Miracle/Chords - Revision history

Lériendil: Lériendil moved page Chords of miracle to Miracle/Chords

2025-06-22T21:50:15Z

Lériendil moved page Chords of miracle to Miracle/Chords

← Older revision	Revision as of 21:50, 22 June 2025
(No difference)

FloraC: Cleanup

2025-01-07T11:25:51Z

Cleanup

← Older revision		Revision as of 11:25, 7 January 2025
Line 1:		Line 1:
	Below are listed the [[dyadic chord]]s of 11-limit [[~~Miracle~~\|miracle temperament]]. They are listed in order of increasing [[Graham complexity]], with [[hash complexity]] used to break ties.		Below are listed the [[dyadic chord]]s of [[11-limit]] [[miracle\|miracle temperament]]. They are listed in order of increasing [[Graham complexity]], with [[hash complexity]] used to break ties.

	For any linear temperament, if we ~~chose~~ a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2<sup>s</sup> for all s ∊ S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "~~Hash~~" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity.		For any linear temperament, if we choose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If ''S'' is such a set, the sum Σ 2<sup>''s''</sup> for all ''s'' ∊ ''S'' provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity.

	The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the harmonic series (the overtones) and utonal if it is the inversion of an otonal chord (in other words, fitting the subharmonic series), and ambitonal if it can equally well be seen as otonal or utonal.		The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the harmonic series (the overtones) and utonal if it is the inversion of an otonal chord (in other words, fitting the subharmonic series), and ambitonal if it can equally well be seen as otonal or utonal.

	The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord. These include:		The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord. These include:
	* [[Marvel ~~triad~~\|~~marvel~~]], for the tempering of [[225/224]]		* [[Marvel chords\|Marvel]], for the tempering of [[225/224]]
	* [[Keenanismic chords\|~~keenanismic~~]], for the tempering of [[385/384]]		* [[Keenanismic chords\|Keenanismic]], for the tempering of [[385/384]]
	* [[Swetismic chords\|~~swetismic~~]], for the tempering of [[540/539]]		* [[Swetismic chords\|Swetismic]], for the tempering of [[540/539]]
	* [[Rastmic chords\|~~rastmic~~]], for the tempering of [[243/242]]		* [[Rastmic chords\|Rastmic]], for the tempering of [[243/242]]
	* [[Werckismic chords\|~~werckismic~~]], for the tempering of [[441/440]]		* [[Werckismic chords\|Werckismic]], for the tempering of [[441/440]]
	* [[~~undecimal~~ marvel chords\|~~unimarvel~~]], for the tempering of any two of 225/224, 385/384 or 540/539		* [[Undecimal marvel chords\|Unimarvel]], for the tempering of any two of 225/224, 385/384 or 540/539
	* [[Prodigy chords\|~~prodigy~~]], for the tempering of both 225/224 and 441/440		* [[Prodigy chords\|Prodigy]], for the tempering of both 225/224 and 441/440
	* [[Jove chords\|~~jove~~]], for the tempering of any two of 243/242, 441/440 or 540/539		* [[Jove chords\|Jove]], for the tempering of any two of 243/242, 441/440 or 540/539
	* [[Miracle chords\|~~miracle~~]], for the tempering of any three independent commas mentioned above		* [[Miracle chords\|Miracle]], for the tempering of any three independent commas mentioned above

	The generator used below is the standard choice for miracle temperament, the secor, 16/15~15/14. However, it should be noted that the choice of generator does not affect the list of chords, only how those chords are interpreted. Does ~~0-7-13~~ denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.		The generator used below is the standard choice for miracle temperament, the secor, 16/15~15/14. However, it should be noted that the choice of generator does not affect the list of chords, only how those chords are interpreted. Does 0–7–13 denote the major triad or the minor triad? It is on the list of chords either way, but with a secor generator it is the major triad.

	== Triads ==		== Triads ==
	The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of miracle. For instance, Chord ~~0-2-5~~, which is 1/~~1-8/7-7~~/5, occurs for the first time on the fifth generation, and will therefore occur five times in ~~miracle~~[10]. Chord ~~0-3-9~~, which is ~~1/1-11~~/~~9-11~~/6, occurs for the first time on the ninth generation, and therefore appears only once in ~~miracle~~[10].		The chords are ordered by generator steps. This chord ordering is useful because you can tell how often it will occur in a scale of miracle. For instance, Chord 0–2–5, which is 1–8/7–7/5, occurs for the first time on the fifth generation, and will therefore occur five times in Miracle[10]. Chord 0–3–9, which is 1–11/9–11/6, occurs for the first time on the ninth generation, and therefore appears only once in Miracle[10].

