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The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks *imperfect* tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

- Zeitler
- Badyllic

Cardinality | 8 (octatonic) |
---|---|

Pitch Class Set | {0,1,3,5,6,9,10,11} |

Forte Number | 8-Z15 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2767 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 863 |

Deep Scale | no |

Interval Vector | 555553 |

Interval Spectrum | p^{5}m^{5}n^{5}s^{5}d^{5}t^{3} |

Distribution Spectra | <1> = {1,2,3} <2> = {2,3,4} <3> = {3,4,5,6} <4> = {4,5,6,7,8} <5> = {6,7,8,9} <6> = {8,9,10} <7> = {9,10,11} |

Spectra Variation | 2.25 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.616 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3691 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3893 | Phrocryllic | ||||

3rd mode: Scale 1997 | Raga Cintamani | ||||

4th mode: Scale 1523 | Zothyllic | ||||

5th mode: Scale 2809 | Gythyllic | ||||

6th mode: Scale 863 | Pyryllic | This is the prime mode | |||

7th mode: Scale 2479 | Harmonic and Neapolitan Minor Mixed | ||||

8th mode: Scale 3287 | Phrathyllic |

The prime form of this scale is Scale 863

Scale 863 | Pyryllic |

The octatonic modal family [3691, 3893, 1997, 1523, 2809, 863, 2479, 3287] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3691 is 2767

Scale 2767 | Katydyllic |

Only scales that are chiral will have an enantiomorph. Scale 3691 is chiral, and its enantiomorph is scale 2767

Scale 2767 | Katydyllic |

T_{0} | 3691 | T_{0}I | 2767 | |||||

T_{1} | 3287 | T_{1}I | 1439 | |||||

T_{2} | 2479 | T_{2}I | 2878 | |||||

T_{3} | 863 | T_{3}I | 1661 | |||||

T_{4} | 1726 | T_{4}I | 3322 | |||||

T_{5} | 3452 | T_{5}I | 2549 | |||||

T_{6} | 2809 | T_{6}I | 1003 | |||||

T_{7} | 1523 | T_{7}I | 2006 | |||||

T_{8} | 3046 | T_{8}I | 4012 | |||||

T_{9} | 1997 | T_{9}I | 3929 | |||||

T_{10} | 3994 | T_{10}I | 3763 | |||||

T_{11} | 3893 | T_{11}I | 3431 |

These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone.

Scale 3689 | Katocrian | |||

Scale 3693 | Stadyllic | |||

Scale 3695 | Kodygic | |||

Scale 3683 | Dycrian | |||

Scale 3687 | Zonyllic | |||

Scale 3699 | Galyllic | |||

Scale 3707 | Rynygic | |||

Scale 3659 | Polian | |||

Scale 3675 | Monyllic | |||

Scale 3627 | Kalian | |||

Scale 3755 | Phryryllic | |||

Scale 3819 | Aeolanygic | |||

Scale 3947 | Ryptygic | |||

Scale 3179 | Daptian | |||

Scale 3435 | Prokofiev | |||

Scale 2667 | Byrian | |||

Scale 1643 | Locrian Natural 6 |

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.