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
- Monyllic

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

Pitch Class Set | {0,1,3,4,6,9,10,11} |

Forte Number | 8-13 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2895 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 735 |

Deep Scale | no |

Interval Vector | 556453 |

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

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

Spectra Variation | 2.5 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3675 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3885 | Styryllic | ||||

3rd mode: Scale 1995 | Aeolacryllic | ||||

4th mode: Scale 3045 | Raptyllic | ||||

5th mode: Scale 1785 | Tharyllic | ||||

6th mode: Scale 735 | Sylyllic | This is the prime mode | |||

7th mode: Scale 2415 | Lothyllic | ||||

8th mode: Scale 3255 | Daryllic |

The prime form of this scale is Scale 735

Scale 735 | Sylyllic |

The octatonic modal family [3675, 3885, 1995, 3045, 1785, 735, 2415, 3255] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3675 is 2895

Scale 2895 | Aeoryllic |

Only scales that are chiral will have an enantiomorph. Scale 3675 is chiral, and its enantiomorph is scale 2895

Scale 2895 | Aeoryllic |

T_{0} | 3675 | T_{0}I | 2895 | |||||

T_{1} | 3255 | T_{1}I | 1695 | |||||

T_{2} | 2415 | T_{2}I | 3390 | |||||

T_{3} | 735 | T_{3}I | 2685 | |||||

T_{4} | 1470 | T_{4}I | 1275 | |||||

T_{5} | 2940 | T_{5}I | 2550 | |||||

T_{6} | 1785 | T_{6}I | 1005 | |||||

T_{7} | 3570 | T_{7}I | 2010 | |||||

T_{8} | 3045 | T_{8}I | 4020 | |||||

T_{9} | 1995 | T_{9}I | 3945 | |||||

T_{10} | 3990 | T_{10}I | 3795 | |||||

T_{11} | 3885 | T_{11}I | 3495 |

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 3673 | Ranian | |||

Scale 3677 | ||||

Scale 3679 | Rycrygic | |||

Scale 3667 | Kaptian | |||

Scale 3671 | Aeonyllic | |||

Scale 3659 | Polian | |||

Scale 3691 | Badyllic | |||

Scale 3707 | Rynygic | |||

Scale 3611 | ||||

Scale 3643 | Kydyllic | |||

Scale 3739 | Epanyllic | |||

Scale 3803 | Epidygic | |||

Scale 3931 | Aerygic | |||

Scale 3163 | Rogian | |||

Scale 3419 | Magen Abot 1 | |||

Scale 2651 | Panian | |||

Scale 1627 | Zyptian |

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