Sensi - Revision history

FloraC: /* Music */ copypaste one from 46edo

2026-05-07T14:17:05Z

Music: copypaste one from 46edo

← Older revision		Revision as of 14:17, 7 May 2026
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	; [[Budjarn Lambeth]]		; [[Budjarn Lambeth]]
	* [https://www.youtube.com/watch?v=qc0CkUKj7t4 Music in Sensi Temperament (+ Tempered Octaves) ~~– Mar~~ 2024]		* [https://www.youtube.com/watch?v=qc0CkUKj7t4 ''Music in Sensi Temperament (+ Tempered Octaves)''] (2024)

			; [[Claudi Meneghin]]
			* [https://www.youtube.com/watch?v=rmgWC_jruSg ''Sensi Fugue''] (2024) – fugue for two organs, in sensi, 46edo tuning

	[[Category:Sensi\| ]] <!-- Main article -->		[[Category:Sensi\| ]] <!-- Main article -->

ArrowHead294 at 18:14, 6 March 2026

2026-03-06T18:14:53Z

← Older revision		Revision as of 18:14, 6 March 2026
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	\| Mapping = 1; 7 9 13 10		\| Mapping = 1; 7 9 13 10
	\| Generators = 9/7 \| Generators tuning = 443.3 \| Optimization method = CWE		\| Generators = 9/7 \| Generators tuning = 443.3 \| Optimization method = CWE
	\| MOS scales = [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]]		\| MOS scales = [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]]
	\| Pergen = (P8, ccP5/7)		\| Pergen = (P8, ccP5/7)
	\| Odd limit 1 = 7 \| Mistuning 1 = 7.5 \| Complexity 1 = 19		\| Odd limit 1 = 7 \| Mistuning 1 = 7.5 \| Complexity 1 = 19

FloraC: Cleanup on infobox

2026-02-09T09:39:31Z

Cleanup on infobox

← Older revision		Revision as of 09:39, 9 February 2026
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	{{interwiki		{{interwiki
			\| en = Sensi
	\| de = Sensi		\| de = Sensi
	~~\| en = Sensi~~
	}}		}}
	{{Infobox regtemp		{{Infobox regtemp
	\| Title = Sensi		\| Title = Sensi
	\| Subgroups = 2.3.5.7, 2.3.5.7.13		\| Subgroups = 2.3.5.7, 2.3.5.7.13
	\| Comma basis = [[~~245~~/~~243~~]], [[~~126~~/~~125~~]] (7-limit); <br> [[91/90]], [[126/125]], [[169/168]] (2.3.5.7.13)		\| Comma basis = [[126/125]], [[245/243]] (7-limit); <br>[[91/90]], [[126/125]], [[169/168]] (2.3.5.7.13)
	\| Edo join 1 = 19 \| Edo join 2 = 27		\| Edo join 1 = 19 \| Edo join 2 = 27
	\| ~~Generator~~ = 9/7 \| ~~Generator~~ tuning = 443.3 \| Optimization method = CWE		\| Mapping = 1; 7 9 13 10
			\| Generators = 9/7 \| Generators tuning = 443.3 \| Optimization method = CWE
	\| MOS scales = [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]]		\| MOS scales = [[3L 2s]], [[3L 5s]], [[8L 3s]], [[8L 11s]]
	~~\| Mapping = 1; 7 9 13 10~~
	\| Pergen = (P8, ccP5/7)		\| Pergen = (P8, ccP5/7)
	\| Odd limit 1 = 7 \| Mistuning 1 = 7.5 \| Complexity 1 = 19		\| Odd limit 1 = 7 \| Mistuning 1 = 7.5 \| Complexity 1 = 19
	\| Odd limit 2 = (2.3.5.7.13) 21 \| Mistuning 2 = 11.1 \| Complexity 2 = 27		\| Odd limit 2 = 2.3.5.7.13 21 \| Mistuning 2 = 11.1 \| Complexity 2 = 27
	}}		}}
	'''Sensi''' is a [[rank-2 temperament\|rank-2]] [[regular temperament]] that is [[generator\|generated]] by an extremely sharp major third of between 442 and 445{{cent}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1\|6th harmonic]] is therefore split into seven, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.		'''Sensi''' is a [[rank-2 temperament\|rank-2]] [[regular temperament]] that is [[generator\|generated]] by an extremely sharp major third of between 442 and 445{{cent}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1\|6th harmonic]] is therefore split into seven, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.

