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
- Manyllic

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

Pitch Class Set | {0,2,3,4,5,7,8,11} |

Forte Number | 8-17 |

Rotational Symmetry | none |

Reflection Axes | 3.5 |

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 | [7] |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 2493 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 1647 | Polyllic | ||||

3rd mode: Scale 2871 | Stanyllic | ||||

4th mode: Scale 3483 | Mixotharyllic | ||||

5th mode: Scale 3789 | Eporyllic | ||||

6th mode: Scale 1971 | Aerynyllic | ||||

7th mode: Scale 3033 | Doptyllic | ||||

8th mode: Scale 891 | Ionilyllic | This is the prime mode |

The prime form of this scale is Scale 891

Scale 891 | Ionilyllic |

The octatonic modal family [2493, 1647, 2871, 3483, 3789, 1971, 3033, 891] (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 2493 is 1971

Scale 1971 | Aerynyllic |

T_{0} | 2493 | T_{0}I | 1971 | |||||

T_{1} | 891 | T_{1}I | 3942 | |||||

T_{2} | 1782 | T_{2}I | 3789 | |||||

T_{3} | 3564 | T_{3}I | 3483 | |||||

T_{4} | 3033 | T_{4}I | 2871 | |||||

T_{5} | 1971 | T_{5}I | 1647 | |||||

T_{6} | 3942 | T_{6}I | 3294 | |||||

T_{7} | 3789 | T_{7}I | 2493 | |||||

T_{8} | 3483 | T_{8}I | 891 | |||||

T_{9} | 2871 | T_{9}I | 1782 | |||||

T_{10} | 1647 | T_{10}I | 3564 | |||||

T_{11} | 3294 | T_{11}I | 3033 |

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 2495 | Aeolocrygic | |||

Scale 2489 | Mela Gangeyabhusani | |||

Scale 2491 | Layllic | |||

Scale 2485 | Harmonic Major | |||

Scale 2477 | Harmonic Minor | |||

Scale 2461 | Sagian | |||

Scale 2525 | Aeolaryllic | |||

Scale 2557 | Dothygic | |||

Scale 2365 | Sythian | |||

Scale 2429 | Kadyllic | |||

Scale 2237 | Epothian | |||

Scale 2749 | Katagyllic | |||

Scale 3005 | Gycrygic | |||

Scale 3517 | Epocrygic | |||

Scale 445 | Gocrian | |||

Scale 1469 | Epiryllic |

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.