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- Zeitler
- Katagyllian

Cardinality | 10 (decatonic) |
---|---|

Pitch Class Set | {0,1,2,4,5,6,8,9,10,11} |

Forte Number | 10-4 |

Rotational Symmetry | none |

Reflection Axes | 5 |

Palindromic | no |

Chirality | no |

Hemitonia | 8 (multihemitonic) |

Cohemitonia | 6 (multicohemitonic) |

Imperfections | 2 |

Modes | 9 |

Prime? | no prime: 1919 |

Deep Scale | no |

Interval Vector | 888984 |

Interval Spectrum | p^{8}m^{9}n^{8}s^{8}d^{8}t^{4} |

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

Spectra Variation | 1.2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [10] |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3959 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode: Scale 4027 | Ragyllian | ||||

3rd mode: Scale 4061 | Staptyllian | ||||

4th mode: Scale 2039 | Danyllian | ||||

5th mode: Scale 3067 | Goptyllian | ||||

6th mode: Scale 3581 | Epocryllian | ||||

7th mode: Scale 1919 | Rocryllian | This is the prime mode | |||

8th mode: Scale 3007 | Zyryllian | ||||

9th mode: Scale 3551 | Sagyllian | ||||

10th mode: Scale 3823 | Epinyllian |

The prime form of this scale is Scale 1919

Scale 1919 | Rocryllian |

The decatonic modal family [3959, 4027, 4061, 2039, 3067, 3581, 1919, 3007, 3551, 3823] (Forte: 10-4) is the complement of the modal family [17, 257] (Forte: 2-4)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3959 is 3551

Scale 3551 | Sagyllian |

T_{0} | 3959 | T_{0}I | 3551 | |||||

T_{1} | 3823 | T_{1}I | 3007 | |||||

T_{2} | 3551 | T_{2}I | 1919 | |||||

T_{3} | 3007 | T_{3}I | 3838 | |||||

T_{4} | 1919 | T_{4}I | 3581 | |||||

T_{5} | 3838 | T_{5}I | 3067 | |||||

T_{6} | 3581 | T_{6}I | 2039 | |||||

T_{7} | 3067 | T_{7}I | 4078 | |||||

T_{8} | 2039 | T_{8}I | 4061 | |||||

T_{9} | 4078 | T_{9}I | 4027 | |||||

T_{10} | 4061 | T_{10}I | 3959 | |||||

T_{11} | 4027 | T_{11}I | 3823 |

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 3957 | Porygic | |||

Scale 3955 | Pothygic | |||

Scale 3963 | Aeoryllian | |||

Scale 3967 | Soratic | |||

Scale 3943 | Zynygic | |||

Scale 3951 | Mathyllian | |||

Scale 3927 | Monygic | |||

Scale 3895 | Eparygic | |||

Scale 4023 | Styptyllian | |||

Scale 4087 | Aeolatic | |||

Scale 3703 | Katalygic | |||

Scale 3831 | Ionyllian | |||

Scale 3447 | Mogyllian | |||

Scale 2935 | Modygic | |||

Scale 1911 | Messiaen Mode 3 |

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