Marvel woo - Revision history

ArrowHead294 at 20:09, 11 February 2025

2025-02-11T20:09:06Z

← Older revision		Revision as of 20:09, 11 February 2025
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	* [https://soundcloud.com/morphosyntax-1/cave-of-marvels Cave of Marvels] by [[Herman Miller]] (2017)		* [https://soundcloud.com/morphosyntax-1/cave-of-marvels Cave of Marvels] by [[Herman Miller]] (2017)

	{{~~Scale~~ gallery}}		{{Navbox scale gallery}}

	[[Category:Marvel]]		[[Category:Marvel]]
	[[Category:Listen]]		[[Category:Listen]]

FloraC: -duplicate info. Misc. style improvements (vertical fractions only have a place in display-style math, and raised fractions look dumb with large ratios too)

2025-01-10T17:26:31Z

-duplicate info. Misc. style improvements (vertical fractions only have a place in display-style math, and raised fractions look dumb with large ratios too)

← Older revision		Revision as of 17:26, 10 January 2025
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	'''Marvel woo''' is a particular tuning of ~~Marvel~~ which is optimized for synchronized [[beat]]ing, and which also happens to be very close to the [[~~Tenney-Euclidean_Tuning\|~~TE tuning]] for ~~Marvel~~.		'''Marvel woo''' is a particular tuning of [[marvel\|undecimal marvel]] which is optimized for synchronized [[beat]]ing, and which also happens to be very close to the [[TE tuning]] for marvel.

	[[Marvel family\|Marvel]] is the rank-3 [[Tour of Regular Temperaments\|temperament]] tempering out 225/224, the [https://en.wikipedia.org/wiki/Septimal_kleisma septimal kleisma]. For Marvel woo, we extend Marvel into the 11-limit by tempering out [[385/384]].		The marvel woo [[tuning map]] is {{val\| 1200.643223 1901.313567 2785.029055 3369.469129 4151.317943 }}.

	The marvel woo [[tuning map]] is {{~~map~~\| 1200.643223 1901.313567 2785.029055 3369.469129 4151.317943 }}.
	__TOC__		__TOC__
	== Math ==		== Math ==
	Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo~~]]s~~ (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [{{monzo\| 0 -4 4 4 4 }}, {{monzo\| -21 6 -6 15 8 }}, {{monzo\| 7 -18 18 11 4 }}, {{monzo\| -28 -4 4 32 4 }}, {{monzo\| 0 0 0 0 28 }}]/28. It leads to a tuning where the octave is sharp by {{~~sfrac~~\|{{monzo\| -7 -1 1 1 1 }}\|7~~}} ~~=~~ ~~(~~{{frac\|~~385\|384}})<sup>1/7</sup>, about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only {{~~sfrac~~\|{{monzo\| -49 -26 -2 19 12 }}\|28~~}} ~~=~~ {{sfrac\|~~(385/384)<sup>3/7</sup>\|(225/224)<sup>1/4</sup>}}, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 4:5:6:7:8, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.		Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo\|eigenmonzos (unchanged-intervals)]]. This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [{{monzo\| 0 -4 4 4 4 }}, {{monzo\| -21 6 -6 15 8 }}, {{monzo\| 7 -18 18 11 4 }}, {{monzo\| -28 -4 4 32 4 }}, {{monzo\| 0 0 0 0 28 }}]/28. It leads to a tuning where the octave is sharp by {{nowrap\|{{monzo\| -7 -1 1 1 1 }}/7 = (385/384)<sup>1/7</sup>}}, about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only {{nowrap\|{{monzo\| -49 -26 -2 19 12 }}/28 = (385/384)<sup>3/7</sup>/(225/224)<sup>1/4</sup>}}, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the [[11-odd-limit]] [[tonality diamond]] is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the 11-odd-limit diamond are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 4:5:6:7:8, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.

	== Scales ==		== Scales ==

ArrowHead294 at 18:35, 9 January 2025

2025-01-09T18:35:26Z

← Older revision		Revision as of 18:35, 9 January 2025
Line 6:		Line 6:
	__TOC__		__TOC__
	== Math ==		== Math ==
	Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo]]s (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [{{monzo\| 0 -4 4 4 4 }}, {{monzo\| -21 6 -6 15 8 }}, {{monzo\| 7 -18 18 11 4 }}, {{monzo\| -28 -4 4 32 4 }}, {{monzo\| 0 0 0 0 28 }}]/28. It leads to a tuning where the octave is sharp by {{sfrac\|{{monzo\| -7 -1 1 1 1 }}\|7}} = (385/384)<sup>1/7</sup>, about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only {{sfrac\|{{monzo\| -49 -26 -2 19 12 }}\|28}} = {{sfrac\|(385/384)<sup>3/7</sup>\|(225/224)<sup>1/4</sup>}}, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 4:5:6:7:8, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.		Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo]]s (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [{{monzo\| 0 -4 4 4 4 }}, {{monzo\| -21 6 -6 15 8 }}, {{monzo\| 7 -18 18 11 4 }}, {{monzo\| -28 -4 4 32 4 }}, {{monzo\| 0 0 0 0 28 }}]/28. It leads to a tuning where the octave is sharp by {{sfrac\|{{monzo\| -7 -1 1 1 1 }}\|7}} = ({{frac\|385\|384}})<sup>1/7</sup>, about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only {{sfrac\|{{monzo\| -49 -26 -2 19 12 }}\|28}} = {{sfrac\|(385/384)<sup>3/7</sup>\|(225/224)<sup>1/4</sup>}}, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 4:5:6:7:8, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.

