THE

HISTORY OF MUSIC LIBRARY

THE HISTORY OF MUSIC (art and Science) FROM THE EARLIEST RECORDS TO THE FALL OF THE ROMAN EMPIRE.

THE GREEKS

CHAPTER IV.

AND now, as to the ancient Octave system, which has been implicitly followed by the moderns, even in the present mathematical divisions of the scale.

Greek music did not attain so high a level for many centuries after the death of Pythagoras. The Greek scale adopted by the modems was devised in the second century of the Christian era, and no further improvement has been effected since that date.

It is certain that Pythagoras did but import the Octave system from Egypt or Babylon, where it had existed for ages before his time, yet the vanity of certain Greeks, who were of a different stamp to Herodotus, led them to attribute the discovery to Pythagoras, because he was their countryman. To give circumstance and confirmation to this first fable, they concocted others as to the way in which he had been led to the discovery. These stories are such clumsy inventions, that they carry their own refutation.

The first is, that he was passing a blacksmith's shop, and, hearing the musical consonances of the Fourth, Fifth, and Octave, sounded by the various hammers on the anvils, he was induced to enter and to weigh the hammers. He is then said to have found the cause of the consonances in their respective weights, which were in the proportions of six, eight, nine, and twelve pounds. That of six pounds sounded the Octave to twelve; that of eight, compared with twelve, gave the interval of a Fifth; and those nine and twelve, sounded together were at the interval of a Fourth. It is surprising how often this childish story has been repeated. Demolish it a thousand times and yet it appears again. In the middle ages such a discovery was thought too good for a heathen, and so Pythagoras was declared to be a misnomer for Jubal, and the real blacksmith to have been his brother, Tubal Cain. The first person who seems to have dared to express dissent from a story so generally adopted by the later Greeks was Claudius Ptolemy. He avoided the mention of Pythagoras by name, but cautiously hinted to them that the power of a blow increases loudness, yet does not alter the pitch of any sound, so as to make it higher or lower. Pythagoras should have looked to the anvils, for pitch, instead of to the hammers; as we should look to the bell instead of to its clapper.

The next story is that, pursuing his discovery, Pythagoras took four strings of equal size and length, and fixing them at one end, he passed them over such bridges as were used in musical instruments, (Magades), and then hung weights to the other ends. He employed weights in the same proportions as the hammers in the previous experiment, viz., of six, eight, nine, and twelve pounds; and it is said that he obtained the same results by those weights as with the hammers. Claudius Ptolemy, acting with his usual care not to give offence, only threw doubts upon this story, dissuading his countrymen from placing any reliance upon such an experiment. He did not emphatically deny its truth, but advised that they should trust only to measurement. For that purpose he recommended the kanon harmonikos, consisting of a rule and movable bridges, to be placed under the strings.

So this fable went on uncontradicted, perhaps till the time of that great enquirer after truth, the astronomer Galileo. He seems to have been the first to point out that, to produce such results as Pythagoras was said to have obtained by tension upon equal-sized strings, the weights should have been the squares of those he is said to have employed; i.e., instead of six pounds, he should have used six times six; and instead of eight, eight times eight, and so on.

The above stories are detailed by Nicomachus, by Gaudentius, by Boethius, and by a host of later writers.

If the third, and only possible account, had been left alone, it would have pointed too clearly to Egypt, or Babylon, as the source from which the knowledge of Pythagoras was derived. He is said, and probably with truth, to have next taken the measurement of the strings upon a stringed instrument with a rule and a movable bridge under them. Some said it was a Monochord, or one-stringed instrument, but if so, he could only have divided a string into two parts, as in the Magadis. Nicomachus says that many called the supposed Monochord a Phandura, perhaps because they imagined the measurements to have been taken upon such an instrument, but that Pythagoreans entitled it a Kanon.

If Pythagoras experimented upon consonances, he should have had more than one string to work upon.

It may be noted, that the Greeks had a three-stringed instrument called the Pandoura, or Pandura, which Julius Pollux enumerates after the Monochord, and says, “so called by the Assyrians, who invented it”. The name may have been derived from Assyria, and still the instrument, perhaps slightly varying in form, may have been common to Egypt under another title. Martianus Capella attributes the Pandoura to the latter country. His Nymph, while recounting the good she has done to mortals, says, “I have allowed the Egyptians to try their hands at the Pandura.” Among the Assyrian sculptures we find such an instrument, and it differs but little from the Egyptian Nefer, which may have been the Nabla of the Greeks. The Nabla and Pandoura are not strictly identical.

Athenaeus, after quoting Protagorides of Cyzicus On the Festivals of Daphne, as to the bright sounding Pandoura, states that Pythagoras, who wrote a book about the Red Sea, says that the Troglodytai, (who bordered upon it,) make the Pandoura out of the daphne, i.e., laurel, that grows on the sea shore. Thus the instrument is brought within the knowledge of Pythagoras, and to the southern part of Egypt, or of Ethiopia. It may be added that, in and before the time of Claudius Ptolemy, three strings had been found insufficient for trying and measuring consonances, and that the Greeks then used an instrument to make many sections, called the Helikon. Movable bridges had the effect of fixing the sounds, as the hand pressing strings upon frets.

Aristides Quintilianus states that, when Pythagoras was upon his death-bed, he exhorted his friends to use the Monochord, by which, says he, Pythagoras showed that the intervals in music are rather to be judged intellectually, through numbers, than sensibly, through the ear. Plutarch also attributes this doctrine to Pythagoras, (De Musica) and it became the distinguishing principle of the Pythagorean musicians “Sense is but an uncertain guide; numbers cannot fail”.

We know the opinion of the Egyptians as to the small amount of the Greek knowledge of music before the visit of Pythagoras, from what one of the Egyptian priests said to Solon, in order to suggest an apology for it. Plato, too, seems to have accepted the Egyptian estimate of his countrymen’s acquirements, by repeating the story. The priest accounted for the Greeks having no remote history, because they had but recently begun to commit their records to writing; and, as their country had been swept by a current from heaven, rushing on them like a pestilence, the survivors had been left destitute of literary attainments, and unacquainted with music. And thus, said he, you became young again, as at first, knowing nothing of the events of ancient times, either in our country or in your own (Timaeus). The Egyptians had no record of the great Deluge in their own land.

Pythagoras is supposed, according to the weight of authorities, to have been born about the year 570 BC, and to have visited Egypt in the reign of Amasis, which was one of forty-four years, commencing from about the date of the supposed birth of Pythagoras. The discoveries attributed to Pythagoras are too various and too vast for any one mind to have originated, but they are not beyond what might have been learnt by one person, and carried away from a country of ancient civilisation. Among his reputed discoveries are the doctrines of the Immortality of the Soul, and the musical harmony in the revolutions of the heavenly bodies. The first is clearly referred to the Egyptians by Herodotus, who adds, that “some of the Greeks have adopted this opinion, (some earlier, others later,) as if it were their own; but, although I know their names, I do not mention them”.

The doctrine of the Harmony of the Spheres is referred to the Chaldeans by Philon Judaeus. It was associated with astronomical reckonings, and with the Octave system of music. It must, therefore, have followed the Octave system. The theory was based upon calculations of distances, and of the rapidity of motion, of the stars and planets, from observations which must have been made by a long line of astronomers. This doctrine was adopted by Archytas, by Plato, and by all the philosophers, says Plutarch; for the universe, say they, was framed and constituted by its author on the principles of music.(De Musica)

The ancients accounted for those sounds not reaching mortal ears, as, sometimes owing to the magnitude of the concussions of the air, and, at others, as exceeding our powers of hearing, both in acumen on the one hand, and in gravity on the other. Herein they anticipated philosophical discoveries of the last and of the present centuries, which prove, by resultant sounds, that some concussions of air could only produce sounds too high, and other experiments prove that sounds may also be too low, for our hearing. Again, they argued that there are many sounds in nature of which we know nothing, some, on account of the feebleness of the concussion; others, on account of their great distance; and, again, others, on account of their excess being too great for our organs to endure. Our ears, said Archytas, are like narrow-necked phials, out of which, if it be attempted to pour rapidly, nothing will come.

As to the Octave system of music, the earliest extant notice of it among the Greeks is included in some fragments of the writings of Philolaos, the successor of Pythagoras, who is reputed to have been the first to publish the Pythagorean doctrines. The part concerning the Octave system of music, or Harmonia, supplies the old Pythagorean musical terms, which, not being generally known, are here printed, with, their proportions as musical intervals. Some of the terms were afterwards rejected and others retained. A few have already been explained. Proportions will be more fully explained hereafter. The following is the passage :

The extent of the Octave system is a Fourth and a Fifth;

but the Fifth is greater than the Fourth by a Tone; [proportion of 9 to 8.]

for, from the lowest string to the middle string is a Fourth; [E to A]

but from middle to highest string a Fifth; [A to E]

from the highest to third string [from the top] a Fourth; [E to B]

from the third to the lowest a Fifth; [B to E]

between the middle string and third is a Tone. [A to B] .

The Fourth is in the proportion of 4 to 3;

the Fifth is in the proportion of 3 to 2;

the Octave in that of 2 to 1.

Thus the Octave system is of five Tones and two Semitones;

the Fifth is of three Tones and a Semitone;

the Fourth of two Tones and a Semitone.

These intervals will be found verified in the following scale for the seven-stringed lyre.

The first observation to be made upon the above is, that we have diesis here used for a semitone, like the modern French diese; but diesis was afterwards transferred to the smaller interval of either a third part, or of a quarter, of a tone, in the Chromatic and Enharmonic scales; and this Diatonic semitone, or hemitone, was then called a limma or remnant by the Pythagoreans, and hemitone only by the Aristoxenians. Next, the distinction is to be here observed between Harmonia, the Octave system of music, and Diapason, the Octave itself. Plutarch tells us that Pythagoras limited the doctrines, of Harmonia to the sounds that are included in the Diapason, or Octave. That was the original definition, and one Octave suffices to exemplify every other. Philolaos defines Harmonia as altogether composed of opposites, for it is the union of many ingredients, and the connection, in two ways, of varying, or different-meaning, parts. The two ways may be assumed to mean by Fourth and Fifth, and by Fifth and Fourth, whether up or down in the Octave, as defined in the preceding quotation from the same author.

The Octave system, new to the Greeks, was called Harmonia, and this name seems not to have been derived from Harmonia, the wife of the Phoenician, or Egyptian, Cadmus, the reputed founder of Thebes, and teacher of the alphabet, for there is no apparent connection between her and music : it was more probably taken from the verb harmozein, to fit together, because it fitted in, and dove-tailed the only two lesser consonances of the Greeks, viz., the Fourth and the Fifth, within the greater consonance, the Octave. (The older system had no such fitting in). The perfect participle of this verb was also used in music as an adjective, hermosmenos, meaning “fitting according to the laws of music” or musical. Pythagorean musicians took the name of Harmonici, (although others called them Canonici, from their measurements by a rule,) and Aristoxenus charges some of them with having continued to teach the following seven-stringed system exclusively, and calling that Harmonia, long after lyres had been made to carry eight and even fifteen strings. The charge of Aristoxenus against his predecessors, of having taught only the Enharmonic system, must be received with some qualification, for, against it, we have the above Diatonic system from Philolaos; we have it also in the Timaeus of Plato; and Ptolemy has preserved the scales of Archytas in the three genera.

The seven strings of the lyre were soon increased to eight. The manner in which that addition was made, will be best seen by placing the two systems side by side, as in the following :

THE DISJUNCT, OR OCTAVE SYSTEM.

The intermediate tone, or tone of disjunction, is, in both cases, immediately above the key note.

The notes which are here ascribed to the strings are taken from the Hypo-Dorian, which was the Common Greek scale, and is our Natural scale, or A minor, with a minor Seventh. Aristotle describes it as most suited to the Kithara, being the most stately and stable. It was no doubt the general scale, because it is within the natural compass of a man’s voice.

Boeckh found a difficulty about the name of the third string from the top in the seven-stringed system, b, from its being called Paramese by some, while Philolaos seems to call it Trite. But while Philolaos speaks of it as the Third (Trite) in numbering it from the highest string of the tetrachord, he also explains that it is at the interval of a Fourth from the highest, and of a Fifth from the lowest string; therefore, even if differing in name, there is no difference in meaning. Aristotle says that the Trite of the eight-stringed lyre was the omitted string. It is very clear why this string (c, in the above scale), was omitted in preference to any other. It made a minor Third from the key-note upwards, (a to C,) and a major Third from the highest string downwards, (e to c) and Thirds, as they tuned them, were discords. The ancients wanted Fourths and Fifths in preference, because they were consonances. By the above arrangement there was, from the key note, a, upwards, a Fourth, (a to d;) and a Fifth, (a to e;) and in coming down from e, there was the choice of a Fourth to b, or of a Fifth to a. Again, b made a Fifth to the lower e. The improvement in this system over the preceding one was very great. The tone interposed between the two Fourths or tetrachords, made the compass an Octave, instead of a discordant minor Seventh. This tone was called diazeutic, (tonos diazeuktikos,) or the tone of disjunction, because it separated the two tetrachords. The scale then became like ours, in what is called one key, instead of turning out of the scale of A minor at the fifth ascending note, as it would if b flat had been retained, instead of b natural. So the upper tetrachord began one note higher in the Octave systems, viz., on b natural instead of a.

Some lyres of large size were upon stands; but those of a portable character, like the Kithara, were held on the left side of the body, with the left arm behind the instrument, for the purpose of reaching the base strings, which were furthest from the player. The left hand took the lower tetrachord, the thumb being on Mese, the key-note. The little finger was not used. The forefinger of the left hand gave the name of Lichanos to the string next below the key-note. The right hand held the plectrum, and touched only the treble strings, which were nearest to the body of the player. The plectrum was of horn, ivory, bone, or of any hard wood.

The left arm had to contribute to the support of the lyre, but the right was more disengaged, and was sometimes flourished about, to assist in declamation, or held out as if addressing the audience. The principal duty fell upon the thumb of the left hand, because it was upon the key-note.

When the lyre had eight strings, the five from the key-note upwards completed the notes of the Fifth, and then its older name, Dioxia, gave way to that of Diapente, through five. No change was made in the word Diapason (the Octave), because through all was as applicable to eight strings as to seven.