ArrowHead294: /* BPS */

2026-02-04T20:28:10Z

BPS

← Older revision		Revision as of 20:28, 4 February 2026
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	: ''Main article: [[Relationship between Bohlen–Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen.E2.80.93Pierce.E2.80.93Stearns temperament to octave-ful temperaments\|Relationship between Bohlen–Pierce and octave-ful temperaments]].		: ''Main article: [[Relationship between Bohlen–Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen.E2.80.93Pierce.E2.80.93Stearns temperament to octave-ful temperaments\|Relationship between Bohlen–Pierce and octave-ful temperaments]].

	Since the sensamagic comma, 245/243, contains no 2 in its [[monzo\|factorization]], only primes 3, 5, and 7, it can be tempered out in a [[3/1\|tritave (3/1)]]-repeating, [[3.5.7 subgroup]] context, where the generator (9/7) is now the tritave-reduced 7th subharmonic, two of which give the 5th harmonic. This is known as [[BPS\|~~Bohlen-Pierce-Stearns~~ (BPS)]] temperament, and it generates a [[4L 5s (3/1-equivalent)\|4L 5s]] scale against the tritave (sometimes known as ''Lambda''). Where this temperament connects to sensi is that, at 7 generators, BPS reaches an interval that it identifies with [[125/63]], which is rather close to the octave; sensi is obtained by treating this interval as the mapping of 2/1, which provides the interesting notion of using sensi in a 3/1-periodic 3.5.7.2 setting.		Since the sensamagic comma, 245/243, contains no 2 in its [[monzo\|factorization]], only primes 3, 5, and 7, it can be tempered out in a [[3/1\|tritave (3/1)]]-repeating, [[3.5.7 subgroup]] context, where the generator (9/7) is now the tritave-reduced 7th subharmonic, two of which give the 5th harmonic. This is known as [[BPS\|Bohlen–Pierce–Stearns (BPS)]] temperament, and it generates a [[4L 5s (3/1-equivalent)\|4L 5s]] scale against the tritave (sometimes known as ''Lambda''). Where this temperament connects to sensi is that, at 7 generators, BPS reaches an interval that it identifies with [[125/63]], which is rather close to the octave; sensi is obtained by treating this interval as the mapping of 2/1, which provides the interesting notion of using sensi in a 3/1-periodic 3.5.7.2 setting.

	== Chords and harmony ==		== Chords and harmony ==

ArrowHead294 at 20:27, 4 February 2026

2026-02-04T20:27:38Z

← Older revision		Revision as of 20:27, 4 February 2026
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	'''Sensi''' is a [[rank-2 temperament\|rank-2]] [[regular temperament]] that is [[generator\|generated]] by an extremely sharp major third of between 442 and 445{{cent}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1\|6th harmonic]] is therefore split into seven, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.		'''Sensi''' is a [[rank-2 temperament\|rank-2]] [[regular temperament]] that is [[generator\|generated]] by an extremely sharp major third of between 442 and 445{{cent}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1\|6th harmonic]] is therefore split into seven, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.

	The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (hence the 8-note ([[3L 5s]], checkertonic) and 11-note ([[8L 3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).		The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (hence the 8-note ([[3L 5s]], checkertonic) and 11-note ([[8L 3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).

	Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), as well as [[46edo]] (generator 17\46; {{nowrap\| L/s {{=}} 7/5 }}, more optimized for sensi temperament) and [[65edo]] (generator 24\65; {{nowrap\| L/s {{=}} 10/7 }}) using the 65f [[val]] with a flat 13.		Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), as well as [[46edo]] (generator 17\46; {{nowrap\| L/s {{=}} 7/5 }}, more optimized for sensi temperament) and [[65edo]] (generator 24\65; {{nowrap\| L/s {{=}} 10/7 }}) using the 65f [[val]] with a flat 13.
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	It is worth noting that sensi distinguishes itself from other structures, the [[sensamagic clan\|sensamagic temperaments]], based around 245/243 (whose basic form in the 2.9/7.5/3 subgroup is known as [[sentry]]) by virtue of its minor third (6/5) being ''flattened'' from just rather than sharpened. This results in the supermajor third being sharpened even more than is typical, so much so that it is tuned [[interseptimal]]ly and may not fulfill all the functions that [[~]]9/7 is intended to have.		It is worth noting that sensi distinguishes itself from other structures, the [[sensamagic clan\|sensamagic temperaments]], based around 245/243 (whose basic form in the 2.9/7.5/3 subgroup is known as [[sentry]]) by virtue of its minor third (6/5) being ''flattened'' from just rather than sharpened. This results in the supermajor third being sharpened even more than is typical, so much so that it is tuned [[interseptimal]]ly and may not fulfill all the functions that [[~]]9/7 is intended to have.

