I am a Pythagorean myself, and regard the Aristoxenians as silly folk who misinterpret Aristoxenus--and he merely walked slipshod in the footsteps of Pythagoras. Accordingly, I increased the mean tones (_ab_, _cd_, _de_, _fg_, _ga_) to major tones, and decreased the mean semitones (_bc_, _ef_) proportionately; and then I put _a_¹ and _a_² at about a quarter and a half of a mean tone above _a_, and _b_¹ and _b_² at rather less than an eighth and a quarter of a minor tone above _b_, and so on with the other notes. I worked out the vibrations for one complete tetrachord; and (omitting decimals) they were 243, 246, 249 for _b_, _b_¹, _b_², 256, 263, 271 for _c_, _c_¹, _c_², 288, 296, 304 for _d_, _d_¹, _d_², and 324 for _e_. And then I got Messrs Broadwood to make me a set of tuning-forks to test it--a troublesome piece of work, to which their Mr Hipkins gave a great deal of his valuable time and skill and knowledge. The error in the forks was negligible. The intervals were very curious, and unpleasant at first hearing; but, on getting used to them, I got impatient with the piano for having nothing but mean semitones. As the piano and all keyed instruments have equal temperament now, they ought to have black keys and white alternately all through, and the music could be rewritten in a simpler form. It is ridiculous to keep to five black keys and seven white, instead of six of each, now we have dropped the system on which the seven and five were based. I did not build my instrument of seventy strings, as I did not see how it could be kept in tune--a tuner would never get these subtle notes quite true, when his daily work was with the tempered scale. And there were practical difficulties about an instrument of seventy tuning-forks. Somebody asked me what I meant to call the instrument, and I said Cacophone. That was before I grew accustomed to the intervals, and came to like them. But my answer reached some people’s ears in Paris; and I read in the _Revue Critique_, 27 July 1896, that I had invented a series of sounds “inexécutables par aucune voix humaine ou même féline,” in fact a “miaulement,” which “mérite complètement le nom de Cacophone, sous laquelle, dit-on, il l’a désignée.” Anyway, my cat-squall was antique, and their tempered scale was not; and I retorted with some vigour in that journal, 12 October 1896.