The strings of the lyre were usually counted from the lowest and longest, as No. 1, and the highest and shortest was the last. This is, at least, the way in which Nicomachus and Aristides Quintilianus count them, Trite, for the third string from the top, seems to have been exceptional. It may have been because it was at the interval of a Third, both from the key-note and from the highest string.

For all purposes of declamation, and for a simple chant, the Octave lyre was a sufficient instrument. The reciter could take his key-note at a comfortable pitch, so that he could sing a Fifth up, and a Fourth down, in his natural voice, without exertion. The compass was ample for such a purpose. This use of the lyre for recitation continued for ages after the time of Dionysius of Halicarnassus. Aristides Quintilianus also contended that orations, as well as poetry, lost much of their effect upon the hearers if unaccompanied by a musical instrument.

It is essential to bear in mind the difference between this Greek one-octave vocal scale, and the Octave of modern times. By an Octave scale, we mean one that begins on the key-note, and ends on its Octave above or below; but a Greek single Octave began on the Fourth below the key-note, and ended on the Fifth above it. That was the better arrangement for singing, because the Greek had a few notes on each side of his key-note, and we have either all above, or all below. But when the Greeks extended their scale to two Octaves, their arrangement was the same as ours. They added a Fourth to the top, and a Fifth to the bottom of their one-octave scale.

It is surprising what a difficulty this slight variation of habit has occasioned to the moderns. All the supposed inscrutability of the Greek modes rests upon the misunderstanding of this simple point the difference between a complete Greek scale of two Octaves, and a single Octave of the same. It is that difference only which made them an insolvable riddle to Sir John Hawkins, as well as to others; both before and after his time.

And now, as to this important key-note, important in all music, but especially so in Greek. It was always called Mese, whether it occupied the place of middle string, which the word means, or not. When the lyre had but seven strings, Mese was in the middle, but when the number was increased to eight, there could no longer be any middle string; for, as Aristotle says, in referring to it, eight has no middle. Still, it was the centre of every complete two-octave scale. If the Greeks would but have changed the name of their key-note to one less misleading, when they made their lyres of eight or ten strings, it can hardly be supposed that their system could have remained for so long a time a mystery to the modems; or that the thorough identity of the Greek with our old minor scale should not have been perceived. The name, Mese, was retained because, although the number of strings might vary, the system of tuning the lyre to Mese made it ever the centre and turning point of the scale. When Bacchius asks, What is change of system? (metabole sustematike), he gives the answer, “When we change from one system [i.e. scale] into another, making another string Mese”. Euclid says the same. Aristides Quintilianus says that systems without mutation are those with one key-note (Mese), and that mutable systems have several. Euclid the same. As there could not be several middle strings to a lyre, it must be evident that Mese has a second meaning. Change of system is change of scale. It would, indeed, include such a change as from Diatonic to Chromatic, but as that would not alter Mese, these writers can only mean change from one key to another, or, as the Greeks would call it, from one mode to another, as Dorian to Hypo-Dorian, or to Phrygian. Mese may or may not have been middle string, but, in Greek music, it had the invariable meaning of key-note. It was equally the pitch-note for reciting. The name, Mese, say Aristotle, was taken into the Octave system from the seven-stringed lyre. Euclid says that all other notes are tuned to Mese. Here again, it must be key-note. So also, Baochius says, Mese is the string from which, in the Octave lyre, the Fourth is tuned down, and the Fifth up, and from which the two-octave scale is tuned both down and up. Mese is the leader and sole ruler of the scale, says Aristotle. Why, though all the strings be in tune except Mese, says Aristotle again, does the whole scale appear out of tune; and yet, if any other string be out of tune, that single string only is affected? He answers that, in all good poetical recitation or song, Mese [the key-note] must be constantly used, and that all good composers do so. When they quit it, they return to it quickly, but to no other in a similar way. He compares Mese to the conjunctions in language, and says that if we take away such as te and kai, it will no longer be Greek speech, but that words of another kind might, be omitted from the language without such inconvenience, for the conjunctions are in constant requisition, while others are so but little in comparison with them. In the same way, says he, Mese [the key-note] is the conjunction of sounds, and, especially of the sweet ones, because its sound exists in them. Mese remains at this day the key-note of our minor scales, which were inherited from the Greeks, and not from the Western Church. The scales of the latter had not true key-notes.

Having quoted freely from Aristotle’s Problems, it is perhaps here the place to refer to a supposed difficulty in Problems 7, 8, 12, and 13 of Section 19, as to the lowest sound of the Octave being the antiphon to the highest, rather than vice versa, and as to the low sound absorbing the Melos of the high one. The lower sound of the Octave is the generator of the upper, which is its first harmonic; and as the upper vibrates as two to one of the lower, it is more quickly over. The difficulty has been only created by misunderstanding the word Melos to mean melody, as if the lower took the tune away from the upper, but Melos means only a succession of sounds that vary in pitch, up and down, whether in speech or in music, and it is quite as applicable to any under part as to an upper. If we hear the voices of men and women singing together in a room, the more rapid vibrations of a woman’s voice seem to give it superior power; but if a chorus of men’s and women’s voices be heard singing the same subject at a distance, especially in the open air, the women’s voices will seem to give brilliancy to the men’s, and to die away in them, for the slower vibrations of the men’s voices continue after those of the women have ceased. The effect of the longer duration of sound in a low note than a high one, may be tested on a pianoforte by striking low and high together. The higher the note, the shorter will be its duration.

The above answer to the difficulty in Aristotle’s Problems applies equally to the similar passages of Plutarch in his Convivial Questions,, and in his Conjugal Precepts.

Further examples may be desired, and having referred to Melos in Aristotle’s Problems, and in Plutarch, as meaning only the undulations of succeeding sounds, it becomes expedient to show how wide were the senses in which the word was applied. Plato says that Melos is compounded out of three things, out of speech, out of music, and out of rhythm; and Aristides Quintilianus says that Melos is indeed perfect when it combines speech, music, and rhythm, but that the more precise meaning of the word, as in music, is the linking together of sounds that differ as to acuteness and gravity. Bryennius includes the same words. Aristoxenus opens his treatise by describing the different kinds of Melos, and, after that of music, he says : “There is also some Melos, so called, in speech, which is compounded out of the accents that accompany it; for it is natural to raise and to lower the pitch of the voice in conversation”. Ezekiel 1. 10, which, in the Septuagint version, is threnos kai melos kai ouai, is rendered in our English version lamentations, and mourning, and woe. According to the Greek, it might have been translated lamentation, and wailing, and woe, for Eastern mourning is intended, and implied in the word Melos. In the Electra of Euripides the rising and falling sound of the battle cry is Melos boes. The Melos of rhythm; to which Plato refers, is, according to Aristides Quintilianus, the rise and fall of the voice between the up and down beats, the arsis and the thesis, which together constituted a pous, or foot, in verse. When applied to musical instruments, Melos expresses the rise and fall of their sounds, while Melodia applies only to those of the voice. To connect Melos or Melodia with modem melody, so as to exclude recitation by unmusical intervals, required the addition of an adjective (such asteleion, or hermosmenon), unless explained by the context. Our modem melody comes within the Greek definitions of Melodia and Melos, but they are far from being its synonyms, because, in neither of the Greek words was it indispensable that there should have been music, in our sense of the word. In fact, if we require more precise definitions of Melos, we may turn to the instructions for making it, under the head of Melopoeia, in the treatises on music, and we shall there find it explained as the rise and fall of the voice, either by gradual ascent and descend or by any intervals up and down. These were to be varied by pauses, or by iteration of the same sound. It was Melopoeia that brought out the force of elocution in tragedy. Aristotle says that there are six necessities for tragedy, the most important being the language, and that, of the remaining five, Meloppeia, or due inflection of the voice, is the greatest charm. It is somewhat remarkable that all this should have been left unexplained by historians of music.

CHAPTER V.

WHENEVER the Greeks wished to compliment an eminent poet-musician upon his having introduced some novelty in the style of his poetry and recitation, they chose to express it by the figure of speech, that he had added a new string to the lyre. The phrase was happily selected to express that he had enlarged the powers of instrument and voice; but it was as purely figurative, as if we were now to say familiarly of a man who had made some useful discovery, that it would be a feather in his cap. In later ages this mere idiom dame to be appropriated by certain Greeks in a literal, instead of a figurative, sense, and hence the long and conflicting list of double and even triple claimants for every string to the lyre, such as that copied by Boethius, into his treatise upon music.

As to the addition of one or more strings to the Octave system, even if the scale had not been borrowed entire, it would have required no genius to make such a discovery as, that, if one note had its Octave, another must have the same. The first Octave sound discovered was the clue to the whole series, as is sufficiently proved by the Magadis and the double flute, which are older by many ages than the Greek claimants for the added strings.

It was the same with the tetrachord system. One tetrachord having been joined on to another, nothing was easier than to add a third. In the time of Terpander the number of strings had thus been increased from four to seven, by the addition of an entire tetrachord; and in the time of Ion, of Chios, by another tetrachord, from seven to ten. There was no such gradual progress as seven, eight, nine, and ten strings. For these additions by tetrachords we have the best evidence, in the authors themselves, and it is by far the more probable mode of increase.

The Conjunct system never extended beyond eleven notes, and then the eleventh string was borrowed from the Octave system, and added on at the base of the scale, to make an Octave to the key note.

When thus completed, the scale obtained the name of the Conjunct, or the Lesser System Complete, and retained it until Claudius Ptolemy disallowed the claim of the Lesser System to be considered complete, because it did not include the consonances of Octave with Fifth, nor of the double Octave.

A system, says Euclid, is compounded of one or more intervals, but Aristoxenus says, a system is to be understood as something compounded of more than one interval. In either case, a Fourth, (being compounded of two tones and a semitone,) and a Fifth, (of-three tones and a semitone,) were systems, and hence the necessity of the addition complete, (teleion) to signify an entire scale. Claudius Ptolemy differs from earlier writers in his definition of a complete system. He admits of nothing less than two Octaves, because any smaller compass cannot include the whole of the consonances.

According to Suidas, Ion, the contemporary of Sophocles and of Pericles, produced his first tragedy in the 82nd Olympiad, (453 BC) and was dead before the year 421 BC.

The following lines, from a hymn by Ion, are quoted in Euclid’s Introduction to Music, where they follow immediately after the lines already cited from a hymn by Terpander.

Having the ten-note scale,

Combining threefold consonance:

Till now with seven-string lyres the Greeks hymned thee,

Upraising stinted song.

From the above fragment of a hymn, and from that of Terpander, which is also part of a hymn, it would appear that the ancient scale of conjoined tetrachords was kept in use, and was perhaps, at that time, chiefly reserved for purposes of religion. It is difficult to find another reason for its vitality, after so very superior a system as that of the Octave had been discovered.

The three consonances to which Ion refers can only be the three tetrachords conjoined. He could not intend the Octave system, because, instead of only three consonances from ten strings, there would have been five even from seven strings, viz., two Fourths, two Fifths, and an Octave, as already shown in the extract from Philolaos.

The new scale of Ion’s was called Episynaphe, or Conjunction upon Conjunction, Here, then, in Athens, two hundred years after Egypt had been opened to them, the Greeks had but just added the third conjunct tetrachord to their old defective scale, which was still maintained, at least for hymns, in the most polished city of Greece. Diodorus Siculus alludes to this conservative spirit of the Athenians, who, being an Egyptian colony, had derived their institutions from the parent country, and Plutarch refers to the same as characteristic of the second Egyptian colony of Argos. It is related, says he, that the people of Argos prohibited by law any extension, or alteration, of their musical system, imposing a fine upon the first person who should venture to increase the number of strings of the lyre beyond seven. That law was aimed at checking, extravagances in recitation, it could not have been intended to limit music in the modem sense.

Of the like spirit as existing among the ancient Egyptians, in regard to their hymns to the gods, Plato says, that such was the reputed antiquity and sanctity of some of the hymns, that they were ascribed to Isis, and were held to be ten thousand years old.

The additional tetrachord of Ion made a great musical improvement because it supplied the lower D to the Octave in the Dorian scale, (our D minor, with a minor Seventh,) and thus the b flat in that scale was properly brought into play. When the eleventh note was added, (viz., the A at the base of the scale), it equally completed an Octave of the Hypo-Dorian scale, (our A minor,) from base A to tenor a, because the lower B in the scale was natural, as required for the key of A minor, although the upper b was flat, as required for D minor. How completely does this foreshadow, and tell the origin of the ecclesiastical scales of later days, with the lower B, natural, and the upper b flat!

This scale, with the added tetrachord of Ion, is one of two scales that Meibom misunderstood, and his account includes another error, which Dr. Burney too hastily adopted from him.

The original seven strings had seven different names, but no additional names were given to the strings of the tetrachord added by Ion. It therefore became necessary to distinguish between the new and the old series by adding to the name of each string that of the tetrachord to which it belonged. So the name, Hypate (E), became lengthened into Hypate Meson, i.e., of the middle tetrachord; and the newly added Hypate (B) was Hypate Hypaton, i. e., of the lowest tetrachord.

When A, the Octave below the key note, was added under Ion’s tetrachord, the above scale became identical, as to this lower Octave, with the other scale upon the Octave system, viz., from base A to tenor a. The divergence of the two systems commenced from tenor a. The preceding scale of eleven notes turned off to b flat, c, and d, and there stopped; while the larger scale, of fifteen notes or two complete Octaves, followed on its course with an upper Octave in the same key as the lower, viz., from tenor a to treble a.

This will be seen by comparing it with the following:

In the above scale a second name (Diatonos) has been added to the Paranete and to the Lichanos strings, which occupy corresponding positions in the tetrachords. The first named are in tetrachords above the key-note, and the second in those below it. The additional name arose in this way. When the lyre was tuned for the Enharmonic, or for the Chromatic scale, the two inner strings of each tetrachord were altered in pitch, and so represented variable, or movable sounds, (kinomenoi, keklimnoi, or, phermenoi). The outer strings of all tetrachords, and the Octave below Mese, were immovable. The chief alteration was in the Lichanos, and its equivalent, the Paranete string of a tetrachord. They were changed in pitch for both Chromatic and Enharmonic scales. At first Diatonos was added to the name of Lichanos, when for the Diatonic scale; and afterwards, for brevity, it was sometimes called Diatonos only. In other cases it was called Lichanos Enarmonios, or Lichanos Chromatike, according to which of the two the scale might be.

