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
- Kaptian

Cardinality | 7 (heptatonic) |
---|---|

Pitch Class Set | {0,1,4,6,9,10,11} |

Forte Number | 7-Z12 |

Rotational Symmetry | none |

Reflection Axes | 5 |

Palindromic | no |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 671 |

Deep Scale | no |

Interval Vector | 444342 |

Interval Spectrum | p^{4}m^{3}n^{4}s^{4}d^{4}t^{2} |

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

Spectra Variation | 2.857 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [10] |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3667 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 3881 | Morian | ||||

3rd mode: Scale 997 | Rycrian | ||||

4th mode: Scale 1273 | Ronian | ||||

5th mode: Scale 671 | Stycrian | This is the prime mode | |||

6th mode: Scale 2383 | Katorian | ||||

7th mode: Scale 3239 | Mela Tanarupi |

The prime form of this scale is Scale 671

Scale 671 | Stycrian |

The heptatonic modal family [3667, 3881, 997, 1273, 671, 2383, 3239] (Forte: 7-Z12) is the complement of the pentatonic modal family [107, 1411, 1549, 2101, 2753] (Forte: 5-Z12)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3667 is 2383

Scale 2383 | Katorian |

T_{0} | 3667 | T_{0}I | 2383 | |||||

T_{1} | 3239 | T_{1}I | 671 | |||||

T_{2} | 2383 | T_{2}I | 1342 | |||||

T_{3} | 671 | T_{3}I | 2684 | |||||

T_{4} | 1342 | T_{4}I | 1273 | |||||

T_{5} | 2684 | T_{5}I | 2546 | |||||

T_{6} | 1273 | T_{6}I | 997 | |||||

T_{7} | 2546 | T_{7}I | 1994 | |||||

T_{8} | 997 | T_{8}I | 3988 | |||||

T_{9} | 1994 | T_{9}I | 3881 | |||||

T_{10} | 3988 | T_{10}I | 3667 | |||||

T_{11} | 3881 | T_{11}I | 3239 |

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 3665 | Stalimic | |||

Scale 3669 | Mothian | |||

Scale 3671 | Aeonyllic | |||

Scale 3675 | Monyllic | |||

Scale 3651 | ||||

Scale 3659 | Polian | |||

Scale 3683 | Dycrian | |||

Scale 3699 | Galyllic | |||

Scale 3603 | ||||

Scale 3635 | Katygian | |||

Scale 3731 | Aeryrian | |||

Scale 3795 | Epothyllic | |||

Scale 3923 | Stoptyllic | |||

Scale 3155 | Ladimic | |||

Scale 3411 | Enigmatic | |||

Scale 2643 | Raga Hamsanandi | |||

Scale 1619 | Prometheus Neapolitan |

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.