BPS - Revision history

FloraC: - "3.5.7.9 tetrad" (not a tetrad under 3/1 equivalence); improve links

2026-09-12T08:49:55Z

- "3.5.7.9 tetrad" (not a tetrad under 3/1 equivalence); improve links

← Older revision		Revision as of 08:49, 12 September 2026
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	}}		}}
	{{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]].

	As the generator of the Bohlen–Pierce scale, and the simplest decently accurate temperament of the 3.5.7 subgroup, this temperament fulfills a niche similar to [[meantone]] of the 2.3.5 subgroup, allowing for the 3:5:7 triad ~~or 3:5:7:9 tetrad~~ to serve as BPS' primary consonance, similar to how the 4:5:6 triad serves as meantone's primary consonance.		As the generator of the Bohlen–Pierce scale, and the simplest decently accurate temperament of the 3.5.7 subgroup, this temperament fulfills a niche similar to [[meantone]] of the [[5-limit\|2.3.5 subgroup]], allowing for the [[3:5:7]] triad to serve as BPS' primary consonance, similar to how the [[4:5:6]] triad serves as meantone's primary consonance.

	For technical data, see [[Sensamagic clan #BPS]] or [[No-twos subgroup temperaments #BPS]] (currently, extensions with 2 are stored on the former page and no-~~twos~~ extensions are stored on the latter).		For technical data, see [[Sensamagic clan #BPS]] or [[No-twos subgroup temperaments #BPS]] (currently, extensions with 2 are stored on the former page and no-2's extensions are stored on the latter).

	== Extensions ==		== Extensions ==

CompactStar at 07:22, 18 August 2026

2026-08-18T07:22:10Z

← Older revision		Revision as of 07:22, 18 August 2026
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	'''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]].

	As the generator of the Bohlen–Pierce scale, and the simplest decently accurate temperament of the 3.5.7 subgroup, this temperament fulfills a niche similar to [[meantone]] of the 2.3.5 subgroup, allowing for the 3:5:7:9 tetrad to serve as BPS' primary consonance, similar to how the 4:5:6 triad serves as meantone's primary consonance.		As the generator of the Bohlen–Pierce scale, and the simplest decently accurate temperament of the 3.5.7 subgroup, this temperament fulfills a niche similar to [[meantone]] of the 2.3.5 subgroup, allowing for the 3:5:7 triad or 3:5:7:9 tetrad to serve as BPS' primary consonance, similar to how the 4:5:6 triad serves as meantone's primary consonance.

	For technical data, see [[Sensamagic clan #BPS]] or [[No-twos subgroup temperaments #BPS]] (currently, extensions with 2 are stored on the former page and no-twos extensions are stored on the latter).		For technical data, see [[Sensamagic clan #BPS]] or [[No-twos subgroup temperaments #BPS]] (currently, extensions with 2 are stored on the former page and no-twos extensions are stored on the latter).

FloraC: Cleanup on infobox

2026-02-09T10:04:21Z

Cleanup on infobox

← Older revision		Revision as of 10:04, 9 February 2026
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	{{Infobox ~~Regtemp~~		{{Infobox regtemp
	\| Title = BPS		\| Title = BPS
	\| Subgroups = 3.5.7		\| Subgroups = 3.5.7
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	\| Edo join 1 = b13 \| Edo join 2 = b17		\| Edo join 1 = b13 \| Edo join 2 = b17
	\| Mapping = 1; 2 -1		\| Mapping = 1; 2 -1
	\| ~~Generator~~ = 9/7		\| Generators = 9/7
	\| ~~Generator~~ tuning = 440.7		\| Generators tuning = 440.7
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[4L 1s (3/1-equivalent)\|4L 1s <3/1>]], [[4L 5s (3/1-equivalent)\|4L 5s <3/1>]]		\| MOS scales = [[4L 1s (3/1-equivalent)\|4L 1s <3/1>]], [[4L 5s (3/1-equivalent)\|4L 5s <3/1>]]
	\| Color name =		\| Color name =
	\| Odd limit 1 = 7 \| Mistuning 1 = 4.73 \| Complexity 1 = 4		\| 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		\| Odd limit 2 = 3.5.7 49 \| Mistuning 2 = 9.46 \| Complexity 2 = 9
	}}		}}
	{{Wikipedia\|Bohlen–Pierce scale}}		{{Wikipedia\|Bohlen–Pierce scale}}

FloraC: The formal name is BPS, not the three-word combo

2025-12-24T12:03:27Z

The formal name is *BPS*, not the three-word combo

← Older revision		Revision as of 12:03, 24 December 2025
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	{{Infobox Regtemp		{{Infobox Regtemp
	\| Title = ~~Bohlen–Pierce–Stearns~~		\| Title = BPS
	\| Subgroups = 3.5.7		\| Subgroups = 3.5.7
	\| Comma basis = [[245/243]]		\| Comma basis = [[245/243]]

