Marvel woo: Difference between revisions
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'''Marvel woo''' is a particular tuning of | '''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 {{val| 1200.643223 1901.313567 2785.029055 3369.469129 4151.317943 }}. | |||
The marvel woo [[tuning map]] is | |||
__TOC__ | __TOC__ | ||
== Math == | == 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]] | |||
== Scales == | == Scales == | ||
{| class="sortable wikitable" | {| class="sortable wikitable" | ||
|- | |||
! Size | ! Size | ||
! Name | ! Name | ||
| Line 88: | Line 85: | ||
== 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) | |||
{{Navbox scale gallery}} | |||
[[Category:Marvel]] | [[Category:Marvel]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
Latest revision as of 20:09, 11 February 2025
Marvel woo is a particular tuning of undecimal marvel which is optimized for synchronized beating, 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].
Math
Marvel woo is the marvel tuning with 10/3, 7/2 and 11 as 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 [[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 (385/384)1/7, about 0.643 cents. In this tuning, 9/5 and 12/7 are sharp by only (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 ratios 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
| 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
- Cave of Marvels by Herman Miller (2017)
| View • Talk • EditScale galleries | |
|---|---|
| JI scales | 12-tone JI scales • Combination product sets • CS scales • Maximal harmony epimorphic scales • MOS transversals • Non-octave JI scales • Wakalixes • Z-polygon transversals • Other JI scales Full list: Category:Just intonation scales |
| Tempered scales | 12-tone tempered scales • Clippers • Essentially tempered scales • Marvel woo scales • MOS cradle scales • Non-octave tempered scales • Scalesmith systematic scales • Other tempered scales Full list: Category:Tempered scales |
| ET subsets | 11edo modes, 19edo modes, 22edo modes, 24edo scales, 31edo modes |
All other scale gallery pages are included in Category:Lists of scales | |