More About Tunings

Thanks to the improved workflow in QuteCsound, it’s getting easier to experiment with alternate tuning systems. Also, I’ve learned a couple of tricks for organizing Csound scores.

While enjoying the pure sounds of just intonation, I’ve been realizing that I don’t actually mind 12-tone equal temperament (12ET, for short). It has a beautifully developed harmonic language, which is not the case with any alternate tuning.

Also — and this is a subtle point — with equal temperament, you always know where you are. If you’re composing in just intonation, arbitrarily tiny micro-intervals can flit around like gnats, and every chord root will tend to grow a different forest of harmonic possibilities.

Csound has a very nice opcode (cpsxpch) for experimenting with equal temperaments. So last night I thought I’d play around  little with 31-tone ET. 19ET and 31ET are notable because their triads and seventh-chords are closer to perfect intonation than those in 12ET. I’ve played around quite a bit over the years with 19ET, mostly using a MIDI keyboard. I know the chord fingerings in 19ET, but 31ET just has too darn many steps to lay it out conveniently on a conventional keyboard, so I’ve never explored it.

The triads and seventh-chords in 31ET are wonderful — very warm and consonant. Yet the chromatic resources of this scale are bizarre and almost unfathomable.

The smallest scale steps (I’ve started calling them chroma-steps) are so close together as to be almost, yet not quite, indistinguishable.

The perfect fifth (from C to G, if we want to preserve that nomenclature — and why not preserve it?) is 18 chroma-steps wide, which means that it can be divided into two, three, or six equal steps (or nine, obviously). A triad consisting of the steps 00-09-18 is neither major nor minor, it’s balanced or neutral. But it doesn’t sound especially neutral; it sounds quite unsettled and disturbing. The scale 00-06-12-18-24 has a vaguely pentatonic flavor, yet the ear, which is accustomed to hearing diatonic scales, is entirely unable to assign any identity to the 06 and 12 notes. They’re floating somewhere.

Augmented and diminished chords in 31ET don’t close at the octave. The augmented chord is 00-10-20-30, so the top note is one chroma-step shy of the octave. This gives the voicing a sad, muted flavor. The diminished seventh, on the other hand (00-08-16-24-32, with 32 being 01 in the next octave) is a bit edgy because the “octave” note is one chroma-step too high.

Fourth-chords and stacked fifths, however, sound very natural.

If we construct an equal-tone scale in which each step is 4 chroma-steps wide, not only does the scale not repeat at the octave, but it misses almost all of the white keys. (The white keys, for reference, are 00-05-10-13-18-23-28.) The interval of 4 chroma-steps is easily wide enough to hear as a scale step, but the scale doesn’t mesh well with our expectations.

Each whole-step divides into 5 chroma-steps, which means that if we try to play a 12-note chromatic scale, the “black keys” won’t be equally spaced between the white keys. The scale will be a succession like 3-2-3-2-3-3-2. I haven’t tried that one yet, but I’m expecting it to sound strange and unsettling.

I may try writing a few microtonal studies. I enjoy exploring uncharted wilderness, especially when I can do it from the comfort of my home studio.

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