	== Scales ==		== Scales ==

ArrowHead294 at 18:34, 9 January 2025

2025-01-09T18:34:23Z

← Older revision		Revision as of 18:34, 9 January 2025
Line 6:		Line 6:
	__TOC__		__TOC__
	== Math ==		== Math ==
	Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo]]s (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [{{monzo\| 0 -4 4 4 4 }}, {{monzo\| -21 6 -6 15 8 }}, {{monzo\| 7 -18 18 11 4 }}, {{monzo\| -28 -4 4 32 4 }}, {{monzo\| 0 0 0 0 28 }}]/28. It leads to a tuning where the octave is sharp by {{sfrac\|{{monzo\| -7 -1 1 1 1 }}\|7}}~~ ~~= (385/384)<sup>1/7</sup>, about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only {{sfrac\|{{monzo\| -49 -26 -2 19 12 }}\|28}}~~ ~~= {{sfrac\|(385/384)<sup>3/7</sup>\|(225/224)<sup>1/4</sup>}}, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 4:5:6:7:8, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.		Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo]]s (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [{{monzo\| 0 -4 4 4 4 }}, {{monzo\| -21 6 -6 15 8 }}, {{monzo\| 7 -18 18 11 4 }}, {{monzo\| -28 -4 4 32 4 }}, {{monzo\| 0 0 0 0 28 }}]/28. It leads to a tuning where the octave is sharp by {{sfrac\|{{monzo\| -7 -1 1 1 1 }}\|7}} = (385/384)<sup>1/7</sup>, about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only {{sfrac\|{{monzo\| -49 -26 -2 19 12 }}\|28}} = {{sfrac\|(385/384)<sup>3/7</sup>\|(225/224)<sup>1/4</sup>}}, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 4:5:6:7:8, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.

	== Scales ==		== Scales ==

ArrowHead294 at 18:34, 9 January 2025

2025-01-09T18:34:06Z

← Older revision		Revision as of 18:34, 9 January 2025
Line 3:		Line 3:
	[[Marvel family\|Marvel]] is the rank-3 [[Tour of Regular Temperaments\|temperament]] tempering out 225/224, the [https://en.wikipedia.org/wiki/Septimal_kleisma septimal kleisma]. For Marvel woo, we extend Marvel into the 11-limit by tempering out [[385/384]].		[[Marvel family\|Marvel]] is the rank-3 [[Tour of Regular Temperaments\|temperament]] tempering out 225/224, the [https://en.wikipedia.org/wiki/Septimal_kleisma septimal kleisma]. For Marvel woo, we extend Marvel into the 11-limit by tempering out [[385/384]].

	The marvel woo [[tuning map]] is ~~<~~1200.643223 1901.313567 2785.029055 3369.469129 4151.317943\|.		The marvel woo [[tuning map]] is {{map\| 1200.643223 1901.313567 2785.029055 3369.469129 4151.317943 }}.
	__TOC__		__TOC__
	== Math ==		== Math ==
			Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo]]s (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [{{monzo\| 0 -4 4 4 4 }}, {{monzo\| -21 6 -6 15 8 }}, {{monzo\| 7 -18 18 11 4 }}, {{monzo\| -28 -4 4 32 4 }}, {{monzo\| 0 0 0 0 28 }}]/28. It leads to a tuning where the octave is sharp by {{sfrac\|{{monzo\| -7 -1 1 1 1 }}\|7}} = (385/384)<sup>1/7</sup>, about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only {{sfrac\|{{monzo\| -49 -26 -2 19 12 }}\|28}} = {{sfrac\|(385/384)<sup>3/7</sup>\|(225/224)<sup>1/4</sup>}}, about 0.0018 cents. Putting 10/3, 7/2, 11, and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 4:5:6:7:8, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.
	Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo]]s (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [\|0 -4 4 4 4~~>~~, \|-21 6 -6 15 8~~>~~, \|7 -18 18 11 4~~>~~, \|-28 -4 4 32 4~~>~~, \|0 0 0 0 28~~>~~]/28. It leads to a tuning where the octave is sharp by \|-7 -1 1 1 1>/7 = (385/384)^(1/7), about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only \|-49 -26 -2 19 12>~~/28~~ = (385/384)^(3/7)/(225/224)^(1/4), about 0.0018 cents. Putting 10/3, 7/2, 11 and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 1-5~~/4-3/2-~~7~~/4-2~~, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.

