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
- Mixonyllic

Cardinality | 8 (octatonic) |
---|---|

Pitch Class Set | {0,1,2,3,5,6,10,11} |

Forte Number | 8-4 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3783 |

Hemitonia | 6 (multihemitonic) |

Cohemitonia | 4 (multicohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 447 |

Deep Scale | no |

Interval Vector | 655552 |

Interval Spectrum | p^{5}m^{5}n^{5}s^{5}d^{6}t^{2} |

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

Spectra Variation | 3 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3183 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3639 | Paptyllic | ||||

3rd mode: Scale 3867 | Storyllic | ||||

4th mode: Scale 3981 | Phrycryllic | ||||

5th mode: Scale 2019 | Palyllic | ||||

6th mode: Scale 3057 | Phroryllic | ||||

7th mode: Scale 447 | Thyphyllic | This is the prime mode | |||

8th mode: Scale 2271 | Poptyllic |

The prime form of this scale is Scale 447

Scale 447 | Thyphyllic |

The octatonic modal family [3183, 3639, 3867, 3981, 2019, 3057, 447, 2271] (Forte: 8-4) is the complement of the tetratonic modal family [39, 897, 2067, 3081] (Forte: 4-4)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3183 is 3783

Scale 3783 | Phrygyllic |

Only scales that are chiral will have an enantiomorph. Scale 3183 is chiral, and its enantiomorph is scale 3783

Scale 3783 | Phrygyllic |

T_{0} | 3183 | T_{0}I | 3783 | |||||

T_{1} | 2271 | T_{1}I | 3471 | |||||

T_{2} | 447 | T_{2}I | 2847 | |||||

T_{3} | 894 | T_{3}I | 1599 | |||||

T_{4} | 1788 | T_{4}I | 3198 | |||||

T_{5} | 3576 | T_{5}I | 2301 | |||||

T_{6} | 3057 | T_{6}I | 507 | |||||

T_{7} | 2019 | T_{7}I | 1014 | |||||

T_{8} | 4038 | T_{8}I | 2028 | |||||

T_{9} | 3981 | T_{9}I | 4056 | |||||

T_{10} | 3867 | T_{10}I | 4017 | |||||

T_{11} | 3639 | T_{11}I | 3939 |

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 3181 | Rolian | |||

Scale 3179 | Daptian | |||

Scale 3175 | Eponian | |||

Scale 3191 | Bynyllic | |||

Scale 3199 | Thaptygic | |||

Scale 3151 | Pacrian | |||

Scale 3167 | Thynyllic | |||

Scale 3119 | ||||

Scale 3247 | Aeolonyllic | |||

Scale 3311 | Mixodygic | |||

Scale 3439 | Lythygic | |||

Scale 3695 | Kodygic | |||

Scale 2159 | ||||

Scale 2671 | Aerolyllic | |||

Scale 1135 | Katolian |

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.