Chords of magic - Revision history

FloraC at 12:18, 4 February 2026

2026-02-04T12:18:57Z

← Older revision		Revision as of 12:18, 4 February 2026
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			{{Breadcrumb\|Magic}}
	Below is a complete list of the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[magic\|magic temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[chord #Inversion\|inversions]]; only one is listed, that being the inversion where all notes are a nonnegative number of major third [[generator]]s above the root.		Below is a complete list of the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[magic\|magic temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[chord #Inversion\|inversions]]; only one is listed, that being the inversion where all notes are a nonnegative number of major third [[generator]]s above the root.

FloraC: FloraC moved page Magic/Chords to Chords of magic over a redirect without leaving a redirect: Not the main article of the chords and harmony section

2026-02-04T12:18:34Z

FloraC moved page Magic/Chords to Chords of magic over a redirect without leaving a redirect: Not the main article of the chords and harmony section

← Older revision	Revision as of 12:18, 4 February 2026
(No difference)

FloraC: Improve intro. Unimarvel -> marvel11

2026-02-04T12:13:33Z

Improve intro. Unimarvel -> marvel11

← Older revision		Revision as of 12:13, 4 February 2026
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	Below ~~are listed~~ the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[magic\|magic temperament]]. ~~Typing the~~ chords ~~requires consideration of the fact that magic conflates~~ [[10/9]] ~~and~~ [[11/10]] ~~and so also [[9/5]] and [[20/~~11]]. ~~If a~~ [[~~transversal~~]] ~~can be found which shows the chord to be essentially just, that transversal~~ is listed ~~along with a typing as otonal~~, ~~utonal, or ambitonal. If~~ the ~~chord is essentially tempered, it is analyzed in terms~~ of the ~~transversal which employs 10/9 and 9/5~~.		Below is a complete list of the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[magic\|magic temperament]]. Note that there are many common chords, for example [[8:10:12:15]], which are not listed; in this case due to [[15/8]] not being in the 11-odd-limit. Every chord listed has multiple [[chord #Inversion\|inversions]]; only one is listed, that being the inversion where all notes are a nonnegative number of major third [[generator]]s above the root.

	~~Chords requiring tempering only by~~ [[~~225~~/~~224~~]] ~~are labeled~~ [[~~marvel chords\|marvel~~]]~~, by~~ [[~~245~~/~~243~~]] [[~~sensamagic chords\|sensamagic]], by [[100~~/99]] [[~~ptolemismic chords\|ptolemismic~~]], ~~by [[896/891]]~~ [[~~pentacircle chords\|pentacircle~~]], by [[~~385/384]] [[keenanismic chords\|keenanismic~~]], ~~and by~~ [[~~540/539]] [[swetismic chords\|swetismic~~]]. ~~Those requiring any two of 225/224~~, ~~100/99 or 896/891 are labeled apollo, any two~~ of ~~100/99, 245/243 or 540/539 octarod, any two~~ of ~~245/243~~, ~~896/891 or 385/384 [[undecimal sensamagic chords\|sensamagic11]], any two~~ of ~~225/224, 385/384, or 540/539 [[undecimal marvel chords\|unimarvel]]. Chords requiring both 100~~/99 and ~~385~~/~~384 are labeled [[keemic chords\|keemic]]. Finally, anything requiring three independent commas among those discussed above is labeled [[magic chords\|magic]]~~.		Typing the chords requires consideration of the fact that magic conflates [[10/9]] and [[11/10]] and so also [[9/5]] and [[20/11]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as [[otonal]], [[utonal]], or [[ambitonal]]. If the chord is essentially tempered, it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 10/9 and 9/5.

	Magic has [[mos scale]]s of ~~sizes~~ 7, 10, 13, 16, 19, and 22 notes. It may be seen that even the ~~seven~~-note mos is not without a few harmonic resources, and the larger ones do much better.		Chords requiring tempering only by [[225/224]] are labeled [[marvel chords\|marvel]], by [[245/243]] [[sensamagic chords\|sensamagic]], by [[100/99]] [[ptolemismic chords\|ptolemismic]], by [[896/891]] [[pentacircle chords\|pentacircle]], by [[385/384]] [[keenanismic chords\|keenanismic]], and by [[540/539]] [[swetismic chords\|swetismic]]. Those requiring any two of 100/99, 225/224 or 896/891 are labeled [[apollo chords\|apollo]], any two of 100/99, 245/243 or 540/539 [[octarod chords\|octarod]], any two of 245/243, 896/891 or 385/384 [[undecimal sensamagic chords\|sensamagic11]], any two of 225/224, 385/384, or 540/539 [[undecimal marvel chords\|marvel11]]. Chords requiring both 100/99 and 385/384 are labeled [[keemic chords\|keemic]]. Finally, anything requiring three independent commas among those discussed above is labeled [[magic chords\|magic]].