The reader of Dr. Burney’s account of Greek music will not have discovered from it that there were two distinct systems of Greek music in use simultaneously, as here just exhibited. Burney regarded the two only as one General System of the Ancients, and termed what are properly the third and fourth ascending tetrachords of the Greater System, the fourth and fifth. With him, the b flat tetrachord of the Lesser System was the third; and the fourth (as he termed it) was supposed to commence by a descent from the top of this third tetrachord, viz., from D to B and then to reascend. It is something of the dodging kind, said he, that is to be found in the scale of Guido, divided into hexachords. The way he fell into this error was by copying Meibom’s ready-made diagram in his notes upon Euclid, and, with it, the word system in the singular number.

And now, as to the Greek musical keys, or modes (tropoi). The principal three, for the voice, were Dorian, Phrygian, and Lydian. They had, for a long time, no settled pitch, even in relation to one another, for the names were first used in reference to the character of poetry to be recited, and not as to pitch. They denoted the general tenor of a composition, a certain style of poetry with its appropriate metre, and the spirit of a song.

The ancients were not agreed as to what were the characteristics of any of the modes except the Dorian, of which Plato says, that it was the only true Greek style. That was severe, firm, and manly. The Phrygian mode was reputed by some to be enthusiastic and orgiastic, deriving its character from the Phrygian style of worship. Aristotle, for instance, described it as enthusiastic and bacchic; but Plato, on the contrary, as smooth and fit for prayer. Again, the Lydian mode was esteemed by some as modest, decorous, and fit for boys; by others, as plaintive and erotic, (or fit for love songs); by others again as expressive of mournful affections.

The reason for these conflicting descriptions is to be found in the fact that particular metres were appropriated to particular modes; and, unless all poets could first have been induced to agree in the appropriation of one style of song to each particular metre, there could be no general agreement as to the character of the mode. A martial song and a hymn may now be written in the same metre and be played in the same key there will be a wide difference in the character of the words of the two, and in the spirit of the music, but no change in the notes of the key, in which they may both be played. The notes of the key constitute the musical mode.

Boeckh has collected various estimates of the characters of the modes among the ancients; but, musically speaking, the only difference was one of pitch, which, in itself, could confer no character, because all the Greek modes were tuned in the same way. Difference of character in modern keys of music arises solely from imperfection in tuning them, one scale being left less perfect, in order to improve another. We must, therefore, look exclusively to the metre of the poetry and to the spirit of the words, which the style of music would follow, for any attributed difference which has been marked between one Greek mode and another. Dorian gravity would be fitted by spondaic metre and common time, while the more lively strains would require more rapid feet, and some would be better fitted by triple time.

The relative pitch of the modes was long unsettled. Aristoxenus has noted some of the ancient vagaries, such as placing Dorian and Hypo-Dorian only a tone apart, and the Mixo-Lydian between them. Again, Athenaeus gives several quotations which show that Aeolian, at an early date, held the position afterwards assigned to Hypo-Dorian just as Mixo-Lydian was transferred, and became synonymous with Hyper-Dorian. This will explain a passage about a combination of Aeolian and Dorian modes, quoted from Pindar by the Scholiast on Pyth., II. 127, and which has been a musical crux :

Αίλεύσ έβαινε Δώριον ύμνών.

So Pindar refers to the Greek Conjunct system, in which the b flat gave the option of the Dorian mode, joined on to the Hypo-Dorian, or natural scale. This modulation to the Fourth above was the usual hymnal one from the date of Terpander to that of Ion, and even down to existing specimens of Greek hymns, which will hereafter be presented to the reader, and for the first time, in an intelligible form. In the time of Plato, however, the modes seem to have acquired an established order of succession, and therewith obtained that secondary meaning of relative pitch, which is their more important feature in a strictly musical view of the subject. In the same way, the secondary meaning of Mese, as keynote, is far more important than the primary, for it has afforded a far greater insight into Greek music, than the mere fact that it was originally the middle string of the lyre.

Aristides Quintilianus, after saying that Dorian, Phrygian, and Lydian were the principal modes for the voice, adds that the others were rather for musical instruments. Bacchius Senior puts the question: If three modes only are sung, which are they?. The answer is (inverting the usual order) Lydian, Phrygian, and Dorian.  And if seven? Answer: Mixo-Lydian, Lydian, Phrygian, and Dorian, and the Hypos, or Dominants, of the last three. He numbers the vocal scales in order of descent, the Mixo-Lydian g being the highest. The modes were not always called tropoi, which carried with the name an implied character, or style, but sometimes only as taxeis or syntagmata (positions or arrangements of notes in musical scales,) as in preceding quotations, and by Aristotle.

In the time of Aristoxenus, who was a pupil of Aristotle, there were thirteen Diatonic scales, viz., one for each of the twelve semitones of the Octave, and one for the Octave itself. In the time of Alypius (said to be about 115 BC), the number had been increased to fifteen, by giving to each of the five principal scales its Hypo and its Hyper, the one beginning the Fourth below and the other a Fourth above. Thus there were three scales beyond the compass of an Octave, and they were necessarily duplicates of others that were the same notes an Octave lower.

The following is the enumeration of the modes, according to Alypius, with their relative pitch. It is only necessary to remark that the Mixo-Lydian (not here included by name) is the same scale as the Hyper-Dorian, viz., g, it being a Fourth above the Dorian. The letters prefixed refer to the lowest note of the scales, or the Octave below their Mese.

The order begins with the Hypos, as the lowest scales, viz., A to C#; then the Principals, D to F # ; and lastly the Hypers, G to b. The highest three Hypers, a, b b, and  b, are the same notes as the three lowest Hypos, but are the Octave above them. These were unnecessary except in relation to their Principals. The entire compass of the scales was three Octaves and a tone from a fixed pitch.

When the Greeks modulated from one key into another, they did so exactly as we do now, by some sound common to both keys. They did not always fly to discords to change to a connected key, as was the fashion even in the present century. The greater the connection between the two scales, the better was the modulation esteemed by them, as by us.

They had four kinds of modulation, called mutation, or change, (Metabole). One kind was described as according to genus, being such as a transition from the Diatonic to the Chromatic or Enharmonic scale; a second was a change of system, as from the Conjunct to the Disjunct scale, or vice versa; the third was a change of key or mode as from Dorian to Phrygian; and the Fourth a change of Melopoeia, i.e., in the style of singing or chanting, as from grave to gay, or from, a. love song to a martial one.

When a Greek system, or scale, was called a metabole, or, without mutation, such a translation as the ordinary one, immutable, conveys a wrong impression, for it means nothing more than an ordinary scale, tuned to one key-note, and usually a Diatonic scale.

There is a passage referring to the added Octave tone at the basis of the Greek two-octave scale, in Plutarch’s Commentary on the Timaeus of Plato, which has created a difficulty for many writers on Greek music. It has led them to suppose that this tone, called Proslambanomenos, was originally at the top of the scale, and not at its base. Boeckh erroneously inferred from the passage that the Octave below the key note was not in use in the time of Plato.

Plutarch’s complaint is that innovators, (neoteroi) by adding Proslambanomenos as an Octave below the key-note, at the base of the Greater System or two-octave scale, had introduced a tone below Hypate, which was formerly the lowest sound. By which, said he, they have made the ascending sequence of the consonances to differ from the order of nature, for they have-thus placed a Fifth below a Fourth, whereas the Fourth ought to have been the lowest interval of all. It is clear, he adds, that Plato added on to the acute part of the scale. He does not there say that Plato fixed the particular string, called Proslambanomenos, at the top of the scale, as some former readers have understood.

The passage about Plato’s additions to the scale is not to be found exactly as Plutarch expresses it in the Timaeus, but Plato there speaks of circles within circles, and of musical proportions, which must have been calculated by some disciple of his school, who then reduced them to a scale. It is quite a celestial scale, for it refers only to the music of the heavens. The substance of those calculations is stated by Plutarch’s contemporary, Theon of Smyrna, (who quotes from Adrastus,) as well as by Proclus. It does not bear out Plutarch’s words as to the Octave below the key-note having been excluded from the computation, but only that Plato extended the greater system of the Diatonic scale to four Octaves, a Fifth, and a Tone. Therefore he included this lowest note. The rest is Plutarch’s surmise; but, very possibly, a correct one, so far as the heavenly bodies were concerned. The passages in both authors relate to the harmony of the universe, which had first been adapted by the Greeks to their shorter musical scale, and Hypate then represented Saturn, the slowest in motion of the planets, and furthest from the earth. Saturn was then placed at the distance represented by a musical Fourth, from the Sun; in other words, there were two planets, Jupiter and Mars, between Saturn and the Sun, and the Sun, as the centre of the planetary system, was Mese, the key-note to the whole, Saturn being Hypate, represented by the lowest note as to pitch.

The systems of Copernicus, Kepler, and Newton, as to the planets revolving round the Sun, were prefigured by Pythagoras, and there can be no doubt that his knowledge of the revolutions of planets in their orbits, as well as his general system, were derived from the observations that had been made for many preceding ages by Egyptian and Babylonian astronomers. It was Claudius Ptolemy, some six centuries after Pythagoras, who first propounded the doctrine that the earth is the unmoved centre of the universe, a theory which took such hold of Roman Pontiffs as to cause the retention of the book of Copernicus in the Index Expurgatorius of Rome, until the decree of Paul V was revoked by Pius VII, so recently as in 1821.

Whether the confusion of order among the heavenly bodies has been so great as represented by Plutarch, in consequence of the addition of a note to the musical scale, is a question we must leave to be determined by Pythagorean philosophers, and by our present learned Mousikoi, the astronomers. As to mere mundane music, it is not so, and we must even defend the supposed innovators from their part of the charge made by Plutarch; for, long before the date of Plato, Anacreon had used the Egyptian Magadis, and still a thousand years before that, the Egyptian lute, or Nefer, had its two-octave scale. The double flutes, Egyptian and Greek, the antiphons, antistrophes, and all the musical antis of the Greeks, signified an Octave below another note, so that any compass of one Octave must have thereby created a two-octave scale.

CHAPTER VI.

It is clear that ancient Greek singing must often have caused a severe strain to the voice. If we take the lowest of the five principal middle scales, the manly and severe Dorian, the key-note was tenor d, in the space immediately below the treble clef, and the Octave below it was D on the third line of the bass. Suppose only the small lyre or Kithara, if an Octave in compass. It would extend a Fourth below the key note, viz., to tenor a, and a Fifth above it, to treble a. That is a high chest note for an ordinary tenor voice.

Our ancient Greek must have thrown back his head, and have filled his chest to the fullest, if he wished to declaim his severe, firm, and manly addresses to Apollo from so high a key-note as D. Aristotle says that few persons could sing the Nomes, called Nomoi orthioi, on account of their high notes. That may readily be imagined. The comment, however, tends to show that regard was paid to pitch; and Plutarch says of Nomes, that they were not to be transposed. Yet, on the other hand, are we to assume that all were debarred from chanting to Apollo who could not sing so high? Some of the ancients invited the god to supper, and must then have addressed him. Perhaps they only took part in a paean.

The public crier is now out of fashion in large towns; but many may recollect him in former days, with his old French Oyez! oyez! (Hear! hear.!) corrupted into O yes! O yes! and how he assumed the highest possible pitch of voice for his announcements. With all due respect for antiquity, we can but fancy the singing of an ancient Greek to the gods to have been something of the same kind; and, considering that the most correct Nomes were upon three notes, it would be difficult now to decide whether such singing differed widely from that of the ancient Greek crier, with his Akouete Leo! Hear, ye people.

Apollo seems to have been addressed as if he had been troubled with deafness, or was supposed to be a long way off; and, perhaps, that was the general style of heathen antiquity. It recalls Elijah’s mockery of the priests of Baal telling them to cry aloud: peradventure he sleepeth, and must be awakened.

It may be assumed that the Greek key-notes were fixed so much higher than the conversational tone of the human voice with the object of being more distinctly audible to a large assemblage, especially to one in the open air. Modern speakers, about to address a crowd, often adopt the same course, though, perhaps, in a modified form. They assume the high pitch in order that their voices may not be mixed up and lost in the conversations of those who are around or beneath them.

The Phrygia mode may well have sounded enthusiastic or bacchic, if sung from the chest voice, with tenor e as key note. It would cause a great strain upon ordinary lungs; and, as to the mournful and plaintive character attributed to the Lydian, it can but have been mainly, if not altogether, owing to the necessity of employing the head voice to squeeze out the high notes. The singer must have resembled the high tenor, who sings the accepted lover’s part in modern operas. Few men could avoid resorting to the head voice, if they were to sing with such a key note as the high f sharp of a tenor voice. Plutarch states that the reason why Plato would not tolerate the Lydian mode was on account of its acuteness and fitness to express and excite plaintive and mournful affections.

On the other hand, it is not to be supposed that any large majority of voices could have distinctly audible notes below our A in the base; so that the variation between ancient and modern pitch cannot have been very material. In all probability a tone was the extreme, unless the human voice has diminished in compass, which is a theory not to be upheld. Aristoxenus and Euclid fixed the limit of the most extensive voice at two Octaves and a Fifth, which is much the same as now. There is also this against the theory: that Hypo-Dorian was included in Dorian, and, for general voices, it answered far better to the character of firmness and manliness ascribed to the mode, than its principal.

The Hypo-Dorian compass upon the Octave lyre would have been from E to e, with the intermediate a for key-note, which, was, and still is, quite within the reach of men’s ordinary voices. Suppose only half a tone lower to be allowed, for variation between ancient and modern pitch, there would be but an exceptionally low base voice that could not sing to the highest of the notes. Moreover, Euclid prefaces the name of the Hypo-Dorian scale with the title of Common, as well as of Locrian (for Locrian songs,) which were erotic, or Anacreontic. Aristotle says it was most suited to the Kithara, as being the most stately and stable of modes; and Athenaeus says that Hypo-Dorian songs were sung by nearly everybody.

