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Polynesian Mythology and Ancient Traditional History of the New Zealand Race


page 225

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,* 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 of interval, by which, while

* Cicero.

Cicero, Orat.

page 226 they kept within the limits of the 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 be amiss, before going further 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, * 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 on the tetrachord or 4th.

The principal scales and genera were three; the diatonic, the chromatic, and the enharmonic. The diatonic (genus) consisted

* Ptolomæus the Magian, Mr. Vincent's paper in “Notices et Extraits des MSS.,” tom. xvi. Paris.

page 227 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 one 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, 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;* others again 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: “Diatoni vero quod naturalis est facilior est intervallorum distantia;” of the enharmonic he says:

* Smith.


page 228 “Est autem harmoniæ modulatio ab arte concepta, et ea re cautio ejus maximè 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 (Περι` Μουσικη^ς) 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 were 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,* 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 (Περι` Μουσικη^ς), 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.

* “De poematum Cantu.”

page 229

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 πεθλναρηκέναι).*

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, having an extraordinary attachment to dissonances and irrational intervals” (περιττά … ήάλογα), 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 (i. 433), in his History of Music, from various authorities, concludes that this genus (the close enharmonic) was almost exclusively in use before Aristoxenus (about the time of

* That the enharmonic has no foundation in nature is false, for what tree tapers “per saltum?”—what river flows in heaps?—this gradation is nature's life-stream; the other scales may be compared to the proportional parts, the enharmonic to the continuous procession.

page 230 Alexander the Great), and we gather from Aristoxenus that there were exercises in it for practice, and this observation is corroborated in the “Notices et 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, “The intervals of the close enharmonic tetrachord A section of sheet music. 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* says of the canoon (κα`γωγ) 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, 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 * gives a most scientific description of an elaborate instrument made at Paris, exhibited at the Institut, on which the

* Lane's “Modern Egypt.”

Lay Tradescant's “Chinese as they are.”

* “Notices et Extraits des MSS.,” tom xvi.

page 231 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,* 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 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.

A section of sheet music.

This Scale would approximate to the Scotch, or rather to that given as Chinese by Dr. Russell.

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 half-note interval with which we have to do; A section of sheet music. 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.

* “Mémoire de la Société Royale de Lille.”

Περι` Μουσικη^ς

Burney, vol. i.

page 232

Suffice it to say, that many Chinese airs, of which I have two, show the diesic modulation 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 Harmonics it is the limma of equal temperament. Sometimes the moderns use the term for the double sharp. It was Rameau's diese 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 82768/82805 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 248/256 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 being given by Vincent as 115 5/7:112½, that of 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 / 112½ or 117 / 114

If any wish to examine this matter more closely, they can consult the Treatises on Harmonics. 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 page 233 assert that sometimes these songs may not change into one of the chromatic χρόαι, 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, 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.