Bohpier: Difference between revisions
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{{Infobox regtemp | |||
| Title = Bohpier | |||
| Subgroups = 2.3.5.7, 2.3.5.7.11, 2.3.5.7.11.13 | |||
| Comma basis = [[245/243]], [[3125/3087]] (7-limit); <br>[[100/99]], [[245/243]], [[1344/1331]] (11-limit; <br>[[100/99]], [[144/143]], [[196/195]], [[275/273]]<br>(13-limit) | |||
| Edo join 1 = 41 | Edo join 2 = 49f | |||
| Mapping = 1; 13 19 23 12 14 | |||
| Generators = 12/11 | |||
| Generators tuning = 146.5 | |||
| Optimization method = CWE | |||
| MOS scales = [[1L 7s]], [[8L 1s]], [[8L 9s]], [[8L 17s]] | |||
| Odd limit 1 = 9 | Mistuning 1 = 6.53 | Complexity 1 = 25 | |||
| Odd limit 2 = 13-limit 21 | Mistuning 2 = 12.5 | Complexity 2 = 41 | |||
}} | |||
'''Bohpier''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] which can be described as the [[Bohlen–Pierce]] scale with [[2/1|octaves]]. From this strong relation it derives its name. In this temperament, like in Bohlen–Pierce, 13 generator steps give the [[3/1|3rd harmonic]], 19 give the [[5/1|5th harmonic]], and 23 give the [[7/1|7th harmonic]], [[tempering out]] the sensamagic comma ([[245/243]]) and the gariboh comma ([[3125/3087]]). The only difference is the addition of the [[period]] of an octave. | '''Bohpier''' is a [[rank-2 temperament|rank-2]] [[regular temperament|temperament]] which can be described as the [[Bohlen–Pierce]] scale with [[2/1|octaves]]. From this strong relation it derives its name. In this temperament, like in Bohlen–Pierce, 13 generator steps give the [[3/1|3rd harmonic]], 19 give the [[5/1|5th harmonic]], and 23 give the [[7/1|7th harmonic]], [[tempering out]] the sensamagic comma ([[245/243]]) and the gariboh comma ([[3125/3087]]). The only difference is the addition of the [[period]] of an octave. | ||
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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: ~27/25 = 146.4741{{c}} | |||
| CWE: ~27/25 = 146.4739{{c}} | |||
| POTE: ~27/25 = 146.4741{{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: ~12/11 = 146.4441{{c}} | |||
| CWE: ~12/11 = 146.5009{{c}} | |||
| POTE: ~12/11 = 146.5446{{c}} | |||
|} | |||
{| class="wikitable mw-collapsible mw-collapsed" | |||
|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings | |||
|- | |||
! rowspan="2" | | |||
! colspan="3" | Euclidean | |||
|- | |||
! Constrained | |||
! Constrained & skewed | |||
! Destretched | |||
|- | |||
! Tenney | |||
| CTE: ~12/11 = 146.4006{{c}} | |||
| CWE: ~12/11 = 146.5230{{c}} | |||
| POTE: ~12/11 = 146.6027{{c}} | |||
|} | |||
[[TOP tuning|TOP generators]]: | [[TOP tuning|TOP generators]]: | ||
* 7-limit: ~2 = 1200.00000, ~27/25 = 146.47407 | * 7-limit: ~2 = 1200.00000{{c}}, ~27/25 = 146.47407{{c}} | ||
* 11-limit: ~2 = 1199.23623, ~12/11 = 146.45131 | * 11-limit: ~2 = 1199.23623{{c}}, ~12/11 = 146.45131{{c}} | ||
* 13-limit: ~2 = 1198.55643, ~12/11 = 146.42630 | * 13-limit: ~2 = 1198.55643{{c}}, ~12/11 = 146.42630{{c}} | ||
=== Tuning spectrum === | === Tuning spectrum === | ||
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[[Category:Sensamagic clan]] | [[Category:Sensamagic clan]] | ||
[[Category:Gariboh clan]] | [[Category:Gariboh clan]] | ||
[[Category: | [[Category:Canopic clan]] | ||
[[Category:Bohlen–Pierce]] | [[Category:Bohlen–Pierce]] | ||