Marvel woo

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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 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