118edo: Difference between revisions
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It has two reasonable mappings for 13. The [[patent val]] tempers out [[196/195]], [[352/351]], [[625/624]], [[729/728]], [[1001/1000]], [[1575/1573]] and [[4096/4095]]. The 118f val tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1573/1568]], [[1716/1715]] and [[2080/2079]]. It is, however, better viewed as a no-13 19-limit temperament, on which subgroup it is consistent through the [[21-odd-limit]]. | It has two reasonable mappings for 13. The [[patent val]] tempers out [[196/195]], [[352/351]], [[625/624]], [[729/728]], [[1001/1000]], [[1575/1573]] and [[4096/4095]]. The 118f val tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1573/1568]], [[1716/1715]] and [[2080/2079]]. It is, however, better viewed as a no-13 19-limit temperament, on which subgroup it is consistent through the [[21-odd-limit]]. | ||
Since the [[Pythagorean comma]] maps to 2 steps of 118edo, it can be interpreted as a stack of 10 [[12edo]]<nowiki/>s minus the said comma. | Since the [[Pythagorean comma]] maps to 2 steps of 118edo, it can be interpreted as a stack of 10 [[12edo]]<nowiki/>s minus the said comma. | ||
118edo is the 17th [[The Riemann Zeta Function and Tuning|zeta peak edo]]. | 118edo is the 17th [[The Riemann Zeta Function and Tuning|zeta peak edo]]. | ||
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{{primes in edo|118}} | {{primes in edo|118}} | ||
==Table of intervals== | ==Table of intervals== | ||
{| class="wikitable" | |||
|+Selected 118 EDO intervals | |||
!Step | |||
!Name | |||
!Associated ratio | |||
|- | |||
|0 | |||
|unison | |||
|1/1 exact | |||
|- | |||
|2 | |||
|comma | |||
|[[531441/524288]], [[81/80]] | |||
|- | |||
|9 | |||
|limma | |||
|[[256/243]] | |||
|- | |||
|11 | |||
|apotome | |||
|[[2187/2048]] | |||
|- | |||
|20 | |||
|whole tone | |||
|[[9/8]] | |||
|- | |||
|23 | |||
|septimal second | |||
|[[8/7]] | |||
|- | |||
|26 | |||
|septimal third | |||
|[[7/6]] | |||
|- | |||
|29 | |||
|Pythagorean minor 3rd | |||
|[[32/27]] | |||
|- | |||
|31 | |||
|Classical minor 3rd | |||
|[[6/5]] | |||
|- | |||
|38 | |||
|Classical major 3rd | |||
|[[5/4]] | |||
|- | |||
|40 | |||
|Pythagorean major 3rd | |||
|[[81/64]] | |||
|- | |||
|49 | |||
|perfect 4th | |||
|[[4/3]] | |||
|- | |||
|59 | |||
|symmetric tritone | |||
| | |||
|- | |||
|69 | |||
|perfect 5th | |||
|[[3/2]] | |||
|- | |||
|78 | |||
|Pythagorean minor 6th | |||
|[[128/81]] | |||
|- | |||
|80 | |||
|Classical minor 6th | |||
|[[8/5]] | |||
|- | |||
|87 | |||
|Classical major 6th | |||
|[[5/3]] | |||
|- | |||
|89 | |||
|Pythagorean major 6th | |||
|[[27/16]] | |||
|- | |||
|118 | |||
|perfect 8ve | |||
|2/1 exact | |||
|} | |||
== Regular temperament properties == | == Regular temperament properties == | ||