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]]. | [[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 | 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 | |||
== Scales == | == Scales == | ||
{| class="sortable wikitable" | {| class="sortable wikitable" | ||
|- | |||
! Size | ! Size | ||
! Name | ! Name | ||
Revision as of 18:34, 9 January 2025
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 (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 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 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)