3限纯律

3限纯律 由分子和分母为质数2和3的任意次乘积的纯律音程组成，如3/2, 16/9. 3限纯律音程的一般形式为<math>2^a3^b<\math>, 其中a, b为整数。

历史

先秦时期的《管子·地员篇》记载了三分损益律：取一段弦“三分损一”（均分弦为三段，舍一留二）便得到 3/2f（f为弦的原频率），三分益一（弦均分三段后再加一段）便得到 4/3f. 这种生律方式得到的是3限纯律的子集：<math>\{2^a3^b\}<\math>, 其中a为整数，b为非负整数。

Edo approximation

Edos which do relatively well at approximating 3-limit intervals can be found as the denominators of the convergents and semiconvergents of the continued fraction for the logarithm of 3 base 2. These are 模板:EDOs (模板:OEIS)

Another approach is to find edos which have more accurate approximation to 3 than all smaller edos. This results in 模板:EDOs, … (模板:OEIS)

A stricter approach is to find edos with an increasingly stronger consistent circle of 3/2. These are 模板:EDOs (with strengths 1, 1, 2, 3, 11, 28, … respectively)