AND A COMPARISON OF THE INTERVALS DISCERNIBLE IN THEM WITH THE INTERVALS STATED TO HAVE BEEN PERFORMED BY THE ANCIENT GREEKS IN SOME OF THEIR DIVISIONS OF THE MUSICAL SCALE, CALLED γένοσ ἐναρμονικὸν {Greek génos e?narmonikòn}, on BY OTHERS ἁρμονία {Greek a!rmonía}.
ALL nations, perhaps, without excepting any, have some method of expressing the more energetic emotions beyond mere speaking or acting; a sense of joy or pain, naturally calling forth ejaculations and vociferations exceeding in limit the tone of voice used in ordinary discourse. The cry of war, the encouraging to battle, the shout of victory, or the lament of the vanquished, the wailing over a deceased friend, grief at the departure of a lover, each in its turn has prompted or suggested some modification of sound beyond the ordinary range of mere tame every-day discourse; and this modification of voice we may call, in a wide sense, natural music.
But as the highest art is to conceal the art, 1 and to imitate nature, that mighty nation, the Greeks, with an art almost peculiarly their own, having observed these expressions of sentiment, thence deduced certain laws 2 of interval, by which, while they kept within the limits of art, they took care not to transgress those of nature, but judiciously to
adopt, and as nearly as possible to define, with mathematical exactness, those intervals which the uncultured only approach by the irregular modulation of natural impulses; so their art was the schooling of nature by the more exact observance of her laws, and by training nature by perfect art, they made art like nature, and corrected nature by art, as the sculptor or painter gives the classic embodiment or personification, not the commonplace, and often defective representation of an object.
This I opine to have been the real nature of the enharmonic scale of the Greeks; and hence I conceive the reason of the remnant of that scale being found among most of those nations who have been left to the impulses of a 'nature-taught' song rather than been cramped by the trammels of a conventional system--the result of education and civilisation.
It may not he amiss, before going farther into this analogy of nature, and of an art reciprocally reflecting back that nature, to endeavour to give the uninitiated an idea of what is meant by the 'enharmonic: genus ' of the Greeks.
I must first remark that while we have, properly speaking, only one scale of musical notes and two genera, the Greeks had three scales and five genera. For we have only the diatonic scale, but by a certain introduction of one or more semitones, we make what is called the chromatic.
Whereas, the Greeks had three scales, comprising five genera, or, according to some, nine 1, all differing not only, as ours do, in the position of intervals, but in the intervals themselves; this difference of interval (rather than position of interval) gave rise to the expression 'genera of a
system', and depended on the distribution of two intermediate sounds in the tetrachord or 4th.
The principal scales and genera were three; the diatonic, the chromatic, and the enharmonic. The diatonic (genus) consisted of a limma or minor half tone, a major tone, and a major tone ascending, this had another modification, by which, while it retained the same semitone, it contracted the next tone, and extended the last; the latter was called soft diatonic.
The chromatic, which consisted of semitone, semitone, one tone and a half interval, or nearly our minor third, was called tonaæon, and had two modifications, one called hemiolion, and the other malakon; these shades or modifications seem of later invention, and soon to have fallen into disuse.
The enharmonic consisted of a quarter tone, a quarter tone and an interval of two tones, an interval somewhat greater than our third major.
Wallis says that we have no idea of these intervals at the present day, as in any way connected with a scale, since they amount to little more than an imperfect elevation or depression of the voice within the limits of what we call a sound or harmonic note; though a certain use is made of the term enharmonic, and the existence of the interval is admitted in the higher researches on music, and said to be apparent in the so-called tierce wolf of the organ, in untempered instruments, and in the systems of equal temperament.
Writers of the present day, greatly differ as to the existence or use of these χρόαι {Greek xróai}, or shades of distinction, some wishing to modify them by a modern application of the term, amounting to those shades, 'nuances' or slurs, which the best vocalists or performers are sometimes heard to introduce 1; others again 2 declaring them to be in practice
impossible; and all for the most part alleging that, whatever might have been the case in former times, no such modifications do exist in practice at the present day.
Now, with regard to the existence of them in ancient times, innumerable authorities might be quoted; but, not to exceed a reasonable limit, I shall only cite one or two testimonies, and shall confine myself to those referring to the enharmonic.
