The Exciting Universe Of Music Theory

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- Zeitler
- Badygic

Cardinality | 9 (nonatonic) |
---|---|

Pitch Class Set | {0,1,2,4,7,8,9,10,11} |

Forte Number | 9-2 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3391 |

Hemitonia | 7 (multihemitonic) |

Cohemitonia | 6 (multicohemitonic) |

Imperfections | 3 |

Modes | 8 |

Prime? | no prime: 767 |

Deep Scale | no |

Interval Vector | 777663 |

Interval Spectrum | p^{6}m^{6}n^{7}s^{7}d^{7}t^{3} |

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

Spectra Variation | 2.444 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3991 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode: Scale 4043 | Phrocrygic | ||||

3rd mode: Scale 4069 | Starygic | ||||

4th mode: Scale 2041 | Aeolacrygic | ||||

5th mode: Scale 767 | Raptygic | This is the prime mode | |||

6th mode: Scale 2431 | Gythygic | ||||

7th mode: Scale 3263 | Pyrygic | ||||

8th mode: Scale 3679 | Rycrygic | ||||

9th mode: Scale 3887 | Phrathygic |

The prime form of this scale is Scale 767

Scale 767 | Raptygic |

The nonatonic modal family [3991, 4043, 4069, 2041, 767, 2431, 3263, 3679, 3887] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3991 is 3391

Scale 3391 | Aeolynygic |

Only scales that are chiral will have an enantiomorph. Scale 3991 is chiral, and its enantiomorph is scale 3391

Scale 3391 | Aeolynygic |

T_{0} | 3991 | T_{0}I | 3391 | |||||

T_{1} | 3887 | T_{1}I | 2687 | |||||

T_{2} | 3679 | T_{2}I | 1279 | |||||

T_{3} | 3263 | T_{3}I | 2558 | |||||

T_{4} | 2431 | T_{4}I | 1021 | |||||

T_{5} | 767 | T_{5}I | 2042 | |||||

T_{6} | 1534 | T_{6}I | 4084 | |||||

T_{7} | 3068 | T_{7}I | 4073 | |||||

T_{8} | 2041 | T_{8}I | 4051 | |||||

T_{9} | 4082 | T_{9}I | 4007 | |||||

T_{10} | 4069 | T_{10}I | 3919 | |||||

T_{11} | 4043 | T_{11}I | 3743 |

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 3989 | Sythyllic | |||

Scale 3987 | Loryllic | |||

Scale 3995 | Ionygic | |||

Scale 3999 | Dydyllian | |||

Scale 3975 | ||||

Scale 3983 | Thyptygic | |||

Scale 4007 | Doptygic | |||

Scale 4023 | Styptyllian | |||

Scale 4055 | Dagyllian | |||

Scale 3863 | Eparyllic | |||

Scale 3927 | Monygic | |||

Scale 3735 | ||||

Scale 3479 | Rothyllic | |||

Scale 2967 | Madyllic | |||

Scale 1943 |

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