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
- Saptyllic

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

Pitch Class Set | {0,2,3,4,6,8,9,10} |

Forte Number | 8-25 |

Rotational Symmetry | 6 semitones |

Reflection Axes | 0, 3 |

Palindromic | yes |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 4 |

Modes | 3 |

Prime? | no prime: 1495 |

Deep Scale | no |

Interval Vector | 464644 |

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

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

Spectra Variation | 1 |

Maximally Even | no |

Maximal Area Set | yes |

Interior Area | 2.732 |

Myhill Property | no |

Balanced | yes |

Ridge Tones | [0,6] |

Propriety | Proper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1885 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode: Scale 1495 | Messiaen Mode 6 | This is the prime mode | |||

3rd mode: Scale 2795 | Van der Horst Octatonic | ||||

4th mode: Scale 3445 | Messiaen Mode 6 Inverse |

The prime form of this scale is Scale 1495

Scale 1495 | Messiaen Mode 6 |

The octatonic modal family [1885, 1495, 2795, 3445] (Forte: 8-25) is the complement of the tetratonic modal family [325, 1105] (Forte: 4-25)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1885 is itself, because it is a palindromic scale!

Scale 1885 | Saptyllic |

T_{0} | 1885 | T_{0}I | 1885 | |||||

T_{1} | 3770 | T_{1}I | 3770 | |||||

T_{2} | 3445 | T_{2}I | 3445 | |||||

T_{3} | 2795 | T_{3}I | 2795 | |||||

T_{4} | 1495 | T_{4}I | 1495 | |||||

T_{5} | 2990 | T_{5}I | 2990 | |||||

T_{6} | 1885 | T_{6}I | 1885 | |||||

T_{7} | 3770 | T_{7}I | 3770 | |||||

T_{8} | 3445 | T_{8}I | 3445 | |||||

T_{9} | 2795 | T_{9}I | 2795 | |||||

T_{10} | 1495 | T_{10}I | 1495 | |||||

T_{11} | 2990 | T_{11}I | 2990 |

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 1887 | Aerocrygic | |||

Scale 1881 | Katorian | |||

Scale 1883 | ||||

Scale 1877 | Aeroptian | |||

Scale 1869 | Katyrian | |||

Scale 1901 | Ionidyllic | |||

Scale 1917 | Thydyllian | |||

Scale 1821 | Aeradian | |||

Scale 1853 | Maryllic | |||

Scale 1949 | Mathyllic | |||

Scale 2013 | Mocrygic | |||

Scale 1629 | Synian | |||

Scale 1757 | ||||

Scale 1373 | Storian | |||

Scale 861 | Rylian | |||

Scale 2909 | Mocryllic | |||

Scale 3933 | Ionidygic |

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.