Vitruvius (lib. v, c. 5) says: 'Diatonic vero quod naturalis est facilior est intervallorum distantia'; of the enharmonic he says: 'Est autem harmonia, modulatio ab arte concepta et ea re cantio ejus maxime gravem et egregiam habet auctoritatem.' The graveness and seriousness are given as the striking characteristics of this genus.
We may here incidentally remark that. though he says 'ab arte concepta', it does not prove that it might not have been art imitating nature; and more, it is not impossible that these, at present so-called uncivilised and savage nations, might have retained this character of song from a period of the highest state of civilisation, at an epoch of great antiquity.
Plutarch (Περὶ Μουσικῆσ {Greek Perì Mousikh^s}) remarks, that the most beautiful of the musical genera is the enharmonic, on account of its grave and solemn character, and that it was formerly most in esteem.
Aristides Quintilian tells us it was the most difficult of all, and required a most excellent ear.
Aristoxenus observes that it was so difficult, that no one could sing more than two dieses consecutively, and yet the perceptions of a Greek audience wore fully awake to, and their judgment could appreciate, a want of exactness in execution; for Dionysius of Halicarnassus says, he himself has been in the most crowded theatre, where, if a singer or citharoedist mistook the smallest interval (presumed to
be the enharmonic diesis), he was hissed off the stage.
Isaac Vossius 1, from a multitude of authorities, has established, that transitions were made by ancient singers and performers, from the diatonic to the chromatic and enharmonic, with the greatest facility; and he adds: 'which, because the moderns cannot do, they even positively and seriously assert that the ancients could not sing the enharmonic.' Whereas, continues he: 'not only did they sing it, but accompanied it with instruments.'
So Plutarch (Περὶ Μουσικῆσ {Greek Perì Mousikh^s}), who adds a remark, the purport of which is, such persons (who affirm that the ancients could not accompany the enharmonic) forget that if they can accompany greater intervals which were composed of less, there can be no reason why the scale of an instrument might not be so adjusted as to accompany the less intervals which compose those greater.
The doubt of the possibility of using the enharmonic as a scale is not confined to our own day, for Plutarch, as we have seen (and in other places also), speaks of the decline of it; and Athenæus speaks of certain Greeks who, from time to time, retired by themselves to keep up the recollection of the good old music, since the art had become so corrupted.
In Plutarch's time (De Musica) he bitterly complains that certain people 'affirmed the enharmonic diesis to be absolutely undistinguishable,' and that, therefore, it had no place in the scales of nature, and that those who attempted to prove it were mere triflers (pefluarhké?nai) 2
He then makes the remark about the possibility of accompanying the enharmonic intervals with instruments, and adds: 'and these very people who talk about the enharmonic having no foundation in nature, have an extraordinary attachment to dissonances and irrational intervals' (περιττά · · · ῆ ἄλογα {Greek perittá . . . h^ á?loga}), which have no existence in the real science of the proportions of natural intervals, and may be compared to certain irregular tenuities or awkward excrescences on what should be a beautiful tree or other object. For whatever reason, it appears it was wholly laid aside in Plutarch's time, which he attributes to the dulness of the ears of those of his day.
Wallis supposes the genera of the chromatic and enharmonic to have fallen into disuse for many ages; Scaliger, not till Domitian: the enharmonic, because of the extreme difficulty; the chromatic, on account of its softness and effeminacy. Dr Wallis adds: 'modern music never affected to appreciate such subtilty and delicate nicety, for neither voice could execute, nor ear easily distinguish so minute differences, at least so we suppose now-a-days.'
Dr Burney, in his History of Music (i. 433), from various authorities, concludes, that this genus (the close enharmonic) was almost exclusively in use before Aristoxenus (about the time of Alexander the Great), and we gather from Aristoxenus that there were exercises in it for practice, and this observation is corroborated in the Notices of Extraits des MSS., t. xvi., in a most elaborate and clever paper, by Mr Vincent, from certain MSS. in the King of France's library.
Dr Burney, in common with most other modern
writers on the subject, says. 'intervals of the close enharmonic tetrachord
appear wholly strange and unmanageable', and hence it has been concluded that the enharmonic was impossible in practice.
Dr Burney, however, one day received a letter from his friend Dr Russell, regarding the ' state of music in Arabia, and to the Doctor's utter astonishment, he learnt from that letter that the Arabian scale of music was divided into quarter tones; and that an octave, which, upon our keyed instruments is only divided into 12 semitones, in the Arabian scale contained 24, for all of which they had particular denominations.
