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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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! Cents*
! Cents*
! Ratios
! Ratios
|-
| 0
|
|
|
|
|
|
| 0
| 0.0
| 1/1
| −8
| 27.8
| 56/55~66/65
| −16
| 55.6
| 28/27~36/35
| −24
| 83.4
| 22/21
|-
|-
| 1
| 1
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| 1109.1
| 1109.1
| 40/21
| 40/21
|-
| 8
| 24
| 1116.6
| 21/11
| 16
| 1144.4
| 27/14~35/18
| 8
| 1172.2
| 55/28~65/33
| 0
| 1200.0
| 2/1
|
|
|
|
|
|
|}
|}
<nowiki/>* In 13-limit CWE tuning
<nowiki/>* In 13-limit CWE tuning
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== Tunings ==
== Tunings ==
[[POTE generator]]:  
{| class="wikitable mw-collapsible mw-collapsed"
* 7-limit: ~27/25 = 146.47407
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
* 11-limit: ~12/11 = 146.54458
|-
* 13-limit: ~12/11 = 146.60266
! 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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|-
|-
! Edo<br>generator
! Edo<br>generator
! [[Eigenmonzo|Eigenmonzo<br>(unchanged-interval)]]
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Generator (¢)
! Comments
! Comments
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* [[Lumatone mapping for bohpier]]
* [[Lumatone mapping for bohpier]]


[[Category:Temperaments]]
[[Category:Bohpier]] <!-- main article -->
[[Category:Bohpier]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Sensamagic clan]]
[[Category:Sensamagic clan]]
[[Category:Gariboh clan]]
[[Category:Gariboh clan]]
[[Category:Mirkwai clan]]
[[Category:Canopic clan]]
[[Category:Bohlen-Pierce]]
[[Category:Bohlen–Pierce]]
Retrieved from "https://en.xen.wiki/w/Bohpier"