Sensamagic - Revision history

Vector at 03:15, 3 June 2026

2026-06-03T03:15:13Z

← Older revision		Revision as of 03:15, 3 June 2026
Line 9:		Line 9:

	This page will focus on tritave and rank-3 Sensamagic.		This page will focus on tritave and rank-3 Sensamagic.
			[[File:Sensamagic9.png\|thumb\|Sensamagic enneatonic (3/1-equivalent) MOS]]
	''TODO: complete page''		''TODO: complete page''

Vector at 01:59, 2 June 2026

2026-06-02T01:59:25Z

← Older revision		Revision as of 01:59, 2 June 2026
Line 1:		Line 1:
			[[File:Sentry8.png\|thumb\|Sentry octatonic MOS]]
	'''Sensamagic''' (b13 & b17), sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''' (BPS), is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s with [[5/3]]; this means that the comma [[245/243]] is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of [[Meantone]], relating the two simplest prime harmonics after the equave with a medium accuracy.		'''Sensamagic''' (b13 & b17), sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''' (BPS), is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s with [[5/3]]; this means that the comma [[245/243]] is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of [[Meantone]], relating the two simplest prime harmonics after the equave with a medium accuracy.

Vector at 04:29, 9 March 2026

2026-03-09T04:29:31Z

← Older revision		Revision as of 04:29, 9 March 2026
Line 70:		Line 70:
	\|		\|
	\|}		\|}
	<nowiki/>* in 3.5.7-subgroup [[CWE]] tuning, tritave reduced		<nowiki>*</nowiki> in 3.5.7-subgroup [[CWE]] tuning, tritave reduced. Intervals may be additionally octave-reduced in rank-3 sensamagic.

	{{Navbox regtemp}}		{{Navbox regtemp}}

Inthar: /* Interval chain */

2026-03-09T04:08:23Z

Interval chain

← Older revision		Revision as of 04:08, 9 March 2026
Line 44:		Line 44:
	\| 6		\| 6
	\| 742.0		\| 742.0
	\| 75/49, 125/27		\| 75/49, 125/81
	\|-		\|-
	\| 7		\| 7

Inthar: /* Interval chain */

2026-03-09T04:07:52Z

Interval chain

← Older revision		Revision as of 04:07, 9 March 2026
Line 44:		Line 44:
	\| 6		\| 6
	\| 742.0		\| 742.0
	\| 75/49		\| 75/49, 125/27
	\|-		\|-
	\| 7		\| 7

Inthar: /* Interval chain */

2026-03-09T04:04:57Z

Interval chain

← Older revision		Revision as of 04:04, 9 March 2026
Line 24:		Line 24:
	\| 1		\| 1
	\| 440.7		\| 440.7
	\| 9/7		\| '''9/7'''
	\|-		\|-
	\| 2		\| 2

Inthar at 04:04, 9 March 2026

2026-03-09T04:04:35Z

← Older revision		Revision as of 04:04, 9 March 2026
Line 10:		Line 10:

	''TODO: complete page''		''TODO: complete page''

			== Interval chain ==
			{\| class="wikitable right-1 right-2"
			\|-
			! #
			! Cents*
			! Approximate ratios
			\|-
			\| 0
			\| 0.0
			\| '''1/1'''
			\|-
			\| 1
			\| 440.7
			\| 9/7
			\|-
			\| 2
			\| 881.3
			\| '''5/3'''
			\|-
			\| 3
			\| 1322.0
			\| 15/7
			\|-
			\| 4
			\| 1762.7
			\| '''25/9'''
			\|-
			\| 5
			\| 301.4
			\| 25/21
			\|-
			\| 6
			\| 742.0
			\| 75/49
			\|-
			\| 7
			\| 1182.7
			\|
			\|-
			\| 8
			\| 1623.4
			\|
			\|-
			\| 9
			\| 162.1
			\|
			\|-
			\| 10
			\| 602.7
			\|
			\|-
			\| 11
			\| 1043.4
			\|
			\|-
			\| 12
			\| 1484.1
			\|
			\|}
			<nowiki/>* in 3.5.7-subgroup [[CWE]] tuning, tritave reduced

	{{Navbox regtemp}}		{{Navbox regtemp}}

Inthar at 04:06, 7 March 2026

2026-03-07T04:06:09Z

← Older revision		Revision as of 04:06, 7 March 2026
Line 4:		Line 4:

	* simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as Sentry (11 & 19)		* simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as Sentry (11 & 19)
	* equating the octave to a false octave found on the Sensamagic generator chain, such as 125/63 (resulting in [[Sensi]] (19 & 27)) or 49/25 (resulting in an obscure ~~porcupine~~ extension called "Hedgehog" that splits the octave into two 7/5~10/7 tritones)		* equating the octave to a false octave found on the Sensamagic generator chain, such as 125/63 (resulting in [[Sensi]] (19 & 27)) or 49/25 (resulting in an obscure [[Porcupine]] extension called "Hedgehog" that splits the octave into two 7/5~10/7 tritones)
	* adding the octave as an additional generator, resulting in rank-3 Sensamagic (41 & 19 & 27, or b65 & b30 & b43)		* adding the octave as an additional generator, resulting in rank-3 Sensamagic (41 & 19 & 27, or b65 & b30 & b43)

Inthar at 04:05, 7 March 2026

2026-03-07T04:05:51Z

← Older revision		Revision as of 04:05, 7 March 2026
Line 1:		Line 1:
	'''Sensamagic''' (b13 & b17), sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''' (BPS), is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s with [[5/3]]; this means that the comma [[245/243]] is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of [[~~meantone~~]], relating the two simplest prime harmonics after the equave with a medium accuracy.		'''Sensamagic''' (b13 & b17), sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''' (BPS), is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s with [[5/3]]; this means that the comma [[245/243]] is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of [[Meantone]], relating the two simplest prime harmonics after the equave with a medium accuracy.

	Sensamagic can be used as a temperament with octaves by one of several approaches:		Sensamagic can be used as a temperament with octaves by one of several approaches:

	* simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as Sentry (11 & 19)		* simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as Sentry (11 & 19)
	* equating the octave to a false octave found on the Sensamagic generator chain, such as 125/63 (resulting in [[Sensi]] (19 & 27)) or 49/25 (resulting in an obscure porcupine extension called "~~hedgehog~~" that splits the octave into two 7/5~10/7 tritones)		* equating the octave to a false octave found on the Sensamagic generator chain, such as 125/63 (resulting in [[Sensi]] (19 & 27)) or 49/25 (resulting in an obscure porcupine extension called "Hedgehog" that splits the octave into two 7/5~10/7 tritones)
	* adding the octave as an additional generator, resulting in rank-3 Sensamagic (41 & 19 & 27, or b65 & b30 & b43)		* adding the octave as an additional generator, resulting in rank-3 Sensamagic (41 & 19 & 27, or b65 & b30 & b43)

Inthar at 04:01, 7 March 2026

2026-03-07T04:01:15Z

← Older revision		Revision as of 04:01, 7 March 2026
Line 1:		Line 1:
	'''Sensamagic''' (b13 & b17), sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''', is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s with [[5/3]]; this means that the comma [[245/243]] is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of [[meantone]], relating the two simplest prime harmonics after the equave with a medium accuracy.		'''Sensamagic''' (b13 & b17), sometimes known in a tritave-equivalent context as '''Bohlen-Pierce-Stearns''' (BPS), is the temperament in the 3.5.7 subgroup equating a stack of two [[9/7]]<nowiki/>s with [[5/3]]; this means that the comma [[245/243]] is tempered out. 9/7 is tuned sharp (about 440 cents) and 5/3 is flattened (about 880 cents). It functions as a tritave analog of [[meantone]], relating the two simplest prime harmonics after the equave with a medium accuracy.

	Sensamagic can be used as a temperament with octaves by one of several approaches:		Sensamagic can be used as a temperament with octaves by one of several approaches:

	* simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as ~~"sentry"~~ (11 & 19)		* simply taking the octave as the period instead of the tritave, resulting in a 2.9/7.5/3 subgroup temperament known as Sentry (11 & 19)
	* equating the octave to a false octave found on the ~~sensamagic~~ generator chain, such as 125/63 (resulting in [[~~sensi~~]] (19 & 46)) or 49/25 (resulting in an obscure porcupine extension called "hedgehog" that splits the octave into two 7/5~10/7 tritones)		* equating the octave to a false octave found on the Sensamagic generator chain, such as 125/63 (resulting in [[Sensi]] (19 & 27)) or 49/25 (resulting in an obscure porcupine extension called "hedgehog" that splits the octave into two 7/5~10/7 tritones)
	* adding the octave as an additional generator, resulting in rank-3 ~~sensamagic~~ (41 & 19 & 27, or b65 & b30 & b43)		* adding the octave as an additional generator, resulting in rank-3 Sensamagic (41 & 19 & 27, or b65 & b30 & b43)

	This page will focus on tritave and rank-3 ~~sensamagic~~.		This page will focus on tritave and rank-3 Sensamagic.

	''TODO: complete page''		''TODO: complete page''

	{{Navbox regtemp}}		{{Navbox regtemp}}