10:12:15 - Revision history

Overthink: expand description

2025-12-30T09:32:18Z

expand description

← Older revision		Revision as of 09:32, 30 December 2025
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	{{Infobox Chord\|ColorName=gu or g}}		{{Infobox Chord\|ColorName=gu or g}}

	'''10:12:15''' is a utonal [[minor triad]], known as the '''just minor triad''', '''classical minor triad''', or '''Ptolemaic minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], with the major third replaced by a minor third.		'''10:12:15''' is a utonal [[minor triad]], known as the '''just minor triad''', '''classical minor triad''', or '''Ptolemaic minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], with the major third replaced by a minor third. It occurs as a minor triad in the [[5L 2s\|diatonic]] scale of [[meantone]] temperament, as the minor third formed from stacking three [[4/3\|perfect fourths]] octave reduced, [[32/27]], is equated with [[6/5]] due to vanishing of [[81/80]].

			It is not the only minor triad in [[just intonation]]; other minor triads include [[54:64:81]] (Pythagorean minor triad), [[6:7:9]] (septimal minor triad), and [[16:19:24]].

	== Audio of close voicings ==		== Audio of close voicings ==

Overthink: /* Related chords */ note subharmonics

2025-12-22T08:09:22Z

Related chords: note subharmonics

← Older revision		Revision as of 08:09, 22 December 2025
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	* [[10:12:15:18]] adds [[9/5]]		* [[10:12:15:18]] adds [[9/5]]
	* [[30:36:45:50]] adds [[5/3]]		* [[30:36:45:50]] adds [[5/3]]
	* [[70:84:105:120]] (12:10:8:7) – adds 12/7 (7-limit)		* [[70:84:105:120]] (1/(12:10:8:7)) – adds 12/7 (7-limit)
	* [[60:70:84:105]] (7:6:5:4) – a homonym of the previous chord		* [[60:70:84:105]] (1/(7:6:5:4)) – a homonym of the previous chord

	[[Category:Minor triads\|#@]] <!-- 2-digit first number -->		[[Category:Minor triads\|#@]] <!-- 2-digit first number -->

TallKite: changed the voicings list to a table

2025-11-24T21:08:20Z

changed the voicings list to a table

← Older revision		Revision as of 21:08, 24 November 2025
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	== Notable voicings ==		== Notable voicings ==
	Voicings are ~~identified with~~ [[Kite's thoughts on hi-lo notation\|Hi-lo ~~notation~~]]. AOV ~~and CAOV stand for~~ (~~condensed)~~ [[Odd limit#Proposed extensions\|all-odd voicing]].		Voicings are sorted by [[Wilson norm]]. This list is only a brief overview, see [[Voicings of 10:12:15]] for a more comprehensive list.
			{\| class="wikitable"
	~~3 voices~~:		\|+
			!Voices
	* 10~~:12~~:15 (~~6:5:4~~) - ~~basic voicing~~		![[EFR]]
	* 6:10:15 ~~(5:3:2)~~ - ~~lo3, CAOV~~		![[Kite's thoughts on hi-lo notation\|Hi-lo name]]
	* 3:5:15 (5:~~3:1)~~ - ~~lo3hi5, AOV~~		!Special properties
	* 12:15:20 ~~(5:4:3) -~~ 1st inversion		\|-
	* 15:20:24 ~~(8:6:5) -~~ 2nd inversion		\| rowspan="6" \|3 voices
	* 10:15:24 (12:8:5) - ~~hi3~~		\|3:5:15
			\|lo3hi5
	4 voices:		\|AOV ([[Odd limit#Proposed extensions\|all-odd voicing]])
			\|-
	* 10:12:15:20 ~~(6:5:4:3)~~ - ~~add8~~		\|6:10:15
	* 10:15:20:24 ~~(12:8:6:5) -~~ hi3add8		\|lo3
			\|CAOV (condensed AOV)
			\|-
			\|10:12:15
			\|basic
			\|
			\|-
			\|10:15:24
			\|hi3
			\|
			\|-
			\|12:15:20
			\|hiR
			\|1st inversion
			\|-
			\|15:20:24
			\|lo5
			\|2nd inversion
			\|-
			\| rowspan="2" \|4 voices
			\|10:12:15:20
			\|add8
			\|
			\|-
			\|10:15:20:24
			\|hi3add8
			\|
			\|}

	== Related chords ==		== Related chords ==

TallKite: /* Notable voicings */

2025-11-19T02:36:22Z

Notable voicings

← Older revision		Revision as of 02:36, 19 November 2025
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	3 voices:		3 voices:

	* 10:12:15 (6:5:4) - ~~close~~ voicing		* 10:12:15 (6:5:4) - basic voicing
	* 6:10:15 (5:3:2) - lo3, CAOV		* 6:10:15 (5:3:2) - lo3, CAOV
	* 3:5:15 (5:3:1) - lo3hi5, AOV		* 3:5:15 (5:3:1) - lo3hi5, AOV

TallKite: /* Related chords */

2025-11-19T02:26:14Z

Related chords

← Older revision		Revision as of 02:26, 19 November 2025
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	Melodic inversion: [[4:5:6]].		Melodic inversion: [[4:5:6]].