For ordinary purposes, therefore, the Greek compass was very much the same as that of today, and we might add that Plato’s advice to the singers and reciters of his time would be just as applicable to any who would wish to sing ballads well, as if given by the highest modern authority. It is to make the metre and the air subserve to the sentiment of the words, and not to allow the due expression of the words to be subservient to the time-beats of either metre or music.

In order to remedy the obvious defect of too high key-notes in the principal Greek scales, Claudius Ptolemy proposed, and carried out, the lowering of the seven scales particularized by Bacchius, to the extent of each a Fourth; to bring, as he said, an Octave of all into the middle of the voice instead of its higher extreme. The advantage thus gained will be better brought before the eye of the reader, by first presenting the scales in musical notes in their original keys, and afterwards as transposed by Ptolemy.

The description of the various Greek Octaves, called Lydian, Phrygian, or other, by Euclid, Gaudentius, Bacchius, and other ancient writers, will be found to tally with the intervals of their particular modes, as they begin upon the Octave lyre, in both the preceding sets of scales. Transposition makes no change in that respect. If the lyre were tuned for any one mode specially, the only Greek Octave that could be included, on the Octave lyre, would be from the Fourth below the key note, to the Fifth above it, as here shown in the Dorian. It would have no Octave up from the key-note itself; but then, the Hypo-Dorian, being always timed a Fourth below the Dorian, would, by the same rule, commence on its key-note and include the Octave above it, and no other.

A fifteen-stringed lyre could only include one of the two-octave scales complete. As there are seven scales of different pitches, six more strings would have been required to include fifteen notes of all. So, some of the highest notes of the higher scales, and of the lowest notes of the lower, are necessarily omitted in the preceding diagrams, as they were omitted on the lyre.

The names given to the Greek Octaves, which were thus derived from the changing positions of the eight notes of an Octave in the different modes on the lyre when the Dorian was the central one, have been one of the greatest puzzles to writers on Greek music. Some inferred that each particular kind of Octave belonged exclusively to, and was identical with, its mode; whereas, every kind of Octave is common to every mode or key, and the transposed scales prove that the intervals of all keys are alike if begun upon the same part of their scale. It is a misconception, about Greek Octaves that underlies the Greek names given to the old scales of the Church, now called Gregorian. They are not scales but Octaves in the Dorian or Hypo-Dorian mode, and yet had such names as Lydian and Phrygian assigned to them. To be really Lydian or Phrygian they should have been taken in Lydian or Phrygian keys. If their Octaves had been properly selected from their respective keys, they would have had the same sharps and flats as other music.

One continuous proof runs throughout all ancient treatises on Greek music, that every mode or scale was tuned in precisely the same way, viz., always to its own Mese, or key-note. For that reason alone, if there were no other, Greek scales of the same genus must have been identical as to intervals, just as are modem scales.

I have already remarked that there was no complete major scale among the ancients. Every Greek writer insisted upon the interval of a whole tone, at least, immediately below the key-note. The distances of tone or semitone, for every string, are given by ancient writers, and they invariably make a complete old minor scale. There is no major Third, no major Sixth, no major Seventh, among them; and if one Diatonic scale had differed from another, the mathematical proportions of Euclid, and others, could not have been given as applicable to all. The diagrams of Alypius, of Claudius Ptolemy, and others, down to that of Boethius, all alike prove that one Greek scale differed from another in nothing but pitch. The tones, says Bryennius, differ from one another in no other respect than in their positions as to acuteness and gravity, as has already been shown

Yet this has been termed a laughable assertion by Boeckh, in his Metres of Pindar. He fancied there could be no character attached to a Greek mode, but by changing the order of the intervals of tone and semitone in the scale, as they are changed in ecclesiastical modes, or tones. It must be supposed that he derived his knowledge of what was said to be Greek music, through over-zealous writers on Church music, and had entirely formed his judgment upon them. He cannot have derived it from the Greek treatises on music.

It will be observed, in the preceding diagrams, that as the key-note shifted to the right, another note of the scale was taken in on the left, and so the Octave began upon a different part of every scale.

The form of Octave that began on the second ascending note of its key was called Mixo-Lydian, just as here; that which began on the third was Lydian; on the fourth, Phrygian; on the fifth, Dorian; on the sixth, Hypo-Lydian; on the seventh, Hypo-Phrygian; and the one beginning on the key note, or its Octave, Hypo-Dorian.

The difference between one kind of Octave and another was as to where the two semitones would occur. If the Octave began on the key note, the scale being minor, the semitones would be found in ascending from the second to third, and from the fifth to the sixth strings. If on the second of the key, as the Mixo-Lydian Octave, they would occur in ascending from the first to the second, and from the fourth to the fifth strings. That these are the true distinctions between Greek Octaves may be verified by comparing the above with Euclid’s description of them. The names of the strings of the lyre have been here dispensed with, as they would only perplex the reader; but they may be tested by the curious upon the preceding Greater System.

There was an old plan of teaching singing to boys in English Cathedral schools and one that has been revived as a novelty of late, in which Ut, (or Do,) was always the key-note, like the Mese of the Greeks. This system was identical with that of the Greeks, for every other note in the scale took its name from its position in respect to Ut, as, the Greek did to Mese, and had no fixed sound. With every change of key, Ut became a different note, and every other followed suit. The chorister thus acquired a little knowledge of harmony at the time he was learning to read music; and it was supposed necessary to teach harmony to choristers in those days, although it is sometimes dispensed with at the present date.

Although the Greek names for notes were thus unfixed and variable, according to the positions they might occupy in any mode, or key, they had fixed and distinctive marks or signs for all notes when written down upon paper. These music signs (semeioi mousikoi), were letters of the alphabet, turned about in various directions, and sometimes only parts of letters were used. The Greeks practised writing down music as early, at least, as in the fourth century BC, for Aristoxenus complains that too much had been thought of it, and too much credit had been taken for what was purely mechanical, and not part of the science of music.

The following graceful figure of a girl reading music from a book, is given by Dr. Burney, from an ancient bas-relief in the Ghigi Palace at Rome.

Aristies Quintilianus attributes the system of musical notation for the fifteen modes, and in the three genera, Diatonic, Chromatic, and Enharmonic, to Pythagoras. Whenever we read of musical improvements by Pythagoras, we may fairly suppose them to have been derived from Egypt.

The SYSTEM OF TUNING the seven scales was by first taking a pitch for the key-note of the highest, the Mixo-Lydian, alias Hyper-Dorian, and then tuning by intervals of Fourths down and of Fifths up. Suppose that key-note to be d, as in the transposed scales, tune a Fourth below it, for Dorian (a), then another Fourth down to Hypo-Dorian (E), which is the lowest of the scales. From that, tuning a Fifth up, will give the Phrygian pitch (B), and thence a Fourth down, the Hypo-Phrygian (F #). From this last another Fifth up gives the Lydian (C #), and lastly, a Fourth down, the Hypo-Lydian (G # ). These are the directions of Claudius Ptolemy divested of their Greek technicalities.

From the time of Aristoxenus, and, perhaps, long before it, the Greeks tuned their lyres by a Fourth down, and thence a Fifth up, because it measured the distance of a tone between the two upper notes. The Pythagorean tone was our major tone, it being the difference by which a Fifth overlaps a Fourth.

This tuning will afford an easy experiment as to the ancient major Thirds, called Ditones, to show how they were discords, instead of concords, and the value of the introduction of minor tones. Supposing neither violin, guitar, nor harp to be at hand, let the pianoforte-tuner be asked, on his next visit, to tune four notes perfectly, viz., from C, a Fourth down to G, and thence, a Fifth up to D, for the first major tone, and then from D down to A, and up to E, for the second major tone. Thus, from C to E will be a Pythagorean Third, or Ditone. The interval will be too wide for a true major Third, and quite discordant. If the timer be not asked to tune the intervals perfectly, he will temper them all, so as to bring the major Third just bearable to the ear. Thirds are no longer timed perfectly upon pianofortes, because the notes are wanted for many keys, and keyed instruments are imperfect. If the tuner would then make F a perfect Fourth above C, the hearer could judge also of the Pythagorean limma or remnant, called by the Aristoxenians a semitone, as between E and F. He would thus know practically all that can be written about the systems of Pythagoras, of the Romans, of Boethius, and of all the most ancient tone and semitone scales for voice or instrument. The Fourths, Fifths, and Octaves were at all times the same as now.

Claudius Ptolemy argues against having more than seven scales, or modes, but admits of an eighth, to complete an Octave. He says that, in a Fifth, there are three tones and a limma, which they, (meaning the Aristoxenians,) denominate a semitone; that, in, a Fourth, there are two tones and a limma, thus seven notes for scales in all. If you add to them, says he, you can but multiply divisions that you have already within the seven scales. If the moderns would but be contented with seven scales upon imperfect instruments, they might have them better in tune.

Before touching upon the improvement of the scale by Ptolemy, it is expedient to take up the thread of the Chromatic and Enharmonic systems of the ancients, They are of considerable interest in the history pf the science, as well as of the art.

The Greeks seem originally to have had but one kind of CHROMATIC SCALE, as one Diatonio and one Enharmonic; but they made many experiments upon new ones, which were modifications of the first two, although without any durable success. For instance, Bacchius Senior names but one of each kind, so the varieties had all died away when he wrote.

The principal Chromatic scale, the original and the most enduring, was called, for distinction, the Chroma tonaion, by Aristoxenus. Euclid places it alone in the list of scales in the early part of his treatise, although he afterwards mentions the others, as called Chroai, or colours. We should, perhaps, term them different shades. The principal Chromatic scale ascended by semitone, semitone, and minor Third.

The peculiarity is, that it includes a minor scale without either Fourth or Seventh, and also a major scale without its Fourth and Seventh, or, in other words, a major scale of five tones, without semitones, a pentatonic scale. How truly the ear guided to the omission of the Fourth ascending from the key-note, and of the minor Seventh, is a subject to be explained hereafter.

This Chromatic scale was of very simple formation on the lyre. It was only necessary to lower the forefinger string, and its representative in the higher tetrachords, half a tone below their Diatonic pitch, so as to make the interval between the highest string of a tetrachord and the next to it, a minor Third, instead of a tone. The other three strings of every tetrachord remained as in the Diatonic scale. This may be termed one of the skipping scales. It differs widely from the modem Chromatic, which includes every semitone in the Octave. The Greeks could only have obtained the extra semitones by changes of key, or mode. Still, they might have included all upon the fifteen-stringed lyre.

If the portion of the Greek Chromatic scale which is in a major key, be played in the Lydian mode, our F#; it will be identical with the short keys (usually black) on a pianoforte, according to the reputed, but mistaken, test of ancient Irish and Scottish tunes mistaken, because the Irish and the Scotch had as perfect scales as any of their neighbours, and this peculiarity was but a preference of many among them for the shorter scale.

As to the ENHARMONIC SCALE, the following account of its origin is given by Plutarch, in his De Musica, cap. 11:

To Olympus, as Aristoxenus informs us, the invention of the Enharmonic genus is unanimously ascribed by the scientific world, (the Mousikoi), for, before his time, all was Diatonic or Chromatic. They conjecture such a discovery as this to have been made in the following manner:  While preluding up and down in the Diatonic genus, and frequently passing from Bb,and from A [the key-note] directly down to F [the sixth of the key,] and thus passing over G, [the minor Seventh] in the descent, he observed the beauty of the effect; and, both astonished at, and approving it, he constructed a system strictly analogous to it, in the Dorian mode, for there was no sound in it that was peculiar to the Diatonic scale, neither any that belonged only to the Chromatic, nor to the Enharmonic genus. Such was the first of the Enharmonic scales that of Olympus.

This scale of Olympus was not considered to be Enharmonic either by Aristoxenus, or by Euclid. They name it the Common Genus, or Common to all scale, because it included only sounds that were common to the three genera. It lacked the distinguishing feature of the Enharmonic, viz., the quarter-tone between the lowest two strings. It was but the old Diatonic minor scale, wanting its Fourth and minor Seventh. The three permanent sounds in every tetrachord, whether Diatonic, Chromatic, or Enharmonic, were the two extremes, and the semitone above the lowest. That semitone was usually occupied by the Parhypate string; but, in the Enharmonic genus, Parhypate was moved down to within a quarter-tone of the lowest, and Lichanos took Parhypate’s place. The reason why this scale of Olympus has been such a puzzle, is simply because this movement of one string into the place of another was not thought of.

As to the story about Olympus, it is an indirect way of filing upon him the first discovery that the Fourth and minor Seventh do not properly belong to the scale of the key-note. But there was Egypt, long before him, and hundreds of cases after him, in which that discovery was made by the ear, without any knowledge of what Olympus may have effected. These discoverers by ear were strictly correct, as will be proved hereafter. Those notes belong only to the tetrachord, and not rightly to the Octave system.

Olympus, who, according to Plutarch, was a flute-player of Phrygian extraction, must have flourished a short time after Terpander, says Muller in other words, after Egypt had been thrown open to the Greeks. To have found out the defects of those two notes, a man must have had the Octave system in his ear. It is to be remarked that the Chromatic, as well as the Enharmonic, omits the Fourth and minor Seventh, and that the Chromatic was admittedly older than Olympus. Those two notes have been shunned by susceptible ears in simple melody, in all ages. When the ancient Chromatic and Enharmonic scales fell out of use, we may be sure that music had advanced beyond simple unaided melody into the stage of accompanying the voice with varied harmony.

Now, as to the reason for the introduction of an Enharmonic quarter-tone. While the Chromatic scale made a skip downwards of a minor Third, (as from key-note A to F #,) the Enharmonic made the greater skip of a major Third, (as from A to F #). But there was a string already upon that note, and the question would naturally arise as to what should be done with the unemployed string. It was not required where it stood, and there remained but the interval of one semitone into which it could be packed. So the otherwise useless string was eventually placed at a quarter-tone between the two strings, to give an occasional grace-note. That is the simple origin of quarter-tones in Greek music. It could not have been employed practically in any other way than as a grace-note.

