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- Zeitler
- Zyptyllic

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

Pitch Class Set | {0,1,2,5,6,8,10,11} |

Forte Number | 8-Z15 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3287 |

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 3431 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3763 | Modyllic | ||||

3rd mode: Scale 3929 | Aeolothyllic | ||||

4th mode: Scale 1003 | Ionyryllic | ||||

5th mode: Scale 2549 | Rydyllic | ||||

6th mode: Scale 1661 | Gonyllic | ||||

7th mode: Scale 1439 | Rolyllic | ||||

8th mode: Scale 2767 | Katydyllic |

The prime form of this scale is Scale 863

Scale 863 | Pyryllic |

The octatonic modal family [3431, 3763, 3929, 1003, 2549, 1661, 1439, 2767] (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 3431 is 3287

Scale 3287 | Phrathyllic |

Only scales that are chiral will have an enantiomorph. Scale 3431 is chiral, and its enantiomorph is scale 3287

Scale 3287 | Phrathyllic |

T_{0} | 3431 | T_{0}I | 3287 | |||||

T_{1} | 2767 | T_{1}I | 2479 | |||||

T_{2} | 1439 | T_{2}I | 863 | |||||

T_{3} | 2878 | T_{3}I | 1726 | |||||

T_{4} | 1661 | T_{4}I | 3452 | |||||

T_{5} | 3322 | T_{5}I | 2809 | |||||

T_{6} | 2549 | T_{6}I | 1523 | |||||

T_{7} | 1003 | T_{7}I | 3046 | |||||

T_{8} | 2006 | T_{8}I | 1997 | |||||

T_{9} | 4012 | T_{9}I | 3994 | |||||

T_{10} | 3929 | T_{10}I | 3893 | |||||

T_{11} | 3763 | T_{11}I | 3691 |

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 3429 | Marian | |||

Scale 3427 | Zacrian | |||

Scale 3435 | Prokofiev | |||

Scale 3439 | Lythygic | |||

Scale 3447 | Mogyllian | |||

Scale 3399 | Zonian | |||

Scale 3415 | Ionaptyllic | |||

Scale 3367 | Moptian | |||

Scale 3495 | Banyllic | |||

Scale 3559 | Thophygic | |||

Scale 3175 | Eponian | |||

Scale 3303 | Mylyllic | |||

Scale 3687 | Zonyllic | |||

Scale 3943 | Zynygic | |||

Scale 2407 | Zylian | |||

Scale 2919 | Molyllic | |||

Scale 1383 | Pynian |

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