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{{Infobox regtemp
| Title = BPS
| Subgroups = 3.5.7
| Comma basis = [[245/243]]
| Edo join 1 = b13 | Edo join 2 = b17
| Mapping = 1; 2 -1
| Generators = 9/7
| Generators tuning = 440.7
| Optimization method = CWE
| MOS scales = [[4L 1s (3/1-equivalent)|4L 1s <3/1>]], [[4L 5s (3/1-equivalent)|4L 5s <3/1>]]
| Color name =
| Odd limit 1 = 7 | Mistuning 1 = 4.73 | Complexity 1 = 4
| Odd limit 2 = 3.5.7 49 | Mistuning 2 = 9.46 | Complexity 2 = 9
}}
{{Wikipedia|Bohlen–Pierce scale}}
{{Wikipedia|Bohlen–Pierce scale}}
'''BPS''' (for ''Bohlen–Pierce–Stearns'') is a [[non-octave]] [[regular temperament|temperament]] in the 3.5.7 [[subgroup]] generated by a sharp [[~]][[9/7]] (or equivalently a flat ~[[7/3]]), [[tempering out]] the sensamagic comma ([[245/243]]) so that a stack of two generators represents [[5/3]] in addition to 81/49. This generates a [[mos scale]] of {{mos scalesig|4L 5s<3/1>|link=1}}, known as the Bohlen–Pierce ''Lambda'' scale. The "canonical" tuning for the generator is [[13edt|3\13edt]], representing the equal-tempered [[Bohlen–Pierce]] scale, but a range of other tunings are valid, including [[17edt|4\17edt]], [[30edt|7\30edt]], and [[43edt|10\43edt]].
'''BPS''' (for ''Bohlen–Pierce–Stearns'') is a [[non-octave]] [[regular temperament|temperament]] in the 3.5.7 [[subgroup]] generated by a sharp [[~]][[9/7]] (or equivalently a flat ~[[7/3]]), [[tempering out]] the sensamagic comma ([[245/243]]) so that a stack of two generators represents [[5/3]] in addition to 81/49. This generates a [[mos scale]] of {{mos scalesig|4L 5s<3/1>|link=1}}, known as the Bohlen–Pierce ''Lambda'' scale. The "canonical" tuning for the generator is [[13edt|3\13edt]], representing the equal-tempered [[Bohlen–Pierce]] scale, but a range of other tunings are valid, including [[17edt|4\17edt]], [[30edt|7\30edt]], and [[43edt|10\43edt]].
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<nowiki/>* In 3.5.7-targeted [[DKW theory|DKW]] tuning
<nowiki/>* In 3.5.7-targeted [[DKW theory|DKW]] tuning


== Tuning spectrum ==
== Tunings ==
=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 3.5.7-subgroup norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~9/7 = 441.1431{{c}}
| CWE: ~9/7 = 440.6646{{c}}
| POTE: ~9/7 = 440.4881{{c}}
|}
 
=== Other tunings ===
* [[DKW theory|DKW]] (3.5.7): ~3 = 1901.955{{c}}, ~9/7 = 440.554{{c}}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
{| class="wikitable center-all left-4"
|-
|-
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|  
|  
| 432.263
| 432.263
|
|-
| [[35edt|8\35]]
|
| 434.733
|  
|  
|-
|-
|  
|  
| [[7/3]]
| [[9/7]]
| 435.084
| 435.084
| 0-comma
| Untempered
|-
|-
| [[61edt|14\61]]
| [[48edt|11\48]]
|
| 436.514
|  
|  
|-
| 435.865
|  
|  
| 3645/2401
| 437.449
| 1/6-comma
|-
|-
| [[100edt|23\100]]
| [[61edt|14\61]]
|  
|  
| 437.450
| 436.514
|  
|  
|-
|-
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|-
|-
|  
|  
| [[49/45]]
| [[135/49]]
| 438.632
| 438.632
| 1/4-comma
| 1/4-comma
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|-
|-
|  
|  
| [[7/5]]
| [[15/7]]
| 439.814
| 439.814
| 1/3-comma
| 1/3-comma
|-
| [[108edt|25\108]]
|
| 440.267
|
|-
|-
|  
|  
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|-
|-
|  
|  
| 2/1
| [[2/1]]
| 443.136
| 443.136
| [[Sensi]] mapping of 2/1 to ~125/63
| [[Sensi]] mapping of 2/1 to ~125/63
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|  
|  
| 443.790
| 443.790
|
|-
| [[77edt|18\77]]
|
| 444.613
|  
|  
|-
|-
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|}
|}
<nowiki/>* Besides the [[3/1|tritave]]
<nowiki/>* Besides the [[3/1|tritave]]
=== Other tunings ===
* [[DKW theory|DKW]] (3.5.7): ~3 = 1901.955, ~9/7 = 440.554


[[Category:BPS| ]] <!-- main article -->
[[Category:BPS| ]] <!-- main article -->
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