524edo: Difference between revisions
Created page with "524 equal division divides the octave into steps of 2.29 cents each. == Theory == {{Harmonics in equal|524}} 524edo is excellent in the 2.7.13.19 subgroup, and good in the no..." |
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524edo is excellent in the 2.7.13.19 subgroup, and good in the no-threes 19-limit. In the 3-limit, it is wise to treat 524edo as a dual-fifth system. | 524edo is excellent in the 2.7.13.19 subgroup, and good in the no-threes 19-limit. In the 3-limit, it is wise to treat 524edo as a dual-fifth system. | ||
524 years is the length of a calendar leap week cycle with 93 leap weeks, creating a 93 out of 524 maximum evenness scale, represented by the 93 & 524 temperament. In addition, both 93 and 524 represent well the 13:17:19 harmonics. The corresponding comma list is 16807/16796, 157339/157216, 47071232/47045881. Eliora proposes that this temperament be named '''ostara''', after the feast of the spring equinox, which 93\524 leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231, 97 & 400, and 52 & 293 already have their identities and names. | 524 years is the length of a calendar leap week cycle with 93 leap weeks, creating a 93 out of 524 maximum evenness scale, represented by the 93 & 524 temperament. In addition, both 93 and 524 represent well the 13:17:19 harmonics. The corresponding comma list in the 2.7.13.17.19 subgroup is 16807/16796, 157339/157216, 47071232/47045881. Eliora proposes that this temperament be named '''ostara''', after the feast of the spring equinox, which 93\524 leap week rule approximates well. Other spring equinoctial temperaments, such as 41 & 231, 97 & 400, and 52 & 293 already have their identities and names. | ||
In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655. | |||
== Regular temperament properties == | |||
Based on treating 524edo as a no-threes system: | |||
{| class="wikitable center-4 center-5 center-6" | |||
! rowspan="2" |Subgroup | |||
! rowspan="2" |[[Comma list]] | |||
! rowspan="2" |[[Mapping]] | |||
! rowspan="2" |Optimal | |||
8ve stretch (¢) | |||
! colspan="2" |Tuning error | |||
|- | |||
![[TE error|Absolute]] (¢) | |||
![[TE simple badness|Relative]] (%) | |||
|- | |||
|2.5 | |||
|{{Monzo|1217 0 -524}} | |||
|[{{val|524 1217}}] | |||
| -0.152 | |||
|0.153 | |||
|6.66 | |||
|- | |||
|2.5.7 | |||
|{{Monzo|33 0 -13 -1}}, {{Monzo|-4 0 -43 37}} | |||
|[{{val|524 1217 1471}}] | |||
| -0.087 | |||
|0.155 | |||
|6.79 | |||
|- | |||
|2.5.7.11 | |||
|1835008/1830125, {{Monzo|3 0 7 3 -8}}, {{Monzo|-13 0 -5 10 -1}} | |||
|[{{val|524 1217 1471 1813}}] | |||
| -0.108 | |||
|0.139 | |||
|6.07 | |||
|- | |||
|2.5.7.11.13 | |||
|1001/1000, 742586/741125, 2097152/2093663, 14201915/14172488 | |||
|[{{val|524 1217 1471 1813 1939}}] | |||
| -0.082 | |||
|0.135 | |||
|5.87 | |||
|- | |||
|2.5.7.11.13.17 | |||
|1001/1000, 6664/6655, 54080/54043, 147968/147875, 285719/285610 | |||
|[{{val|524 1217 1471 1813 1939 2142}}] | |||
| -0.084 | |||
|0.122 | |||
| | |||
|} | |||