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- Zeitler
- Katydyllic

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

Pitch Class Set | {0,1,2,3,6,7,9,11} |

Forte Number | 8-Z15 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3691 |

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 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 2767 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3431 | Zyptyllic | ||||

3rd mode: Scale 3763 | Modyllic | ||||

4th mode: Scale 3929 | Aeolothyllic | ||||

5th mode: Scale 1003 | Ionyryllic | ||||

6th mode: Scale 2549 | Rydyllic | ||||

7th mode: Scale 1661 | Gonyllic | ||||

8th mode: Scale 1439 | Rolyllic |

The prime form of this scale is Scale 863

Scale 863 | Pyryllic |

The octatonic modal family [2767, 3431, 3763, 3929, 1003, 2549, 1661, 1439] (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 2767 is 3691

Scale 3691 | Badyllic |

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

Scale 3691 | Badyllic |

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

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

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

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

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

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

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

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

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

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

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

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

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 2765 | Lydian Diminished | |||

Scale 2763 | Mela Suvarnangi | |||

Scale 2759 | Mela Pavani | |||

Scale 2775 | Godyllic | |||

Scale 2783 | Gothygic | |||

Scale 2799 | Lyryllian | |||

Scale 2703 | Galian | |||

Scale 2735 | Gynyllic | |||

Scale 2639 | Dothian | |||

Scale 2895 | Aeoryllic | |||

Scale 3023 | Mothygic | |||

Scale 2255 | Dylian | |||

Scale 2511 | Aeroptyllic | |||

Scale 3279 | Pythyllic | |||

Scale 3791 | Stodygic | |||

Scale 719 | Kanian | |||

Scale 1743 | Epigyllic |

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