	Each of the triads generated has three "inversions", i.e., can be written starting on any one of the three tones in the triad.		Each of the triads generated has three rotations ("inversions"), i.e., can be written starting on any one of the three tones in the triad.

	This ordering does create results that may seem surprising: ~~For~~ example, chord #21, 1/~~1-6/5-8~~/5, is the first inversion of ~~1/1-5~~/~~4-3~~/2; in this list, ~~1/1-5~~/~~4-3~~/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.		This ordering does create results that may seem surprising: for example, chord #21, 1–6/5–8/5, is the first inversion of 1–5/4–3/2; in this list, 1–5/4–3/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.

	All three inversions for all 63 chords are notated in this [[Media:41-EDO-Miracle-scale-and-triads.pdf\|PDF]] and can be heard using a [[Media:41 EDO Miracle - scale and triads - piano.mp3\|piano]], a [[Media:41 EDO Miracle - scale and triads - steel gtr.mp3\|steel-stringed guitar]], a [[Media:41 EDO Miracle - scale and triads - nylon guitar.mp3\|nylon-stringed guitar]], and a [[Media:41 EDO Miracle - scale and triads - strings.mp3\|string ensemble]]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using ~~41 EDO~~ sagittal notation ([[Media:41 EDO Miracle - scale and triads.mus2\|get Mus2 file]]), exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a [[Media:41 EDO Miracle - scale and triads.mid\|tuned MIDI file]]. The sequence is: chord as generated, first inversion, second inversion, quarter-note rest.		All three inversions for all 63 chords are notated in this [[Media:41-EDO-Miracle-scale-and-triads.pdf\|PDF]] and can be heard using a [[Media:41 EDO Miracle - scale and triads - piano.mp3\|piano]], a [[Media:41 EDO Miracle - scale and triads - steel gtr.mp3\|steel-stringed guitar]], a [[Media:41 EDO Miracle - scale and triads - nylon guitar.mp3\|nylon-stringed guitar]], and a [[Media:41 EDO Miracle - scale and triads - strings.mp3\|string ensemble]]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using 41edo sagittal notation ([[Media:41 EDO Miracle - scale and triads.mus2\|get Mus2 file]]), exported to tuned [[MIDI]], and rendered with [[Timidity++]] using soundfonts.) Finally, here is a [[Media:41 EDO Miracle - scale and triads.mid\|tuned MIDI file]]. The sequence is: chord as generated, first inversion, second inversion, quarter-note rest.

	{\| class="wikitable"		{\| class="wikitable center-1"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
Line 607:		Line 607:

	== Tetrads ==		== Tetrads ==
			{\| class="wikitable center-1"
	{\| class="wikitable"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
Line 1,732:		Line 1,731:

	== Pentads ==		== Pentads ==
			{\| class="wikitable center-1"
	{\| class="wikitable"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal
Line 2,181:		Line 2,179:

	== Hexads ==		== Hexads ==
			{\| class="wikitable center-1"
	{\| class="wikitable"
	\|-		\|-
	! ~~Number~~		! #
	! Chord		! Chord
	! Transversal		! Transversal

Xenllium: fixed typo

2023-10-16T10:23:41Z

fixed typo

← Older revision		Revision as of 10:23, 16 October 2023
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	* [[Werckismic chords\|werckismic]], for the tempering of [[441/440]]		* [[Werckismic chords\|werckismic]], for the tempering of [[441/440]]
	* [[undecimal marvel chords\|unimarvel]], for the tempering of any two of 225/224, 385/384 or 540/539		* [[undecimal marvel chords\|unimarvel]], for the tempering of any two of 225/224, 385/384 or 540/539
	* [[Jove chords\|jove]], for the tempering of both 225/224 and 243/242
	* [[Prodigy chords\|prodigy]], for the tempering of both 225/224 and 441/440		* [[Prodigy chords\|prodigy]], for the tempering of both 225/224 and 441/440
			* [[Jove chords\|jove]], for the tempering of any two of 243/242, 441/440 or 540/539
	* [[Miracle chords\|miracle]], for the tempering of any three independent commas mentioned above		* [[Miracle chords\|miracle]], for the tempering of any three independent commas mentioned above