As to the quarter-tones, says Aristoxenus, no voice could sing three of them in succession, neither can the singer sing less than a quarter-tone correctly, nor the hearer judge of it. There are numerous comments upon the quarter-tone to this effect, and to its unfitness for harmony. When, therefore, we read of the Enharmonic genus having been so much in use before the time of Aristoxenus, as almost to exclude the other genera, we should think of it as of an ordinary scale without either Fourth or Seventh, adding only thereto the possibility of an attempt at a quarter-tone by the singer.

As to the intermediate quarter-tones of the modem Enharmonic, says Plutarch, these do not seem to have constituted any part of the invention of Olympus, and the difference between the two methods may be immediately perceived by any one, on hearing a piece played in the ancient manner; as, in that case, no division is made of the semitone. He adds that the division of the semitone came afterwards into use in the Lydian and Phrygian modes. It might have been suspected in the Lydian only, for such a refinement was best fitted for tearful, or very amatory ditties.

When Aristoxenus complains that his predecessors had taught only the Enharmonic division of the scale, and the compass of but one Octave, it is to be understood in a general sense, and of immediate predecessors only. In proof, Archytas of Tarentum, the cotemporary of Plato, defined the three genera, and suggested a new division of the intervals, which has been preserved by Claudius Ptolemy. Plato did not limit himself to one genus; neither did Aristotle. Nor can it be understood of still earlier men, such as Philolaos, from whom quotations have been here given.

When the Enharmonic system was greatly in vogue in Greece, it took the name of Harmonia, as if the only system of Music. Aristoxenus, who complains of this, himself calls it Harmonia at the beginning of his treatise (pages 2, 7, and 8), and Enharmonia at pages 19, 21, 24, 25, and 26. In the last-named page, he uses Harmonia once, and Enharmonia thrice. Aristoxenus entitles his own treatise Harmonike and that became eventually the more general name for Music proper, and prevented confusion between the two meanings of the earlier word. Aristotle seems occasionally to have used Harmonia, where it is to be understood of only the one branch, viz., Enharmonia; but, at other times, he distinguishes that system by its more limited name of Enharmonia. It is not always possible to tell which of the two may have been intended by him. Euclid draws the line between the two words.

After the time of Aristoxenus, there was little else than complaint in the opposite direction, viz., that the Enharmonic and Chromatic scales were neglected, and that nothing but the Diatonic was used. This continued till Greece fell under the dominion of the Romans, who may be said to have employed no other than Diatonic scales.

There were certain variations from the usual Diatonic and Chromatic scales, through a different tuning of the intervals. These were called Chroai, or shades of colour. The notice of them by Aristoxenus proves that mathematicians had been at work, at an early date, to obtain new sounds from the scale; but, owing to the vague Aristoxenian mode of describing the notes as thirds, or quarters of tones, we cannot tell what mathematical proportions were adopted, except through the comparatively late work of Claudius Ptolemy, who preserves the divisions of Archytas, of Eratosthenes, and of Didymus. Neither the Octave itself, nor any musical interval within it, is divisible into equal parts; therefore, thirds and quarters of tones never were, and never could be; but there was an approach to those proportions in some of the scales.

The Diatonic had two Chroai, or shades, viz., the Diatonon suntonon, (strained tight,) or called simply Diatonon, it being the chief characteristic of the genus, as before described, and the Diatonon malakon, or Soft Diatonic, in which the forefinger string was relaxed about a quarter of a tone, so as to leave, roughly speaking, only three-quarters of a tone between it and the next lower string, instead of a tone. Plato alludes to these two kinds of Diatonic; therefore even the second of them must have had an early origin. .

The Chromatic had three Chroai, or shades. First, the ordinary Chroma, or Chroma tonaion, before described. Secondly, the Chroma hemilion, or Sesquialteral Chromatic, in which intervals of about three-eighths of a tone (an eighth added to each quarter-tone) were substituted for the semitones; and thirdly, Chroma malakon, or Soft Chromatic, in which intervals of about a third of a tone were similarly employed.

There was but one Enharmonic.

To know only the proportions of one Fourth, in a Greek scale, is a sufficient index to the composition of the entire two-octave scale; because, at the base of each Octave was a diazeuctic, or major tone, and after it, two conjunct tetrachords completed the Octave in our form, i.e., counting it upwards from the key-note.

To show the divisions of one of these tetrachords, without fractions, the plan of Claudius Ptolemy is here adopted in preference to that of Aristoxenus, or of Euclid. (Introductio Harmonica, pp. 11, 12.)

Aristoxenus and Euclid count six for a semitone, and twelve for a tone; so that a Fourth, being made up of two tones and a semitone, counted as 30. Ptolemy doubled those numbers, because the Sesquialteral Chromatic must otherwise have been expressed by 4'1/2. With him, therefore, a quarter-tone, (or Enharmonic diesis), is 6; a semitone is 12 ; and a tone 24; thus representing the complete tetrachord by 60.

The six scales are here placed side by side to facilitate comparison, although the three principals, here in larger letters, have already been explained.

DIATONIC (Ditonon suntonon).................. 12, 24, 24=60.

Soft Diatonic ...(Ditonon malakon).............. 12, 18, 30=60.

CHROMATIC ...(Chroma tonaion) ............... 12, 12, 36=60.

SOFT CHROMATIC...(Chroma malakon) ...... 8, 8, 44=60.

SESQUIALTERAL

CHROMATIO (Chroma hemiolion)................. 9, 9,42=60.

ENHARMONIC ............................................... 6, 6, 48=60.

Aristides Quintilianus describes six other scales as Enharmonic, which, according to all earlier authorities, are mixed modes, having Enharmonic quarter-tones. He reports them as very ancient. The internal evidence of this treatise shows that Meibom ascribed too remote a date to the writer. Meibom seems to have been desirous of magnifying the importance of the addition he was about to make to musical history, by being the first to publish Aristides treatise. He ranks the author as preceding Claudius Ptolemy, quite overlooking the fact that he borrows the above division of the scale into 60 parts from Ptolemy. I can hardly suppose Aristides Quintilianus to have lived earlier than in the fourth century, and more probably a century or two nearer to our own time. In the first place, he is the only Greek writer who places G and G# at the base of his scale. As to this G, (which mediaeval writers distinguished as Gamma, because there was already a capital letter, G, an Octave above it, in the ecclesiastical scale), Guido describes it as a note added by the moderns. Next, Aristides must surely have lived when all scales but the one common Diatonic were forgotten. He would not otherwise have misinterpreted Plato in a musical term relating to one of the forgotten scales; or suppose that he intended to apply the adjective, suntonon, to an Enharmonic division of the tetrachord, when there was but one Enharmonic. The Enharmonic is the very opposite to suntonon, viz., the malakotaton of all scales, the first meaning tightly drawn, and the second the softest or most relaxed in the tuning. Plato refers to the two kinds of Diatonic-Lydian, and, therefore, he adds the otherwise unnecessary prefix of suntonon to the principal one, and applies malakon to the other.

The Enharmonic scale, to which Aristides Quintilianus has given the name of Suntono-Lydian, is what every other Greek writer, early and late, has termed Hypo-Lydian; and the inference to be drawn is, that the mistake originated with the copyist of the old manuscript which he used, and that he lived at too late a period to detect it. He himself says that the Enharmonic scale is indivisible; therefore, there cannot have been any second kind, and no prefix to the name could be required.

A third argument for the late date of this author is, that his system of musical notation has many changes from the system of Alypius, so that the one will not serve throughout to explain the other. The system of Aristides Quintilianus is a universal one for all modes, and he gives the notation for every semitone in the entire scale. This is a great improvement, but one unknown to Boethius, who wrote in the sixth century yet Aristides does not give it as his own system, or as any novelty, but   recognised plan.

The date that Meibom has assigned to him has been so universally adopted by the learned, that it has become necessary to show cause for dissent. The scale that Aristides named Suntono-Lydian in the ancient set of scales may be seen to be Hypo-Lydian, by having its key-note on the third ascending string of its Octave on the lyre.

Scales were hardly Meibons forte, or else he would have discovered this to be Hypo-Lydian. In his notes upon Euclid he formed a set of scales so erroneously as to base the tetrachords upon the inner movable strings, instead of upon the outer, fixed sounds. Again, in his comments upon this author, he tells the reader that the two most ancient tetrachords were joined together by one string common to both, and that it was called Hypate Meson, the lowest of the middle tetrachord. Aristotle says that the string was Mese. It is clear that Meibom had not read Aristotle’s Problems, and was guessing. In the following scales his conjectural emendations are not infrequently in the wrong places, as he might have discovered if he had drawn out a diagram of them, according to their key-notes on the lyre. The text of Aristides is undoubtedly very faulty in the copy Meibom used, but still, all scales were formed according to laws about which there is no disagreement among ancient writers.

The following are the six ancient scales of Aristides according to the inaccurate revision of Meibom. The figure of 1/4 is intended for the Enharmonic diesis or quarter-tone :

In the above, the Dorian interval to its key-note is in its right place, as fourth of the series, according with the text. It has an ascent of two tones from the forefinger string, and its diazeuctic tone is next above it. But the Phrygian is in the wrong place. It should be on the string next above the Dorian, and so one degree to the right in the scale. Meibom added one of the above quarter-tones to fill up its Octave, so as to make it agree with another line in the text, but he ought to have placed the added quarter-tone to the left, instead of to the right, of the key-note. As it now stands, Dorian and Phrygian key-notes are on one string, which was impossible. The curious may pursue the analysis further by comparing the Greek text with his translation at p. 21, and with the diagram at p. 22. I subjoin the principal seven Enharmonic scales according to their proper order. The diagonal line from one figure of 2 to another shows the ascent to the Mese, or key-note of each, and its diazeuctic tone is in the next division to the right of it.

The Iastian has no place in the following, because it could only occupy the position of one of the seven scales already figured; and it was for such reasons that Claudius Ptolemy recommended the reduction of the number of scales to seven :

The value of the treatise of Aristides Quintilianus is but little affected by a slip about ancient fanciful scales, and as to a musical term which had fallen into disuse at the time when he was writing. It would not be impossible, even now, to find a very learned man who could not define a musical scale of Chaucer’s age, and who might, perhaps, be puzzled with one even of the time of Queen Elizabeth.

CHAPTER VII.

No subject connected with ancient music has been discussed with more earnestness, or at greater length, than as to whether the Greeks did, or did not, practise simultaneous consonances, and intermix them with discords; thus making harmony in the modern technical sense of the word.

The great discussion arose in the seventeenth century, from the discovery that the Greek word, Harmonia, is not a synonyme for simultaneous concordant sounds; although the world had been taught to regard it in that light, and had incorporated it into modem languages in that sense. So far the discoverers were right, for Symphonia is the Greek word for consonance. But then, instead of pursuing the inquiry by comparing Greek definitions of Harmonia, some of the disputants jumped to the hasty conclusion that the word had, at no time, the sense of simultaneous consonances, but meant only a succession of intervals, in single notes, according to their scale. Next, they defined Melodia as a succession of sounds, according to time, measure, and cadence and, thirdly, Symphonia as differing only from Harmonia and Melodia in that its sequences were limited to such intervals as would make up Fourths, Fifths, and Octaves; and that it did not permit any intermixture of Seconds, Thirds, Sixths, or Sevenths. So they denied simultaneous consonance even to Symphonia.

Thus, from a promising opening, the investigators rushed into error in the opposite extreme. If the enquiry had been pursued in the only proper way, by searching for, and comparing, Greek definitions of Harmonia, its meaning would inevitably have been traced to be the Theory and Practice of Music, and identical with the later word, Harmonike. Harmonia includes poetry united with music, but not poetry alone, and so it has a more restricted sense than Mousike. Again, the chanting of poetry, though unregulated by musical intervals, is Melodia, and the metre of the poetry brings it within the denomination of Mousike; but it is not Harmonia. So that the primary translation of the word Harmonia is our Music.

The original question might, at any time, have been settled by referring to the precise explanation of Harmonia, by Philolaos. The only point to have been recollected was that, in the time of Philolaos, Greek science and Greek practice were limited to an Octave; and that any other Octave could be but a repetition of the first. Therefore, as Plutarch says, Pythagoras limited the science of Harmonia to the sounds that are within an Octave.

The passage in Philolaos was probably passed by and neglected, on account of the difficulty of understanding its technicalities. To those who had not learned anything of Greek music, some of the words would not have been intelligible.

Although it is popularly supposed that men who undertake to write about Greek music are acquainted with some of the elementary treatises, the controversy about Harmonia clearly proves that many of the disputants had not thought it necessary. The passage from Philolaos might have been found, quoted by Nicomachus; and his treatise is included in the collection of Greek authors upon music, edited by Meibom, and printed in 1652. Therefore, the extract was perfectly accessible, and every one might have read it for himself.

The controversy has been carried on intermittingly for full two hundred years. In the last century English scholars engaged warmly in it, but among them, some, rather to show their powers of argument and classic lore, than from any reasonable expectation of throwing new light upon the meaning; for the Greek authors upon music had formed no part of their reading. In the present century, the discussion has been going on chiefly in France, in Belgium, and in Germany. It is not even yet concluded; for, since the harmony of the ancients must form the subject of the present chapter, it becomes necessary to controvert the strange hallucinations of the latest writer upon ancient music F. J. Ftis, of whose History a third and posthumous volume has been recently announced.

The theory of Fétis was perhaps peculiar to himself. It was that the Greeks had no other simultaneous harmony than an uninterrupted succession of Fourths, a similar succession of Fifths, or a succession of Octaves.

This would bring the polished Greeks down to the barbarian level of Hucbald, in the middle ages. Such a theory is in absolute contradiction to Plato and to Aristotle two authors whose works seem only to have entered into Fétis’s reading, if at all, through the medium of translations, many of which are not remarkable for accuracy as to the musical parts of those authors. The slender peg upon which Fétis hung his extraordinary theory was not derived from any Greek author, but from two lines of Horace. Further than this, not only was the idea borrowed, but even the author was misinterpreted.

As Fétis held the high position of Director of the Conservatoire of Music in Brussels, he was looked up to as of some authority, and his fluent writings seem to have had a larger share of currency in France than those of learned French and Belgian writers. He says, in his Biographie Universelle des Musiciens, in which he devotes twenty-five columns to his own life, and but three and a-half to that of Auber, that he wrote the musical articles for three French journals at the same time, and often penned three criticisms in a night upon one new work, and all from different points of view. Add to the three journals the Biographie des Musiciens, in which he included living authors and composers, as well as the dead, and we have a formidable man; one not to be needlessly provoked by musicians who hoped for favourable report of their works, either with their contemporaries or with posterity. This must surely have been one reason why his extraordinary vagaries were allowed to have such free sway.

