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
- Epaptian

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

Pitch Class Set | {0,1,2,4,6,7,10} |

Forte Number | 7-28 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3429 |

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 |

Maximal Area Set | no |

Interior Area | 2.549 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 1239 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 2667 | Byrian | ||||

3rd mode: Scale 3381 | Katanian | ||||

4th mode: Scale 1869 | Katyrian | ||||

5th mode: Scale 1491 | Mela Namanarayani | ||||

6th mode: Scale 2793 | Eporian | ||||

7th mode: Scale 861 | Rylian |

The prime form of this scale is Scale 747

Scale 747 | Lynian |

The heptatonic modal family [1239, 2667, 3381, 1869, 1491, 2793, 861] (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 1239 is 3429

Scale 3429 | Marian |

Only scales that are chiral will have an enantiomorph. Scale 1239 is chiral, and its enantiomorph is scale 3429

Scale 3429 | Marian |

T_{0} | 1239 | T_{0}I | 3429 | |||||

T_{1} | 2478 | T_{1}I | 2763 | |||||

T_{2} | 861 | T_{2}I | 1431 | |||||

T_{3} | 1722 | T_{3}I | 2862 | |||||

T_{4} | 3444 | T_{4}I | 1629 | |||||

T_{5} | 2793 | T_{5}I | 3258 | |||||

T_{6} | 1491 | T_{6}I | 2421 | |||||

T_{7} | 2982 | T_{7}I | 747 | |||||

T_{8} | 1869 | T_{8}I | 1494 | |||||

T_{9} | 3738 | T_{9}I | 2988 | |||||

T_{10} | 3381 | T_{10}I | 1881 | |||||

T_{11} | 2667 | T_{11}I | 3762 |

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 1237 | Salimic | |||

Scale 1235 | Messiaen Truncated Mode 2 | |||

Scale 1243 | Epylian | |||

Scale 1247 | Aeodyllic | |||

Scale 1223 | Phryptimic | |||

Scale 1231 | Logian | |||

Scale 1255 | Chromatic Mixolydian | |||

Scale 1271 | Kolyllic | |||

Scale 1175 | Epycrimic | |||

Scale 1207 | Aeoloptian | |||

Scale 1111 | Sycrimic | |||

Scale 1367 | Leading Whole-Tone Inverse | |||

Scale 1495 | Messiaen Mode 6 | |||

Scale 1751 | Aeolyryllic | |||

Scale 215 | ||||

Scale 727 | Phradian | |||

Scale 2263 | Lycrian | |||

Scale 3287 | Phrathyllic |

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.