	One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as [[31/24]]~[[40/31]] is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29). There are also alternative mappings of 7, including [[sensei]] (+32 generators, with a tuning flat of 65edo) and [[warrior]] (~~-33~~ generators, with a tuning between 65edo and 46edo); warrior combines well with the mapping of sensible, and sensei with sendai.		One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as {{nowrap\|[[31/24]]~[[40/31]]}} is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29). There are also alternative mappings of 7, including [[sensei]] (+32 generators, with a tuning flat of 65edo) and [[warrior]] (−33 generators, with a tuning between 65edo and 46edo); warrior combines well with the mapping of sensible, and sensei with sendai.

	==== BPS ====		==== BPS ====
	: ''Main article: [[Relationship between Bohlen–Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen.E2.80.93Pierce.E2.80.93Stearns temperament to octave-ful temperaments\|Relationship between Bohlen–Pierce and octave-ful temperaments]].		: ''Main article: [[Relationship between Bohlen–Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen.E2.80.93Pierce.E2.80.93Stearns temperament to octave-ful temperaments\|Relationship between Bohlen–Pierce and octave-ful temperaments]].

	Since the sensamagic comma, 245/243, contains no 2 in its [[monzo\|factorization]], only primes 3, 5, and 7, it can be tempered out in a [[3/1\|tritave (3/1)]]-repeating, [[3.5.7 subgroup]] context, where the generator (9/7) is now the tritave-reduced 7th subharmonic, two of which give the 5th harmonic. This is known as [[BPS\|Bohlen-Pierce-Stearns (BPS)]] temperament, and it generates a [[4L 5s (3/1-equivalent)\|4L 5s]] scale against the tritave (sometimes known as ''Lambda''). Where this temperament connects to sensi is that, at 7 generators, BPS reaches an interval that it identifies with [[125/63]], which is rather close to the octave; sensi is obtained by treating this interval as the mapping of 2/1, which provides the interesting notion of using sensi in a 3/1-periodic 3.5.7.2 setting.		Since the sensamagic comma, 245/243, contains no 2 in its [[monzo\|factorization]], only primes 3, 5, and 7, it can be tempered out in a [[3/1\|tritave (3/1)]]-repeating, [[3.5.7 subgroup]] context, where the generator (9/7) is now the tritave-reduced 7th subharmonic, two of which give the 5th harmonic. This is known as [[BPS\|Bohlen-Pierce-Stearns (BPS)]] temperament, and it generates a [[4L 5s (3/1-equivalent)\|4L 5s]] scale against the tritave (sometimes known as ''Lambda''). Where this temperament connects to sensi is that, at 7 generators, BPS reaches an interval that it identifies with [[125/63]], which is rather close to the octave; sensi is obtained by treating this interval as the mapping of 2/1, which provides the interesting notion of using sensi in a 3/1-periodic 3.5.7.2 setting.

	== Chords and harmony ==		== Chords and harmony ==

Overthink: - typo

2025-12-29T10:06:32Z

- typo

← Older revision		Revision as of 10:06, 29 December 2025
Line 17:		Line 17:
	'''Sensi''' is a [[rank-2 temperament\|rank-2]] [[regular temperament]] that is [[generator\|generated]] by an extremely sharp major third of between 442 and 445{{cent}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1\|6th harmonic]] is therefore split into seven, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.		'''Sensi''' is a [[rank-2 temperament\|rank-2]] [[regular temperament]] that is [[generator\|generated]] by an extremely sharp major third of between 442 and 445{{cent}}, which is taken in the [[7-limit]] to represent a sharpened [[9/7]]. The most important equivalence in sensi (i.e. [[tempering out]] the comma [[245/243]]) is known as ''sensamagic'', by which two of these thirds stack to a major sixth which approximates [[5/3]]. Sensi then makes the additional tempering of [[126/125]], through which three of these major sixths approximate [[7/6]], two octaves up. The [[6/1\|6th harmonic]] is therefore split into seven, and [[5/4]] is divided into three parts, each identified with [[15/14]]. Furthermore, since the supermajor third is tempered so sharply, it makes sense to have it represent both 9/7 and [[13/10]], which means [[91/90]] is tempered out in the 2.3.5.7.13 [[subgroup]]. There the 15/14 interval also represents [[14/13]] and [[13/12]], which results in [[169/168]] and [[196/195]] being tempered out.