Fétis wrote upon the music of all styles and all ages, but it is only with his theories about ancient music that I have here any concern.

In Greek music, Fétis had the courage to correct Aristoxenus and other Greeks, as well as Josephus upon Hebrew words and upon Jewish musical instruments. Fétis was quite persuaded that Aristoxenus, Juba, and other great writers, did not understand Greek musical instruments, but that he, who seems not to have known the forms of the Greek letters sufficiently to look out a word in a Lexicon, could set them all right. He had evidently arrived at the age when certain men consider themselves infallible an age that has hardly been sufficiently recognised; indeed, the symptoms have not always been so strongly developed as in the late M. Fétis. We have a proverb that young men think old men fools, but old men know that young men are so. For that we must have been indebted to an infallible. Fétis asserted his claims as early as 1850. He then announced in his journal that he would give the definite solution to the difficulties before which the genius, and learning of the greatest men, such as Descartes, Leibnitz, Newton, d’Alembert, Euler, and Lagrange, had succumbed.

Fétis has a new way of making Greek tetrachords. It differs wholly from that of any of the Greek authors. They all made tetrachords to consist of two tones and a half, but his are only of two tones. He can only have attained to his own system by inspiration; for there has been nothing like it, either before or since. He is equally original in his teaching about the present musical scale. In writing the memoir of Boethius, (Boece), he praises him for not having adopted the false proportions of Didymus and of Ptolemy. If we grant that Fétis may be supposed to have known what he was writing about, he recommends the world to give up consonant major and minor Thirds, and to return to the discordant Thirds, or Ditones, of Pythagoras.

These are slight samples of the peculiar teaching of the author of the most recently published general history of music. His horror of mathematicians in music is sufficiently proved by the careful way in which he singles out the greatest of them for his supposed triumph. Didymus and Ptolemy were mathematicians as well as the other great men named. Fétis felt no need of mathematicians. He could, and did, write books on the theory of music, without having even troubled himself to learn the proportions of musical intervals, or the laws of natural sounds.

Fétis ascribes to the Greeks two different systems of music at different periods, one for those who lived from the time of Pythagoras to that of Aristoxenus, when, according to him, all was plain song or Gregorian music; and, for those Greeks who had the good luck to be born at later dates, he allows such charms of harmony as successions of Fourths, and successions of Fifths. This uncomplimentary theory has no support from any Greek author. Fétis derived the idea that he thus harped upon from Claude Perrault, one of the numerous disputants about ancient harmony in the seventeenth century; and Perrault took his idea from misunderstanding two lines of an epode of Horace.

Sonante mixtum tibiis carmen lyra,

Hac Dorium, illis barbarum.

Fétis pursued the illis barbarum all round the circle, till he had proved, to his own satisfaction, that barbarum must mean the Mixo-Lydian mode, and that it was simultaneously employed with the Dorian, (or the keys of G and D together,) so as to make perpetual Fourths; or else it was Dorian and Hyper-Phrygian (D and A,) so as to make a constant succession of Fifths.

It is clear that Perrault had not read Aristotle’s 19th Section of Problems, in which it is said, over and over again, that the Greeks did not sing sequences of Fourths, and did not sing successions of Fifths. As to the two lines of Horace, we shall refer to them again, but will no farther follow M. Fétis through his positive solution of the difficulties before which genius and learning had succumbed, than to take one passage that he employed, through the medium of an indifferent translation of Plato, to show that it has the directly opposite meaning to that for which he employed it.

The translation adopted by Fétis was one by Victor Cousin; and, to strengthen public belief in it as an authority, he added that Cousin was assisted by Nicolo Poulo, a Greek of Smyrna, who was employed in the library of the Institut de France. Also that Poulo was fort instruit dans la musique. Nevertheless, it does not follow that he should have understood the technicalities of ancient music, and it appears so, almost at the first word; for, where Plato recommended the lyre to be played in unison with the voice, (so as to guide the learner to the right notes), Poulo missed the sense of the word proschorda, which means a string in unison. Again, to suppose that Plato could have intended to establish symphony and antiphony between density and rarity, and between quickness and slowness, imagines some peculiar process quite unknown to the modems. Whately says: As muddy water is likely to be thought deeper than it is, from your not being able to see to the bottom, while water that is very clear always looks shallower than it is; so, in language, obscurity is often mistaken for depth. That seems to have formed the reliance of the translator in his rendering of this passage. It may have been a crux, because it goes a little more deeply into ancient music than the modems have usually pursued the subject.

The following is an attempt to give the sense of the author rather than the most literal translation, because a trifling amplification promises to render it more generally intelligible to those who have hot taken up the subject of ancient music. The original and Cousin’s translations are subjoined in a note. Plato says : On this account, therefore, both the player on the Kithara and the learner ought to avail themselves of the sounds of the lyre, for the sake of the exactitude of its notes, to play in unison with the voice, note for note. But, as for playing different passages and flourishes upon the lyre, when the notes for the instrument vary from those intended for the voice, or, when close intervals of the Chromatic and Enharmonic scales are opposed to the wider intervals of the Diatonic; also, when there are quick to slow, or high to low notes, thus making varied harmony, or running together in Octaves. And in like manner, as to adapting the manifold diversities of rhythm to the notes of the lyre, it is unnecessary that all these things should be learned by those who have to acquire a serviceable knowledge of the art and science of music within three years, on account of the speed that is demanded, for opposite principles, confusing one another, cause slowness in learning.

Three years would not have been required only to learn to accompany the voice in unison with the lyre. That was but one branch of Harmonia, and Harmonia itself but one branch of that Mousike, from which we have taken the word Music, through the Latin Musica. Mousike was reputed by the Greeks to be the encyclopaedia of learning. Although, in the course of general education, boys were only taught so far as to play in unison with the voice, the Greeks practised every variety of vocal accompaniment. Aristotle’s opinion was that all consonances are more pleasing than simple sounds, and he justly adds that the sweetest of consonances is the Octave. His estimate of the Octave has been fully shared by the moderns; for, the sets of variations upon an air, so much in favour some years ago, would have been thought incomplete if there had not been one among them specially devoted to playing passages in Octaves. Greek ears, and those of the moderns, again coincide in forbidding the playing of Fourths or Fifths in sequences, and in only allowing them to be intermixed with other intervals.

The development of harmony was much less favoured by the national instrument of the Greeks than it is by those of the moderns. The lyre was made to serve the triple purposes of the rhapsodist, of the orator, and of the musician. Orators now speak without the accompaniment of music, and every house is furnished with a less portable, but more complete, musical instrument than the lyre.

Plato, Plutarch, and some others of the ancients, valued music more highly for educational than for any other purpose, and, desiring to make the knowledge universal, they advocated a return to the ancient simplicity of style. Plato would have banished from his model republic all musical instruments that had an extensive compass of notes. He objected to flutes as having too many sounds.

Plutarch commended the ancient Nomes of Olympus, which were upon three notes; and he expressed his regret that the limitation of melodies to the compass of a few sounds had become obsolete in his own time. Yet the instrumental accompaniments played by the very ancients to whom he refers were certainly compounded of concords mixed with occasional discords; for he states that, in the strict spondaean mode, they played such notes as D, in dissonance with C, or B, and in  harmony with A or G. In these were the passing discords of one tone against the next; of the minor Third (esteemed a discord on account of the imperfect tuning), and the concords of the Fourth, and of the Fifth. In spite, however, of his advocacy of limit to the number of notes, Plutarch admitted music to be also a suitable attendant on conviviality; and, in his judgment, the art is never more beneficial than in seasons of festive relaxation and indulgence. He thought, too, that music has the power of allaying the stimulating effects of wine.

Many more proofs of the employment of harmony might be derived from Plutarch’s Dialogue on Music as when he states that the reason assigned for the exclusive use of the ordinary Diatonic and Chromatic scales in his own time, and for the rejection of all such refinements as Chromatic thirds, and Enharmonic quarters, of tones, was the inapplicability of such minute divisions for harmony; and again, in his references to Plato and to Aristotle .

Aristotle speaks of playing Mese and singing Paramese; i.e., striking the key-note and singing the tone above it necessarily a discord. Plato, in the preceding quotation, alluded to playing or singing one of the small intervals of the Chromatic or Enharmonic scale against the Diatonic. In both cases those would be discords, made, as we commonly do, in passing from one interval to another. Gaudentius describes Paraphones as holding a middle place between consonances and dissonances, but as sounding like consonances when played together upon an instrument. He classes Ditones and Tritones among them. (He is the only Greek author who includes Tritones.) Plutarch speaks of a practice among the lyrists, in his time, of altering the tuning of the lyre, and of invariably flattening the forefinger strings. This is strong testimony to the goodness of their ears. The object was, no doubt, to get rid of the Fourth and minor Seventh, and so to make better melody with other parts of the scale. He adds, that they lowered the fixed sounds to suit this system.

Athenaeus quotes Phaenias the Peripatetic, one of the immediate disciples of Aristotle, as saying, in book I. of his Treatise on Poets, that Stratonicus, the Athenian, was the first person reputed to have introduced full chords in simple harp-playing, (without the voice,) and that he was the first who took pupils in music, and who composed diagrams of music; perhaps meaning that he was the first who wrote down his compositions upon wood or papyrus. The credit of having been the first instrumentalist is, however, disputed by others. Harmony is implied in the one fact of Stratonicus having played chords upon his instrument. Again, the Epigoneion was an instrument of the harp kind, with forty strings; and even if it had but half that number, some of them could only have been useful for harmony, as the voice would very rarely extend beyond fifteen notes. Although the Epigoneion is now transformed in the upright psaltery, says Athenaeus, it still preserves the name of the man who was the first to use it. Epigonus was by birth an Ambraciot, but he was subsequently, made a citizen of Sicyon, and he was a man of great skill in music, so that he played with his hands, without a plectrum; for the Alexandrians have great skill in all the above-named instruments, and in all kinds of flutes. This quotation is another evidence that the Egyptian custom of playing instruments of the harp kind with both hands had extended, at an early date, from Alexandria to Greece. Again, to Epigonus is attributed, on the authority of Philochorus, that he was the first who introduced duets between harp and flute, and who instituted a chorus.

Several passages from Latin authors have also been brought into the discussion about ancient harmony, and among them the ninth epode of Horace, before referred to. Horace proposes to celebrate the victory of Actium with Maecenas, at his villa, the song with the lyre being intermingled with flutes, a Dorian strain on the one side, and for those yonder, Phrygian or some other.

Sober and manly Dorian might have suited the tastes of Maecenas and of Horace, but there were others, Horace thought, who would prefer something more lively, more enthusiastic, bacchic, or even erotic for such a joyous celebration.

It seems almost needless to remark upon this passage that the intermingling is of the voice, the lyre, and the flutes, and not of the Dorian and Phrygian songs, which are sufficiently kept apart by the words hac and illis. Yet the Fétis theory was built upon a directly opposite construction. He omitted, however, to elucidate one part of his system, viz., how he proposed that the words, the rhythm, and the time, of two songs of opposite character were to be made to harmonize together. Something more than a succession of Fourths and Fifths was required for that purpose. Yet it was upon this passage that he built up an imaginary system of music for the Greeks, and as it was his only proof, he was under the necessity of coupling together les Grecs et les Romains, in the title of his book.

While on the subject of the Romans, there is a passage in the 84th Epistle of Seneca, that was long after borrowed from him by Macrobius, and which refers both to the ancient chorus, and to harmony, while it gives a curious picture of music at the public celebrations of Imperial Rome. It begins thus :

Do you not observe of how many persons voices a chorus consists? and yet but one sound is produced from all. One has a high voice, another low, a third a middle voice; the tones of women are added to those of men; flutes are intermingled. No single voice is distinguishable; it is heard only as a portion of the whole. I am speaking of the chorus with which the ancient philosophers were acquainted; for, in our public celebrations, there are more singers than there were formerly spectators in the theatre. When our array of singers has filled up every passage between the seats in the amphitheatre when the audience part is girt round by trumpeters, and all kinds of pipes and other instruments have sounded in concert from the stage out of these differing sounds is harmony produced. Thus would I have it with our minds.

Another allusion to harmony is found in his 88th Epistle, which is on the subject of consolation in adversity. He there says :

And now to music, you teach how voices high and low make harmony together, how concord may arise from strings of varying sounds, teach, rather, how my mind may be in concord with itself, and my thoughts be free from discord. You point out modes fittest for mournful strains, but, in my adversity, show rather how I may restrain the utterance of any mournful note.

There is another equally unequivocal passage from Cicero, relating to music in parts, which will be found in the second book of his Republic:

For, as in strings or pipes, or in vocal music, a certain consonance is to be maintained out of different sounds, which, if changed or made discrepant, educated ears cannot endure; and as this consonance, arising from the control of dissimilar voices, is yet proved to be concordant and agreeing, so, out of the highest, the lowest, the middle, and the intermediate orders of men, as in sounds, the state becomes of accord through the controlled relation, and by the agreement of dissimilar ranks; and that which, in music, is by musicians called harmony, the same is concord in a state

Cicero’s mere definition of the word concentus, in his Republic, ought to have been enough to prove the whole case :Hie [sonus] qui. . . acuta cum gravibus temperans varios sequabiliter concentus efficit. (Rep., VI. 18.) Again, if any of the disputants had read Section 19 of Aristotle’s Problems, and especially No. 39, in which he says that all concordant sounds are more agreeable than single notes, and that of concords the Octave is the most agreeable, that ought to have sufficed to prove the Greek case. But, in truth, floating upon the surface of music has been for ages more popular than diving.

It is now curious to look back upon the ardent discussions about the harmony, or the no-harmony, of the ancients, and to read the number of distinguished names among those who took part in them.

Dr. Burney devotes nearly forty pages of his History of Music to a dissertation upon this subject, and concludes with his own summing up, which is not the least curious part.

