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.

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
- Phryryllic

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

Pitch Class Set | {0,1,3,5,7,9,10,11} |

Forte Number | 8-21 |

Rotational Symmetry | none |

Reflection Axes | 5 |

Palindromic | no |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 4 |

Modes | 7 |

Prime? | no prime: 1375 |

Deep Scale | no |

Interval Vector | 474643 |

Interval Spectrum | p^{4}m^{6}n^{4}s^{7}d^{4}t^{3} |

Distribution Spectra | <1> = {1,2} <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> = {10,11} |

Spectra Variation | 2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [10] |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3755 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3925 | Thyryllic | ||||

3rd mode: Scale 2005 | Gygyllic | ||||

4th mode: Scale 1525 | Sodyllic | ||||

5th mode: Scale 1405 | Goryllic | ||||

6th mode: Scale 1375 | Bothyllic | This is the prime mode | |||

7th mode: Scale 2735 | Gynyllic | ||||

8th mode: Scale 3415 | Ionaptyllic |

The prime form of this scale is Scale 1375

Scale 1375 | Bothyllic |

The octatonic modal family [3755, 3925, 2005, 1525, 1405, 1375, 2735, 3415] (Forte: 8-21) is the complement of the tetratonic modal family [85, 1045, 1285, 1345] (Forte: 4-21)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3755 is 2735

Scale 2735 | Gynyllic |

T_{0} | 3755 | T_{0}I | 2735 | |||||

T_{1} | 3415 | T_{1}I | 1375 | |||||

T_{2} | 2735 | T_{2}I | 2750 | |||||

T_{3} | 1375 | T_{3}I | 1405 | |||||

T_{4} | 2750 | T_{4}I | 2810 | |||||

T_{5} | 1405 | T_{5}I | 1525 | |||||

T_{6} | 2810 | T_{6}I | 3050 | |||||

T_{7} | 1525 | T_{7}I | 2005 | |||||

T_{8} | 3050 | T_{8}I | 4010 | |||||

T_{9} | 2005 | T_{9}I | 3925 | |||||

T_{10} | 4010 | T_{10}I | 3755 | |||||

T_{11} | 3925 | T_{11}I | 3415 |

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 3753 | Phraptian | |||

Scale 3757 | Raga Mian Ki Malhar | |||

Scale 3759 | Darygic | |||

Scale 3747 | Myrian | |||

Scale 3751 | Aerathyllic | |||

Scale 3763 | Modyllic | |||

Scale 3771 | Katodyllian | |||

Scale 3723 | Myptian | |||

Scale 3739 | Epanyllic | |||

Scale 3787 | Kagyllic | |||

Scale 3819 | Aeolanygic | |||

Scale 3627 | Kalian | |||

Scale 3691 | Badyllic | |||

Scale 3883 | Kyryllic | |||

Scale 4011 | Styrygic | |||

Scale 3243 | Mela Rupavati | |||

Scale 3499 | Hamel | |||

Scale 2731 | Neapolitan Major | |||

Scale 1707 | Dorian Flat 2 |

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. Bibliography