Xenharmonic Wiki

Marvel woo: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>FREEZE
No edit summary
ArrowHead294 (talk | contribs)
14,512 edits
mNo edit summary
 
(11 intermediate revisions by 5 users not shown)
Line 1: Line 1:
[[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|undecimal marvel]] which is optimized for synchronized [[beat]]ing, and which also happens to be very close to the [[TE tuning]] for marvel.


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


=Math=
== Scales ==
{| 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]]
|}


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&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 cents. 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 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..
== 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]]


=7 notes=
* [https://soundcloud.com/morphosyntax-1/cave-of-marvels Cave of Marvels] by [[Herman Miller]] (2017)
[[max7amarvwoo|max7amarvwoo]]


=12 notes=
{{Navbox scale gallery}}
[[genus1125marvwoo|genus1125marvwoo]]


[[duohexmarvwoo|duohexmarvwoo]]
[[Category:Marvel]]
 
[[Category:Listen]]
[[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]]
 
=24 notes=
[[bimarveldenewoo|bimarveldenewoo]]
 
=Music=
[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]
Retrieved from "https://en.xen.wiki/w/Marvel_woo"