1553edo: Difference between revisions

Regular temperament properties: rework as a dual-fifth temp
Theory: the prime subgroup doesn't look any useful. 2.9.5.7.13 arguably makes more sense
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{{EDO intro|1553}}
{{EDO intro|1553}}
== Theory ==
== Theory ==
1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. Assume the [[patent val]], 1553et tempers out 200120949/200000000 in the 7-limit; 102487/102400, 759375/758912, 2359296/2358125, and 369140625/369098752 in the 11-limit; 1716/1715, 40656/40625, 59535/59488, 105644/105625, 196625/196608, 200000/199927, 823875/823543, 8859375/8859136, 34034175/34027136, and 75000000/74942413, in the 13-limit.
1553edo is only [[consistent]] to the 5-odd-limit and harmonic 3 is about halfway between its steps. It has a reason approximation of the 2.9.5.7.13 [[subgroup]], where it notably tempers out [[4096/4095]] and 140625/140608.  


=== Odd harmonics ===
=== Odd harmonics ===