Sensamagic - Revision history

Overthink: /* Tunings */ mark section to be added

2026-03-12T19:12:36Z

Tunings: mark section to be added

← Older revision		Revision as of 19:12, 12 March 2026
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	\| POTE: ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}}		\| POTE: ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}}
	\|}		\|}

			=== Tuning spectrum ===
			{{Todo\|complete section\|inline=1}}

	[[Category:Sensamagic\| ]] <!-- main article -->		[[Category:Sensamagic\| ]] <!-- main article -->

FloraC: /* Tunings */ - typos

2026-03-12T15:31:31Z

Tunings: - typos

← Older revision		Revision as of 15:31, 12 March 2026
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	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~3/2 = 703.7424{{c}}, ~9/7 = ~~443~~.9020{{c}}		\| CTE: ~3/2 = 703.7424{{c}}, ~9/7 = 440.9020{{c}}
	\| CWE: ~3/2 = 703.7411{{c}}, ~9/7 = 440.9017{{c}}		\| CWE: ~3/2 = 703.7411{{c}}, ~9/7 = 440.9017{{c}}
	\| POTE: ~3/2 = 703.7424{{c}}, ~9/7 = ~~443~~.9020{{c}}		\| POTE: ~3/2 = 703.7424{{c}}, ~9/7 = 440.9020{{c}}
	\|}		\|}

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	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~3/2 = 703.7737{{c}}, ~9/7 = ~~443~~.9186{{c}}		\| CTE: ~3/2 = 703.7737{{c}}, ~9/7 = 440.9186{{c}}
	\| CWE: ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}		\| CWE: ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}
	\| POTE: ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}}		\| POTE: ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}}

FloraC: Expand on intro, explaining how prime 11 can fit the structure.

2026-03-12T15:23:08Z

Expand on intro, explaining how prime 11 can fit the structure.

← Older revision		Revision as of 15:23, 12 March 2026
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	\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 5.11 \| Complexity 2 = ?		\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 5.11 \| Complexity 2 = ?
	}}		}}
	'''Sensamagic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as the [[2.3.7 subgroup]], while identifying the [[5/~~4\|classical major third (5/4)~~]] as a stack ~~consisting~~ of two [[9/7\|supermajor thirds ~~(9/7)]] and a [[3/2\|perfect fifth]] [[octave reduction\|octave reduced]]~~, [[tempering out]] [[245/243]]. It is the head of the [[sensamagic family]], and ~~the~~ canonical [[11-limit]] [[extension]] ~~adding~~ [[385/384]] and [[896/891]] to the comma list makes it a member of both [[keenanismic temperaments]] and [[pentacircle clan]].		'''Sensamagic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as the [[2.3.7 subgroup]], while identifying the [[5/3]] major sixth as a stack of two [[9/7]] supermajor thirds, [[tempering out]] [[245/243]]. It is the head of the [[sensamagic family]].

			It favors a sharp supermajor third, and subtracting such a third from a [[4/3\|perfect fourth]] produces a narrow subminor second of [[28/27]][[~]][[36/35]]. The canonical [[11-limit]] [[extension]] identifies this interval with [[33/32]], so that [[11/8]] is that plus a perfect fourth. This adds [[385/384]] and [[896/891]] to the comma list and makes it a member of both [[keenanismic temperaments]] and [[pentacircle clan]].

	The temperament was named after the corresponding comma, which was named by [[Gene Ward Smith]] in 2010. See [[245/243 #Etymology]].		The temperament was named after the corresponding comma, which was named by [[Gene Ward Smith]] in 2010. See [[245/243 #Etymology]].