This latter observation would seem to tally very well with what Mr Lane 1 says of the canoon (κάνων {Greek kánwn}) of the present Arabs, which, he says, has 24 treble notes. Only, that he adds, each note has three strings to it, which (later, as we shall see) he affirms to have been thirds of tones. If so, the system is a shade of the chromatic; and if Mr Lane is right (and he gives a drawing of the instrument), Dr Russell must err, or speak of another instrument. I should be inclined to give preference to Lane, because of the great pains he has taken in describing the instrument.
Mr Lay Tradescant 2, speaking of the Chinese intervals, says that 'it is impossible to obtain the intervals of their scale on our keyed instruments, but they may be perfectly effected on the violin.'
Mr Vincent 1 gives a most scientific description of an elaborate instrument made at Paris, exhibited at the Institut, on which the quarter tones were most correctly illustrated, and observes, that a much less interval than the quarter-tone, perhaps eight or ten times less, is discernible, as proved by a M. Delezenne 2, 1827; and our own ears attest that universally in the modulations of the voice of the so-called savage tribes, and in the refined and anomalously-studied Chinese, there are intervals which do not correspond to any notes on our keyed instruments, and which to an untrained ear appear almost monotonous.
There is another matter with which incidentally we have to do, namely, an apparent difference of opinion between ancient authors themselves about the enharmonic. Plutarch 3 says that Aristoxenus (in a book not now extant) informs us that Olympus was the inventor of an enharmonic, but of a kind consisting of a scale in which certain notes, the 'lichani' or 'indicatrices', were omitted, and that the airs of Olympus were so simple and beautiful, that there was nothing like them.
This Scale would approximate to the Scotch, or rather to that given as Chinese by Dr Russell. 4 But there is nothing repugnant in this, to the division of the intermediate half-note between this saltus; and, as here, it is the division of the halfnote interval with which we have to do;
the discussion as to the variety or difference introduced by Olympus--(as to whether he made use of this design or not)--is not of any importance to our subject, our object being merely to show that the smaller interval, called a quarter tone, has its representative in modern times.
Suffice it to say, that many Chinese airs, of which I have two, show the diesic modulations and the saltus combined; but the majority of the New Zealand airs which I have heard are softer and more 'ligate', and have a great predominance of the diesic element.
It may not be amiss to define in what sense we wish 'diesis' to be understood, for sometimes, by modern writers especially, it is used for the simple minor half-tone of 24/25 in contradistinction to the major of 15/16. In Dr Smith's Harmonies it is the limma of equal temperament. Sometimes the moderns use the term for the double sharp. It was Rameau's these major; Henfling's Harmonia; Boyce's quarter-note; the Earl of Stamford's tierce wolf; observed in the tuning of an organ. Dr Maxwell makes 2025/2048 the maj. diesis, and 32768/32805 the min. But the sense in which I shall use it is that of the ancient quarter-tone, being an approach to the quarter of a tone major, or rather the division of the limma 243/256 into two unequal parts; this is called the Aristoxenian diesis quadrantalis; which is represented nearly by 120 being the lowest note; then 116.60: 113.39.
I shall not trouble the reader with chronological or scholastic differences; the diesis of Archytas; that of being given by Vincent as 115 5/7: 112½, Eratosthenes as 117: 114, for keen indeed must be the ear that could discern between 15/16 and 24/25 (except in harmony); much more difficult still would it be to discover a difference between 116.60. 113.39 and 115 5/7 / 112 ½ or 117/114.
If any wish to examine this matter more closely, they can consult the Treatises on Harmonies. Mr Vincent has calculated these differences by logarithms to the 60 root of 2.
My point is, to prove that the ancients did possess and practise a modulation which contained much less intervals than ours, and that such, or an approach to such, modulation (though probably but imperfect) is still retained among some people, and that the principles on which the Greeks founded their enharmonic genus, still survive in natural song, though I will not be bold enough to assert that sometimes these songs may not change into one of the chromatic Χρόαι {Greek Xróai}, which, for want of practice, I might not be able to decide. One thing, however, is certain, that, as Aristoxenus tells us, no perfect ear could modulate more than two dieses at a time (and then there was a 'saltus' or interval of two tones), and as the New Zealand songs frequently exhibit more than two close intervals together, it is more than probable that many of these songs are a chromatic, represented by 120, 114 or 108, or 120, 112½, 108; but it will not be worth while for the present purpose to discuss this nicety, as all we want is a practical approximation.
