Keemic chords - Revision history

FloraC: Recategorize

2025-10-12T10:47:50Z

Recategorize

← Older revision		Revision as of 10:47, 12 October 2025
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	[[Category:Tetrads]]		[[Category:Tetrads]]
	[[Category:Pentads]]		[[Category:Pentads]]
	[[Category:~~Supermagic~~]]		[[Category:Keemic]]

FloraC: Temp rename followup

2025-10-12T10:47:09Z

Temp rename followup

← Older revision		Revision as of 10:47, 12 October 2025
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	A '''~~supermagic~~ chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in the [[~~supermagic~~]] temperament. Since 100/99 is tempered out, [[ptolemismic chords]] are also ~~supermagic~~ chords; since 385/384 is tempered out, [[keenanismic chords]] are also ~~supermagic~~ chords. Aside from these, there are also essentially ~~supermagic~~ tempered chords.		A '''keemic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in the [[keemic]] temperament. Since [[100/99]] is [[tempering out\|tempered out]], [[ptolemismic chords]] are also keemic chords; since [[385/384]] is tempered out, [[keenanismic chords]] are also keemic chords. Aside from these, there are also essentially keemic tempered chords.

	The most basic of these is the '''magical seventh chord''', consisting of three sharp [[6/5\|classical minor thirds]] and a [[8/7\|septimal whole tone]], which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[tempering out\|tempered out]]. This means the chord is the tempering of		The most basic of these is the '''magical seventh chord''', consisting of three sharp [[6/5\|classical minor thirds]] and a [[8/7\|septimal whole tone]], which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[tempering out\|tempered out]]. This means the chord is the tempering of
	* 1–6/5–16/11–7/4 with steps 6/5, 6/5, 6/5, 8/7.		* 1–6/5–16/11–7/4 with steps 6/5, 6/5, 6/5, 8/7.

	In an optimized tuning for the ~~supermagic~~ temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it does not appear that often.		In an optimized tuning for the keemic temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it does not appear that often.

	Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[doublewide]].		Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[doublewide]].
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	* 1–12/11–6/5–3/2–7/4 with steps 12/11, 11/10, 5/4, 7/6, 8/7.		* 1–12/11–6/5–3/2–7/4 with steps 12/11, 11/10, 5/4, 7/6, 8/7.

	The count of ~~supermagic~~ chords is therefore tetrads: 4, and pentads: 4, for a total of 8.		The count of keemic chords is therefore tetrads: 4, and pentads: 4, for a total of 8.

	[[Category:11-odd-limit chords]]		[[Category:11-odd-limit chords]]

FloraC: FloraC moved page Supermagic chords to Keemic chords: Temp rename followup

2025-10-12T10:45:33Z

FloraC moved page Supermagic chords to Keemic chords: Temp rename followup

← Older revision	Revision as of 10:45, 12 October 2025
(No difference)

FloraC: Complete

2024-10-17T13:38:19Z

Complete

← Older revision		Revision as of 13:38, 17 October 2024
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	The most basic of these is the '''magical seventh chord''', consisting of three sharp [[6/5\|classical minor thirds]] and a [[8/7\|septimal whole tone]], which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[tempering out\|tempered out]]. This means the chord is the tempering of		The most basic of these is the '''magical seventh chord''', consisting of three sharp [[6/5\|classical minor thirds]] and a [[8/7\|septimal whole tone]], which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[tempering out\|tempered out]]. This means the chord is the tempering of
	* 1–6/5–16/11–7/4, with steps 6/5, 6/5, 6/5, 8/7.		* 1–6/5–16/11–7/4 with steps 6/5, 6/5, 6/5, 8/7.

	In an optimized tuning for the supermagic temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it does not appear that often.		In an optimized tuning for the supermagic temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it does not appear that often.

	Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[doublewide]].		Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[doublewide]].

			For other tetrads, there are
			* 1–5/4–16/11–9/5 with steps 5/4, 7/6, 5/4, 10/9;
			* 1–12/11–5/4–9/5 with steps 12/11, 8/7, 16/11, 10/9, and its inverse
			* 1–12/11–6/5–7/4 with steps 12/11, 10/9, 16/11, 8/7.

			For pentads, there are
			* 1–12/11–5/4–3/2–9/5 with steps 12/11, 8/7, 6/5, 6/5, 10/9, and its inverse
			* 1–6/5–11/8–3/2–5/3 with steps 6/5, 8/7, 12/11, 10/9, 6/5;
			* 1–5/4–11/8–3/2–12/7 with steps 5/4, 11/10, 12/11, 8/7, 7/6, and its inverse
			* 1–12/11–6/5–3/2–7/4 with steps 12/11, 11/10, 5/4, 7/6, 8/7.

			The count of supermagic chords is therefore tetrads: 4, and pentads: 4, for a total of 8.

