The Exciting Universe Of Music Theory

presents

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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).

- Messiaen
- Messiaen Truncated Mode 2

- Zeitler
- Dodimic

Cardinality | 6 (hexatonic) |
---|---|

Pitch Class Set | {0,1,3,6,7,9} |

Forte Number | 6-30 |

Rotational Symmetry | 6 semitones |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2665 |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 4 |

Modes | 2 |

Prime? | yes |

Deep Scale | no |

Interval Vector | 224223 |

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

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

Spectra Variation | 1.333 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.366 |

Myhill Property | no |

Balanced | yes |

Ridge Tones | none |

Propriety | Proper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 715 can be rotated to make 2 other scales. The 1st mode is itself.

This is the prime form of this scale.

The hexatonic modal family [715, 2405, 1625] (Forte: 6-30) is the complement of the hexatonic modal family [715, 1625, 2405] (Forte: 6-30)

The inverse of a scale is a reflection using the root as its axis. The inverse of 715 is 2665

Scale 2665 | Aeradimic |

Only scales that are chiral will have an enantiomorph. Scale 715 is chiral, and its enantiomorph is scale 2665

Scale 2665 | Aeradimic |

T_{0} | 715 | T_{0}I | 2665 | |||||

T_{1} | 1430 | T_{1}I | 1235 | |||||

T_{2} | 2860 | T_{2}I | 2470 | |||||

T_{3} | 1625 | T_{3}I | 845 | |||||

T_{4} | 3250 | T_{4}I | 1690 | |||||

T_{5} | 2405 | T_{5}I | 3380 | |||||

T_{6} | 715 | T_{6}I | 2665 | |||||

T_{7} | 1430 | T_{7}I | 1235 | |||||

T_{8} | 2860 | T_{8}I | 2470 | |||||

T_{9} | 1625 | T_{9}I | 845 | |||||

T_{10} | 3250 | T_{10}I | 1690 | |||||

T_{11} | 2405 | T_{11}I | 3380 |

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 713 | Thoptitonic | |||

Scale 717 | Raga Vijayanagari | |||

Scale 719 | Kanian | |||

Scale 707 | ||||

Scale 711 | Raga Chandrajyoti | |||

Scale 723 | Ionadimic | |||

Scale 731 | Ionorian | |||

Scale 747 | Lynian | |||

Scale 651 | Golitonic | |||

Scale 683 | Stogimic | |||

Scale 587 | Pathitonic | |||

Scale 843 | Molimic | |||

Scale 971 | Mela Gavambodhi | |||

Scale 203 | ||||

Scale 459 | Zaptimic | |||

Scale 1227 | Thacrimic | |||

Scale 1739 | Mela Sadvidhamargini | |||

Scale 2763 | Mela Suvarnangi |

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.