			Magic has [[mos scale]]s of 7, 10, 13, 16, 19, and 22 notes. It may be seen that even the 7-note mos is not without a few harmonic resources, and the larger ones do much better.

	[[Kite Giedraitis]] has named the chords using arrows (ups and downs), as described in [[Kite's thoughts on pergens]]. The pergen is (P8, P12/5) fifth-of-a-twelfth, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. One up is 19 generators, octave-reduced. The generator is {{nowrap\| vM3 {{=}} 380{{c}} + ''c''/5 }}, where ''c'' is the amount in cents the tempered fifth exceeds 700{{c}}. The [[Kite's thoughts on enharmonic unisons in ups and downs notation\|enharmonic unison]] is ^<sup>5</sup>dd2, thus {{nowrap\|^<sup>5</sup>C {{=}} Bx}}. To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap\|/1 {{=}} −25''G'' + 3''G'' {{=}} m2 + ^^d8 {{=}} ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma, so {{nowrap\| /C {{=}} ^^Dbb }}, {{nowrap\| \C {{=}} vvB# }}, {{nowrap\| ^^C {{=}} /B# }}, and {{nowrap\| vvC {{=}} \Dbb }}. The cents values of sharps, ups and lifts vary greatly, as this table shows. Note that if the fifth is wider than 22edo's fifth, a lift will actually be descending. Furthermore, if the fifth is narrower than 19edo's, an up will be descending.		[[Kite Giedraitis]] has named the chords using arrows (ups and downs), as described in [[Kite's thoughts on pergens]]. The pergen is (P8, P12/5) fifth-of-a-twelfth, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. One up is 19 generators, octave-reduced. The generator is {{nowrap\| vM3 {{=}} 380{{c}} + ''c''/5 }}, where ''c'' is the amount in cents the tempered fifth exceeds 700{{c}}. The [[Kite's thoughts on enharmonic unisons in ups and downs notation\|enharmonic unison]] is ^<sup>5</sup>dd2, thus {{nowrap\|^<sup>5</sup>C {{=}} Bx}}. To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap\|/1 {{=}} −25''G'' + 3''G'' {{=}} m2 + ^^d8 {{=}} ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma, so {{nowrap\| /C {{=}} ^^Dbb }}, {{nowrap\| \C {{=}} vvB# }}, {{nowrap\| ^^C {{=}} /B# }}, and {{nowrap\| vvC {{=}} \Dbb }}. The cents values of sharps, ups and lifts vary greatly, as this table shows. Note that if the fifth is wider than 22edo's fifth, a lift will actually be descending. Furthermore, if the fifth is narrower than 19edo's, an up will be descending.
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	\| 0–1–2–13		\| 0–1–2–13
	\| 1–12/11–5/4–14/9		\| 1–12/11–5/4–14/9
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–1–11–13		\| 0–1–11–13
	\| 1–12/11–5/4–7/5		\| 1–12/11–5/4–7/5
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–2–12–13		\| 0–2–12–13
	\| 1–12/11–14/9–7/4		\| 1–12/11–14/9–7/4
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–11–12–13		\| 0–11–12–13
	\| 1–12/11–7/5–7/4		\| 1–12/11–7/5–7/4
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–7–8–18		\| 0–7–8–18
	\| 1–7/6–16/11–18/11		\| 1–7/6–16/11–18/11
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–10–11–18		\| 0–10–11–18
	\| 1–9/8–7/5–18/11		\| 1–9/8–7/5–18/11
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–1–2–11–13		\| 0–1–2–11–13
	\| 1–12/11–5/4–7/5–14/9		\| 1–12/11–5/4–7/5–14/9
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–1–2–12–13		\| 0–1–2–12–13
	\| 1–12/11–5/4–14/9–7/4		\| 1–12/11–5/4–14/9–7/4
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–1–11–12–13		\| 0–1–11–12–13
	\| 1–12/11–5/4–7/5–7/4		\| 1–12/11–5/4–7/5–7/4
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–2–11–12–13		\| 0–2–11–12–13
	\| 1–12/11–7/5–14/9–7/4		\| 1–12/11–7/5–14/9–7/4
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–2–12–13–20		\| 0–2–12–13–20
	\| 1–12/11–14/11–14/9–7/4		\| 1–12/11–14/11–14/9–7/4
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–7–8–18–20		\| 0–7–8–18–20
	\| 1–7/6–14/11–16/11–18/11		\| 1–7/6–14/11–16/11–18/11
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|		\|
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	\| 0–1–2–11–12–13		\| 0–1–2–11–12–13
	\| 1–12/11–5/4–7/5–14/9–7/4		\| 1–12/11–5/4–7/5–14/9–7/4
	\| ~~Unimarvel~~		\| Marvel11
	\|		\|
	\|-		\|-

