Is there a general equal-tempered tunings theory?
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Anuman_mp3
- KVRer
- Topic Starter
- 9 posts since 29 Sep, 2021
I was searching a little bit about it, but for now I've only found advice for harmonic sounds, with the just octave as the interval of equivalence. I'm wondering if there are also practical theories for inharmonic-derived tunings?
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BertKoor - KVRAF
- 14235 posts since 8 Mar, 2005 from Utrecht, Holland
Ehrm... this?
wikipedia wrote: An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, which gives an equal perceived step size as pitch is perceived roughly as the logarithm of frequency.
[...]
Other equal temperaments divide the octave differently. For example, some music has been written in 19-TET and 31-TET, while the Arab tone system uses 24-TET.
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jancivil
- KVRAF
- 24102 posts since 20 Oct, 2007 from gonesville
The book definition of inharmonic is the frequency of an overtone is not reducible to a two-integer ratio.
Technically the only true harmonic in 12tET is that octave, @ 2:1.
Conventionally the 12 represent the natural rational intervals of a “just” intonation. (EG: 3:2 representing a perfect fifth, while the 12tET P5 is a couple of cents sharp of that, in an ‘irrational’ mathematical construct, <12th root of 2>.
So this is perhaps nothing to the problem you brought up. But inharmonicity captured in notation is complex enough to kinda want to avoid, a wild goose chase.
Technically the only true harmonic in 12tET is that octave, @ 2:1.
Conventionally the 12 represent the natural rational intervals of a “just” intonation. (EG: 3:2 representing a perfect fifth, while the 12tET P5 is a couple of cents sharp of that, in an ‘irrational’ mathematical construct, <12th root of 2>.
So this is perhaps nothing to the problem you brought up. But inharmonicity captured in notation is complex enough to kinda want to avoid, a wild goose chase.