Overthink: scale sizes

2025-12-24T01:36:31Z

scale sizes

← Older revision		Revision as of 01:36, 24 December 2025
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	\| MOS scales = [[4L 1s (3/1-equivalent)\|4L 1s <3/1>]], [[4L 5s (3/1-equivalent)\|4L 5s <3/1>]]		\| MOS scales = [[4L 1s (3/1-equivalent)\|4L 1s <3/1>]], [[4L 5s (3/1-equivalent)\|4L 5s <3/1>]]
	\| Color name =		\| Color name =
	\| Odd limit 1 = 7 \| Mistuning 1 = 4.73 \| Complexity 1 =		\| Odd limit 1 = 7 \| Mistuning 1 = 4.73 \| Complexity 1 = 4
	\| Odd limit 2 = (3.5.7) 49 \| Mistuning 2 = 9.46 \| Complexity 2 =		\| Odd limit 2 = (3.5.7) 49 \| Mistuning 2 = 9.46 \| Complexity 2 = 9
	}}		}}
	{{Wikipedia\|Bohlen–Pierce scale}}		{{Wikipedia\|Bohlen–Pierce scale}}

Overthink: + infobox

2025-12-24T01:35:20Z

+ infobox

← Older revision		Revision as of 01:35, 24 December 2025
Line 1:		Line 1:
			{{Infobox Regtemp
			\| Title = Bohlen–Pierce–Stearns
			\| Subgroups = 3.5.7
			\| Comma basis = [[245/243]]
			\| Edo join 1 = b13 \| Edo join 2 = b17
			\| Mapping = 1; 2 -1
			\| Generator = 9/7
			\| Generator 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 =
			\| Odd limit 2 = (3.5.7) 49 \| Mistuning 2 = 9.46 \| Complexity 2 =
			}}
	{{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]].

FloraC: + tunings

2025-10-12T09:58:56Z

+ tunings

@@ Line 67: / Line 67: @@
 <nowiki/>* In 3.5.7-targeted [[DKW theory|DKW]] tuning
-== Tuning spectrum ==
+== Tunings ==
 {| class="wikitable center-all left-4"
 |-
@@ Line 191: / Line 212: @@
 |}
 <nowiki/>* Besides the [[3/1|tritave]]
 [[Category:BPS| ]] <!-- main article -->

Lériendil: /* Tuning spectrum */

2025-10-09T13:50:46Z

Tuning spectrum

← Older revision		Revision as of 13:50, 9 October 2025
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	\|		\|
	\|-		\|-
			\| [[35edt\|8\35]]
	\|		\|
	\| [[7/3]]		\| 434.733
			\|
			\|-
			\|
			\| [[9/7]]
	\| 435.084		\| 435.084
	\| 0-~~comma~~		\| Untempered
			\|-
			\| [[48edt\|11\48]]
			\|
			\| 435.865
			\|
	\|-		\|-
	\| [[61edt\|14\61]]		\| [[61edt\|14\61]]
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	\| 436.514		\| 436.514
	\|		\|
	\|-
	\|
	~~\| 3645/2401~~
	~~\| 437.449~~
	~~\| 1/6-comma~~
	\|-		\|-
	\|		\|
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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

Lériendil: /* Tuning spectrum */

2025-10-09T13:47:17Z

Tuning spectrum

← Older revision		Revision as of 13:47, 9 October 2025
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	\| 437.449		\| 437.449
	\| 1/6-comma		\| 1/6-comma
	\|-
	~~\| [[100edt\|23\100]]~~
	\|
	~~\| 437.450~~
	\|
	\|-		\|-
	\|		\|
Line 119:		Line 114:
	\| 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~~
	\|		\|
	\|-		\|-

Lériendil: /* Tuning spectrum */

2025-10-09T13:46:30Z

Tuning spectrum

← Older revision		Revision as of 13:46, 9 October 2025
Line 169:		Line 169:
	\| 442.921		\| 442.921
	\|		\|
			\|-
			\|
			\| 2/1
			\| 443.136
			\| [[Sensi]] mapping of 2/1 to ~125/63
	\|-		\|-
	\| [[30edt\|7\30]]		\| [[30edt\|7\30]]
Line 174:		Line 179:
	\| 443.790		\| 443.790
	\|		\|
	\|-
	\|
	~~\| 175/81~~
	~~\| 444.544~~
	~~\| 2/3-comma~~
	\|-		\|-
	\| [[77edt\|18\77]]		\| [[77edt\|18\77]]

BPS - Revision history

FloraC: - "3.5.7.9 tetrad" (not a tetrad under 3/1 equivalence); improve links

CompactStar at 07:22, 18 August 2026

FloraC: Cleanup on infobox

FloraC: The formal name is *BPS*, not the three-word combo

Overthink: scale sizes

Overthink: + infobox

FloraC: + tunings

Lériendil: /* Tuning spectrum */

Lériendil: /* Tuning spectrum */

Lériendil: /* Tuning spectrum */

FloraC: The formal name is BPS, not the three-word combo