Back in the ultramodern 1920s, quartertones seemed like the next logical step for deeper exploration of pitch language. The theory of acoustical tuning wasn’t taught in those days; thinkers as brilliant as Schoenberg and Cowell went around insisting that the 11th harmonic of C was F# (it’s 551 cents, halfway between F and F#, not 600 cents), and no one really believed that you could hear such tiny pitch differences. In addition, the nature of musical instruments, especially that behemoth the piano, was not going to change any time soon, but if you put two pianos together, you could tune one down 50 cents, and between them you’d have a quarter-tone scale, 24 equal steps to the octave. It was an interval not of acoustic necessity, but of convenience. Thinkers like Ferruccio Busoni theorized about splitting the half-step into three and four equal parts as well. In those days of talk about splitting the atom, it must have been in the air.
And so a number of composers wrote music in quartertones. Chief among these were (for quality) the American Charles Ives and (for quantity) the Czech Alois Hába. Ives’s main contribution was Three Pieces for Quarter-Tone Pianos, completed in 1926, one of his last works. His article “Some Quarter-Tone Impressions” (published by Norton with his Essays Before a Sonata) theorizes about what kind of harmonies quartertones would support. He postulates a triad in-between major and minor, say, C and G with a pitch between Eb and E; the chord sounds more stable, he claims, if you add a seventh halfway between Bb and B. The Quarter-Tone Pieces carry out these theories beautifully. The only recording I’ve ever found, however (and there are several), that really has the pianos exactly a quarter-tone apart is the old vinyl recording on Odyssey. All the others miss slightly.
Alois Hába (1893-1973) wrote a considerable amount of quartertone music. He also wrote string quartets that divided the whole step in to five equal parts (fifth-tone, or 30 equal steps to the octave) and six equal parts (or 36 steps to the octave). Haba’s opera The Mother is in quartertones, and is recorded on Supraphon. Another composer of divided half-steps is the Russian Ivan Wyschnegradsky (1893-1979), who had a vision in the street one day that he was supposed to write microtonal music. Musicians at McGill University, including the Mather-LePage Duo, put out two recordings of Wyschnegradsky’s multiple piano works, one for two pianos tuned a quarter-tone apart, another for three pianos tuned a sixth-tone apart. It’s visionary music, like Scriabin but creepily in-between-the-keys. The Arditti Quartet has supposedly made a recording of Wyschnegradsky’s string quartets that was released in Europe, but I’ve never found it.
Mexico’s Julian Carrillo also made a career out of what he portentously called “the Thirteenth Tone,” although what he actually did was to divide the half-step into four parts for 48 equal steps per octave. His Preludio a Cristobal Colon, published in Henry Cowell’s New Music Edition, is written for an ensemble in his special notation.
Ezra Sims of Boston has gone even further, writing in a special notation for 72 pitches per octave. Sweet, haunting, sometimes folk-music-based, Sims’s music sounds natural but is very careful about its intonation, not compromising on commas and raised and lower leading tones.
Each of these divisions has certain acoustical features in its favor; the more divisions, the more acoustical accuracy and the less convenience of notation and performance. Quartertone tuning captures several 11-based intervals, intervals based on the 11th harmonic:
11/8 = 551 cents
11/9 = 347 cents
11/6 = 1049 cents
12/11 = 151 cents
All are very close to quartertones. However, seven-based intervals are just as out of tune in quartertone music as they are in 12-tone equal temperament.
The 36-tone equal temperament, or dividing the half-step in three, is better for capturing intervals based on the 7th harmonic, or 7-based intervals.
7/4 = 969 cents
7/6 = 267 cents
8/7 = 231 cents
9/7 = 435 cents
Each of these is approximately 33 cents above or below an equal-tempered pitch. Sims’s 72-pitch tuning combines these possibilities, allowing pitches both 33 and 50 cents away from the 12 standard ones, and also allows much closer approximations of standard major and minor thirds. The use of 72-tone equal temperament allows perfect transposibility in eleven-limit tuning, but at the price of tremendous inefficiency. Partch, after all, gets perfect eleven-limit tuning with only 43 pitches, and I’ve never succeeding in needing more than 31.
Other intervals are possible with equal temperaments not derived from the whole- or half-step, but from circles of fifths.