Marvel woo: Difference between revisions

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[[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|385/384]]. Marvel woo is a particular tuning of Marvel which is optimized for synchronized beating, 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 which is optimized for synchronized beating, and which also happens to be very close to the [[Tenney-Euclidean_Tuning|TE tuning]] for Marvel.


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


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


Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as eigenmonzos. 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 cents. 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 ratios 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 19.968, 11.977, 6.997 and 8 respectively..
Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as eigenmonzos. 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 cents. 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 ratios 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 19.968, 11.977, 6.997 and 8 respectively..


=7 notes=
== Scales ==
[[max7amarvwoo|max7amarvwoo]]
 
=12 notes=
[[genus1125marvwoo|genus1125marvwoo]]
 
[[duohexmarvwoo|duohexmarvwoo]]
 
[[bluesmarvwoo|bluesmarvwoo]]
 
[[dwarf12_11marvwoo|dwarf12_11marvwoo]]
 
[[glummamarvwoo|glummamarvwoo]]
 
[[tertiadie3marvwoo|tertiadie3marvwoo]]
 
[[sixtetwoo|sixtetwoo]]
 
=14 notes=
[[pum14marvwoo|pum14marvwoo]]
 
=15 notes=
[[pummelmarvwoo|pummelmarvwoo]]
 
[[dwarf15marvwoo|dwarf15marvwoo]]
 
[[dekanymarvwoo|dekanymarvwoo]]
 
[[genus5625marvwoo|genus5625marvwoo]]
 
=16 notes=
[[stellarhexmarvwoo|stellarhexmarvwoo]]
 
=17 notes=
[[diam7plusmarvwoo|diam7plusmarvwoo]]
 
[[dwarf17marvwoo|dwarf17marvwoo]]
 
[[elf17marvwoo|elf17marvwoo]]
 
[[diamond_chess11marvwoo|diamond_chess11marvwoo]]
 
[[rectsp6amarvwoo|rectsp6amarvwoo]]
 
[[chalmers_17marvwoo|chalmers_17marvwoo]]
 
[[genus3375plusmarvwoo|genus3375plusmarvwoo]]
 
=18 notes=
[[genus28125marvwoo|genus28125marvwoo]]
 
=19 notes=
[[marvel19woo|marvel19woo]]
 
=20 notes=
[[genus16875marvwoo|genus16875marvwoo]]
 
=21 notes=
[[dcon9marvwoo|dcon9marvwoo]]
 
[[blackwoo|blackwoo]]
 
=22 notes=
[[marvel22woo|marvel22woo]]


[[marvel22_11woo|marvel22_11woo]]
{| class="sortable wikitable"
! Size
! Name
|-
| 7 notes
| [[max7amarvwoo]]
|-
| rowspan="7" | 12 notes
| [[genus1125marvwoo]]
|-
| [[duohexmarvwoo]]
|-
| [[bluesmarvwoo]]
|-
| [[dwarf12_11marvwoo]]
|-
| [[glummamarvwoo]]
|-
| [[tertiadie3marvwoo]]
|-
| [[sixtetwoo|sixtetwoo]]
|-
| 14 notes
| [[pum14marvwoo]]
|-
| rowspan="4" | 15 notes
| [[pummelmarvwoo]]
|-
| [[dwarf15marvwoo]]
|-
| [[dekanymarvwoo]]
|-
| [[genus5625marvwoo]]
|-
| 16 notes
| [[stellarhexmarvwoo]]
|-
| rowspan="7" | 17 notes
| [[diam7plusmarvwoo]]
|-
| [[dwarf17marvwoo]]
|-
| [[elf17marvwoo]]
|-
| [[diamond_chess11marvwoo]]
|-
| [[rectsp6amarvwoo]]
|-
| [[chalmers_17marvwoo]]
|-
| [[genus3375plusmarvwoo]]
|-
| 18 notes
| [[genus28125marvwoo]]
|-
| 19 notes
| [[marvel19woo]]
|-
| 20 notes
| [[genus16875marvwoo]]
|-
| rowspan="2" | 21 notes
| [[dcon9marvwoo]]
|-
| [[blackwoo]]
|-
| rowspan="2" | 22 notes
| [[marvel22woo]]
|-
| [[marvel22_11woo]]
|-
| 24 notes
| [[bimarveldenewoo]]
|}


=24 notes=
== Music ==
[[bimarveldenewoo|bimarveldenewoo]]
* [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]]


=Music=
[[Category:Marvel]]
[http://micro.soonlabel.com/marvel/20140425_diam7_plus_woo.mp3 The Mysteries of Motivation] in diam7plusmarvwoo by [http://chrisvaisvil.com/the-mysteries-of-motivation-piano-tuned-to-marvel-woo/ Chris Vaisvil]

Revision as of 08:15, 25 October 2018

Marvel woo is a particular tuning of Marvel which is optimized for synchronized beating, and which also happens to be very close to the TE tuning for Marvel.

Marvel is the rank-3 temperament tempering out 225/224, the 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|.

Math

Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as eigenmonzos. 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 cents. 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 ratios 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 19.968, 11.977, 6.997 and 8 respectively..

Scales

Size Name
7 notes max7amarvwoo
12 notes genus1125marvwoo
duohexmarvwoo
bluesmarvwoo
dwarf12_11marvwoo
glummamarvwoo
tertiadie3marvwoo
sixtetwoo
14 notes pum14marvwoo
15 notes pummelmarvwoo
dwarf15marvwoo
dekanymarvwoo
genus5625marvwoo
16 notes stellarhexmarvwoo
17 notes diam7plusmarvwoo
dwarf17marvwoo
elf17marvwoo
diamond_chess11marvwoo
rectsp6amarvwoo
chalmers_17marvwoo
genus3375plusmarvwoo
18 notes genus28125marvwoo
19 notes marvel19woo
20 notes genus16875marvwoo
21 notes dcon9marvwoo
blackwoo
22 notes marvel22woo
marvel22_11woo
24 notes bimarveldenewoo

Music

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