编辑“︁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 ==
[[Edo]]s which do relatively well at approximating 3-limit intervals can be found as the denominators of the convergents and semiconvergents of the [[wikipedia: Continued fraction|continued fraction]] for the logarithm of 3 base 2. These are {{EDOs| 1, 2, 3, 5, 7, 12, 17, 29, 41, 53, 94, 147, 200, 253, 306, 359, 665, … }} ({{OEIS|A206788}})

Another approach is to find edos which have more accurate approximation to 3 than all smaller edos. This results in {{EDOs|1, 2, 3, 5, 7, 12, 29, 41, 53, 200, 253, 306, 359, 665, 8286, 8951, 9616, 10281, 10946, 11611, 12276, 12941, 13606, 14271, 14936, 15601, 31867 }}, … ({{OEIS|A060528}})

A stricter approach is to find edos with an increasingly stronger [[consistent circle]] of 3/2. These are {{EDOs|1, 2, 12, 53, 665, 190537, … }} (with strengths 1, 1, 2, 3, 11, 28, … respectively)



[[Category:律制]]