	Plausible [[Chord homonym\|homonyms]]: 12:15:20, a maj6no5 chord.		Plausible [[Chord homonym\|homonyms]]: 12:15:20 (1/1 - 5/4 - 5/3), a maj6no5 chord.

	Notable extensions (5-limit except where noted):		Notable extensions (5-limit except where noted):

TallKite: added a plausible homonym

2025-11-19T02:18:55Z

added a plausible homonym

← Older revision		Revision as of 02:18, 19 November 2025
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	== Related chords ==		== Related chords ==
	Melodic inversion: [[4:5:6]]		Melodic inversion: [[4:5:6]].

			Plausible [[Chord homonym\|homonyms]]: 12:15:20, a maj6no5 chord.

	Notable extensions (5-limit except where noted):		Notable extensions (5-limit except where noted):

TallKite: major rewrite

2025-11-19T01:51:00Z

major rewrite

← Older revision		Revision as of 01:51, 19 November 2025
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	{{Infobox Chord\|ColorName=gu or g}}		{{Infobox Chord\|ColorName=gu or g}}

	'''10:12:15''' is a utonal [[minor triad]], known as the '''just minor triad''', '''classical minor triad''', or '''Ptolemaic minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third ~~swapped with~~ a minor third.		'''10:12:15''' is a utonal [[minor triad]], known as the '''just minor triad''', '''classical minor triad''', or '''Ptolemaic minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], with the major third replaced by a minor third.

	== ~~Rotations around the octave~~ ==		== Audio of close voicings ==
	[[File:SculpEufaDem10-12-15-onD.mp3\|none\|thumb\|10:12:15 "Root position"]]		[[File:SculpEufaDem10-12-15-onD.mp3\|none\|thumb\|10:12:15 Root position]]
	[[File:SculpEufaDem12-15-20-onD.mp3\|none\|thumb\|12:15:20 "1st inversion"]]		[[File:SculpEufaDem12-15-20-onD.mp3\|none\|thumb\|12:15:20 1st inversion]]
	[[File:SculpEufaDem15-20-24-onD.mp3\|none\|thumb\|15:20:24 "2nd inversion"]]		[[File:SculpEufaDem15-20-24-onD.mp3\|none\|thumb\|15:20:24 2nd inversion]]

	== ~~Voicings and rotations around two octaves~~ ==		== Notable voicings ==
	{\| ~~class="wikitable sortable" style="text~~-~~align:center;"~~		Voicings are identified with [[Kite's thoughts on hi-lo notation\|Hi-lo notation]]. AOV and CAOV stand for (condensed) [[Odd limit#Proposed extensions\|all-odd voicing]].
	\|+
	~~! style="width:90px;" {{diagonal split header\|Rotation\|Voicing}}~~		3 voices:
	~~! style="width:90px;" \| Root~~
	~~! style="width:90px;" \| '~~3		* 10:12:15 (6:5:4) - close voicing
	~~! style="width~~:~~90px;" \| '15~~		* 6:10:15 (5:3:2) - lo3, CAOV
	~~! style="width:90px;" \| '''<nowiki/>'''<nowiki/>'3'15~~		* 3:5:15 (5:3:1) - lo3hi5, AOV
	\|-		* 12:15:20 (5:4:3) - 1st inversion
	~~! style="width:90px;" \| On 3~~		* 15:20:24 (8:6:5) - 2nd inversion
	~~\| style="width~~:~~90px;" data-sort-value="012-015-040" \|~~ 12:15:40		* 10:15:24 (12:8:5) - hi3
	~~\| style="width~~:~~90px;" data~~-~~sort-value="006-010-015" \|~~ 6:10:15
	~~\| style="width~~:~~90px;" data-sort-value="006-015-020" \| 6~~:15:20		4 voices:
	~~\| style="width~~:~~90px;" data~~-~~sort-value="012-015-020" \| ''~~12:15:20''
	\|-		* 10:12:15:20 (6:5:4:3) - add8
	~~! style="width~~:~~90px;" \| On 5~~		* 10:15:20:24 (12:8:6:5) - hi3add8
	~~\| style="width~~:~~90px;" data-sort-value="010-012-015" \| ''10~~:12:~~15''~~
	~~\| style="width:90px;" data-sort-value="010-015-024" \|~~ 10:15:24
	~~\| style="width~~:~~90px;" data~~-~~sort-value="005-006-015" \| 5~~:~~6:15~~
	~~\| style="width:90px;" data-sort-value="005-012-015" \| 5~~:12:15
	\|-
	~~! style="width~~:~~90px;" \| On 15~~
	~~\| style="width~~:~~90px;" data-sort-value="015-040-048" \| 15~~:40:48
	~~\| style="width:90px;" data-sort-value="015-024~~-~~040" \| 15:24:40~~
	~~\| style="width~~:~~90px;" data-sort-value="015-020-024" \| ''~~15:20:24''
	~~\| style="width~~:~~90px;" data-sort-value="015-020-048" \| 15~~:20:48
	\|}

