40ed10: Difference between revisions
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The '''division of the 10th harmonic into 40 equal parts''' is related to [[12edo]], but with 10/1 instead of 2/1 being just. The step size (99.657843 [[cent]]s) of this [[equal-step tuning]] very close to 1\12 (one step of 12 EDO). | The '''division of the 10th harmonic into 40 equal parts''' is related to [[12edo]], but with 10/1 instead of 2/1 being just. The step size (99.657843 [[cent]]s) of this [[equal-step tuning]] is very close to 1\12 (one step of 12 EDO). | ||
It is possible to call this division a form of '''decibel tuning''' or '''kilobyte tuning''', as | It is possible to call this division a form of '''decibel tuning''' or '''kilobyte tuning''', as | ||
Revision as of 22:16, 5 June 2021
The division of the 10th harmonic into 40 equal parts is related to 12edo, but with 10/1 instead of 2/1 being just. The step size (99.657843 cents) of this equal-step tuning is very close to 1\12 (one step of 12 EDO).
It is possible to call this division a form of decibel tuning or kilobyte tuning, as
[math]\displaystyle{ 10^{\frac{1}{10}} \approx 2^{\frac{1}{3}} = 1.2589254 \approx 1.2599210 }[/math];
which lies in the basis of the definition of decibel. In addition, as a consequence of the previous formula,
[math]\displaystyle{ 2^{10} \approx 10^{3} = 1024 \approx 1000 }[/math];
which lies in the basis of using a "decimal" prefix to an otherwise binary unit of information. The octave, which is 12\40 = 3\10, is compressed by about 4.1 cents.
Theory
Since 40ed10 has relations to the proximity of 1024 to 1000, just like 12edo it tempers out the lesser diesis of 128/125. However in this situation the tempering has a different interpretation, namely that "in favor of 1000".