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
- Aeolonyllic

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

Pitch Class Set | {0,1,2,3,5,7,10,11} |

Forte Number | 8-11 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3751 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 4 (multicohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 703 |

Deep Scale | no |

Interval Vector | 565552 |

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

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

Spectra Variation | 2.75 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.616 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3247 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3671 | Aeonyllic | ||||

3rd mode: Scale 3883 | Kyryllic | ||||

4th mode: Scale 3989 | Sythyllic | ||||

5th mode: Scale 2021 | Katycryllic | ||||

6th mode: Scale 1529 | Kataryllic | ||||

7th mode: Scale 703 | Aerocryllic | This is the prime mode | |||

8th mode: Scale 2399 | Zanyllic |

The prime form of this scale is Scale 703

Scale 703 | Aerocryllic |

The octatonic modal family [3247, 3671, 3883, 3989, 2021, 1529, 703, 2399] (Forte: 8-11) is the complement of the tetratonic modal family [43, 1409, 1541, 2069] (Forte: 4-11)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3247 is 3751

Scale 3751 | Aerathyllic |

Only scales that are chiral will have an enantiomorph. Scale 3247 is chiral, and its enantiomorph is scale 3751

Scale 3751 | Aerathyllic |

T_{0} | 3247 | T_{0}I | 3751 | |||||

T_{1} | 2399 | T_{1}I | 3407 | |||||

T_{2} | 703 | T_{2}I | 2719 | |||||

T_{3} | 1406 | T_{3}I | 1343 | |||||

T_{4} | 2812 | T_{4}I | 2686 | |||||

T_{5} | 1529 | T_{5}I | 1277 | |||||

T_{6} | 3058 | T_{6}I | 2554 | |||||

T_{7} | 2021 | T_{7}I | 1013 | |||||

T_{8} | 4042 | T_{8}I | 2026 | |||||

T_{9} | 3989 | T_{9}I | 4052 | |||||

T_{10} | 3883 | T_{10}I | 4009 | |||||

T_{11} | 3671 | T_{11}I | 3923 |

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 3245 | Mela Varunapriya | |||

Scale 3243 | Mela Rupavati | |||

Scale 3239 | Mela Tanarupi | |||

Scale 3255 | Daryllic | |||

Scale 3263 | Pyrygic | |||

Scale 3215 | Katydian | |||

Scale 3231 | Kataptyllic | |||

Scale 3279 | Pythyllic | |||

Scale 3311 | Mixodygic | |||

Scale 3119 | ||||

Scale 3183 | Mixonyllic | |||

Scale 3375 | ||||

Scale 3503 | Zyphygic | |||

Scale 3759 | Darygic | |||

Scale 2223 | Konian | |||

Scale 2735 | Gynyllic | |||

Scale 1199 | Magian |

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.