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
- Solian

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

Pitch Class Set | {0,1,3,6,8,9,10} |

Forte Number | 7-25 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2653 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 733 |

Deep Scale | no |

Interval Vector | 345342 |

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

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

Spectra Variation | 2.286 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 1867 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 2981 | Ionolian | ||||

3rd mode: Scale 1769 | Blues Heptatonic II | ||||

4th mode: Scale 733 | Donian | This is the prime mode | |||

5th mode: Scale 1207 | Aeoloptian | ||||

6th mode: Scale 2651 | Panian | ||||

7th mode: Scale 3373 | Lodian |

The prime form of this scale is Scale 733

Scale 733 | Donian |

The heptatonic modal family [1867, 2981, 1769, 733, 1207, 2651, 3373] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1867 is 2653

Scale 2653 | Sygian |

Only scales that are chiral will have an enantiomorph. Scale 1867 is chiral, and its enantiomorph is scale 2653

Scale 2653 | Sygian |

T_{0} | 1867 | T_{0}I | 2653 | |||||

T_{1} | 3734 | T_{1}I | 1211 | |||||

T_{2} | 3373 | T_{2}I | 2422 | |||||

T_{3} | 2651 | T_{3}I | 749 | |||||

T_{4} | 1207 | T_{4}I | 1498 | |||||

T_{5} | 2414 | T_{5}I | 2996 | |||||

T_{6} | 733 | T_{6}I | 1897 | |||||

T_{7} | 1466 | T_{7}I | 3794 | |||||

T_{8} | 2932 | T_{8}I | 3493 | |||||

T_{9} | 1769 | T_{9}I | 2891 | |||||

T_{10} | 3538 | T_{10}I | 1687 | |||||

T_{11} | 2981 | T_{11}I | 3374 |

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 1865 | Thagimic | |||

Scale 1869 | Katyrian | |||

Scale 1871 | Aeolyllic | |||

Scale 1859 | ||||

Scale 1863 | Pycrian | |||

Scale 1875 | Persichetti Scale | |||

Scale 1883 | ||||

Scale 1899 | Moptyllic | |||

Scale 1803 | ||||

Scale 1835 | Byptian | |||

Scale 1931 | Stogian | |||

Scale 1995 | Aeolacryllic | |||

Scale 1611 | Dacrimic | |||

Scale 1739 | Mela Sadvidhamargini | |||

Scale 1355 | Raga Bhavani | |||

Scale 843 | Molimic | |||

Scale 2891 | Phrogian | |||

Scale 3915 |

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