FloraC: Sort intervals by size

2026-02-03T20:30:38Z

Sort intervals by size

Show changes

FloraC: Label the chords

2026-02-03T20:06:23Z

Label the chords

Show changes

FloraC: Cleanup

2026-02-03T11:41:19Z

Cleanup

Show changes

FloraC: Temp rename followup

2025-10-12T11:02:31Z

Temp rename followup

← Older revision		Revision as of 11:02, 12 October 2025
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	Below are listed the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[magic\|magic temperament]]. Typing the chords requires consideration of the fact that magic conflates [[10/9]] and [[11/10]] and so also [[9/5]] and [[20/11]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 10/9 and 9/5.		Below are listed the [[11-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[magic\|magic temperament]]. Typing the chords requires consideration of the fact that magic conflates [[10/9]] and [[11/10]] and so also [[9/5]] and [[20/11]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If the chord is essentially tempered, it is analyzed in terms of the transversal which employs 10/9 and 9/5.

	Chords requiring tempering only by [[225/224]] are labeled [[marvel chords\|marvel]], by [[245/243]] [[sensamagic chords\|sensamagic]], by [[100/99]] [[ptolemismic chords\|ptolemismic]], by [[896/891]] [[pentacircle chords\|pentacircle]], by [[385/384]] [[keenanismic chords\|keenanismic]], and by [[540/539]] [[swetismic chords\|swetismic]]. Those requiring any two of 225/224, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 [[undecimal sensamagic chords\|sensamagic11]], any two of 225/224, 385/384, or 540/539 [[undecimal marvel chords\|unimarvel]]. Chords requiring both 100/99 and 385/384 are labeled [[~~supermagic~~ chords\|~~supermagic~~]]. Finally, anything requiring three independent commas among those discussed above is labeled [[magic chords\|magic]].		Chords requiring tempering only by [[225/224]] are labeled [[marvel chords\|marvel]], by [[245/243]] [[sensamagic chords\|sensamagic]], by [[100/99]] [[ptolemismic chords\|ptolemismic]], by [[896/891]] [[pentacircle chords\|pentacircle]], by [[385/384]] [[keenanismic chords\|keenanismic]], and by [[540/539]] [[swetismic chords\|swetismic]]. Those requiring any two of 225/224, 100/99 or 896/891 are labeled apollo, any two of 100/99, 245/243 or 540/539 octarod, any two of 245/243, 896/891 or 385/384 [[undecimal sensamagic chords\|sensamagic11]], any two of 225/224, 385/384, or 540/539 [[undecimal marvel chords\|unimarvel]]. Chords requiring both 100/99 and 385/384 are labeled [[keemic chords\|keemic]]. Finally, anything requiring three independent commas among those discussed above is labeled [[magic chords\|magic]].

