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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.

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
- Lygyllic

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

Pitch Class Set | {0,1,3,4,6,7,10,11} |

Forte Number | 8-18 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2919 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 879 |

Deep Scale | no |

Interval Vector | 546553 |

Interval Spectrum | p^{5}m^{5}n^{6}s^{4}d^{5}t^{3} |

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

Spectra Variation | 2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3291 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3693 | Stadyllic | ||||

3rd mode: Scale 1947 | Byptyllic | ||||

4th mode: Scale 3021 | Stodyllic | ||||

5th mode: Scale 1779 | Zynyllic | ||||

6th mode: Scale 2937 | Phragyllic | ||||

7th mode: Scale 879 | Aeranyllic | This is the prime mode | |||

8th mode: Scale 2487 | Dothyllic |

The prime form of this scale is Scale 879

Scale 879 | Aeranyllic |

The octatonic modal family [3291, 3693, 1947, 3021, 1779, 2937, 879, 2487] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3291 is 2919

Scale 2919 | Molyllic |

Only scales that are chiral will have an enantiomorph. Scale 3291 is chiral, and its enantiomorph is scale 2919

Scale 2919 | Molyllic |

T_{0} | 3291 | T_{0}I | 2919 | |||||

T_{1} | 2487 | T_{1}I | 1743 | |||||

T_{2} | 879 | T_{2}I | 3486 | |||||

T_{3} | 1758 | T_{3}I | 2877 | |||||

T_{4} | 3516 | T_{4}I | 1659 | |||||

T_{5} | 2937 | T_{5}I | 3318 | |||||

T_{6} | 1779 | T_{6}I | 2541 | |||||

T_{7} | 3558 | T_{7}I | 987 | |||||

T_{8} | 3021 | T_{8}I | 1974 | |||||

T_{9} | 1947 | T_{9}I | 3948 | |||||

T_{10} | 3894 | T_{10}I | 3801 | |||||

T_{11} | 3693 | T_{11}I | 3507 |

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 3289 | Lydian Sharp 2 Sharp 6 | |||

Scale 3293 | Saryllic | |||

Scale 3295 | Phroptygic | |||

Scale 3283 | Mela Visvambhari | |||

Scale 3287 | Phrathyllic | |||

Scale 3275 | Mela Divyamani | |||

Scale 3307 | Boptyllic | |||

Scale 3323 | Lacrygic | |||

Scale 3227 | Aeolocrian | |||

Scale 3259 | ||||

Scale 3163 | Rogian | |||

Scale 3419 | Magen Abot 1 | |||

Scale 3547 | Sadygic | |||

Scale 3803 | Epidygic | |||

Scale 2267 | Padian | |||

Scale 2779 | Shostakovich | |||

Scale 1243 | Epylian |

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. Bibliography