	== Related chords ==		== Related chords ==
	~~Common tetrads based on this triad~~ (5-limit except where noted):		Melodic inversion: [[4:5:6]]

			Notable extensions (5-limit except where noted):

	* [[4:5:6]] – chord inversion
	* [[10:12:15:18]] adds [[9/5]]		* [[10:12:15:18]] adds [[9/5]]
	* [[30:36:45:50]] adds [[5/3]]		* [[30:36:45:50]] adds [[5/3]]
	* [[~~60:~~70:84:105]] – adds 8/7 ~~below root~~ (7-limit)		* [[70:84:105:120]] (12:10:8:7) – adds 12/7 (7-limit)
	* [[70:84:105~~:120~~]] ~~– adds 12/7~~ (7~~-limit~~); homonym of ~~60:70:84:105~~		* [[60:70:84:105]] (7:6:5:4) – a homonym of the previous chord

	[[Category:Minor triads\|#@]] <!-- 2-digit first number -->		[[Category:Minor triads\|#@]] <!-- 2-digit first number -->

Overthink: /* Related chords */ revised section

2025-11-18T23:02:17Z

Related chords: revised section

← Older revision		Revision as of 23:02, 18 November 2025
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	* [[10:12:15:18]] adds [[9/5]]		* [[10:12:15:18]] adds [[9/5]]
	* [[30:36:45:50]] adds [[5/3]]		* [[30:36:45:50]] adds [[5/3]]
	* [[60:70:84:105]] – adds 8/7 (7-limit)		* [[60:70:84:105]] – adds 8/7 below root (7-limit)
			* [[70:84:105:120]] – adds 12/7 (7-limit); homonym of 60:70:84:105

	[[Category:Minor triads\|#@]] <!-- 2-digit first number -->		[[Category:Minor triads\|#@]] <!-- 2-digit first number -->

FloraC: "Just minor triad" isn't less precise

2025-11-11T11:15:54Z

"Just minor triad" isn't less precise

← Older revision		Revision as of 11:15, 11 November 2025
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	{{Infobox Chord\|ColorName=gu or g}}		{{Infobox Chord\|ColorName=gu or g}}

	'''10:12:15''' is ~~the~~ utonal [[minor triad]], ~~also~~ known as the '''~~classical~~ minor triad, classical minor triad,''' or ~~more generally - albeit less precisely - as the~~ '''~~just~~ minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third swapped with a minor third.		'''10:12:15''' is a utonal [[minor triad]], known as the '''just minor triad''', '''classical minor triad''', or '''Ptolemaic minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third swapped with a minor third.

	== Rotations around the octave ==		== Rotations around the octave ==
Line 39:		Line 39:
	Common tetrads based on this triad (5-limit except where noted):		Common tetrads based on this triad (5-limit except where noted):

	* [[4:5:6]] - chord inversion		* [[4:5:6]] – chord inversion
	* [[10:12:15:18]] adds [[9/5]]		* [[10:12:15:18]] adds [[9/5]]
	* [[30:36:45:50]] adds [[5/3]]		* [[30:36:45:50]] adds [[5/3]]
	* [[60:70:84:105]] - adds 8/7 (7-limit)		* [[60:70:84:105]] – adds 8/7 (7-limit)

	[[Category:Minor triads\|#@]] <!-- 2-digit first number -->		[[Category:Minor triads\|#@]] <!-- 2-digit first number -->

Overthink: fixed major to minor

2025-11-10T20:30:38Z

fixed major to minor

← Older revision		Revision as of 20:30, 10 November 2025
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	{{Infobox Chord\|ColorName=gu or g}}		{{Infobox Chord\|ColorName=gu or g}}

	'''10:12:15''' is the utonal [[minor triad]], also known as the '''classical minor triad, classical minor triad,''' or more generally - albeit less precisely - as the '''just ~~major~~ triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third swapped with a minor third.		'''10:12:15''' is the utonal [[minor triad]], also known as the '''classical minor triad, classical minor triad,''' or more generally - albeit less precisely - as the '''just minor triad'''. It is a common chord that appears as a counterpart to the widespread otonal major triad of [[4:5:6]], the major third swapped with a minor third.

	== Rotations around the octave ==		== Rotations around the octave ==