Unidec: Difference between revisions
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Rework on intro |
→Tunings: + basic norm-based tunings |
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== Tunings == | == Tunings == | ||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~80/63 = 416.9403{{c}} | |||
| CWE: ~80/63 = 416.8688{{c}} | |||
| POTE: ~80/63 = 416.8385{{c}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~14/11 = 416.9262{{c}} | |||
| CWE: ~14/11 = 416.8543{{c}} | |||
| POTE: ~14/11 = 416.8350{{c}} | |||
|} | |||
=== Tuning spectrum === | === Tuning spectrum === | ||
{| class="wikitable center-all left-3" | {| class="wikitable center-all left-3" | ||
Revision as of 13:36, 16 November 2025
Unidec is a temperament generated by a wide major third representing 80/63 which can be taken as 14/11 from the 11-limit onwards. Two generators minus a semi-octave period make a ~8/7, and three ~8/7's make a perfect fifth of 3/2, tempering out 1029/1024, the gamelisma, and 4375/4374, the ragisma, with the 11-limit extension adding 385/384 or 441/440 to the comma list.
Unidec has two viable 13-limit extensions: hendec and ekadash.
See Gamelismic clan #Unidec for technical data.
Chords and harmony
Scales
Tunings
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~80/63 = 416.9403 ¢ | CWE: ~80/63 = 416.8688 ¢ | POTE: ~80/63 = 416.8385 ¢ |
| Euclidean | |||
|---|---|---|---|
| Constrained | Constrained & skewed | Destretched | |
| Tenney | CTE: ~14/11 = 416.9262 ¢ | CWE: ~14/11 = 416.8543 ¢ | POTE: ~14/11 = 416.8350 ¢ |
Tuning spectrum
| Eigenmonzo (unchanged interval) |
Generator (¢) | Comments |
|---|---|---|
| 13/12 | 415.357 | |
| 7/4 | 415.587 | |
| 13/10 | 416.198 | |
| 11/8 | 416.227 | |
| 13/9 | 416.338 | |
| 15/13 | 416.516 | |
| 7/6 | 416.641 | |
| 7/5 | 416.730 | 7-odd-limit minimax |
| 11/6 | 416.737 | |
| 11/10 | 416.785 | |
| 9/7 | 416.792 | 9- and 11-odd-limit minimax |
| 15/14 | 416.813 | |
| 11/9 | 416.839 | |
| 15/11 | 416.848 | |
| 5/3 | 416.872 | |
| 5/4 | 416.938 | 5-, 13- and 15-odd-limit minimax |
| 15/8 | 416.957 | |
| 3/2 | 416.993 | |
| 11/7 | 417.508 | |
| 9/5 | 417.596 | |
| 13/11 | 417.842 | |
| 13/7 | 417.925 | |
| 13/8 | 420.264 |
Music
- "Hypnocloudsmack 2" from Newbeams