The following is the catalogue of names from his eighth Section of vol. I. It does not include those who enlisted, or were drawn into the discussion after 1776, neither does it affect to be complete as to those who preceded that date :

FRENCH.  Charles Perrault, Claude Perrault, Boileau, Racine, La Bruyere, Fontenelle, Abbé Fraguier, Abbé Roussier, Mersenne, Burette, Chateauneuf, de Chabanon, Father Boujeant, Father Cerceau, and Jean Jacques Rousseau.

ITALIANS.  Franchinus Gaffurius, Glareanus, Marsilius Ficinus, Zarlino, Vincenzo Galilei, G. B. Doni, Zaccharia Tevo, Bottrigari, Artusi, Tartini, Bontempi, and Padre Martini.

SPANIARDS.Salinas and Cerone.

GERMANS AND HOLLANDERS. Kepler, Athanasius Kircher, Isaac Vossius, Meibomius, and Marpurg.

ENGLISH. Dr. John Wallis, the mathematician; Sir Isaac Newton, Sir William Temple, Wooton, Boyle, Dr. Bentley, Swift (in The Battle of the Books, Stillingfleet, Mason, Dr. Jortin, and, lastly, Dr. Burney.

There would be no difficulty in adding largely to Dr. Burney’s list, but it suffices to show the great interest formerly taken in this subject. In his summing up, Dr Burney adopted an erroneous definition of The Harmony of the Ancients, from Mason, and in translating Aristotle, he missed the distinction between the Greek Sumphona and Antiphona.

In the history of literature there is perhaps no one thing more singular than that, with the number of learned men of all ages, and of all nations, who have enquired into the history of ancient music, no one of them should ever have thought of making an adequate investigation as to the meaning of the everyday words, which have been incorporated into modern languages through the Latin. In some, the cause may have been implicit faith in all Church usages and traditions; but that alone is an insufficient excuse; and yet, to what other cause are we to attribute it? One thing is certain, it is mainly owing to that lack of enquiry that Greek music has so long remained a mystery, and that passages relating to music in classical authors have been so long misunderstood.

There are no extant specimens of ancient Greek or Roman harmony, but there remain three of Greek hymnal melody, which will form the subject of the next chapter.

CHAPTER VIII.

VINCENZO GALILEI, father of the great astronomer and mathematician, Galileo Galilei, was the first to publish three ancient Greek hymns with their music, in his Dialogo della Musica Antica e Moderna, at Florence, in 1581. They were copied from a Greek manuscript that was then in the library of Cardinal St. Angelo, at Rome.

A second Greek manuscript, which included the same hymns, was found among the papers of Archbishop Usher, in Ireland, after his decease, and was bought by Bernard, a Fellow of St. John’s College, who took it to Oxford. The hymns were printed from that manuscript, under the editorship of the Rev. Edward Chilmead of Christ Church, at the end of the Greek edition of the astronomical poems of Aratus, published by the University in 1672.

During the seventeenth century there was great earnestness among the learned at Oxford in reviving ancient Greek literature, including that of music. When Mark Meibom, or Meybaum, (in Latin, Meibomius,) undertook to edit a collection of the works of Greek authors upon music, and to publish them at Antwerp, he received most hearty encouragement and assistance from eminent members of the University, and particularly from Selden, from Patrick Young (who had been librarian to James I and Charles I), and from Gerard Langbaine, Provost of Queen’s College, and keeper of the Archives of the University. They lent, or procured for him, the loan of valuable Greek manuscripts from private libraries, and both Selden and Gerard Langbaine copied and compared transcripts; the latter collating with the best of the numerous Greek manuscripts in the libraries of the University. Chilmead gave up his prepared edition of Gaudentius in Meibon’s favour, and all concurred in promoting and in giving publicity to his work. Many copies must have been bought in England, for no books upon ancient music have been more commonly found in private libraries, when sold by auction, than the Antiques Musicae Auctores Septem. Nevertheless, for want of sufficiently general encouragement, and, as Dr. Wallis adds, scarcity of means, Meibom found himself unable to carry the series further. Then Dr. John Wallis, who was Savilian Professor of Geometry in the University, included the remaining unpublished treatises of Claudius Ptolemy, of Porphyry, and of Bryennius, with his own works, (giving the Greek texts with Latin translations, and with large and useful comments upon them,) and these were published by the University in 1693-99. It may therefore be said that, within that half century, Oxford did more towards advancing the knowledge of this most ancient music than has been accomplished by any University in Europe, whether before or after.

In 1720, M. Burette found a third manuscript containing these hymns, in the King of France’s library at Paris, No. 3221, and he reprinted them in the fifth volume of Mémoires de l'Académie des Inscriptions, 1720.

The Florentine edition agrees with that of Oxford, but the French edition adds six introductory lines, without music, to the Hymn to Apollo, and supplies three or four missing notes.

These hymns are the only trustworthy remains of ancient Greek music; for although the first eight verses of the first Pythian of Pindar were printed by Athanasius Kircher in his Musurgia, in 1650, and were asserted to have been discovered by him in the famous Sicilian library of the Monastery of St. Saviour, near the port of Messina, he was by far too imaginative ever to be followed with safety, and especially in this case. Although every possible search was made for the aforesaid manuscript soon after his announcement, and all the manuscripts in the Monastery were catalogued, this could never be found.

The Te Deum Laudamus that Meibomius printed at the commencement of his Antiquae Musicae Auctores, and which Sir John Hawkins mistook for an ancient copy, was but an exercise of Meibom’s ingenuity in turning Church Plain Song into Greek musical notation, just to show how it would look; and as it was then the custom in Germany to sing the B flat in the Te Deum, although the flat was not marked in the Plain Song, he adopted the Greek sign for B flat, but left that note natural in the ecclesiastical notation. For the understanding of English readers there should be one flat at the signature, so as to make it correspond with his Greek music.

The first of the three ancient Greek hymns is to the Muse Calliope, and it includes an address to Apollo, as leader of the Muses. The second is a hymn of greater length, addressed to Apollo, and the third, which is imperfect as to music, is dedicated to Nemesis. No fair estimate of the former state of music in any country can be adequately formed from the remains of its hymns. Sacred music has always been in arrear of the secular, and no one would suppose that a piece of ordinary hymnal music of the present century would fairly represent the present state of music in Europe, although such a specimen might, by some similar chance, survive for many centuries to come. Yet even these hymns throw some light upon the ancient state of the art.

Before Burette’s time they were printed as Plain Chant, without any attempt at timing the notes. He was the first who reduced them according to length of syllables, and barred them so; and after him, Dr. Burney, and others. The plan they adopted was to mark every long vowel, or syllable, by a minim, and every short one by a crotchet. As the metre was often irregular, this arrangement threw them out of rhythm, and it may be objected that it was not the system that should have been adopted to represent ancient music fairly in modem notation. In the time of the Ptolemies, the Alexandrian grammarians discovered that the poems of Homer included a large number of irregular lines, which they then set themselves to rectify; but those irregularities were held to be sufficiently accounted for and excused, because the poems were written for chanting, and were intended always to be rhapsodised, or chanted. In music, it is not necessary that the exact syllabic reading-length of words should be adhered to. It would thereby be deprived of all variety, and become monotonous in the extreme. Music has the power both of prolonging and of shortening the duration of words, and thereby of covering irregularities in metre. For instance, we chant the Te Deum, the Jubilate, and the Psalms rhythmically as to music, although written as prose. Rhythm is the parent of melody, and even savages beat regular time to their songs. How much more then must rhythm have been an essential part of Greek music, when it was from the Greeks that the laws of rhythm were derived!

Burette’s copy is now but little in the hands of English readers, therefore further remarks, although of general application, may be limited to Dr. Burney’s later version, which is in the same style as that of Burette.

First, as to the imaginary difficulties in adding a base to the music of these hymns. Dr. Burney says : Upon the whole, these melodies are so little susceptible of harmony, or the accompaniment of many parts, that it would be even difficult to make a tolerable base to any one of them, especially the first.

Seeing no sufficient reason for this comment, I selected this first of the hymns to have a base added to it. My learned and kind friend, Professor G. A. Macfarren, of the Royal Academy of Music, has obligingly contributed two kinds of harmony, one in the Greek view of the key, and one in the modem. So the reader will now judge for himself how far Dr. Burney was from the mark when he spoke of the insusceptibility of these Greek hymns for harmony.

Dr. Burney printed all three in the key of F sharp minor, because, says he, It was discovered that these hymns were sung in the Lydian mode of the Diatonic genus, by comparing the notes with those given by Alypius. That all the notes are to be found in the Lydian mode is undoubtedly correct, but a little further comparison would have shown that they are equally to be found in the Hypo-Lydian mode, with C# as Mese. The one note that a modem musician might not expect to find in the key is d natural in the upper Octave, but it is essential to the Conjunct, or Synemmenon, tetrachord of that mode. Therefore the question between the modes has to be determined by Aristotle’s law, which of the two notes, F sharp or C sharp, more nearly complies with the required conditions, as the Mese in question? In that view there can hardly be a doubt but that C sharp, and not F sharp, is the nominal Mese. So the hymn is to be taken in the usual hymnal scale of the Lesser Perfect System, with a semitone, instead of a tone, above that string.

The particular use of the semitone above the keynote, (as of this d natural in a mode having C sharp as Mese,) was that it enabled the player to modulate from the Hypo to its parent key, as here from Hypo-Lydian to Lydian, the latter being a Fourth higher. If we look back to the tuning of Terpander’s seven-stringed lyre, and of Ion’s ten strings, we may find the same semitone above Mese, and so the three scales. Terpander’s, Ion’s, and this, may fairly be said to establish the long continuance of this ancient and favourite hymnal modulation. Herein, too, we trace the origin of the b flat above a in the Plain Chant of the Western Church; and how, in its most ancient form, it allowed of the modulation from Hypo-Dorian to Dorian. If it were but for this one hitherto unnoticed link between the two, these hymns would be of considerable historical interest.

Another point to be observed is that, even in the seventh century BC, Terpander had exactly the same number, and the same aeries, of notes down from his key-note as in these hymns, although he had but a Fourth above it, whereas the hymns extend to the Sixth, and one to the minor Seventh.

The lyre for the hymns was perhaps one of ten strings, since the compass of the voice-part does not exceed ten notes. The Mese of the Hypo-Lydian mode is the tenor c sharp, that is, one ledger line above the base staff and one ledger line below the treble. The vocal compass extends to a Fourth below it, viz., to G sharp, and rises upwards to a, the minor Sixth, and, in the Hymn to Nemeois, to b, the minor Seventh.

In writing out the Hymn to Calliope according to the strict quantity of syllables, the metre being irregular, Dr. Burney adopted the system of making four changes of time, from triple to common, and vice versa, within the first line of the music. He included two lines of poetry within these seven bars, and began the eighth bar with a rest.

It would have puzzled any chorodidáskalos, or Dr. Burney himself, to have kept singers in time with such interruptions of rhythm. It is strange that he should have printed it so, after having remarked but a few pages before that Greek music was all rhythm. The time of notes, says Gaudentius, is to be ruled by the rhythm of the poetry. There is not a shade of probability that the hymn can have been intended to be sung in the hobbling, unrhythmical style adopted by Burney. Even if it had been desired to throw ridicule upon ancient music, as one way of disposing of a troublesome subject, no more effectual means could have been adopted.

The hymn is described in the text as irregular iambic, and the irregularity begins with the second line. The first is what was called Dimeter, or Two Measure iambic, consisting of four poetic feet. This was formerly called Minstrel Measure in England.

The iambus is a poetic foot having the first syllable short and the second long. The spondee has two long syllables.

In irregular metres, the law which overrules the strict timing of syllables is the Measure of the verse. A Measure consists of two poetic feet, which are not necessarily of the same kind, and is the equivalent to the bar in music. The one difference between the two is that the bar of music begins on the thesis, or down beat, which is the stronger accent. That order was once reversed for dancing, as the arsis, or up-spring, was the strong one that began the movement; whereas, in beating time with the hand, as for music, the strong beat is downwards, and the arsis is weak. In the case of iambic verse, or other beginning with a weak syllable, i.e., with the arsis, or up-beat, that syllable is placed before the bar. So the music has the appearance of the reverse of iambic, viz., of trochaic, or the first syllable long and the second short. The length of irregular syllabic quantities has to subserve and to be fitted into the arsis and thesis, or up and down beats of the foot of verse, in the measure that has been adopted. Instead, then, of such constant changes of time as those adopted by Dr. Burney, which make equally constant changes of the rhythm, one rhythm should have been preserved. The syllables should have been brought into the beats of the bar, in the best way the sense would permit, and with all the regard that could be paid to relative quantities. Proportion may be preserved when exact length cannot, it is but as quicker or slower speaking.

Thus verse and music will go together. When the same number of beats can be brought into each line of a poem, or into corresponding lines of stanzas, there should be no difficulty in writing out the music. A musician will be further guided in this by the notes themselves, which often indicate to him the author’s design. Therefore in a musical system so identical with our own as is the Greek, Dr. Burney could have been one of the best interpreters if he would have thought more of musical rhythm and less of the equal duration of syllables. In the state in which the hymns have hitherto been presented to readers, it is doubtful whether anyone can have noticed a single phrase of tune in any one of them. Those phrases of tune are now brought out.

There are so many cases in which music is to be found in old timeless notes, but written over poetry, which gives the measure, that many a fine old melody may yet be rescued from oblivion by a musician who will adopt this course. In the hymns as now printed, there has been little change from Burney’s copy as to notes, but much in their time, in order to preserve rhythm.

Anciently, the Long and the Breve in music were equivalent in duration to the long and the short syllable in recitation, and they took their names from the long and short syllables. But the system of musical notation has been changing century after century in favour of notes that will occupy less space, that can be more rapidly written, and that can be tied together so as to form a guide for the eye at one glance as to the duration of several notes; until at last, the crotchet and quaver, or even the quaver and semiquaver, now, represent the long and short syllable of ancient times. I therefore recommend that the notes be first copied over the words as crotchets, and that the precise time of the former be determined afterwards. Then that the line of poetry be divided into two, by scanning, or by the ictus, or accents in reading, and a bar drawn to the music before the down-beat of the second half. This one bar is a sufficient division for short metres, as in the first Greek hymn, but in the case of longer lines, or of triple time, the lines may require to be further divided. Then let the notes be timed within those bars according to the reading of the words, and as the phrases of music appear to require. If some of the accents should fall badly, there are still parallel cases in modem music. With such care there seems but little probability of material variation from the original design, and it is perhaps the only way of arriving at it. To bar music by accents is a comparatively modem practice. When bars were first introduced, they were mere measures of time, therefore old barring is not to be followed implicitly.

