The Exciting Universe Of Music Theory

presents

more than you ever wanted to know about...

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
- Stanyllic

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

Pitch Class Set | {0,1,2,4,5,8,9,11} |

Forte Number | 8-17 |

Rotational Symmetry | none |

Reflection Axes | 0.5 |

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 | [1] |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 2871 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3483 | Mixotharyllic | ||||

3rd mode: Scale 3789 | Eporyllic | ||||

4th mode: Scale 1971 | Aerynyllic | ||||

5th mode: Scale 3033 | Doptyllic | ||||

6th mode: Scale 891 | Ionilyllic | This is the prime mode | |||

7th mode: Scale 2493 | Manyllic | ||||

8th mode: Scale 1647 | Polyllic |

The prime form of this scale is Scale 891

Scale 891 | Ionilyllic |

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

Scale 3483 | Mixotharyllic |

T_{0} | 2871 | T_{0}I | 3483 | |||||

T_{1} | 1647 | T_{1}I | 2871 | |||||

T_{2} | 3294 | T_{2}I | 1647 | |||||

T_{3} | 2493 | T_{3}I | 3294 | |||||

T_{4} | 891 | T_{4}I | 2493 | |||||

T_{5} | 1782 | T_{5}I | 891 | |||||

T_{6} | 3564 | T_{6}I | 1782 | |||||

T_{7} | 3033 | T_{7}I | 3564 | |||||

T_{8} | 1971 | T_{8}I | 3033 | |||||

T_{9} | 3942 | T_{9}I | 1971 | |||||

T_{10} | 3789 | T_{10}I | 3942 | |||||

T_{11} | 3483 | T_{11}I | 3789 |

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 2869 | Ionian Augmented | |||

Scale 2867 | Socrian | |||

Scale 2875 | Ganyllic | |||

Scale 2879 | Stadygic | |||

Scale 2855 | Epocrain | |||

Scale 2863 | Aerogyllic | |||

Scale 2839 | Lyptian | |||

Scale 2903 | Gothyllic | |||

Scale 2935 | Modygic | |||

Scale 2999 | Chromatic and Permuted Diatonic Dorian Mixed | |||

Scale 2615 | Thoptian | |||

Scale 2743 | Staptyllic | |||

Scale 2359 | Gadian | |||

Scale 3383 | Zoptyllic | |||

Scale 3895 | Eparygic | |||

Scale 823 | Stodian | |||

Scale 1847 | Thacryllic |

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.