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
- Byrian

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

Pitch Class Set | {0,1,3,5,6,9,11} |

Forte Number | 7-28 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2763 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 747 |

Deep Scale | no |

Interval Vector | 344433 |

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

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

Spectra Variation | 2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 2667 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 3381 | Katanian | ||||

3rd mode: Scale 1869 | Katyrian | ||||

4th mode: Scale 1491 | Mela Namanarayani | ||||

5th mode: Scale 2793 | Eporian | ||||

6th mode: Scale 861 | Rylian | ||||

7th mode: Scale 1239 | Epaptian |

The prime form of this scale is Scale 747

Scale 747 | Lynian |

The heptatonic modal family [2667, 3381, 1869, 1491, 2793, 861, 1239] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2667 is 2763

Scale 2763 | Mela Suvarnangi |

Only scales that are chiral will have an enantiomorph. Scale 2667 is chiral, and its enantiomorph is scale 2763

Scale 2763 | Mela Suvarnangi |

T_{0} | 2667 | T_{0}I | 2763 | |||||

T_{1} | 1239 | T_{1}I | 1431 | |||||

T_{2} | 2478 | T_{2}I | 2862 | |||||

T_{3} | 861 | T_{3}I | 1629 | |||||

T_{4} | 1722 | T_{4}I | 3258 | |||||

T_{5} | 3444 | T_{5}I | 2421 | |||||

T_{6} | 2793 | T_{6}I | 747 | |||||

T_{7} | 1491 | T_{7}I | 1494 | |||||

T_{8} | 2982 | T_{8}I | 2988 | |||||

T_{9} | 1869 | T_{9}I | 1881 | |||||

T_{10} | 3738 | T_{10}I | 3762 | |||||

T_{11} | 3381 | T_{11}I | 3429 |

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 2665 | Aeradimic | |||

Scale 2669 | Jeths' Mode | |||

Scale 2671 | Aerolyllic | |||

Scale 2659 | Katynimic | |||

Scale 2663 | Lalian | |||

Scale 2675 | Chromatic Lydian | |||

Scale 2683 | Thodyllic | |||

Scale 2635 | Gocrimic | |||

Scale 2651 | Panian | |||

Scale 2603 | Gadimic | |||

Scale 2731 | Neapolitan Major | |||

Scale 2795 | Van der Horst Octatonic | |||

Scale 2923 | Baryllic | |||

Scale 2155 | ||||

Scale 2411 | Aeolorian | |||

Scale 3179 | Daptian | |||

Scale 3691 | Badyllic | |||

Scale 619 | Double-Phrygian Hexatonic | |||

Scale 1643 | Locrian Natural 6 |

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.