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
- Aeolonian

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

Pitch Class Set | {0,2,4,5,6,10,11} |

Forte Number | 7-15 |

Rotational Symmetry | none |

Reflection Axes | 2 |

Palindromic | no |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 471 |

Deep Scale | no |

Interval Vector | 442443 |

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

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

Spectra Variation | 2.286 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [4] |

Coherence | no |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3189 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1821 | Aeradian | ||||

3rd mode: Scale 1479 | Mela Jalarnava | ||||

4th mode: Scale 2787 | Zyrian | ||||

5th mode: Scale 3441 | Thacrian | ||||

6th mode: Scale 471 | Dodian | This is the prime mode | |||

7th mode: Scale 2283 | Aeolyptian |

The prime form of this scale is Scale 471

Scale 471 | Dodian |

The heptatonic modal family [3189, 1821, 1479, 2787, 3441, 471, 2283] (Forte: 7-15) is the complement of the pentatonic modal family [327, 453, 1137, 2211, 3153] (Forte: 5-15)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3189 is 1479

Scale 1479 | Mela Jalarnava |

T_{0} | 3189 | T_{0}I | 1479 | |||||

T_{1} | 2283 | T_{1}I | 2958 | |||||

T_{2} | 471 | T_{2}I | 1821 | |||||

T_{3} | 942 | T_{3}I | 3642 | |||||

T_{4} | 1884 | T_{4}I | 3189 | |||||

T_{5} | 3768 | T_{5}I | 2283 | |||||

T_{6} | 3441 | T_{6}I | 471 | |||||

T_{7} | 2787 | T_{7}I | 942 | |||||

T_{8} | 1479 | T_{8}I | 1884 | |||||

T_{9} | 2958 | T_{9}I | 3768 | |||||

T_{10} | 1821 | T_{10}I | 3441 | |||||

T_{11} | 3642 | T_{11}I | 2787 |

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 3191 | Bynyllic | |||

Scale 3185 | Messiaen Mode 5 Inverse | |||

Scale 3187 | Koptian | |||

Scale 3193 | Zathian | |||

Scale 3197 | Gylyllic | |||

Scale 3173 | Zarimic | |||

Scale 3181 | Rolian | |||

Scale 3157 | Zyptimic | |||

Scale 3125 | ||||

Scale 3253 | Mela Naganandini | |||

Scale 3317 | Katynyllic | |||

Scale 3445 | Messiaen Mode 6 Inverse | |||

Scale 3701 | Bagyllic | |||

Scale 2165 | ||||

Scale 2677 | Thodian | |||

Scale 1141 | Rynimic |

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