Monday 28 February 2011

N-tone equal temperament vs Just Intonation

Some swift number-crunching later and I have several tables of relative pitches (relative to the octave) for N-tone equal temperament scales where 12<=N<=35 and Just Intonation. What surprises me the most is how closely to Just Intonation 12-Tone Equal Temperament actually is! The average difference between the ratios of the notes to the octave in 12-TET and JI is 0.006157 to 6dp. Contrast this with 13-TET having 0.014749, the second-least closely fitting scale in of those considered. In fact, the next nearest reasonable scale in 19-TET, closely followed by 22-TET.

Specifically, 12-TET differs by 0.006157, 32-TET by 0.005659, 35-TET by 0.005402, 19-TET by 0.005342, 33-TET by 0.005320, 22-TET by 0.004979, 31-TET by 0.003342 and 34-TET by 0.002679.

You don't want to see the rest of them; they're worse fits than 12-TET and so of little value.

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