	[[Category:11-odd-limit chords]]		[[Category:11-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Tetrads]]		[[Category:Tetrads]]
			[[Category:Pentads]]
	[[Category:Supermagic]]		[[Category:Supermagic]]

FloraC: FloraC moved page Magical seventh chord to Supermagic chords: The magical seventh chord is a specific instance of the supermagic chords

2024-10-17T13:18:26Z

FloraC moved page Magical seventh chord to Supermagic chords: The magical seventh chord is a specific instance of the supermagic chords

← Older revision	Revision as of 13:18, 17 October 2024
(No difference)

FloraC: Rework into an article to collect all supermagic chords

2024-10-17T13:17:38Z

Rework into an article to collect all supermagic chords

← Older revision		Revision as of 13:17, 17 October 2024
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	A '''~~magical seventh~~''' is an [[11-limit]] [[essentially tempered ~~dyadic~~ chord]] consisting of three sharp [[6/5\|classical minor thirds]] and a [[8/7\|septimal whole tone]], which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[tempering out\|tempered out]]. This means ~~that in the 11-limit [[supermagic]] [[planar temperament]] tempering these out,~~ the chord is the tempering of		A '''supermagic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] in the [[supermagic]] temperament. Since 100/99 is tempered out, [[ptolemismic chords]] are also supermagic chords; since 385/384 is tempered out, [[keenanismic chords]] are also supermagic chords. Aside from these, there are also essentially supermagic tempered chords.

			The most basic of these is the '''magical seventh chord''', consisting of three sharp [[6/5\|classical minor thirds]] and a [[8/7\|septimal whole tone]], which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[tempering out\|tempered out]]. This means the chord is the tempering of
	* 1–6/5–16/11–7/4, with steps 6/5, 6/5, 6/5, 8/7.		* 1–6/5–16/11–7/4, with steps 6/5, 6/5, 6/5, 8/7.

FloraC: Improve readability; recategorize

2024-10-17T13:11:43Z

Improve readability; recategorize

← Older revision		Revision as of 13:11, 17 October 2024
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	A '''magical seventh''' is an [[11-limit]] [[essentially tempered dyadic chord]] consisting of three sharp [[6/5\|minor thirds]] and an [[8/7]]~~, in other words a 6/5-6/5-6/5-8/7 chord~~, which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[~~Tempering~~ out\|tempered out]]. This means that in the 11-limit ~~4&7&15~~ [[~~Planar temperaments\|~~planar temperament]] tempering these out, the chord is the tempering of 1-6/5~~-16~~/~~11-~~7/4.		A '''magical seventh''' is an [[11-limit]] [[essentially tempered dyadic chord]] consisting of three sharp [[6/5\|classical minor thirds]] and a [[8/7\|septimal whole tone]], which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[tempering out\|tempered out]]. This means that in the 11-limit [[supermagic]] [[planar temperament]] tempering these out, the chord is the tempering of
			* 1–6/5–16/11–7/4, with steps 6/5, 6/5, 6/5, 8/7.

	In an optimized tuning for the ~~4&7&15~~ temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it ~~doesn't~~ appear that often.		In an optimized tuning for the supermagic temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it does not appear that often.

	Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[doublewide]].		Other temperaments that feature this chord prominently include 11-limit [[keemun]], [[superkleismic]], [[porcupine]] and [[doublewide]].

	[[Category:11-odd-limit]]		[[Category:11-odd-limit chords]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Pentads~~]]		[[Category:Tetrads]]
	[[Category:Supermagic]]		[[Category:Supermagic]]

FloraC: Recategorize

2023-05-23T12:06:12Z

Recategorize

← Older revision		Revision as of 12:06, 23 May 2023
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:~~Pentad~~]]		[[Category:Pentads]]
	[[Category:Supermagic]]		[[Category:Supermagic]]

FloraC: Recategorize

2023-04-28T07:17:43Z

Recategorize

← Older revision		Revision as of 07:17, 28 April 2023
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	A ''magical seventh'' is an [[11-limit]], [[essentially tempered dyadic chord]] consisting of three sharp [[6/5\|minor thirds]] and an [[8/7]], in other words a 6/5-6/5-6/5-8/7 chord, which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[Tempering out\|tempered out]]. This means that in the 11-limit 4&7&15 [[Planar temperaments\|planar temperament]] tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.		A '''magical seventh''' is an [[11-limit]] [[essentially tempered dyadic chord]] consisting of three sharp [[6/5\|minor thirds]] and an [[8/7]], in other words a 6/5-6/5-6/5-8/7 chord, which closes at the [[octave]] since both [[100/99]] and [[385/384]] (and therefore [[875/864]]) are [[Tempering out\|tempered out]]. This means that in the 11-limit 4&7&15 [[Planar temperaments\|planar temperament]] tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.

	In an optimized tuning for the 4&7&15 temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it doesn't appear that often.		In an optimized tuning for the 4&7&15 temperament, the [[marvel]] comma [[225/224]] shrinks in size and may reverse direction, and adding it to the list of commas does little tuning [[damage]]; this results in 11-limit [[magic]] temperament, which has the same [[optimal patent val]] ([[104edo]]). Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a [[Graham complexity]] of 12, so it doesn't appear that often.
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	~~[[Category:Dyadic]]~~
	~~[[Category:Magic]]~~
	[[Category:Pentad]]		[[Category:Pentad]]
			[[Category:Supermagic]]

Fredg999 category edits: Removing from Category:Chords using Cat-a-lot

2023-04-28T03:51:55Z

Removing from Category:Chords using Cat-a-lot

← Older revision		Revision as of 03:51, 28 April 2023
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	[[Category:11-odd-limit]]		[[Category:11-odd-limit]]
	~~[[Category:Chords]]~~
	[[Category:Essentially tempered chords]]		[[Category:Essentially tempered chords]]
	[[Category:Dyadic]]		[[Category:Dyadic]]
	[[Category:Magic]]		[[Category:Magic]]
	[[Category:Pentad]]		[[Category:Pentad]]