1178edo: 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" |
m →Regular temperament properties: comma basis |
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! 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| -1867 1178 }} | ||
| {{ | | {{Mapping| 1178 1867 }} | ||
| +0.0276 | | +0.0276 | ||
| 0.0276 | | 0.0276 | ||
| Line 31: | Line 31: | ||
|- | |- | ||
| 2.3.5 | | 2.3.5 | ||
| {{ | | {{Monzo| -14 -19-19 }}, {{monzo| -99 61 1 }} | ||
| {{ | | {{Mapping| 1178 1867 2735 }} | ||
| +0.0522 | | +0.0522 | ||
| 0.0415 | | 0.0415 | ||
| Line 39: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 4375/4374, 703125/702464, {{monzo| -52 -5 -2 23 }} | | 4375/4374, 703125/702464, {{monzo| -52 -5 -2 23 }} | ||
| {{ | | {{Mapping| 1178 1867 2735 3307 }} | ||
| +0.0450 | | +0.0450 | ||
| 0.0380 | | 0.0380 | ||
| Line 46: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 3025/3024, 4375/4374, 234375/234256, {{monzo| -27 3 -4 10 1 }} | | 3025/3024, 4375/4374, 234375/234256, {{monzo| -27 3 -4 10 1 }} | ||
| {{ | | {{Mapping| 1178 1867 2735 3307 4075 }} | ||
| +0.0484 | | +0.0484 | ||
| 0.0347 | | 0.0347 | ||
| Line 52: | Line 52: | ||
|- | |- | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 3025/3024, 4225/4224, 4375/4374, 78125/78078, | | 3025/3024, 4225/4224, 4375/4374, 78125/78078, 655473/655360 | ||
| {{ | | {{Mapping| 1178 1867 2735 3307 4075 4359 }} | ||
| +0.0457 | | +0.0457 | ||
| 0.0322 | | 0.0322 | ||
| Line 60: | Line 60: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 2500/2499, 3025/3024, 4225/4224, 4375/4374, 4914/4913, 14875/14872 | | 2500/2499, 3025/3024, 4225/4224, 4375/4374, 4914/4913, 14875/14872 | ||
| {{ | | {{Mapping| 1178 1867 2735 3307 4075 4359 4815 }} | ||
| +0.0403 | | +0.0403 | ||
| 0.0327 | | 0.0327 | ||
| Line 67: | Line 67: | ||
| 2.3.5.7.11.13.17.19 | | 2.3.5.7.11.13.17.19 | ||
| 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4225/4224, 4375/4374, 4914/4913 | | 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4225/4224, 4375/4374, 4914/4913 | ||
| {{ | | {{Mapping| 1178 1867 2735 3307 4075 4359 4815 5004 }} | ||
| +0.0370 | | +0.0370 | ||
| 0.0318 | | 0.0318 | ||
| Line 77: | Line 77: | ||
|+ 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 90: | Line 90: | ||
|- | |- | ||
| 19 | | 19 | ||
| 489\1178<br | | 489\1178<br>(7\1178) | ||
| 498.13<br | | 498.13<br>(7.13) | ||
| 4/3<br | | 4/3<br>(225/224) | ||
| [[Enneadecal]] | | [[Enneadecal]] | ||
|- | |- | ||
| 31 | | 31 | ||
| 581\1178<br | | 581\1178<br>(11\1178) | ||
| 591.851<br | | 591.851<br>(11.205) | ||
| 936/665<br | | 936/665<br>(?) | ||
| [[31st-octave temperaments#217 & 1178|217 & 1178]] | | [[31st-octave temperaments#217 & 1178|217 & 1178]] | ||
|- | |- | ||
| 38 | | 38 | ||
| 260\1178<br | | 260\1178<br>(12\1178) | ||
| 264.86<br | | 264.86<br>(12.22) | ||
| 500/429<br | | 500/429<br>(144/143) | ||
| [[Semihemienneadecal]] | | [[Semihemienneadecal]] | ||
|- | |- | ||
| 38 | | 38 | ||
| 489\1178<br | | 489\1178<br>(7\1178) | ||
| 498.13<br | | 498.13<br>(7.13) | ||
| 4/3<br | | 4/3<br>(225/224) | ||
| [[Hemienneadecal]] | | [[Hemienneadecal]] | ||
|} | |} | ||
<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 | <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 | ||
== Music == | == Music == | ||