253edo: Difference between revisions
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" |
→Regular temperament properties: + link to retrotonic |
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| Line 17: | Line 17: | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br | ! rowspan="2" | Optimal<br>8ve stretch (¢) | ||
! colspan="2" | Tuning error | ! colspan="2" | Tuning error | ||
|- | |- | ||
| Line 24: | Line 24: | ||
|- | |- | ||
| 2.3 | | 2.3 | ||
| {{ | | {{Monzo| 401 -253 }} | ||
| {{ | | {{Mapping| 253 401 }} | ||
| −0.007 | | −0.007 | ||
| 0.007 | | 0.007 | ||
| Line 32: | Line 32: | ||
| 2.3.5 | | 2.3.5 | ||
| 32805/32768, {{monzo| -4 -37 27 }} | | 32805/32768, {{monzo| -4 -37 27 }} | ||
| {{ | | {{Mapping| 253 401 587 }} | ||
| +0.300 | | +0.300 | ||
| 0.435 | | 0.435 | ||
| Line 39: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 2401/2400, 32805/32768, 390625/387072 | | 2401/2400, 32805/32768, 390625/387072 | ||
| {{ | | {{Mapping| 253 401 587 710 }} | ||
| +0.335 | | +0.335 | ||
| 0.381 | | 0.381 | ||
| Line 46: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 385/384, 1375/1372, 4000/3993, 19712/19683 | | 385/384, 1375/1372, 4000/3993, 19712/19683 | ||
| {{ | | {{Mapping| 253 401 587 710 875 }} | ||
| +0.333 | | +0.333 | ||
| 0.341 | | 0.341 | ||
| Line 53: | Line 53: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 325/324, 385/384, 1375/1372, 1575/1573, 2200/2197 | | 325/324, 385/384, 1375/1372, 1575/1573, 2200/2197 | ||
| {{ | | {{Mapping| 253 401 587 710 875 936 }} | ||
| +0.323 | | +0.323 | ||
| 0.312 | | 0.312 | ||
| Line 60: | Line 60: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 325/324, 375/374, 385/384, 595/594, 1275/1274, 2200/2197 | | 325/324, 375/374, 385/384, 595/594, 1275/1274, 2200/2197 | ||
| {{ | | {{Mapping| 253 401 587 710 875 936 1034 }} | ||
| +0.298 | | +0.298 | ||
| 0.295 | | 0.295 | ||
| Line 70: | Line 70: | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
|- | |- | ||
! Periods<br | ! Periods<br>per 8ve | ||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br | ! Associated<br>ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 87: | Line 87: | ||
| 448/405 | | 448/405 | ||
| [[Sesquiquartififths]] | | [[Sesquiquartififths]] | ||
|- | |||
| 1 | |||
| 48\253 | |||
| 227.67 | |||
| 154/135 | |||
| [[Retrotonic]] | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 98: | Line 104: | ||
| 583.40 | | 583.40 | ||
| 7/5 | | 7/5 | ||
| [[Cotritone]] | | [[Cotritone]] (11-limit) | ||
|} | |} | ||
<nowiki />* | <nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | ||
== Scales == | == Scales == | ||