Magic chords - Revision history

FloraC: Undecimal sensamagic was missing

2025-10-12T11:11:11Z

Undecimal sensamagic was missing

← Older revision		Revision as of 11:11, 12 October 2025
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	A '''magic chord''' is an [[essentially tempered chord]] of the [[magic]] temperament; they are included among those listed as [[chords of magic]]. Aside from the [[marvel chords\|marvel]], [[sensamagic chords\|sensamagic]], [[ptolemismic chords\|ptolemismic]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], [[pentacircle chords\|pentacircle]], [[apollo chords\|apollo]], [[octarod chords\|octarod]], [[undecimal marvel chords\|~~unimarvel~~]] and [[keemic chords]] listed there, there are 23 further essentially magic chords in the [[11-odd-limit]].		A '''magic chord''' is an [[essentially tempered chord]] of the [[magic]] temperament; they are included among those listed as [[chords of magic]]. Aside from the [[marvel chords\|marvel]], [[sensamagic chords\|sensamagic]], [[ptolemismic chords\|ptolemismic]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], [[pentacircle chords\|pentacircle]], [[apollo chords\|apollo]], [[octarod chords\|octarod]], [[undecimal marvel chords\|undecimal marvel]], [[undecimal sensamagic chords\|undecimal sensamagic]] and [[keemic chords]] listed there, there are 23 further essentially magic chords in the [[11-odd-limit]].

	The two magic tetrads are in inverse relationship:		The two magic tetrads are in inverse relationship:

FloraC: Temp rename followup

2025-10-12T11:09:59Z

Temp rename followup

← Older revision		Revision as of 11:09, 12 October 2025
Line 1:		Line 1:
	A '''magic chord''' is an [[essentially tempered chord]] of the [[magic]] temperament; they are included among those listed as [[chords of magic]]. Aside from the [[marvel chords\|marvel]], [[sensamagic chords\|sensamagic]], [[ptolemismic chords\|ptolemismic]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], [[pentacircle chords\|pentacircle]], [[apollo chords\|apollo]], [[octarod chords\|octarod]], [[undecimal marvel chords\|unimarvel]] and [[~~supermagic~~ chords]] listed there, there are 23 further essentially magic chords in the 11-odd-limit.		A '''magic chord''' is an [[essentially tempered chord]] of the [[magic]] temperament; they are included among those listed as [[chords of magic]]. Aside from the [[marvel chords\|marvel]], [[sensamagic chords\|sensamagic]], [[ptolemismic chords\|ptolemismic]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], [[pentacircle chords\|pentacircle]], [[apollo chords\|apollo]], [[octarod chords\|octarod]], [[undecimal marvel chords\|unimarvel]] and [[keemic chords]] listed there, there are 23 further essentially magic chords in the [[11-odd-limit]].

	The two magic tetrads are in inverse relationship:		The two magic tetrads are in inverse relationship:

FloraC: Re-link

2024-10-17T14:52:20Z

Re-link

← Older revision		Revision as of 14:52, 17 October 2024
Line 1:		Line 1:
	A '''magic chord''' is an [[essentially tempered chord]] of the [[magic]] temperament; they are included among those listed as [[chords of magic]]. Aside from the [[marvel chords\|marvel]], [[sensamagic chords\|sensamagic]], [[ptolemismic chords\|ptolemismic]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], [[pentacircle chords\|pentacircle]], [[apollo chords\|apollo]], [[octarod chords\|octarod]], [[undecimal marvel chords\|unimarvel]] and [[~~magical seventh chord\|~~supermagic]] ~~chords~~ listed there, there are 23 further essentially magic chords in the 11-odd-limit.		A '''magic chord''' is an [[essentially tempered chord]] of the [[magic]] temperament; they are included among those listed as [[chords of magic]]. Aside from the [[marvel chords\|marvel]], [[sensamagic chords\|sensamagic]], [[ptolemismic chords\|ptolemismic]], [[keenanismic chords\|keenanismic]], [[swetismic chords\|swetismic]], [[pentacircle chords\|pentacircle]], [[apollo chords\|apollo]], [[octarod chords\|octarod]], [[undecimal marvel chords\|unimarvel]] and [[supermagic chords]] listed there, there are 23 further essentially magic chords in the 11-odd-limit.

