328edo: Difference between revisions

Overthink (talk | contribs)
Theory: important fact
Line 17: Line 17:
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br />8ve stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
! colspan="2" | Tuning error
|-
|-
Line 25: Line 25:
| 2.3.5.7
| 2.3.5.7
| 2401/2400, 3136/3125, 589824/588245
| 2401/2400, 3136/3125, 589824/588245
| {{mapping| 328 520 762 921 }}
| {{Mapping| 328 520 762 921 }}
| −0.298
| −0.298
| 0.229
| 0.229
Line 32: Line 32:
| 2.3.5.7.11
| 2.3.5.7.11
| 2401/2400, 3136/3125, 9801/9800, 19712/19683
| 2401/2400, 3136/3125, 9801/9800, 19712/19683
| {{mapping| 328 520 762 921 1135 }}
| {{Mapping| 328 520 762 921 1135 }}
| −0.303
| −0.303
| 0.205
| 0.205
Line 39: Line 39:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 676/675, 1001/1000, 1716/1715, 3136/3125, 10648/10647
| 676/675, 1001/1000, 1716/1715, 3136/3125, 10648/10647
| {{mapping| 328 520 762 921 1135 1214 }}
| {{Mapping| 328 520 762 921 1135 1214 }}
| −0.295
| −0.295
| 0.188
| 0.188
Line 46: Line 46:
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 3136/3125
| 676/675, 936/935, 1001/1000, 1156/1155, 1716/1715, 3136/3125
| {{mapping| 328 520 762 921 1135 1214 1341 }}
| {{Mapping| 328 520 762 921 1135 1214 1341 }}
| −0.293
| −0.293
| 0.174
| 0.174
Line 58: Line 58:
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|-
! Periods<br />per 8ve
! Periods<br>per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br />ratio*
! Associated<br>ratio*
! Temperaments
! Temperaments
|-
|-
Line 83: Line 83:
|-
|-
| 2
| 2
| 111\328<br />(53\328)
| 53\328
| 406.10<br />(193.90)
| 193.90
| 495/392<br />(28/25)
| 28/25
| [[Semihemiwürschmidt]]
| [[Semihemiwürschmidt]]
|-
|-
| 8
| 8
| 136\328<br />(13\328)
| 13\328
| 497.56<br />(47.56)
| 47.56
| 4/3<br />(36/35)
| 36/35
| [[Twilight]]
| [[Twilight]]
|-
|-
| 41
| 41
| 49\328<br />(1\328)
| 1\328
| 179.27<br />(3.66)
| 3.66
| 567/512<br />(352/351)
| 352/351
| [[Hemicountercomp]]
| [[Hemicountercomp]]
|}
|}
<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/>* In [[normal forms #Minimal-generator form|minimal-generator form]]


[[Category:Hemiwürschmidt]]
[[Category:Hemiwürschmidt]]
[[Category:Semiporwell]]
[[Category:Semiporwell]]