40ed10

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 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".