The Exciting Universe Of Music Theory

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- Zeitler
- Loptyllian

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

Pitch Class Set | {0,1,2,3,4,5,7,9,10,11} |

Forte Number | 10-2 |

Rotational Symmetry | none |

Reflection Axes | 1 |

Palindromic | no |

Chirality | no |

Hemitonia | 8 (multihemitonic) |

Cohemitonia | 7 (multicohemitonic) |

Imperfections | 2 |

Modes | 9 |

Prime? | no prime: 1535 |

Deep Scale | no |

Interval Vector | 898884 |

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

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

Spectra Variation | 1.6 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [2] |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3775 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode: Scale 3935 | Kataphyllian | ||||

3rd mode: Scale 4015 | Phradyllian | ||||

4th mode: Scale 4055 | Dagyllian | ||||

5th mode: Scale 4075 | Katyllian | ||||

6th mode: Scale 4085 | Sydyllian | ||||

7th mode: Scale 2045 | Katogyllian | ||||

8th mode: Scale 1535 | Mixodyllian | This is the prime mode | |||

9th mode: Scale 2815 | Aeradyllian | ||||

10th mode: Scale 3455 | Ryptyllian |

The prime form of this scale is Scale 1535

Scale 1535 | Mixodyllian |

The decatonic modal family [3775, 3935, 4015, 4055, 4075, 4085, 2045, 1535, 2815, 3455] (Forte: 10-2) is the complement of the modal family [5, 1025] (Forte: 2-2)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3775 is 4015

Scale 4015 | Phradyllian |

T_{0} | 3775 | T_{0}I | 4015 | |||||

T_{1} | 3455 | T_{1}I | 3935 | |||||

T_{2} | 2815 | T_{2}I | 3775 | |||||

T_{3} | 1535 | T_{3}I | 3455 | |||||

T_{4} | 3070 | T_{4}I | 2815 | |||||

T_{5} | 2045 | T_{5}I | 1535 | |||||

T_{6} | 4090 | T_{6}I | 3070 | |||||

T_{7} | 4085 | T_{7}I | 2045 | |||||

T_{8} | 4075 | T_{8}I | 4090 | |||||

T_{9} | 4055 | T_{9}I | 4085 | |||||

T_{10} | 4015 | T_{10}I | 4075 | |||||

T_{11} | 3935 | T_{11}I | 4055 |

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 3773 | Raga Malgunji | |||

Scale 3771 | Katodyllian | |||

Scale 3767 | Chromatic Bebop | |||

Scale 3759 | Darygic | |||

Scale 3743 | Thadygic | |||

Scale 3807 | Bagyllian | |||

Scale 3839 | Mixolatic | |||

Scale 3647 | Eporygic | |||

Scale 3711 | Dycryllian | |||

Scale 3903 | Aeogyllian | |||

Scale 4031 | Godatic | |||

Scale 3263 | Pyrygic | |||

Scale 3519 | Raga Sindhi-Bhairavi | |||

Scale 2751 | Sylygic | |||

Scale 1727 | Sydygic |

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