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
- Katydian

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

Pitch Class Set | {0,1,2,3,7,10,11} |

Forte Number | 7-3 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3623 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 4 (multicohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 319 |

Deep Scale | no |

Interval Vector | 544431 |

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

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

Spectra Variation | 3.714 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3215 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 3655 | Mathian | ||||

3rd mode: Scale 3875 | Aeryptian | ||||

4th mode: Scale 3985 | Thadian | ||||

5th mode: Scale 505 | Sanian | ||||

6th mode: Scale 575 | Ionydian | ||||

7th mode: Scale 2335 | Epydian |

The prime form of this scale is Scale 319

Scale 319 | Epodian |

The heptatonic modal family [3215, 3655, 3875, 3985, 505, 575, 2335] (Forte: 7-3) is the complement of the pentatonic modal family [55, 1795, 2075, 2945, 3085] (Forte: 5-3)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3215 is 3623

Scale 3623 | Aerocrian |

Only scales that are chiral will have an enantiomorph. Scale 3215 is chiral, and its enantiomorph is scale 3623

Scale 3623 | Aerocrian |

T_{0} | 3215 | T_{0}I | 3623 | |||||

T_{1} | 2335 | T_{1}I | 3151 | |||||

T_{2} | 575 | T_{2}I | 2207 | |||||

T_{3} | 1150 | T_{3}I | 319 | |||||

T_{4} | 2300 | T_{4}I | 638 | |||||

T_{5} | 505 | T_{5}I | 1276 | |||||

T_{6} | 1010 | T_{6}I | 2552 | |||||

T_{7} | 2020 | T_{7}I | 1009 | |||||

T_{8} | 4040 | T_{8}I | 2018 | |||||

T_{9} | 3985 | T_{9}I | 4036 | |||||

T_{10} | 3875 | T_{10}I | 3977 | |||||

T_{11} | 3655 | T_{11}I | 3859 |

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 3213 | Eponimic | |||

Scale 3211 | Epacrimic | |||

Scale 3207 | ||||

Scale 3223 | Thyphian | |||

Scale 3231 | Kataptyllic | |||

Scale 3247 | Aeolonyllic | |||

Scale 3279 | Pythyllic | |||

Scale 3087 | ||||

Scale 3151 | Pacrian | |||

Scale 3343 | ||||

Scale 3471 | Gyryllic | |||

Scale 3727 | Tholyllic | |||

Scale 2191 | Thydimic | |||

Scale 2703 | Galian | |||

Scale 1167 | Aerodimic |

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.