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.

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
- Polyllic

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

Pitch Class Set | {0,1,2,3,5,6,9,10} |

Forte Number | 8-17 |

Rotational Symmetry | none |

Reflection Axes | 1.5 |

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 | [3] |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1647 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 2871 | Stanyllic | ||||

3rd mode: Scale 3483 | Mixotharyllic | ||||

4th mode: Scale 3789 | Eporyllic | ||||

5th mode: Scale 1971 | Aerynyllic | ||||

6th mode: Scale 3033 | Doptyllic | ||||

7th mode: Scale 891 | Ionilyllic | This is the prime mode | |||

8th mode: Scale 2493 | Manyllic |

The prime form of this scale is Scale 891

Scale 891 | Ionilyllic |

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

Scale 3789 | Eporyllic |

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

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

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

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

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

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

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

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

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

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

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

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

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 1645 | Dorian Flat 5 | |||

Scale 1643 | Locrian Natural 6 | |||

Scale 1639 | Aeolothian | |||

Scale 1655 | Katygyllic | |||

Scale 1663 | Lydygic | |||

Scale 1615 | Sydian | |||

Scale 1631 | Rynyllic | |||

Scale 1583 | Salian | |||

Scale 1711 | Adonai Malakh | |||

Scale 1775 | Lyrygic | |||

Scale 1903 | Rocrygic | |||

Scale 1135 | Katolian | |||

Scale 1391 | Aeradyllic | |||

Scale 623 | Sycrian | |||

Scale 2671 | Aerolyllic | |||

Scale 3695 | Kodygic |

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