The Exciting Universe Of Music Theory

presents

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- Zeitler
- Gonyllic

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

Pitch Class Set | {0,2,3,4,5,6,9,10} |

Forte Number | 8-Z15 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1997 |

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 1661 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 1439 | Rolyllic | ||||

3rd mode: Scale 2767 | Katydyllic | ||||

4th mode: Scale 3431 | Zyptyllic | ||||

5th mode: Scale 3763 | Modyllic | ||||

6th mode: Scale 3929 | Aeolothyllic | ||||

7th mode: Scale 1003 | Ionyryllic | ||||

8th mode: Scale 2549 | Rydyllic |

The prime form of this scale is Scale 863

Scale 863 | Pyryllic |

The octatonic modal family [1661, 1439, 2767, 3431, 3763, 3929, 1003, 2549] (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 1661 is 1997

Scale 1997 | Raga Cintamani |

Only scales that are chiral will have an enantiomorph. Scale 1661 is chiral, and its enantiomorph is scale 1997

Scale 1997 | Raga Cintamani |

T_{0} | 1661 | T_{0}I | 1997 | |||||

T_{1} | 3322 | T_{1}I | 3994 | |||||

T_{2} | 2549 | T_{2}I | 3893 | |||||

T_{3} | 1003 | T_{3}I | 3691 | |||||

T_{4} | 2006 | T_{4}I | 3287 | |||||

T_{5} | 4012 | T_{5}I | 2479 | |||||

T_{6} | 3929 | T_{6}I | 863 | |||||

T_{7} | 3763 | T_{7}I | 1726 | |||||

T_{8} | 3431 | T_{8}I | 3452 | |||||

T_{9} | 2767 | T_{9}I | 2809 | |||||

T_{10} | 1439 | T_{10}I | 1523 | |||||

T_{11} | 2878 | T_{11}I | 3046 |

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 1663 | Lydygic | |||

Scale 1657 | Ionothian | |||

Scale 1659 | Maqam Shadd'araban | |||

Scale 1653 | Minor Romani Inverse | |||

Scale 1645 | Dorian Flat 5 | |||

Scale 1629 | Synian | |||

Scale 1597 | Aeolodian | |||

Scale 1725 | Minor Bebop | |||

Scale 1789 | Blues Enneatonic II | |||

Scale 1917 | Thydyllian | |||

Scale 1149 | Bydian | |||

Scale 1405 | Goryllic | |||

Scale 637 | Debussy's Heptatonic | |||

Scale 2685 | Ionoryllic | |||

Scale 3709 | Katynygic |

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