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
- Aeolynygic

Cardinality | 9 (nonatonic) |
---|---|

Pitch Class Set | {0,1,2,3,4,5,8,10,11} |

Forte Number | 9-2 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3991 |

Hemitonia | 7 (multihemitonic) |

Cohemitonia | 6 (multicohemitonic) |

Imperfections | 3 |

Modes | 8 |

Prime? | no prime: 767 |

Deep Scale | no |

Interval Vector | 777663 |

Interval Spectrum | p^{6}m^{6}n^{7}s^{7}d^{7}t^{3} |

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

Spectra Variation | 2.444 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3391 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode: Scale 3743 | Thadygic | ||||

3rd mode: Scale 3919 | Lynygic | ||||

4th mode: Scale 4007 | Doptygic | ||||

5th mode: Scale 4051 | Ionilygic | ||||

6th mode: Scale 4073 | Sathygic | ||||

7th mode: Scale 1021 | Ladygic | ||||

8th mode: Scale 1279 | Sarygic | ||||

9th mode: Scale 2687 | Thacrygic |

The prime form of this scale is Scale 767

Scale 767 | Raptygic |

The nonatonic modal family [3391, 3743, 3919, 4007, 4051, 4073, 1021, 1279, 2687] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3391 is 3991

Scale 3991 | Badygic |

Only scales that are chiral will have an enantiomorph. Scale 3391 is chiral, and its enantiomorph is scale 3991

Scale 3991 | Badygic |

T_{0} | 3391 | T_{0}I | 3991 | |||||

T_{1} | 2687 | T_{1}I | 3887 | |||||

T_{2} | 1279 | T_{2}I | 3679 | |||||

T_{3} | 2558 | T_{3}I | 3263 | |||||

T_{4} | 1021 | T_{4}I | 2431 | |||||

T_{5} | 2042 | T_{5}I | 767 | |||||

T_{6} | 4084 | T_{6}I | 1534 | |||||

T_{7} | 4073 | T_{7}I | 3068 | |||||

T_{8} | 4051 | T_{8}I | 2041 | |||||

T_{9} | 4007 | T_{9}I | 4082 | |||||

T_{10} | 3919 | T_{10}I | 4069 | |||||

T_{11} | 3743 | T_{11}I | 4043 |

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 3389 | Socryllic | |||

Scale 3387 | Aeryptyllic | |||

Scale 3383 | Zoptyllic | |||

Scale 3375 | ||||

Scale 3359 | Bonyllic | |||

Scale 3423 | Lothygic | |||

Scale 3455 | Ryptyllian | |||

Scale 3519 | Raga Sindhi-Bhairavi | |||

Scale 3135 | ||||

Scale 3263 | Pyrygic | |||

Scale 3647 | Eporygic | |||

Scale 3903 | Aeogyllian | |||

Scale 2367 | Laryllic | |||

Scale 2879 | Stadygic | |||

Scale 1343 | Zalyllic |

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.