The Exciting Universe Of Music Theory

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The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks *imperfect* tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

- Zeitler
- Eporyllic

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

Pitch Class Set | {0,2,3,6,7,9,10,11} |

Forte Number | 8-17 |

Rotational Symmetry | none |

Reflection Axes | 4.5 |

Palindromic | no |

Chirality | no |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 891 |

Deep Scale | no |

Interval Vector | 546652 |

Interval Spectrum | p^{5}m^{6}n^{6}s^{4}d^{5}t^{2} |

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

Spectra Variation | 2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [9] |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3789 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 1971 | Aerynyllic | ||||

3rd mode: Scale 3033 | Doptyllic | ||||

4th mode: Scale 891 | Ionilyllic | This is the prime mode | |||

5th mode: Scale 2493 | Manyllic | ||||

6th mode: Scale 1647 | Polyllic | ||||

7th mode: Scale 2871 | Stanyllic | ||||

8th mode: Scale 3483 | Mixotharyllic |

The prime form of this scale is Scale 891

Scale 891 | Ionilyllic |

The octatonic modal family [3789, 1971, 3033, 891, 2493, 1647, 2871, 3483] (Forte: 8-17) is the complement of the tetratonic modal family [153, 531, 801, 2313] (Forte: 4-17)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3789 is 1647

Scale 1647 | Polyllic |

T_{0} | 3789 | T_{0}I | 1647 | |||||

T_{1} | 3483 | T_{1}I | 3294 | |||||

T_{2} | 2871 | T_{2}I | 2493 | |||||

T_{3} | 1647 | T_{3}I | 891 | |||||

T_{4} | 3294 | T_{4}I | 1782 | |||||

T_{5} | 2493 | T_{5}I | 3564 | |||||

T_{6} | 891 | T_{6}I | 3033 | |||||

T_{7} | 1782 | T_{7}I | 1971 | |||||

T_{8} | 3564 | T_{8}I | 3942 | |||||

T_{9} | 3033 | T_{9}I | 3789 | |||||

T_{10} | 1971 | T_{10}I | 3483 | |||||

T_{11} | 3942 | T_{11}I | 2871 |

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 3791 | Stodygic | |||

Scale 3785 | Epagian | |||

Scale 3787 | Kagyllic | |||

Scale 3781 | Gyphian | |||

Scale 3797 | Rocryllic | |||

Scale 3805 | Moptygic | |||

Scale 3821 | Epyrygic | |||

Scale 3725 | Kyrian | |||

Scale 3757 | Raga Mian Ki Malhar | |||

Scale 3661 | Mixodorian | |||

Scale 3917 | Katoptyllic | |||

Scale 4045 | Gyptygic | |||

Scale 3277 | Mela Nitimati | |||

Scale 3533 | Thadyllic | |||

Scale 2765 | Lydian Diminished | |||

Scale 1741 | Lydian Diminished |

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. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org). Peruse this Bibliography.