The Exciting Universe Of Music Theory

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- Zeitler
- Aeogyllian

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

Pitch Class Set | {0,1,2,3,4,5,8,9,10,11} |

Forte Number | 10-1 |

Rotational Symmetry | none |

Reflection Axes | 0.5 |

Palindromic | no |

Chirality | no |

Hemitonia | 9 (multihemitonic) |

Cohemitonia | 8 (multicohemitonic) |

Imperfections | 2 |

Modes | 9 |

Prime? | no prime: 1023 |

Deep Scale | no |

Interval Vector | 988884 |

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

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

Spectra Variation | 1.8 |

Maximally Even | no |

Myhill Property | yes |

Balanced | no |

Ridge Tones | [1] |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3903 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode: Scale 3999 | Dydyllian | ||||

3rd mode: Scale 4047 | Thogyllian | ||||

4th mode: Scale 4071 | Rygyllian | ||||

5th mode: Scale 4083 | Bathyllian | ||||

6th mode: Scale 4089 | Katoryllian | ||||

7th mode: Scale 1023 | Dodyllian | This is the prime mode | |||

8th mode: Scale 2559 | Zogyllian | ||||

9th mode: Scale 3327 | Madyllian | ||||

10th mode: Scale 3711 | Dycryllian |

The prime form of this scale is Scale 1023

Scale 1023 | Dodyllian |

The decatonic modal family [3903, 3999, 4047, 4071, 4083, 4089, 1023, 2559, 3327, 3711] (Forte: 10-1) is the complement of the modal family [3, 2049] (Forte: 2-1)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3903 is 3999

Scale 3999 | Dydyllian |

T_{0} | 3903 | T_{0}I | 3999 | |||||

T_{1} | 3711 | T_{1}I | 3903 | |||||

T_{2} | 3327 | T_{2}I | 3711 | |||||

T_{3} | 2559 | T_{3}I | 3327 | |||||

T_{4} | 1023 | T_{4}I | 2559 | |||||

T_{5} | 2046 | T_{5}I | 1023 | |||||

T_{6} | 4092 | T_{6}I | 2046 | |||||

T_{7} | 4089 | T_{7}I | 4092 | |||||

T_{8} | 4083 | T_{8}I | 4089 | |||||

T_{9} | 4071 | T_{9}I | 4083 | |||||

T_{10} | 4047 | T_{10}I | 4071 | |||||

T_{11} | 3999 | T_{11}I | 4047 |

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 3901 | Bycrygic | |||

Scale 3899 | Katorygic | |||

Scale 3895 | Eparygic | |||

Scale 3887 | Phrathygic | |||

Scale 3871 | Aerynygic | |||

Scale 3935 | Kataphyllian | |||

Scale 3967 | Soratic | |||

Scale 4031 | Godatic | |||

Scale 3647 | Eporygic | |||

Scale 3775 | Loptyllian | |||

Scale 3391 | Aeolynygic | |||

Scale 2879 | Stadygic | |||

Scale 1855 | Gaptygic |

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