FloraC: Recategorize

2023-05-23T11:37:24Z

Recategorize

← Older revision		Revision as of 11:37, 23 May 2023
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	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Miracle]]		[[Category:Miracle]]
	[[Category:~~Pentad~~]]		[[Category:Triads]]
	[[Category:~~Tetrad~~]]		[[Category:Tetrads]]
	[[Category:~~Triad~~]]		[[Category:Pentads]]
			[[Category:Hexads]]

Fredg999 category edits: Moving from Category:Chords to Category:Lists of chords using Cat-a-lot

2023-04-28T03:50:35Z

Moving from Category:Chords to Category:Lists of chords using Cat-a-lot

← Older revision		Revision as of 03:50, 28 April 2023
Line 2,275:		Line 2,275:
	\|}		\|}

	[[Category:~~Chords~~]]		[[Category:Lists of chords]]
	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Miracle]]		[[Category:Miracle]]

Wolftune: adjusted "overtone series" to "harmonic series" but kept references to "overtones" to explain the use of "otonal"

2022-01-22T20:49:45Z

adjusted "overtone series" to "harmonic series" but kept references to "overtones" to explain the use of "otonal"

← Older revision		Revision as of 20:49, 22 January 2022
Line 3:		Line 3:
	For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2<sup>s</sup> for all s ∊ S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity.		For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2<sup>s</sup> for all s ∊ S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity.

	The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the ~~overtone~~ series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal.		The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the harmonic series (the overtones) and utonal if it is the inversion of an otonal chord (in other words, fitting the subharmonic series), and ambitonal if it can equally well be seen as otonal or utonal.

	The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord. These include:		The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord. These include:
Line 25:		Line 25:
	This ordering does create results that may seem surprising: For example, chord #21, 1/1-6/5-8/5, is the first inversion of 1/1-5/4-3/2; in this list, 1/1-5/4-3/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.		This ordering does create results that may seem surprising: For example, chord #21, 1/1-6/5-8/5, is the first inversion of 1/1-5/4-3/2; in this list, 1/1-5/4-3/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.

	All three inversions for all 63 chords are notated in this [[~~media~~:41-EDO-Miracle-scale-and-triads.pdf\|PDF]] and can be heard using a [[~~media~~:~~41_EDO_Miracle_~~-~~_scale_and_triads_~~-~~_piano~~.mp3\|piano]], a [[~~media~~:~~41_EDO_Miracle_~~-~~_scale_and_triads_~~-~~_steel_gtr~~.mp3\|steel-stringed guitar]], a [[~~media~~:~~41_EDO_Miracle_~~-~~_scale_and_triads_~~-~~_nylon_guitar~~.mp3\|nylon-stringed guitar]], and a [[~~media~~:~~41_EDO_Miracle_~~-~~_scale_and_triads_~~-~~_strings~~.mp3\|string ensemble]]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using 41 EDO sagittal notation ([[~~media~~:~~41_EDO_Miracle_~~-~~_scale_and_triads~~.mus2\|get Mus2 file]]), exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a [[~~media~~:~~41_EDO_Miracle_~~-~~_scale_and_triads~~.mid\|tuned MIDI file]]. The sequence is: chord as generated, first inversion, second inversion, quarter-note rest.		All three inversions for all 63 chords are notated in this [[Media:41-EDO-Miracle-scale-and-triads.pdf\|PDF]] and can be heard using a [[Media:41 EDO Miracle - scale and triads - piano.mp3\|piano]], a [[Media:41 EDO Miracle - scale and triads - steel gtr.mp3\|steel-stringed guitar]], a [[Media:41 EDO Miracle - scale and triads - nylon guitar.mp3\|nylon-stringed guitar]], and a [[Media:41 EDO Miracle - scale and triads - strings.mp3\|string ensemble]]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using 41 EDO sagittal notation ([[Media:41 EDO Miracle - scale and triads.mus2\|get Mus2 file]]), exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a [[Media:41 EDO Miracle - scale and triads.mid\|tuned MIDI file]]. The sequence is: chord as generated, first inversion, second inversion, quarter-note rest.

	{\| class="wikitable"		{\| class="wikitable"

FloraC: +links to each chord page

2021-03-21T14:13:40Z

+links to each chord page

← Older revision		Revision as of 14:13, 21 March 2021
Line 1:		Line 1:
	Below are listed the [[dyadic chord]]s of 11-limit [[Miracle\|miracle temperament]]. They are listed in order of increasing [[Graham complexity]], with [[hash complexity]] used to break ties. For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2<sup>s</sup> for all s ∊ S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity.		Below are listed the [[dyadic chord]]s of 11-limit [[Miracle\|miracle temperament]]. They are listed in order of increasing [[Graham complexity]], with [[hash complexity]] used to break ties.