	== Scales ==		== Scales ==

	{\| class="sortable wikitable"		{\| class="sortable wikitable"
			\|-
	! Size		! Size
	! Name		! Name

BudjarnLambeth: /* Music */ add music

2024-12-06T09:35:08Z

Music: add music

← Older revision		Revision as of 09:35, 6 December 2024
Line 88:		Line 88:
	== Music ==		== Music ==
	* [http://chrisvaisvil.com/the-mysteries-of-motivation-piano-tuned-to-marvel-woo/ The Mysteries of Motivation] ([http://micro.soonlabel.com/marvel/20140425_diam7_plus_woo.mp3 play MP3]) in [[diam7plusmarvwoo]] by [[Chris Vaisvil]]		* [http://chrisvaisvil.com/the-mysteries-of-motivation-piano-tuned-to-marvel-woo/ The Mysteries of Motivation] ([http://micro.soonlabel.com/marvel/20140425_diam7_plus_woo.mp3 play MP3]) in [[diam7plusmarvwoo]] by [[Chris Vaisvil]]

			* [https://soundcloud.com/morphosyntax-1/cave-of-marvels Cave of Marvels] by [[Herman Miller]] (2017)

	{{Scale gallery}}		{{Scale gallery}}

BudjarnLambeth: Scale gallery template

2024-12-02T10:16:35Z

Scale gallery template

← Older revision		Revision as of 10:16, 2 December 2024
Line 88:		Line 88:
	== Music ==		== Music ==
	* [http://chrisvaisvil.com/the-mysteries-of-motivation-piano-tuned-to-marvel-woo/ The Mysteries of Motivation] ([http://micro.soonlabel.com/marvel/20140425_diam7_plus_woo.mp3 play MP3]) in [[diam7plusmarvwoo]] by [[Chris Vaisvil]]		* [http://chrisvaisvil.com/the-mysteries-of-motivation-piano-tuned-to-marvel-woo/ The Mysteries of Motivation] ([http://micro.soonlabel.com/marvel/20140425_diam7_plus_woo.mp3 play MP3]) in [[diam7plusmarvwoo]] by [[Chris Vaisvil]]

			{{Scale gallery}}

	[[Category:Marvel]]		[[Category:Marvel]]
	[[Category:Listen]]		[[Category:Listen]]

Cmloegcmluin: add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group

2023-05-05T23:42:47Z

add unchanged-intervals along with eigenmonzo, per prior agreement on Xenwiki Work Group

← Older revision		Revision as of 23:42, 5 May 2023
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	== Math ==		== Math ==

	Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo]]s. This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [\|0 -4 4 4 4>, \|-21 6 -6 15 8>, \|7 -18 18 11 4>, \|-28 -4 4 32 4>, \|0 0 0 0 28>]/28. It leads to a tuning where the octave is sharp by \|-7 -1 1 1 1>/7 = (385/384)^(1/7), about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only \|-49 -26 -2 19 12>/28 = (385/384)^(3/7)/(225/224)^(1/4), about 0.0018 cents. Putting 10/3, 7/2, 11 and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 1-5/4-3/2-7/4-2, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.		Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as [[eigenmonzo]]s (unchanged-intervals). This gives three monzos with eigenvalue 1, and two with eigenvalue 0, allowing us to construct a projection matrix whose columns (or rows if you prefer) are fractional monzos, which defines the tuning. This matrix is [\|0 -4 4 4 4>, \|-21 6 -6 15 8>, \|7 -18 18 11 4>, \|-28 -4 4 32 4>, \|0 0 0 0 28>]/28. It leads to a tuning where the octave is sharp by \|-7 -1 1 1 1>/7 = (385/384)^(1/7), about 0.643 [[cent]]s. In this tuning, 9/5 and 12/7 are sharp by only \|-49 -26 -2 19 12>/28 = (385/384)^(3/7)/(225/224)^(1/4), about 0.0018 cents. Putting 10/3, 7/2, 11 and 9/5 together with 2 leads to the full 11-limit. This means every interval in the 11-limit tonality diamond is either pure, ±0.0018 cents from pure, or a certain number of octaves away from an interval which is within 0.0018 cents of pure. Because of this, the [[beat ratio]]s of everything in the [[11-limit diamond]] are closely approximated by small integer ratios. For instance, for every eight beats of the [[octave]] in the chord 1-5/4-3/2-7/4-2, the approximate [[5/4]] beats approximately 20 times, [[3/2]] 12 times, and [[7/4]] 7 times; the actual numbers being 8, 19.968, 11.977 and 6.997 respectively.

	== Scales ==		== Scales ==

Xenwolf: +cat

2020-06-08T19:50:29Z

+cat

← Older revision		Revision as of 19:50, 8 June 2020
Line 90:		Line 90:

	[[Category:Marvel]]		[[Category:Marvel]]
			[[Category:Listen]]

Xenwolf: re-added toc

2018-10-25T08:38:12Z

re-added toc

← Older revision		Revision as of 08:38, 25 October 2018
Line 4:		Line 4:

	The marvel woo [[tuning map]] is <1200.643223 1901.313567 2785.029055 3369.469129 4151.317943\|.		The marvel woo [[tuning map]] is <1200.643223 1901.313567 2785.029055 3369.469129 4151.317943\|.
			__TOC__
	== Math ==		== Math ==