2520edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|2520}} | {{EDO intro|2520}} | ||
== Theory == | |||
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 GPV sequence]] for the [[tribilo]] temperament, the 2.3.11 rank-2 temperament tempering out 1771561/1769472. | |||
2520edo tempers out the [[barium comma]], setting [[81/80]] equal to 1/56th of the octave, and it tunes the [[barium]] temperament on the patent val upwards to the 13-limit. In addition, 2520edo tunes a variation of barium in the 2520d val for which has a comma basis of {[[vidar|4225/4224, 4375/4374, 6656/6655]], 1116491110875/1115001192448} and reaches 7th harmonic in 9 generators instead of 5. Eliora proposes the name ''baridar'' for this temperament, being a portmanteau of 'barium' and 'vidar'. Overall, barium is best considered in 2520edo as a no-sevens temperament, where it has a comma basis {4225/4224, 6656/6655, 8862938119652501095929/8859136000000000000000}. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2520}} | {{Harmonics in equal|2520}} | ||
=== 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. | |||
2520edo has subset edos {{EDOs|1, 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 19/7 = 2.714. | |||
Furthermore, one step of 2520edo is 8 pians ([[20160edo|20160/8]]). | |||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
! Periods<br>per 8ve | |||
! Generator | |||
! Cents | |||
! Associated<br>Ratio | |||
! Temperaments | |||
|- | |||
| 9 | |||
| 663\2520<br>(103\2520) | |||
| 315.714<br>(49.048) | |||
| 6/5<br>(36/35) | |||
| [[Ennealimmal]] (2520d) | |||
|- | |||
| 18 | |||
| 523\2520<br>(103\2520) | |||
| 249.047<br>(49.048) | |||
| 231/200<br>(99/98) | |||
| [[Hemiennealimmal]] (2520de) | |||
|- | |||
| 56 | |||
| 1046\2520<br>(11\2520) | |||
| 498.095<br>(5.238) | |||
| 4/3<br>(126/125) | |||
| [[Barium]] | |||
|} | |||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||