			For any linear temperament, if we chose a generator, we may put any octave-equivalent chord of the temperament in a canonical form by representing it as a set of nonnegative integers, starting with 0, which are the number of generator steps giving an octave-equivalent note class in the chord. If S is such a set, the sum Σ 2<sup>s</sup> for all s ∊ S provides a unique odd number encoding the chord, and the logarithm base two of this number is the hash complexity, listed under the heading "Hash" below. The floor of hash complexity, that is, the greatest integer less than the hash complexity, is equal to the Graham complexity.

	The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal.		The heading "transversal" shows a JI chord whose intervals temper to the marvel chord. Under "type" it says otonal if it is an essentially just chord best understood in terms of the overtone series, utonal if it is the inversion of an otonal chord, and ambitonal if it can equally well be seen as otonal or utonal.

	The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord, ~~so that if~~ for ~~example it says "~~werckismic~~" only~~ 441/440 ~~needs to be tempered out. Also~~, ~~"marvel" denotes 9 odd limit (7-limit) marvel~~, ~~whereas "unimarvel" means 11-limit marvel.~~		The other names denote types of essentially tempered chord, giving the least amount of tempering needed to define the chord. These include:
			* [[Marvel triad\|marvel]], for the tempering of [[225/224]]
			* [[Keenanismic chords\|keenanismic]], for the tempering of [[385/384]]
			* [[Swetismic chords\|swetismic]], for the tempering of [[540/539]]
			* [[Rastmic chords\|rastmic]], for the tempering of [[243/242]]
			* [[Werckismic chords\|werckismic]], for the tempering of [[441/440]]
			* [[undecimal marvel chords\|unimarvel]], for the tempering of any two of 225/224, 385/384 or 540/539
			* [[Jove chords\|jove]], for the tempering of both 225/224 and 243/242
			* [[Prodigy chords\|prodigy]], for the tempering of both 225/224 and 441/440
			* [[Miracle chords\|miracle]], for the tempering of any three independent commas mentioned above

	The generator used below is the standard choice for miracle temperament, the secor, 16/15~15/14. However, it should be noted that the choice of generator does not affect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.		The generator used below is the standard choice for miracle temperament, the secor, 16/15~15/14. However, it should be noted that the choice of generator does not affect the list of chords, only how those chords are interpreted. Does 0-7-13 denote the major triad or the minor triad? It's on the list of chords either way, but with a secor generator it's the major triad.

FloraC: Cleanup

2021-03-21T14:00:23Z

Cleanup

Show changes

Jdfreivald: /* Triads */ Added Mus2 file for triads

2020-01-15T21:49:44Z

Triads: Added Mus2 file for triads

← Older revision		Revision as of 21:49, 15 January 2020
Line 14:		Line 14:
	<span style="line-height: 1.5;">This ordering does create results that may seem surprising: For example, chord #21, 1/1-6/5-8/5, is the first inversion of 1/1-5/4-3/2; in this list, 1/1-5/4-3/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.</span>		<span style="line-height: 1.5;">This ordering does create results that may seem surprising: For example, chord #21, 1/1-6/5-8/5, is the first inversion of 1/1-5/4-3/2; in this list, 1/1-5/4-3/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.</span>

	All three inversions for all 63 chords are notated in this [[media:41-EDO-Miracle-scale-and-triads.pdf \| PDF]] and can be heard using a [[media:41_EDO_Miracle_-_scale_and_triads_-_piano.mp3 \| piano]], a [[media:41_EDO_Miracle_-_scale_and_triads_-_steel_gtr.mp3 \| steel-stringed guitar]], a [[media:41_EDO_Miracle_-_scale_and_triads_-_nylon_guitar.mp3 \| nylon-stringed guitar]], and a [[media:41_EDO_Miracle_-_scale_and_triads_-_strings.mp3 \| string ensemble]]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using 41 EDO sagittal notation, exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a [[media:41_EDO_Miracle_-_scale_and_triads.mid \| tuned MIDI file]]. The sequence is: chord as ~~outlined in the list below~~, first inversion, second inversion, quarter-note rest.		All three inversions for all 63 chords are notated in this [[media:41-EDO-Miracle-scale-and-triads.pdf \| PDF]] and can be heard using a [[media:41_EDO_Miracle_-_scale_and_triads_-_piano.mp3 \| piano]], a [[media:41_EDO_Miracle_-_scale_and_triads_-_steel_gtr.mp3 \| steel-stringed guitar]], a [[media:41_EDO_Miracle_-_scale_and_triads_-_nylon_guitar.mp3 \| nylon-stringed guitar]], and a [[media:41_EDO_Miracle_-_scale_and_triads_-_strings.mp3 \| string ensemble]]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using 41 EDO sagittal notation ([[media:41_EDO_Miracle_-_scale_and_triads.mus2 \|get Mus2 file]]), exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a [[media:41_EDO_Miracle_-_scale_and_triads.mid \| tuned MIDI file]]. The sequence is: chord as generated, first inversion, second inversion, quarter-note rest.

