Marvel woo: Difference between revisions

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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 ~~<~~1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|.

__TOC__

== Math ==

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)1/7}}, 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)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-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.

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 ==

{| class="sortable wikitable"

|-

! Size

! Name

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* [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)

[[Category:Marvel]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
-'''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 &lt;1200.643223 1901.313567 2785.029055 3369.469129 4151.317943|.
 __TOC__
 == Math ==
+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.
-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&gt;, |-21 6 -6 15 8&gt;, |7 -18 18 11 4&gt;, |-28 -4 4 32 4&gt;, |0 0 0 0 28&gt;]/28. It leads to a tuning where the octave is sharp by |-7 -1 1 1 1&gt;/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&gt;/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 ==
 {| class="sortable wikitable"
+|-
 ! Size
 ! Name
@@ Line 89: / Line 86: @@
 * [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}}
+* [https://soundcloud.com/morphosyntax-1/cave-of-marvels Cave of Marvels] by [[Herman Miller]] (2017)
+{{Navbox scale gallery}}
 [[Category:Marvel]]
 [[Category:Listen]]