Marvel woo

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

• The Mysteries of Motivation (play MP3) in diam7plusmarvwoo by Chris Vaisvil

• Cave of Marvels by Herman Miller (2017)