In the Hymn to Calliope, the first word of the second line is marked spon, for spondee, or for two spondees, in the line. The two long syllables of a spondee cannot be brought into iambic metre, but iambics can be brought into spondaic or common time, by adding on to the long syllable, or by a pause between each foot. There are several other lines in the hymn which equally require to be in common time. Thus the iambics must become irregular, as they are said to be. The long, or accented syllable, using the word accented in the modern sense of giving quantity, may be further lengthened by a dot or rest, as required in Greek verse for a katalexis to make up the time, or both syllables may be proportionably shortened, according to the necessities of metre.

The music of the hymns is included in five more manuscripts than were known to Burney. Facsimiles of them were printed in Berlin in 1840, by Dr. F. Bellermann, who added a collated text. From this, Bellermann corrected several wrong notes in earlier printed versions. A few notes are deficient in all manuscripts, and they are here supplied in smaller type. 

Greek hymns were a tranquil kind of music, emblematic of a mind at ease. There was no gehenna in the creed of the heathen to disturb their equanimity. Every banqueting party was subjected to a god; and, accordingly, men wore garlands appropriated to the gods, and greeted them with hymns and odes. Thus, Greeks and Romans emulated the Egyptian ladies, in making religion a subject of cheerfulness and festivity.

The following Hymn to Calliope is printed in the Hypo-Lydian mode as transposed a Fourth lower by Claudius Ptolemy, in order to bring it within the reach of ordinary voices. So G sharp is the Mese, distinguished by the A natural above it. At the old pitch, C sharp would have taken the place of G sharp, and the voice part would have ranged up to a, which requires a high tenor voice:

Sing, O Muse, dear to me

My song lead thou:

Let the air of thy groves- ,

Excite my mind;

Calliope, skilled in art,

Who leadest the gladsome Muses,

And you, wise initiator into mysteries

Son of Latona, Delian Apollo,

Be at hand, propitious to me.

Since Dr. Bumey's time other manuscripts of the hymns have been discovered. They supply the deficient ø in the first line, and vary the letter E over the fourth and sixth lines.

THE SAME HYMN TO CALLIOPE. The melody is again harmonized by my friend G. A. Macfaeeen, in the key of E, which has G sharp as its major Third, and to which E, as key-note, aU the progressions point.

The preceding hymn proves two points. First, that it was not indispensable that there should be but a single note to a syllable in Greek music, for here are several cases of two notes to one vowel. Secondly, that a long note might be given to a short vowel as well as to a long one, for spondee is marked over a short vowel. These are strong arguments in favour of the system of bringing them into rhythm, for which I contend. In both cases, we find the same freedom exercised as in music of the present day. There is a Greek passage On the Phrasing of a Composition, by Dionysius of Halicarnassus, that would have been of advantage to Burette and to Burney, if they had known or remembered it. It is: But rhythm and music diminish and augment the quantities of syllables, so as often to change them to their opposites. Time is not to be regulated by syllables, but syllables by time.

That there may be mistakes in the music cannot be wondered at, after the repeated transcripts that have been required in so long an interval of time. No one of the manuscripts from which the above is derived is older than the fourteenth century, and they are mostly of the fifteenth.

The musical notation of Aristides Quintilianus, like that of Alypius, is altogether in capital letters. In the hymns, the capital R represents a broken Beta; the small Sigma represents the capital C, the older form of Sigma; and the small Bau is a substitute for the Greek capital letter. The Greeks noted music by letters upright, inverted, jacent both on the back and on the face, turned right or left, and even by parts of letters. Such notation would be very subject to misconstruction by a copyist who did not understand the musical system; especially the broken letters, as he would most likely attempt to set them right. In some of the manuscripts there are letters that do not even belong to the scale. The Hymn to Apollo seems to begin correctly, but to be wrong in the after part. The authorship of the first two hymns, if not of all three, is attributed to Dionysius, in the Oxford manuscript, by the words Dionysiou Hymnoi at the commencement; but in other manuscripts the third hymn is attributed to Mesodmes, or Mesomedes. The rhythm of the second and third is of twelve syllables, or their equivalents in point of time, for each line of the poetry.

The Hymn to Apollo, saving the six lines of introduction, is set to music throughout; and it rambles about in a less tunable style than the other two. In the Hymn to Nemesis, there are only six lines with music, which is written over the first part of the hymn, except in one manuscript, and yet the poetry consists of twenty lines.

The Greek verses, which are not set to music, are so accessible to the curious, in Dr. Burney’s History of Music and in other sources, that, not being directly within my subject, it seems unnecessary to reprint them. With the same motive of avoiding needless extension, the reprinting of the separate Greek text of the second and third hymns with the Greek music-letters over them, in addition to the modernized version, may be excused. The one example of Greek musical notation over the Hymn to Calliope will probably be thought sufficient. There is, again, but little difference of notes between Dr. Burney’s copy and the following, but much in the time allotted to them, as well as difference of key. The hymn is printed like the last, in the treble clef, and therefore an Octave higher than the real pitch, as if for a man reading music from the treble, or G, clef. In this case, however, it is left in the original scale of Alypius, C# minor, to show how high Greek hymns were, and the necessity for Claudius Ptolemy’s system of transposition.

The Third Hymn is, in one respect, very remarkable; for, although noted, like the others, in the Hypo-Lydian mode, which, at the original pitch, is C sharp minor, it is rather in what we term its relative major, viz., in E. It is so, according to Aristotle’s laws as to Mese, and, except for D natural, would be so by modem laws. By modern laws, D must be sharp to make a major Seventh in the key of E; and as D is natural in the Greek scale, because it is only a semitone, instead of a tone, above, the ancient minor key-note, or Mese, therefore the modem key of E would lose one of its four sharps, and that one its major Seventh. If, then, D is to be natural, the modem key is A major, with three sharps, instead of E major, with four. The hymn is essentially in a major key, and is another of the many instances in which the ear has guided to what is right against the musical laws of ancient times. There could not be a complete major key under Greek musical laws, even down to the close of the thirteenth century, after which Bryennius wrote, but every old minor scale had a major scale within it, by beginning on the third ascending note instead of upon the first, as in A minor to begin on C. So this is irregular music that would have been condemned by the critics of the age, but such as would, nevertheless, please the ear, and which has been sanctioned by the laws of later times.

And now as to the date of this Hymn to Nemesis, and therewith of how far back the practice of a major scale may be traced. The earliest evidence about the hymn, according to Burette, is that it is more ancient than Synethius, a father of the Church, who flourished four hundred and twelve years after Christ; and who, in his ninety-fifth letter, quotes three verses from it as from a hymn that was sung in his time to the sound of the lyre...  It has been attributed by some to a poet, named Mesodmes, who flourished under the emperor Justinian, but Burette thinks the name corrupted from Mesomedes; and Capitolinus, in his life of Antoninus Pius, mentions a lyric poet of that name, from whom that emperor withdrew a part of the pension granted to him by Adrian, for verses which he had written in praise of his favourite, Antinous. Eusebius, in his chronicle, speaks of Mesomedes as a poet originally of Crete, whom he calls a composer of Nomes for the Kithara, which agrees very well with the author of the hymn in question. So says Dr, Burney, quoting Burette, but still the authorship is by no means certain, for these hymns are free compositions, in a very different style from Nomes.

And now, to judge upon strictly musical grounds, which seem not hitherto to have been taken into account. The scale in which the hymns are noted extends here to a Seventh above the keynote; yet they are upon the Lesser Perfect System, because they have the semitone, instead of a tone, above the key-note. No such extension of the Lesser Perfect System is mentioned by Claudius Ptolemy, writing in the first half of the second century of our era. If the compass had extended yet one note higher, so as to make an Octave above the keynote, it would not have been a Lesser System, but one of equal extent with the Greater; and Ptolemy’s objection to it, as not being two Octaves in extent, and, therefore, not being Perfect, would have been removed. It resembles more the scale adopted by the Christian Church, which combined the Greater and Lesser Systems, but which they only employed in the Dorian and Hypo-Dorian modes. A second inference against any very considerable Greek antiquity is the mode in which the music of the hymns is written. We should hardly have expected Apollo or Nemesis to be addressed in the Lydian or Hypo-Lydian mode at any early period of Greek history, but these modes were very much used in comparatively later times. Boethius gives only the musical notation of the Lydian and Hypo-Lydian, and so does the author of a late Greek treatise of an anonymous writer, published by Bellermann. The hymns appear, then, to have been written after the once-attributed characteristics of modes had been forgotten, and they were found to be mere differences of pitch.

These remarks are not offered as sure guides, but they lead to inferences that the date of the hymns is not earlier than from the second to the fourth century of our era. The poetry has been considered to bear strong marks of having been written at a time when Greek poetry was still flourishing; and it would appear, from the subjects, that Paganism must have been at least surviving, if not flourishing, also.

The translation of the music of the second hymn is printed at the old high pitch of the scales of Alypius, but Claudius Ptolemy’s transposition to a Fourth lower is here adopted for this third, as for the first hymn, because they are sufficiently melodious to be sung as curiosities at this day. Both Euclid and Gaudentius say that the scale may be transposed to any semitone within an Octave.

The harmony has been kindly contributed by my friend, G. A. Macfarren, who is the first person who publicly taught a system of harmony founded upon the laws of Nature, in this country, or in any other.

HYMN TO NEMESIS.

Winged Nemesis, turner of the scales of life, 

blue-eyed goddess, daughter of justice, 

who, with your unbending bridle, 

dominate the vain arrogance of men and, 

loathing man's fatal vanity, obliterate black envy; 

beneath your wheel unstable and leaving no imprint, 

the fate of men is tossed; you who come unnoticed, 

in an instant, to subdue the insolent head.

You measure life with your hand, 

and with frowning brows, hold the yoke. 

We glorify you, Nemesis, immortal goddess, 

Victory of the unfurled wings, powerful, infallible, 

who shares the altar of justice and, furious at human pride, 

casts man into the abyss of Tartarus.

The music to the second part of the Hymn to Nemesis has hitherto been found only in one manuscript of the fifteenth century, which is included in the Royal Library at Naples. Like all the other manuscripts, it is in an imperfect state as to the music for some few words, but this is not to be wondered at, considering that the date of the author cannot be later than the fourth century, and is, perhaps, of the second or third. Several intermediate transcriptions had, in all probability, been made. Again, there are some notes so evidently wrong that, in three cases, I have changed one, giving a memorandum of the change at the foot of the page. Having learnt a little of the Greek system, and especially its strong resemblance to our own, I cannot conceive them to have been so written, by the author. There are other cases of a doubtful nature, but the intention of the composer cannot so easily be discerned. These must await the finding of another manuscript. In the meantime, the continuation of the hymn is not equal to the first part.

THE CONTINUATION OF THE HYMN TO NEMESIS.

It seems now so hopeless to anticipate a discovery of any more genuine remains of ancient Greek music, that it may be sufficient to point out the scales of Aristides Quintilianus, in Meibon’s Antiquae Musicae Auctores, as the more probable of the two clues in such a case. In the lower part of that page the enquirer will find, in Greek notation by letters, a complete scale, including every semitone exactly as in our modem Chromatic scale, from Gamma, or the G on the lowest line of the base clef, up to the b, which is three Octaves and a major Third above it. The upper line is for the voice and the under letters are for the lyre. If this clue be copied out over the notes which the letters represent, the process will be found far less tedious than by turning from one mode to another, in the pages of Alypius in the same collection; but his work can also be referred to in case of need. There is no great difference between the two systems, but it is more probable that the clue given by Aristides should serve, than the seemingly earlier one by Alypius, of whose date nothing certain is known, but which has been variously conjectured as of the second, and as of the fourth century of our era.

The difficulties of Greek musical notation have been often exaggerated. Burette is one who indulges in this hyperbole, and Burney quotes the passage:

It is astonishing, says M. Burette, that the ancient Greeks, with all their genius, and in the course of so many ages as music was cultivated by them, never invented a shorter and more commodious way of expressing sounds in writing than by sixteen hundred and twenty notes.(Burney, I. 19.)

Burney argues gravely against this assertion; but neither he, Burette, nor any later historian with whose works I am acquainted, seems to have observed the table of Aristides Quintilianus, which was under their eyes, at p. 27 of his treatise. Besides this, there are other copies of those scales which were sent to Meibom by Selden, and by Gerard Langbaine, at pages 243 and 244 of Meibom’s notes. Learned men of the last century did not turn to original sources overmuch.

The entire notation of all the modes is comprehended by Aristides in thirty-eight double letters (gramimata). Quarter-tones are not included, but as there was but one such sound added in each tetrachoid, and so, two in each Octave, eight more double letter’s would have sufficed. In any case the total must fall far short of sixteen hundred and twenty.

There is a Greek notation by another set of signs, which was employed for rhapsodizing. This system is still employed in the services of the Greek Church in some parts of the world. A similar kind of notation by neumes, or signs for raising and lowering the voice, (pneumata,) was once in use in the Western Church. The conversion of the latter to the purposes of music seems to date only from the middle ages, and will form the subject of a later chapter.

BASIS OF THE SCIENCE OF MUSIC

9.-Its fundamental laws. — Earliest uses of music. — Mathematical divisions of strings not alone sufficient.—Minor tones introduced by Didymus, and followed by Claudius Ptolemy.—Neither the Greek scale nor the modern is properly in one key.—Hence the question whether Elevenths were concords.—How to test intervals.—The true proportions for scales.—Rules for adding and deducting intervals.—Scales of Didymus and of Ptolemy.—Defects of the modern scale.— The law of Nature the only true guide.—Objections to the Fourth and minor Seventh of the present scale.—Causes of Concord and Discord.—Pythagorean ideas realized by modern science.—Sounds too high and too low for our hearing.