FloraC: + infobox

2026-03-12T15:04:19Z

+ infobox

← Older revision		Revision as of 15:04, 12 March 2026
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			{{Infobox regtemp
			\| Title = Sensamagic
			\| Subgroups = 2.3.5.7, 2.3.5.7.11
			\| Comma basis = [[245/243]] (7-limit); <br>[[245/243]], [[385/384]] (11-limit)
			\| Edo join 1 = 19 \| Edo join 2 = 22 \| Edo join 3 = 24
			\| Mapping = 1; 1 1 2 -2; 0 2 -1 -1
			\| Generators = 3/2, 9/7
			\| Generators tuning = 703.8, 440.9
			\| Optimization method = CWE
			\| Odd limit 1 = 9 \| Mistuning 1 = 4.73 \| Complexity 1 = ?
			\| Odd limit 2 = 11-limit 21 \| Mistuning 2 = 5.11 \| Complexity 2 = ?
			}}
	'''Sensamagic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as the [[2.3.7 subgroup]], while identifying the [[5/4\|classical major third (5/4)]] as a stack consisting of two [[9/7\|supermajor thirds (9/7)]] and a [[3/2\|perfect fifth]] [[octave reduction\|octave reduced]], [[tempering out]] [[245/243]]. It is the head of the [[sensamagic family]], and the canonical [[11-limit]] [[extension]] adding [[385/384]] and [[896/891]] to the comma list makes it a member of both [[keenanismic temperaments]] and [[pentacircle clan]].		'''Sensamagic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as the [[2.3.7 subgroup]], while identifying the [[5/4\|classical major third (5/4)]] as a stack consisting of two [[9/7\|supermajor thirds (9/7)]] and a [[3/2\|perfect fifth]] [[octave reduction\|octave reduced]], [[tempering out]] [[245/243]]. It is the head of the [[sensamagic family]], and the canonical [[11-limit]] [[extension]] adding [[385/384]] and [[896/891]] to the comma list makes it a member of both [[keenanismic temperaments]] and [[pentacircle clan]].

FloraC: /* Chords */ -> chords and harmony

2025-10-22T07:13:05Z

Chords: -> chords and harmony

← Older revision		Revision as of 07:13, 22 October 2025
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	Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental module for each prime harmonic. That makes some intervals more intuitive, at the cost of hiding the structure of sensamagic tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 5/3 is a stack of two 9/7's is not revealed, and the related chords can be less convenient.		Alternatively, it can be notated the same as full prime-limit just intonation, with a distinct accidental module for each prime harmonic. That makes some intervals more intuitive, at the cost of hiding the structure of sensamagic tempering. For example, it is customary of the 5/4 to be a major third, and 7/4 to be a minor seventh. As a result, the fact that the 5/3 is a stack of two 9/7's is not revealed, and the related chords can be less convenient.

	== Chords ==		== Chords and harmony ==
	Sensamagic enables [[essentially tempered chord]]s of [[Sensamagic chords\|sensamagic]], [[Keenanismic chords\|keenanismic]], [[Pentacircle chords\|pentacircle]], and [[Undecimal sensamagic chords\|undecimal sensamagic]].		Sensamagic enables [[essentially tempered chord]]s of [[Sensamagic chords\|sensamagic]], [[Keenanismic chords\|keenanismic]], [[Pentacircle chords\|pentacircle]], and [[Undecimal sensamagic chords\|undecimal sensamagic]].

	The [[sensamagic dominant chord]] is a dominant seventh chord useful for tonal harmony in this temperament.		The [[sensamagic dominant chord]] is a dominant seventh chord useful for tonal harmony in this temperament.

	== Tunings ==		== Tunings ==

FloraC: /* Tunings */

2025-10-22T07:11:50Z

Tunings

← Older revision		Revision as of 07:11, 22 October 2025
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	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~3/2 = 703.7424, ~9/7 = 443.9020{{c}}		\| CTE: ~3/2 = 703.7424{{c}}, ~9/7 = 443.9020{{c}}
	\| CWE: ~3/2 = 703.7411, ~9/7 = 440.9017{{c}}		\| CWE: ~3/2 = 703.7411{{c}}, ~9/7 = 440.9017{{c}}
	\| POTE: ~3/2 = 703.7424, ~9/7 = 443.9020{{c}}		\| POTE: ~3/2 = 703.7424{{c}}, ~9/7 = 443.9020{{c}}
	\|}		\|}

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	\|-		\|-
	! Tenney		! Tenney
	\| CTE: ~3/2 = 703.7737, ~9/7 = 443.9186{{c}}		\| CTE: ~3/2 = 703.7737{{c}}, ~9/7 = 443.9186{{c}}
	\| CWE: ~3/2 = 703.7948, ~9/7 = 440.9180{{c}}		\| CWE: ~3/2 = 703.7948{{c}}, ~9/7 = 440.9180{{c}}
	\| POTE: ~3/2 = 703.8004, ~9/7 = 440.9178{{c}}		\| POTE: ~3/2 = 703.8004{{c}}, ~9/7 = 440.9178{{c}}
	\|}		\|}

FloraC: + TE tunings and variants

2025-10-11T16:29:04Z

+ TE tunings and variants

← Older revision		Revision as of 16:29, 11 October 2025
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	The [[sensamagic dominant chord]] is a dominant seventh chord useful for tonal harmony in this temperament.		The [[sensamagic dominant chord]] is a dominant seventh chord useful for tonal harmony in this temperament.

