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
- Gydian

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

Pitch Class Set | {0,4,6,7,8,9,10} |

Forte Number | 7-8 |

Rotational Symmetry | none |

Reflection Axes | 2 |

Palindromic | no |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 5 |

Modes | 6 |

Prime? | no prime: 381 |

Deep Scale | no |

Interval Vector | 454422 |

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

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

Spectra Variation | 3.429 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [4] |

Coherence | no |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 2001 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 381 | Kogian | This is the prime mode | |||

3rd mode: Scale 1119 | Rarian | ||||

4th mode: Scale 2607 | Aerolian | ||||

5th mode: Scale 3351 | Karian | ||||

6th mode: Scale 3723 | Myptian | ||||

7th mode: Scale 3909 | Rydian |

The prime form of this scale is Scale 381

Scale 381 | Kogian |

The heptatonic modal family [2001, 381, 1119, 2607, 3351, 3723, 3909] (Forte: 7-8) is the complement of the pentatonic modal family [93, 1047, 1857, 2571, 3333] (Forte: 5-8)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2001 is 381

Scale 381 | Kogian |

T_{0} | 2001 | T_{0}I | 381 | |||||

T_{1} | 4002 | T_{1}I | 762 | |||||

T_{2} | 3909 | T_{2}I | 1524 | |||||

T_{3} | 3723 | T_{3}I | 3048 | |||||

T_{4} | 3351 | T_{4}I | 2001 | |||||

T_{5} | 2607 | T_{5}I | 4002 | |||||

T_{6} | 1119 | T_{6}I | 3909 | |||||

T_{7} | 2238 | T_{7}I | 3723 | |||||

T_{8} | 381 | T_{8}I | 3351 | |||||

T_{9} | 762 | T_{9}I | 2607 | |||||

T_{10} | 1524 | T_{10}I | 1119 | |||||

T_{11} | 3048 | T_{11}I | 2238 |

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 2003 | Podyllic | |||

Scale 2005 | Gygyllic | |||

Scale 2009 | Stacryllic | |||

Scale 1985 | ||||

Scale 1993 | Katoptian | |||

Scale 2017 | ||||

Scale 2033 | Stolyllic | |||

Scale 1937 | Galimic | |||

Scale 1969 | Stylian | |||

Scale 1873 | Dathimic | |||

Scale 1745 | Raga Vutari | |||

Scale 1489 | Raga Jyoti | |||

Scale 977 | Kocrimic | |||

Scale 3025 | Epycrian | |||

Scale 4049 | Stycryllic |

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