Some years before that time I wrote a little treatise On the Interpretation of Greek Music, and prepared to build an instrument of seventy strings. The ancients had seventy notes, having twenty-one notes to the octave, and a compass of three octaves and a third; but they never had so many strings. They tuned their strings to suit the mode or scale that they were going to use; but my object was to have the notes all there without this tuning.
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 a¹ and a² at about a quarter and a half of a mean tone above a, and b¹ and b² 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, b¹, b², 256, 263, 271 for c, c¹, c², 288, 296, 304 for d, d¹, d², 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.
Various people had published transcripts of bits of ancient music, and had been applauded at the concerts where their transcripts were performed; and they did not like my saying that twenty notes in twenty-one were wrong, and the twenty-first was doubtful. Anyone can calculate the intervals between the notes by means of logarithms and the ratios given by Ptolemy and other ancient authors. These people told me volubly that this was only mathematics—“lascia le muse, e studia le matematiche.” They said that Aristoxenus must have used the tempered scale, as he assumes that six tones make an octave. Euclid, Sectio Canonis, prop. 9, proves with his usual precision that six tones are greater than an octave. Ptolemy, Harmonica, i. 9, says that the Aristoxenians should either have accepted what was proved, or set up something else to take its place; and he would hardly have said that, had they set up the tempered scale.
I have always felt that, if an opinion was worth publishing, it was worth defending; and that was why I defended my views about Greek music in the Revue Critique and elsewhere, and have also defended my views on many other things. Critics often change their tone, when put on their defence. There was a professor of theology at Jena, who was displeased with something that I wrote, and he pitched into me, Berliner Philologische Wochenschrift, 18 June 1898. I wrote an Entgegnung, which appeared there, 27 August 1898, with an Erwiderung from him. I remarked that “was er ein Wasserstrahl nennt, ist nicht anderes als der Heilige Geist,” corrected him on other points, and finished off with “in der That scheint er von der Litteratur der Sache ebensowenig zu wissen als von altchristlicher Kunst.” In his reply he was an injured innocent, although he had come down on me as if he were a Pope and Œcumenical Council all rolled up into one.
I had been writing about some portraits of Christ that can probably be dated at 258 A.D., or shortly after that; and I had used them in support of my opinion that Christ was only a little over twenty years of age at the date of the Crucifixion. I did not expect people to acquiesce in this without demur; but the theologians treated dates as dogmas. I cannot see the merit of believing that something happened in one way, if it happened in another way, or did not happen at all.
One evening, when some friends were staying with me, one of them was speaking of something he had seen in Egypt; and he said that he thought Brugsch’s system was the best, as a rough and ready way of getting at dates. You reckon three generations to a century; and, though this may not be true for a century or two, it comes pretty near the truth on an average of several centuries. Another man looked dubious; so I asked him what was wrong, and he explained. He was descended from William the Conqueror both on his father’s side and on his mother’s, but on one side it was twenty-seven generations, and on the other it was twenty-four; and he was just wondering whether he was a century older or younger than himself.
I wrote a book on Egyptian chronology and its application to the early history of Greece. The evidence required more careful sifting than it had received; and my point of view was that of Ovid, Amores, ii. 2. 57, 58—“viderit ipse licet, credet tamen ipse neganti, | damnabitque oculos, et sibi verba dabit.” I thought of quoting this upon the title-page, but found it rather long, and only gave a part. And then the Guardian reviewed the book, 9 September 1896, and said:—“The motto on the title-page, damnabitque oculos, is, perhaps, the oddest motto that ever graced a scientific treatise issued by a University Press.” Which made it plain that the Guardian had a reviewer who was less familiar with the Latin language than with modern swear-words.