	The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (~~whence~~ the 8-note ([[3L 5s]], checkertonic) and 11-note ([[8L 3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).		The structure whereby 5/3 is split into two supermajor thirds is obviously xenharmonic as this cannot occur in [[12edo]]. But particularly, as the simplest [[EDO]]s with similar structures are [[8edo]] and [[11edo]] (hence the 8-note ([[3L 5s]], checkertonic) and 11-note ([[8L 3s]], flanatonic) [[MOS scale]]s), sensi has a very xenmelodic character compared to many other ways of organizing the 7-limit (such as [[superpyth]], which is based on the familiar [[chain of fifths]], and even [[porcupine]], which is fundamentally heptatonic).

	Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), as well as [[46edo]] (generator 17\46; {{nowrap\| L/s {{=}} 7/5 }}, more optimized for sensi temperament) and [[65edo]] (generator 24\65; {{nowrap\| L/s {{=}} 10/7 }}) using the 65f [[val]] with a flat 13.		Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), as well as [[46edo]] (generator 17\46; {{nowrap\| L/s {{=}} 7/5 }}, more optimized for sensi temperament) and [[65edo]] (generator 24\65; {{nowrap\| L/s {{=}} 10/7 }}) using the 65f [[val]] with a flat 13.

Lériendil: /* Related temperaments */

2025-10-09T20:44:37Z

Related temperaments

← Older revision		Revision as of 20:44, 9 October 2025
Line 242:		Line 242:
	It is worth noting that sensi distinguishes itself from other structures, the [[sensamagic clan\|sensamagic temperaments]], based around 245/243 (whose basic form in the 2.9/7.5/3 subgroup is known as [[sentry]]) by virtue of its minor third (6/5) being ''flattened'' from just rather than sharpened. This results in the supermajor third being sharpened even more than is typical, so much so that it is tuned [[interseptimal]]ly and may not fulfill all the functions that [[~]]9/7 is intended to have.		It is worth noting that sensi distinguishes itself from other structures, the [[sensamagic clan\|sensamagic temperaments]], based around 245/243 (whose basic form in the 2.9/7.5/3 subgroup is known as [[sentry]]) by virtue of its minor third (6/5) being ''flattened'' from just rather than sharpened. This results in the supermajor third being sharpened even more than is typical, so much so that it is tuned [[interseptimal]]ly and may not fulfill all the functions that [[~]]9/7 is intended to have.

	One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as [[31/24]]~[[40/31]] is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29). There are also alternative mappings of 7, including [[sensei]] (+32 generators, with a tuning flat of 65edo) and [[warrior]] (-33 generators, with a tuning between 65edo and 46edo); warrior combines well with the mapping of sensible.		One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as [[31/24]]~[[40/31]] is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29). There are also alternative mappings of 7, including [[sensei]] (+32 generators, with a tuning flat of 65edo) and [[warrior]] (-33 generators, with a tuning between 65edo and 46edo); warrior combines well with the mapping of sensible, and sensei with sendai.

	==== BPS ====		==== BPS ====

Lériendil: /* BPS */

2025-10-09T13:52:27Z

BPS

← Older revision		Revision as of 13:52, 9 October 2025
Line 247:		Line 247:
	: ''Main article: [[Relationship between Bohlen–Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen.E2.80.93Pierce.E2.80.93Stearns temperament to octave-ful temperaments\|Relationship between Bohlen–Pierce and octave-ful temperaments]].		: ''Main article: [[Relationship between Bohlen–Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen.E2.80.93Pierce.E2.80.93Stearns temperament to octave-ful temperaments\|Relationship between Bohlen–Pierce and octave-ful temperaments]].

	Since the sensamagic comma, 245/243, contains no 2 in its [[monzo\|factorization]], only primes 3, 5, and 7, it can be tempered out in a [[3/1\|tritave (3/1)]]-repeating context, where the generator (9/7) is now the tritave-reduced 7th subharmonic, two of which give the 5th harmonic. This is known as [[BPS\|Bohlen-Pierce-Stearns (BPS)]] temperament, and it generates a [[4L 5s (3/1-equivalent)\|4L 5s]] scale against the tritave (sometimes known as ''Lambda''). Where this temperament connects to sensi is that, at 7 generators, BPS reaches an interval that it identifies with [[125/63]], which is rather close to the octave; sensi is obtained by treating this interval as the mapping of 2/1, which provides the interesting notion of using sensi in a 3/1-periodic 3.5.7.2 setting.		Since the sensamagic comma, 245/243, contains no 2 in its [[monzo\|factorization]], only primes 3, 5, and 7, it can be tempered out in a [[3/1\|tritave (3/1)]]-repeating, [[3.5.7 subgroup]] context, where the generator (9/7) is now the tritave-reduced 7th subharmonic, two of which give the 5th harmonic. This is known as [[BPS\|Bohlen-Pierce-Stearns (BPS)]] temperament, and it generates a [[4L 5s (3/1-equivalent)\|4L 5s]] scale against the tritave (sometimes known as ''Lambda''). Where this temperament connects to sensi is that, at 7 generators, BPS reaches an interval that it identifies with [[125/63]], which is rather close to the octave; sensi is obtained by treating this interval as the mapping of 2/1, which provides the interesting notion of using sensi in a 3/1-periodic 3.5.7.2 setting.