	The two magic tetrads are in inverse relationship:		The two magic tetrads are in inverse relationship:

FloraC: Improve readability; recategorize

2024-10-17T13:02:59Z

Improve readability; recategorize

Show changes

Xenllium: Created page with "A '''magic chord''' is an essentially tempered chord of the magic temperament; they are included among those listed as chords of magic. Aside from the marvel, sens..."

2023-08-15T12:29:54Z

Created page with "A '''magic chord''' is an essentially tempered chord of the magic temperament; they are included among those listed as chords of magic. Aside from the marvel, sens..."

New page

A '''magic chord''' is an [[essentially tempered chord]] of the [[magic]] temperament; they are included among those listed as [[chords of magic]]. Aside from the marvel, sensamagic, ptolemismic, keenanismic, swetismic, pentacircle, apollo, octarod, unimarvel and supermagic chords listed there, there are 23 further essentially magic chords in the 11-odd-limit.

The two magic tetrads are in inverse relationship:
* 1-5/4-14/9-9/5 with steps 5/4-5/4-7/6-10/9 and its inverse 1-7/6-16/11-9/5 with steps 7/6-5/4-5/4-10/9;

For pentads, there are seven pairs of chords in inverse relationship:
* 1-9/8-5/4-14/9-9/5 with steps 9/8-10/9-5/4-7/6-10/9 and its inverse 1-9/8-5/4-16/11-9/5 with steps 9/8-10/9-7/6-5/4-10/9;
* 1-5/4-7/5-14/9-9/5 with steps 5/4-9/8-10/9-7/6-10/9 and its inverse 1-9/8-7/5-14/9-9/5 with steps 9/8-5/4-10/9-7/6-10/9;
* 1-12/11-5/4-14/9-9/5 with steps 12/11-8/7-5/4-7/6-10/9 and its inverse 1-12/11-6/5-7/5-7/4 with steps 12/11-10/9-7/6-5/4-8/7;
* 1-12/11-6/5-14/9-7/4 with steps 12/11-10/9-9/7-9/8-8/7 and its inverse 1-12/11-5/4-7/5-9/5 with steps 12/11-8/7-9/8-9/7-10/9;
* 1-7/6-16/11-18/11-9/5 with steps 7/6-5/4-9/8-10/9-10/9 and its inverse 1-9/8-7/5-18/11-9/5 with steps 9/8-5/4-7/6-10/9-10/9;
* 1-7/6-14/11-16/11-9/5 with steps 7/6-12/11-8/7-5/4-10/9 and its inverse 1-12/11-14/11-7/5-7/4 with steps 12/11-7/6-10/9-5/4-8/7;
* 1-9/8-14/11-14/9-9/5 with steps 9/8-9/8-11/9-7/6-10/9 and its inverse 1-9/8-14/11-7/5-18/11 with steps 9/8-9/8-10/9-7/6-11/9.

For hexads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
* 1-9/8-5/4-7/5-14/9-9/5 with steps 9/8-10/9-9/8-10/9-7/6-10/9.

The inversely related pairs of chords are
* 1-12/11-5/4-7/5-14/9-9/5 with steps 12/11-8/7-9/8-10/9-7/6-10/9 and its inverse 1-12/11-6/5-7/5-14/9-7/4 with steps 12/11-10/9-7/6-10/9-9/8-8/7;
* 1-9/8-14/11-7/5-14/9-9/5 with steps 9/8-9/8-10/9-10/9-7/6-10/9 and its inverse 1-9/8-14/11-7/5-18/11-9/5 with steps 9/8-9/8-10/9-7/6-10/9-10/9;
* 1-12/11-14/11-7/5-14/9-7/4 with steps 12/11-7/6-10/9-10/9-9/8-8/7 and its inverse 1-7/6-14/11-16/11-18/11-9/5 with steps 7/6-12/11-8/7-9/8-10/9-10/9.

The count of magic chords is therefore tetrads: 2, pentads: 14, and hexads: 7.

Equal temperaments with magic chords include {{Optimal ET sequence| 19, 22, 41, 60, 63, 85 and 104 }}.

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