			== Tunings ==
			{\| class="wikitable mw-collapsible mw-collapsed"
			\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
			\|-
			! rowspan="2" \|
			! colspan="3" \| Euclidean
			\|-
			! Constrained
			! Constrained & skewed
			! Destretched
			\|-
			! Tenney
			\| CTE: ~3/2 = 703.7424, ~9/7 = 443.9020{{c}}
			\| CWE: ~3/2 = 703.7411, ~9/7 = 440.9017{{c}}
			\| POTE: ~3/2 = 703.7424, ~9/7 = 443.9020{{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: ~3/2 = 703.7737, ~9/7 = 443.9186{{c}}
			\| CWE: ~3/2 = 703.7948, ~9/7 = 440.9180{{c}}
			\| POTE: ~3/2 = 703.8004, ~9/7 = 440.9178{{c}}
			\|}

	[[Category:Sensamagic\| ]] <!-- main article -->		[[Category:Sensamagic\| ]] <!-- main article -->

FloraC: Grammar

2025-10-11T16:19:16Z

Grammar

← Older revision		Revision as of 16:19, 11 October 2025
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	'''Sensamagic''' is ~~the~~ [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as the [[2.3.7 subgroup]], while identifying the [[5/4\|classical major third (5/4)]] as a stack consisting of two [[9/7\|supermajor thirds (9/7)]] and a [[3/2\|perfect fifth]] [[octave reduction\|octave reduced]], [[tempering out]] [[245/243]]. It is the head of the [[sensamagic family]], and the canonical [[11-limit]] [[extension]] adding [[385/384]] and [[896/891]] to the comma list makes it a member of both [[keenanismic temperaments]] and [[pentacircle clan]].		'''Sensamagic''' is a [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as the [[2.3.7 subgroup]], while identifying the [[5/4\|classical major third (5/4)]] as a stack consisting of two [[9/7\|supermajor thirds (9/7)]] and a [[3/2\|perfect fifth]] [[octave reduction\|octave reduced]], [[tempering out]] [[245/243]]. It is the head of the [[sensamagic family]], and the canonical [[11-limit]] [[extension]] adding [[385/384]] and [[896/891]] to the comma list makes it a member of both [[keenanismic temperaments]] and [[pentacircle clan]].

	The temperament was named after the corresponding comma, which was named by [[Gene Ward Smith]] in 2010. See [[245/243 #Etymology]].		The temperament was named after the corresponding comma, which was named by [[Gene Ward Smith]] in 2010. See [[245/243 #Etymology]].

FloraC: Rework on intro

2025-10-11T16:18:47Z

Rework on intro

← Older revision		Revision as of 16:18, 11 October 2025
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	'''Sensamagic''' is the [[~~Rank~~-3 temperament\|rank-3]] [[temperament]] [[tempering out]] [[245/243]], the ~~sensamagic comma. It has a~~ canonical 11-limit [[extension]] adding [[385/384]] and [[896/891]] to the comma list.		'''Sensamagic''' is the [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]] with the same [[lattice]] structure as the [[2.3.7 subgroup]], while identifying the [[5/4\|classical major third (5/4)]] as a stack consisting of two [[9/7\|supermajor thirds (9/7)]] and a [[3/2\|perfect fifth]] [[octave reduction\|octave reduced]], [[tempering out]] [[245/243]]. It is the head of the [[sensamagic family]], and the canonical [[11-limit]] [[extension]] adding [[385/384]] and [[896/891]] to the comma list makes it a member of both [[keenanismic temperaments]] and [[pentacircle clan]].

	The temperament was named after the corresponding comma, which was named by [[Gene Ward Smith]] in 2010. See [[245/243 #Etymology]].		The temperament was named after the corresponding comma, which was named by [[Gene Ward Smith]] in 2010. See [[245/243 #Etymology]].

FloraC: - parent category

2025-04-29T09:54:30Z

- parent category

← Older revision		Revision as of 09:54, 29 April 2025
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	The [[sensamagic dominant chord]] is a dominant seventh chord useful for tonal harmony in this temperament.		The [[sensamagic dominant chord]] is a dominant seventh chord useful for tonal harmony in this temperament.

	~~[[Category:Temperaments]]~~
	[[Category:Sensamagic\| ]] <!-- main article -->		[[Category:Sensamagic\| ]] <!-- main article -->
	[[Category:Rank-3 temperaments]]		[[Category:Rank-3 temperaments]]