# Marvel woo

**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 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 |