The Exciting Universe Of Music Theory

presents

more than you ever wanted to know about...

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
- Dogyllic

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

Pitch Class Set | {0,1,5,6,8,9,10,11} |

Forte Number | 8-4 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2271 |

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 |

Maximal Area Set | no |

Interior Area | 2.366 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3939 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 4017 | Dolyllic | ||||

3rd mode: Scale 507 | Moryllic | ||||

4th mode: Scale 2301 | Bydyllic | ||||

5th mode: Scale 1599 | Pocryllic | ||||

6th mode: Scale 2847 | Phracryllic | ||||

7th mode: Scale 3471 | Gyryllic | ||||

8th mode: Scale 3783 | Phrygyllic |

The prime form of this scale is Scale 447

Scale 447 | Thyphyllic |

The octatonic modal family [3939, 4017, 507, 2301, 1599, 2847, 3471, 3783] (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 3939 is 2271

Scale 2271 | Poptyllic |

Only scales that are chiral will have an enantiomorph. Scale 3939 is chiral, and its enantiomorph is scale 2271

Scale 2271 | Poptyllic |

T_{0} | 3939 | T_{0}I | 2271 | |||||

T_{1} | 3783 | T_{1}I | 447 | |||||

T_{2} | 3471 | T_{2}I | 894 | |||||

T_{3} | 2847 | T_{3}I | 1788 | |||||

T_{4} | 1599 | T_{4}I | 3576 | |||||

T_{5} | 3198 | T_{5}I | 3057 | |||||

T_{6} | 2301 | T_{6}I | 2019 | |||||

T_{7} | 507 | T_{7}I | 4038 | |||||

T_{8} | 1014 | T_{8}I | 3981 | |||||

T_{9} | 2028 | T_{9}I | 3867 | |||||

T_{10} | 4056 | T_{10}I | 3639 | |||||

T_{11} | 4017 | T_{11}I | 3183 |

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 3937 | ||||

Scale 3941 | Stathyllic | |||

Scale 3943 | Zynygic | |||

Scale 3947 | Ryptygic | |||

Scale 3955 | Pothygic | |||

Scale 3907 | ||||

Scale 3923 | Stoptyllic | |||

Scale 3875 | Aeryptian | |||

Scale 4003 | Sadyllic | |||

Scale 4067 | Aeolarygic | |||

Scale 3683 | Dycrian | |||

Scale 3811 | Epogyllic | |||

Scale 3427 | Zacrian | |||

Scale 2915 | Aeolydian | |||

Scale 1891 | Thalian |

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.