	Magic has [[mos scale]]s of sizes 7, 10, 13, 16, 19, and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.		Magic has [[mos scale]]s of sizes 7, 10, 13, 16, 19, and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.
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	\| 0-1-8-9		\| 0-1-8-9
	\| 1-5/4-16/11-9/5		\| 1-5/4-16/11-9/5
	\| ~~Supermagic~~		\| Keemic
	\| Cv^7(^^b5)		\| Cv^7(^^b5)
	\|		\|
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	\| 0-4-8-12		\| 0-4-8-12
	\| 1-6/5-16/11-7/4		\| 1-6/5-16/11-7/4
	\| ~~Supermagic~~		\| Keemic
	\|		\|
	\|		\|
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	\| 0-1-9-13		\| 0-1-9-13
	\| 1-5/4-9/5-12/11		\| 1-5/4-9/5-12/11
	\| ~~Supermagic~~		\| Keemic
	\|		\|
	\|		\|
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	\| 0-4-12-13		\| 0-4-12-13
	\| 1-6/5-7/4-12/11		\| 1-6/5-7/4-12/11
	\| ~~Supermagic~~		\| Keemic
	\|		\|
	\|		\|
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	\| 0-1-5-9-13		\| 0-1-5-9-13
	\| 1-5/4-3/2-9/5-12/11		\| 1-5/4-3/2-9/5-12/11
	\| ~~Supermagic~~		\| Keemic
	\|		\|
	\|		\|
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	\| 0-1-8-9-13		\| 0-1-8-9-13
	\| 1-5/4-16/11-9/5-12/11		\| 1-5/4-16/11-9/5-12/11
	\| ~~Supermagic~~		\| Keemic
	\|		\|
	\|		\|
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	\| 0-4-5-12-13		\| 0-4-5-12-13
	\| 1-6/5-3/2-7/4-12/11		\| 1-6/5-3/2-7/4-12/11
	\| ~~Supermagic~~		\| Keemic
	\|		\|
	\|		\|
Line 1,585:		Line 1,585:
	\| 0-4-8-12-13		\| 0-4-8-12-13
	\| 1-6/5-16/11-7/4-12/11		\| 1-6/5-16/11-7/4-12/11
	\| ~~Supermagic~~		\| Keemic
	\|		\|
	\|		\|

Lériendil: Lériendil moved page Chords of magic to Magic/Chords

2025-06-22T21:49:24Z

Lériendil moved page Chords of magic to Magic/Chords

← Older revision	Revision as of 21:49, 22 June 2025
(No difference)

TallKite: updated EI to EU

2024-12-29T00:25:38Z

updated EI to EU

← Older revision		Revision as of 00:25, 29 December 2024
Line 5:		Line 5:
	Magic has [[mos scale]]s of sizes 7, 10, 13, 16, 19, and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.		Magic has [[mos scale]]s of sizes 7, 10, 13, 16, 19, and 22 notes. It may be seen that even the seven-note mos is not without a few harmonic resources, and the larger ones do much better.

	The chord names use arrows (ups and downs) as described on the [[Pergen]] page. The pergen is (P8, P12/5) fifth-of-a-12th, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. One up is 19 generators, octave-reduced. The generator is {{nowrap\|vM3 {{=}} 380¢ + ''c''/5}}, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. The enharmonic ~~interval~~ is ^<sup>5</sup>dd2, thus {{nowrap\|^<sup>5</sup>C {{=}} B##}}.		The chord names use arrows (ups and downs) as described on the [[Pergen]] page. The pergen is (P8, P12/5) fifth-of-a-12th, #37 in the [http://tallkite.com/misc_files/notation%20guide%20for%20rank-2%20pergens.pdf list of pergens]. One up is 19 generators, octave-reduced. The generator is {{nowrap\|vM3 {{=}} 380¢ + ''c''/5}}, where ''c'' is the amount in cents the tempered fifth exceeds 700¢. The [[Enharmonic unisons in ups and downs notation\|enharmonic unison]] is ^<sup>5</sup>dd2, thus {{nowrap\|^<sup>5</sup>C {{=}} B##}}.

	To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap\|/1 {{=}} −25''G'' + 3''G'' {{=}} m2 + ^^d8 {{=}} ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma, so {{nowrap\|/C {{=}} ^^Dbb\|\C {{=}} vvB#\|^^C {{=}} /B#\|and vvC {{=}} \Dbb}}.		To simplify the chord names, slashes (lifts and drops) are also used. One lift is -22 generators, octave-reduced. Thus {{nowrap\|/1 {{=}} −25''G'' + 3''G'' {{=}} m2 + ^^d8 {{=}} ^^d2}}. Thus a lift equals two ups minus a tempered pythagorean comma, so {{nowrap\|/C {{=}} ^^Dbb\|\C {{=}} vvB#\|^^C {{=}} /B#\|and vvC {{=}} \Dbb}}.

FloraC: Clarify that the scope of this article is currently the 11-odd-limit. -duplicate and out-of-scope chords. Style

2024-12-17T12:08:48Z

Clarify that the scope of this article is currently the 11-odd-limit. -duplicate and out-of-scope chords. Style

Show changes