In proof that a system, of modulation like the above still survives, I shall produce, as nearly as my ear could discern, the modulation of some of
the New Zealand melodies; and shall show a still nearer approach to the system of the real Greek enharmonic, in a Chinese air which I heard and noted.
A few remarks on the system itself, the intervals, and the notation.
SYSTEM
First, that an enharmonic modulation might; exist is admitted by many modern writers. Mr Donkin, for instance, author of the able article on Ancient Music in Dr W. Smith's Dictionary of Greek and Roman Antiquities, observes (under the title of Music) of the different genera less frequently named 1, 'that it would be wrong to conclude hastily, that the others would he impossible in practice, or necessarily unpleasing'; and of the enharmonic he says: 'but it is impossible to form a judgment of its merits without a much greater knowledge of the rules of composition than seems now attainable.'
Mr Lay Tradescant having shown the differences of interval of the Chinese instruments from the intervals generally in use in Europe, adds: 'It will therefore very readily appear from the respective rules, that the character of the music, or, if you please, the mood (he should have said genus), must be very different from our own, and that none of our instruments (he should have said keyed or bored) are capable of doing justice to any air that is played on the kin' (or scholar's lute). He subjoins: 'In my travels I sometimes wrote down the airs that I had heard among the natives, but though I took much pains to learn them accurately,
[paragraph continues] I always found they had lost something of their peculiarity when played upon the violin.
'The reason of this defect seems to have been that the intervals of the Indian music did not agree with those of Europe.' 1
Mr Tradescant might have added, that there will always be some difference in an air played on the guitar and on the violin, though the intervals used axe esteemed the same; and, again, perhaps the learned traveller did not take care to divide the scale of his violin mathematically, like that of the kin, before he tried the effect,; he might also riot have noted the right interval. He concludes: 'There is, however, a connection between the Chinese and old Scotch music, so that when any highly-admired airs of Scotland happen to fall within the compass of the kin, they seem at home when played upon this instrument.'
Mr Lane says the 'canoon' of the Arabians had twenty-four notes. Dr Russell to Burney says that the Arab scale of twenty-four notes was equal to one octave. But Mr Lane adds that 'the most remarkable peculiarity in the Arab system of music is the division of tones into thirds.' Hence, from the system of thirds of tones, I have heard the Egyptian musicians urge against the European systems of music that they are deficient in the number of sounds.
The same remark was made to me by Selim Agar, a Nubian, when singing some Amharic songs: 'Your instrument' (piano), said he, 'is very much out of tune, and jumps very much.'
Mr Lane adds: 'These small and delicate gradations of sound give a peculiar softness to the performances of the Arab musicians, which are generally of a plaintive character; but they are difficult to discriminate with exactness, and therefore seldom
observed in the vocal and instrumental music of those persons who have not made a regular study of the art.'
Had Mr Lane been describing the character and difficulties of the ancient Greek enharmonic or chromatic, he could not have used other terms; they are almost the words of Aristoxenus, Vitruvius, Plutarch, and other ancient writers on these genera; and yet, he adds: 'he took great delight in the more refined kind of music', and found 'the more he became habituated to the style the more he was pleased with it.' He continues: 'He was perfectly charmed with the performance of some female singers, and that the natives are so fascinated as to lavish considerable sums on them.'
Precisely so the Greeks of old.
INTERVALS
We must not suppose that the Greek enharmonic was a consecutive gamut of quarter-tones--no; we are told distinctly by all authors (except, perhaps, Salinas), that there was a quarter-tone, then another quarter-tone, then a great interval completing the fourth; or reversely, a great interval of two major tones, or about our third major, the quarter-tone, mother quarter-tone, thus completing the fourth.
So with these nations, and especially in the Chinese airs I have heard, there is either the two quarter-tones, then an interval of about a third, or, the interval of the third, and then the two dieses or quarter-tones, or it is a mixed genus, and adds a tone or half-tone at either extreme.