	== Chords and harmony ==		== Chords and harmony ==

Lériendil: added discussion of its connection to BPS

2025-10-09T13:42:30Z

added discussion of its connection to BPS

← Older revision		Revision as of 13:42, 9 October 2025
Line 243:		Line 243:

	One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as [[31/24]]~[[40/31]] is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29). There are also alternative mappings of 7, including [[sensei]] (+32 generators, with a tuning flat of 65edo) and [[warrior]] (-33 generators, with a tuning between 65edo and 46edo); warrior combines well with the mapping of sensible.		One way around this is to eschew the generator's interpretation as 9/7 altogether, and focus on the [[5-limit]] part of sensi, which is known as [[sensipent]] (whose comma is [[78732/78125]]). From there, an interpretation of the generator as [[31/24]]~[[40/31]] is apparent. Beyond the 2.3.5.31 subgroup, more accurate interpretations (in comparison to sensi) of sensipent's extended harmony are given by [[sensible]] (adding primes 11, 17, and 23) and [[sendai]] (adding 23 and 29). There are also alternative mappings of 7, including [[sensei]] (+32 generators, with a tuning flat of 65edo) and [[warrior]] (-33 generators, with a tuning between 65edo and 46edo); warrior combines well with the mapping of sensible.

			==== BPS ====
			: ''Main article: [[Relationship between Bohlen–Pierce and octave-ful temperaments#Relationship of rank-2 Bohlen.E2.80.93Pierce.E2.80.93Stearns temperament to octave-ful temperaments\|Relationship between Bohlen–Pierce and octave-ful temperaments]].

			Since the sensamagic comma, 245/243, contains no 2 in its [[monzo\|factorization]], only primes 3, 5, and 7, it can be tempered out in a [[3/1\|tritave (3/1)]]-repeating context, where the generator (9/7) is now the tritave-reduced 7th subharmonic, two of which give the 5th harmonic. This is known as [[BPS\|Bohlen-Pierce-Stearns (BPS)]] temperament, and it generates a [[4L 5s (3/1-equivalent)\|4L 5s]] scale against the tritave (sometimes known as ''Lambda''). Where this temperament connects to sensi is that, at 7 generators, BPS reaches an interval that it identifies with [[125/63]], which is rather close to the octave; sensi is obtained by treating this interval as the mapping of 2/1, which provides the interesting notion of using sensi in a 3/1-periodic 3.5.7.2 setting.

	== Chords and harmony ==		== Chords and harmony ==

Lériendil at 13:35, 9 October 2025

2025-10-09T13:35:39Z

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	Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), as well as [[46edo]] (generator 17\46; {{nowrap\| L/s {{=}} 7/5 }}, more optimized for sensi temperament) and [[65edo]] (generator 24\65; {{nowrap\| L/s {{=}} 10/7 }}) using the 65f [[val]] with a flat 13.		Equal temperaments that support sensi include [[19edo]] (generator 7\19; [[soft]] checkertonic), [[27edo]] (generator 10\27; [[supersoft]] checkertonic), as well as [[46edo]] (generator 17\46; {{nowrap\| L/s {{=}} 7/5 }}, more optimized for sensi temperament) and [[65edo]] (generator 24\65; {{nowrap\| L/s {{=}} 10/7 }}) using the 65f [[val]] with a flat 13.

	See [[Sensipent family #Sensi]] for more technical data, [[sensi extensions]] for extensions of sensi ~~that~~ include the [[11/1\|11th]] and [[17/1\|17th]] harmonics, and [[#Related temperaments]] for alternative interpretations of similar structures to sensi.		See [[Sensipent family #Sensi]] for more technical data, [[sensi extensions]] for extensions of sensi to include the [[11/1\|11th]] and [[17/1\|17th]] harmonics, and [[#Related temperaments]] for alternative interpretations of similar structures to sensi.

	== Theory ==		== Theory ==