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
- Rothyllic

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

Pitch Class Set | {0,1,2,4,7,8,10,11} |

Forte Number | 8-12 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3383 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 4 |

Modes | 7 |

Prime? | no prime: 763 |

Deep Scale | no |

Interval Vector | 556543 |

Interval Spectrum | p^{4}m^{5}n^{6}s^{5}d^{5}t^{3} |

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

Spectra Variation | 2.5 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3479 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3787 | Kagyllic | ||||

3rd mode: Scale 3941 | Stathyllic | ||||

4th mode: Scale 2009 | Stacryllic | ||||

5th mode: Scale 763 | Doryllic | This is the prime mode | |||

6th mode: Scale 2429 | Kadyllic | ||||

7th mode: Scale 1631 | Rynyllic | ||||

8th mode: Scale 2863 | Aerogyllic |

The prime form of this scale is Scale 763

Scale 763 | Doryllic |

The octatonic modal family [3479, 3787, 3941, 2009, 763, 2429, 1631, 2863] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3479 is 3383

Scale 3383 | Zoptyllic |

Only scales that are chiral will have an enantiomorph. Scale 3479 is chiral, and its enantiomorph is scale 3383

Scale 3383 | Zoptyllic |

T_{0} | 3479 | T_{0}I | 3383 | |||||

T_{1} | 2863 | T_{1}I | 2671 | |||||

T_{2} | 1631 | T_{2}I | 1247 | |||||

T_{3} | 3262 | T_{3}I | 2494 | |||||

T_{4} | 2429 | T_{4}I | 893 | |||||

T_{5} | 763 | T_{5}I | 1786 | |||||

T_{6} | 1526 | T_{6}I | 3572 | |||||

T_{7} | 3052 | T_{7}I | 3049 | |||||

T_{8} | 2009 | T_{8}I | 2003 | |||||

T_{9} | 4018 | T_{9}I | 4006 | |||||

T_{10} | 3941 | T_{10}I | 3917 | |||||

T_{11} | 3787 | T_{11}I | 3739 |

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 3477 | Kyptian | |||

Scale 3475 | Kylian | |||

Scale 3483 | Mixotharyllic | |||

Scale 3487 | Byptygic | |||

Scale 3463 | ||||

Scale 3471 | Gyryllic | |||

Scale 3495 | Banyllic | |||

Scale 3511 | Epolygic | |||

Scale 3543 | Aeolonygic | |||

Scale 3351 | Karian | |||

Scale 3415 | Ionaptyllic | |||

Scale 3223 | Thyphian | |||

Scale 3735 | ||||

Scale 3991 | Badygic | |||

Scale 2455 | Bothian | |||

Scale 2967 | Madyllic | |||

Scale 1431 | Phragian |

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.