2520edo: Difference between revisions
Readability; clarify the title row of the rank-2 temp table |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
2520edo is the 18th [[highly composite edo]]. See Subsets and supersets section for the divisors. | 2520edo is the 18th [[highly composite edo]]. See [[#Subsets and supersets]] section for the divisors. | ||
It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472. | It is a good 2.3.5.11.13 [[subgroup]] tuning where it tempers out [[6656/6655]]. The 2520d val tempers out [[2401/2400]] and [[4375/4374]] and provides a tuning for the [[ennealimmal]] temperament and the rank-3 [[ennealimmic]] temperament. The 2520de val is a tuning for the [[hemiennealimmal]] temperament in the 11-limit. The 2520e val is a member of the [[optimal ET sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. | In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. Its subset edos are {{EDOs| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 }}. It is a superabundant edo in addition to being highly composite, with abundancy index of {{nowrap|19/7 {{=}} 2.714}}. | ||
Furthermore, one step of 2520edo is 8 pians ([[20160edo|20160/8]]). | Furthermore, one step of 2520edo is 8 pians ([[20160edo|20160/8]]). | ||
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
! Periods<br>per 8ve | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| 9 | | 9 | ||
| 663\2520<br>(103\2520) | | 663\2520<br />(103\2520) | ||
| 315.714<br>(49.048) | | 315.714<br />(49.048) | ||
| 6/5<br>(36/35) | | 6/5<br />(36/35) | ||
| [[Ennealimmal]] (2520d) | | [[Ennealimmal]] (2520d) | ||
|- | |- | ||
| 18 | | 18 | ||
| 523\2520<br>(103\2520) | | 523\2520<br />(103\2520) | ||
| 249.047<br>(49.048) | | 249.047<br />(49.048) | ||
| 231/200<br>(99/98) | | 231/200<br />(99/98) | ||
| [[Hemiennealimmal]] (2520de) | | [[Hemiennealimmal]] (2520de) | ||
|- | |- | ||
| 56 | | 56 | ||
| 1046\2520<br>(11\2520) | | 1046\2520<br />(11\2520) | ||
| 498.095<br>(5.238) | | 498.095<br />(5.238) | ||
| 4/3<br>(126/125) | | 4/3<br />(126/125) | ||
| [[Barium]] | | [[Barium]] | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||