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.

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
- Badian

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

Pitch Class Set | {0,3,5,6,7,8,9} |

Forte Number | 7-10 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 761 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 607 |

Deep Scale | no |

Interval Vector | 445332 |

Interval Spectrum | p^{3}m^{3}n^{5}s^{4}d^{4}t^{2} |

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

Spectra Variation | 3.143 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 1001 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 637 | Debussy's Heptatonic | ||||

3rd mode: Scale 1183 | Sadian | ||||

4th mode: Scale 2639 | Dothian | ||||

5th mode: Scale 3367 | Moptian | ||||

6th mode: Scale 3731 | Aeryrian | ||||

7th mode: Scale 3913 | Bonian |

The prime form of this scale is Scale 607

Scale 607 | Kadian |

The heptatonic modal family [1001, 637, 1183, 2639, 3367, 3731, 3913] (Forte: 7-10) is the complement of the pentatonic modal family [91, 1547, 1729, 2093, 2821] (Forte: 5-10)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1001 is 761

Scale 761 | Ponian |

Only scales that are chiral will have an enantiomorph. Scale 1001 is chiral, and its enantiomorph is scale 761

Scale 761 | Ponian |

T_{0} | 1001 | T_{0}I | 761 | |||||

T_{1} | 2002 | T_{1}I | 1522 | |||||

T_{2} | 4004 | T_{2}I | 3044 | |||||

T_{3} | 3913 | T_{3}I | 1993 | |||||

T_{4} | 3731 | T_{4}I | 3986 | |||||

T_{5} | 3367 | T_{5}I | 3877 | |||||

T_{6} | 2639 | T_{6}I | 3659 | |||||

T_{7} | 1183 | T_{7}I | 3223 | |||||

T_{8} | 2366 | T_{8}I | 2351 | |||||

T_{9} | 637 | T_{9}I | 607 | |||||

T_{10} | 1274 | T_{10}I | 1214 | |||||

T_{11} | 2548 | T_{11}I | 2428 |

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 1003 | Ionyryllic | |||

Scale 1005 | Radyllic | |||

Scale 993 | ||||

Scale 997 | Rycrian | |||

Scale 1009 | Katyptian | |||

Scale 1017 | Dythyllic | |||

Scale 969 | Ionogimic | |||

Scale 985 | Mela Sucaritra | |||

Scale 937 | Stothimic | |||

Scale 873 | Bagimic | |||

Scale 745 | Kolimic | |||

Scale 489 | Phrathimic | |||

Scale 1513 | Stathian | |||

Scale 2025 | ||||

Scale 3049 | Phrydyllic |

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. Bibliography