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
- Modyllic

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

Pitch Class Set | {0,1,4,5,7,9,10,11} |

Forte Number | 8-Z15 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2479 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 863 |

Deep Scale | no |

Interval Vector | 555553 |

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

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

Spectra Variation | 2.25 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3763 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3929 | Aeolothyllic | ||||

3rd mode: Scale 1003 | Ionyryllic | ||||

4th mode: Scale 2549 | Rydyllic | ||||

5th mode: Scale 1661 | Gonyllic | ||||

6th mode: Scale 1439 | Rolyllic | ||||

7th mode: Scale 2767 | Katydyllic | ||||

8th mode: Scale 3431 | Zyptyllic |

The prime form of this scale is Scale 863

Scale 863 | Pyryllic |

The octatonic modal family [3763, 3929, 1003, 2549, 1661, 1439, 2767, 3431] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3763 is 2479

Scale 2479 | Harmonic and Neapolitan Minor Mixed |

Only scales that are chiral will have an enantiomorph. Scale 3763 is chiral, and its enantiomorph is scale 2479

Scale 2479 | Harmonic and Neapolitan Minor Mixed |

T_{0} | 3763 | T_{0}I | 2479 | |||||

T_{1} | 3431 | T_{1}I | 863 | |||||

T_{2} | 2767 | T_{2}I | 1726 | |||||

T_{3} | 1439 | T_{3}I | 3452 | |||||

T_{4} | 2878 | T_{4}I | 2809 | |||||

T_{5} | 1661 | T_{5}I | 1523 | |||||

T_{6} | 3322 | T_{6}I | 3046 | |||||

T_{7} | 2549 | T_{7}I | 1997 | |||||

T_{8} | 1003 | T_{8}I | 3994 | |||||

T_{9} | 2006 | T_{9}I | 3893 | |||||

T_{10} | 4012 | T_{10}I | 3691 | |||||

T_{11} | 3929 | T_{11}I | 3287 |

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 3761 | Raga Madhuri | |||

Scale 3765 | Dominant Bebop | |||

Scale 3767 | Chromatic Bebop | |||

Scale 3771 | Katodyllian | |||

Scale 3747 | Myrian | |||

Scale 3755 | Phryryllic | |||

Scale 3731 | Aeryrian | |||

Scale 3795 | Epothyllic | |||

Scale 3827 | Bodygic | |||

Scale 3635 | Katygian | |||

Scale 3699 | Galyllic | |||

Scale 3891 | Ryryllic | |||

Scale 4019 | Lonygic | |||

Scale 3251 | Mela Hatakambari | |||

Scale 3507 | Maqam Hijaz | |||

Scale 2739 | Mela Suryakanta | |||

Scale 1715 | Harmonic Minor Inverse |

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.