# 11edt

Jump to navigation
Jump to search
Prime factorization
11 (prime)
Step size
172.905¢
Octave
7\11edt (1210.34¢)

(semiconvergent)
Consistency limit
5
Distinct consistency limit
4

← 10edt | 11edt | 12edt → |

(semiconvergent)

11edt means the division of 3, the tritave, into 11 equal parts of 175.905 cents each, corresponding to 6.940 edo. It can therefore be seen as a very stretched version of 7edo, with octaves sharpened by ten and a third cents. The octave stretching makes the fifth in better tune, and of course the twelfth is the pure 3/1 tritave.

From a no-two point of view, it tempers out 49/45 and 15625/15309 in the 7-limit and 35/33 and 77/75 in the 11-limit.

## Intervals

# | Cents | Hekts | Approximate ratios | Arcturus nonatonic notation (J = 1/1) |
---|---|---|---|---|

0 | 1/1 | J | ||

1 | 172.9 | 118.1 | 11/10, 10/9 | J#, Kb |

2 | 345.8 | 236.2 | 11/9 | K |

3 | 518.7 | 354.3 | 4/3, 27/20 | L |

4 | 691.6 | 472.4 | 3/2, 40/27 | M |

5 | 864.5 | 590.5 | 5/3, 28/17, 105/64 | N |

6 | 1037.4 | 708.6 | 29/16, 20/11, 64/35 | N#, Ob |

7 | 1210.3 | 826.7 | 2/1 | O |

8 | 1383.2 | 944.8 | P | |

9 | 1556.1 | 1062.9 | Q | |

10 | 1729 | 1181 | R | |

11 | 1902 | 1300 | J |

## Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +10.3 | +0.0 | -19.8 | -83.6 | -1.6 | +55.0 | -63.6 | -83.3 | -68.2 | +49.2 | -66.3 |

relative (%) | +6 | +0 | -11 | -48 | -1 | +32 | -37 | -48 | -39 | +28 | -38 | |

Steps (reduced) |
7 (7) |
11 (0) |
16 (5) |
19 (8) |
24 (2) |
26 (4) |
28 (6) |
29 (7) |
31 (9) |
34 (1) |
34 (1) |

## Scala file

Tuning in scala format is as follows:

! E:\cakewalk\scales\11_of_tritave.scl ! 11 in tritave ! 172.90500 345.81000 518.71500 691.62000 864.52500 1037.43000 1210.33500 1383.24000 1556.14500 1729.05000 3/1

## Pieces

Mozart's sonata #11 in A Major K331 in 11 EDT (using a 11 => 12 key mapping so octaves become tritaves)

Frozen Time Occupies Wall Street by Chris Vaisvil =>information about the piece

Molly's Playground by Chris Vaisvil => information about the piece