Polynesian Mythology and Ancient Traditional History of the New Zealand Race
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, another 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 have heard, yet so difficult 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 versâ.
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 page 236 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 any one shall be found who may do more justice to them, I shall be delighted to hear of the result.