MOS substitution: Difference between revisions

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Here the notation ''G''<sup>''k''</sup> denotes repeating the generator ''G'' ''k'' times in the generator sequence.
Here the notation ''G''<sup>''k''</sup> denotes repeating the generator ''G'' ''k'' times in the generator sequence.


These are four of the 8 billiard words that have pattern 5L2m6s. The other four billiard words have length-3 subwords of non-X letters, unlike the MOS substitution scales.
These are four of the 8 [[billiard scale]]s that have pattern 5L2m6s. The other four billiard words have length-3 subwords of non-X letters, unlike the MOS substitution scales.


This scale pattern is available in [[37edo]] with step ratio 5:3:1; the generator sequence in the tuning has 2'''L'''+'''m'''+2'''s''' = 486.5 (~4/3) and 2'''L'''+3'''s''' = 421.6 (~14/11), and notably this tuning represents all primes from 3 to 13 with only 3 being inaccurate. 65edo's 9:7:1 is another optimum for 2.3.5.11.13, and is given by a GS using three 4/3's and one 5/4.
This scale pattern is available in [[37edo]] with step ratio 5:3:1; the generator sequence in the tuning has 2'''L'''+'''m'''+2'''s''' = 486.5 (~4/3) and 2'''L'''+3'''s''' = 421.6 (~14/11), and notably this tuning represents all primes from 3 to 13 with only 3 being inaccurate. 65edo's 9:7:1 is another optimum for 2.3.5.11.13, and is given by a GS using three 4/3's and one 5/4.