I here beg to state that, though with great care and the assistance of a graduated monochord, and an instrument divided like the intervals of the Chinese kin, I have endeavoured to give an idea of those airs of New Zealand which I heard, yet so
difficult is it to discover the exact interval, that I will not vouch for the mathematical exactness: neither will I pledge myself not to have written a chromatic for an enharmonic interval, or vice versa.
I must also, in justice to myself, add, that the singer did not always repeat the musical phrase with precisely the same modulation, though, without a very severe test, this would not have been discernible, nor then to many ears; the general effect being to an European ear very monotonous.
But I may say that, when I sang them from my notation, they were recognised and approved of by competent judges; and that the New Zealander himself said he should 'soon make a singer of me'.
I may also add that I have studied the subject for more than twenty years, and have read something out of almost every book of note that has been written on it; but yet I only offer these airs as an approximation, and if anyone shall be found who may do more justice to them, I shall be delighted to hear of the result.
NOTATION
The notation that I have adopted is, for the enharmonic diesis, the St Andrew's cross or saltier
, quarter tone or half sharp; the usual
for the sharp; and for
three-quarter sharp. In like manner, the
for quarter tone or half flat;
for the flat; and
(or I might have said:
) for the three-quarter flat.
In the Arab ternal division I should use-one third sharp,
; two-third sharp,
; one-third flat,
; two-third flat,
.
In my notation, also, it must be observed, that a sign
or
never conveys its influence beyond the note to which it is attached; thus
would read E half-flat, E natural, E half-sharp, E natural; and is a delicate expression of the chromatic
or of the diatonic
I now give the airs as best I can.
One word as to time. Though I have timed the airs I have given, I am free to confess there was neither metre nor rhythm of any marked character discernible in them; and even in the divisions of the lines or verses, the singer seemed to stop indifferently now at one, now at another word. I have, however, followed in my divisions those given in the book, taking it for granted that the learned author, who has given himself so much pains about the matter, will have chosen the most authentic.
James A. DAVIES 1
Formerly of Trin. Coll., Camb.
Late Private See. to H.R.H. Prince Leopold,
Count of Syracuse, Naples.
17, Great Ormond Street, Queen Square,
September, 1854.
Mr MeGregor gives the following specimens of Arabian Music (see his Eastern Music)
Which I represent thus:
or thus, perhaps clearer:
The run at the end is also met with in the New Zealand songs. The cadence is mixed, i.e. enharmonic and diatonic.
The Chinese Air sung under my window in London:
No. 1
THE WAIATA AROHA: OR, THE BRIDE'S COMPLAINT
Reduced by James Davies. Page 30 1
This last bar would perhaps be better written:
but I have avoided as much as possible
or
as being so very unusual, and it is evident to the musician that D three-quarters sharp is equal to E quarter flat, at least sufficiently near in practice.
No. 2
A LAMENTATION
NO. 3
WHAKARONGO
NO. 4
CHILD'S SONG, TO TEACH SINGING
227:1 Cicero.
227:2 Cicero, Orat.
228:1 Ptolomæus the Magian, Mr. Vincent's paper in Notices et Extraits des MSS., tom. xvi, Paris.
229:1 Smith.
229:2 Burney.
231:1 De Poematum Cantu.
231:2 That the enharmonic has no foundation in nature is false, for what tree tapers 'per saltum?'--'what river flows in heaps?--this gradation is p. 232 nature's life-stream; the other scales may be compared to the proportional parts, the enharmonic to the continuous procession.
233:1 Lane's Modern Egypt.
233:2 Lay Tradescant's Chinese as they Are.
234:1 Notices et Extraits des MSS., tom. xvi.
234:2 Memoire de la Societe Royale de Lille.
234:3 Περὶ Μουσικῆσ {Greek Perì Mousikh^s}.
234:4 Burney, vol. i.
237:1 As the soft diatonic, the hemiolion chromatic, the soft chromatic.
238:1 Lay Tradescant's Chinese as they Are.
241:1 Author of the Papers on the Rhythm of the p. 242 Ancient Greek Orators of the Psalms, Selah, the Evil Eye, read before the Royal Society Of Literature; and of Papers on Accent and Quantity, discovering their true and real difference, from authentic sources. See English Journal of education, February, March, April, June, July, and August; G. Bell, 186, Fleet Street.
243:1 The pages refer to Sir George Grey's collection of New Zealand Songs, Mau Konga moteatea, me nga Haki rara.