	{\| class="wikitable"		{\| class="wikitable"

Jdfreivald: /* Triads */ No, really fixed them this time.

2020-01-15T20:31:11Z

Triads: No, really fixed them this time.

← Older revision		Revision as of 20:31, 15 January 2020
Line 14:		Line 14:
	<span style="line-height: 1.5;">This ordering does create results that may seem surprising: For example, chord #21, 1/1-6/5-8/5, is the first inversion of 1/1-5/4-3/2; in this list, 1/1-5/4-3/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.</span>		<span style="line-height: 1.5;">This ordering does create results that may seem surprising: For example, chord #21, 1/1-6/5-8/5, is the first inversion of 1/1-5/4-3/2; in this list, 1/1-5/4-3/2 is the second inversion of chord #21. Unlike in traditional music theory, there is nothing canonical about these orderings and inversions.</span>

	All three inversions for all 63 chords are notated in this [[media:41-EDO-Miracle-scale-and-triads.pdf PDF]] and can be heard using a [[media:41_EDO_Miracle_-_scale_and_triads_-_piano.mp3 piano]], a [[media:41_EDO_Miracle_-_scale_and_triads_-_steel_gtr.mp3 steel-stringed guitar]], a [[media:41_EDO_Miracle_-_scale_and_triads_-_nylon_guitar.mp3 nylon-stringed guitar]], and a [[media:41_EDO_Miracle_-_scale_and_triads_-_strings.mp3 \| string ensemble]]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using 41 EDO sagittal notation, exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a [[media:41_EDO_Miracle_-_scale_and_triads.mid tuned MIDI file]]. The sequence is: chord as outlined in the list below, first inversion, second inversion, quarter-note rest.		All three inversions for all 63 chords are notated in this [[media:41-EDO-Miracle-scale-and-triads.pdf \| PDF]] and can be heard using a [[media:41_EDO_Miracle_-_scale_and_triads_-_piano.mp3 \| piano]], a [[media:41_EDO_Miracle_-_scale_and_triads_-_steel_gtr.mp3 \| steel-stringed guitar]], a [[media:41_EDO_Miracle_-_scale_and_triads_-_nylon_guitar.mp3 \| nylon-stringed guitar]], and a [[media:41_EDO_Miracle_-_scale_and_triads_-_strings.mp3 \| string ensemble]]. (All linked files are in MP3 format. They were created in [http://www.mus2.com.tr/en/ Mus2] using 41 EDO sagittal notation, exported to tuned MIDI, and rendered with Timidity++ using soundfonts.) Finally, here is a [[media:41_EDO_Miracle_-_scale_and_triads.mid \| tuned MIDI file]]. The sequence is: chord as outlined in the list below, first inversion, second inversion, quarter-note rest.

	{\| class="wikitable"		{\| class="wikitable"

← Older revision		Revision as of 10:23, 16 October 2023
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	* [[Werckismic chords\|werckismic]], for the tempering of [[441/440]]		* [[Werckismic chords\|werckismic]], for the tempering of [[441/440]]
	* [[undecimal marvel chords\|unimarvel]], for the tempering of any two of 225/224, 385/384 or 540/539		* [[undecimal marvel chords\|unimarvel]], for the tempering of any two of 225/224, 385/384 or 540/539
	* [[Jove chords\|jove]], for the tempering of both 225/224 and 243/242
	* [[Prodigy chords\|prodigy]], for the tempering of both 225/224 and 441/440		* [[Prodigy chords\|prodigy]], for the tempering of both 225/224 and 441/440
			* [[Jove chords\|jove]], for the tempering of any two of 243/242, 441/440 or 540/539
	* [[Miracle chords\|miracle]], for the tempering of any three independent commas mentioned above		* [[Miracle chords\|miracle]], for the tempering of any three independent commas mentioned above