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
- Thoptian

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

Pitch Class Set | {0,1,2,4,5,9,11} |

Forte Number | 7-11 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3467 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 379 |

Deep Scale | no |

Interval Vector | 444441 |

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

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

Spectra Variation | 3.143 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 2615 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 3355 | Bagian | ||||

3rd mode: Scale 3725 | Kyrian | ||||

4th mode: Scale 1955 | Sonian | ||||

5th mode: Scale 3025 | Epycrian | ||||

6th mode: Scale 445 | Gocrian | ||||

7th mode: Scale 1135 | Katolian |

The prime form of this scale is Scale 379

Scale 379 | Aeragian |

The heptatonic modal family [2615, 3355, 3725, 1955, 3025, 445, 1135] (Forte: 7-11) is the complement of the pentatonic modal family [157, 929, 1063, 2579, 3337] (Forte: 5-11)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2615 is 3467

Scale 3467 | Katonian |

Only scales that are chiral will have an enantiomorph. Scale 2615 is chiral, and its enantiomorph is scale 3467

Scale 3467 | Katonian |

T_{0} | 2615 | T_{0}I | 3467 | |||||

T_{1} | 1135 | T_{1}I | 2839 | |||||

T_{2} | 2270 | T_{2}I | 1583 | |||||

T_{3} | 445 | T_{3}I | 3166 | |||||

T_{4} | 890 | T_{4}I | 2237 | |||||

T_{5} | 1780 | T_{5}I | 379 | |||||

T_{6} | 3560 | T_{6}I | 758 | |||||

T_{7} | 3025 | T_{7}I | 1516 | |||||

T_{8} | 1955 | T_{8}I | 3032 | |||||

T_{9} | 3910 | T_{9}I | 1969 | |||||

T_{10} | 3725 | T_{10}I | 3938 | |||||

T_{11} | 3355 | T_{11}I | 3781 |

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 2613 | Raga Hamsa Vinodini | |||

Scale 2611 | Raga Vasanta | |||

Scale 2619 | Ionyrian | |||

Scale 2623 | Aerylyllic | |||

Scale 2599 | Malimic | |||

Scale 2607 | Aerolian | |||

Scale 2583 | ||||

Scale 2647 | Dadian | |||

Scale 2679 | Rathyllic | |||

Scale 2743 | Staptyllic | |||

Scale 2871 | Stanyllic | |||

Scale 2103 | ||||

Scale 2359 | Gadian | |||

Scale 3127 | ||||

Scale 3639 | Paptyllic | |||

Scale 567 | Aeoladimic | |||

Scale 1591 | Rodian |

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.