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).

- Arabic
- Maqam Hijaz
- Maqam Hedjaz

- Zeitler
- Ponyllic

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

Pitch Class Set | {0,1,4,5,7,8,10,11} |

Forte Number | 8-18 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 2487 |

Hemitonia | 5 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 3 |

Modes | 7 |

Prime? | no prime: 879 |

Deep Scale | no |

Interval Vector | 546553 |

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

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

Spectra Variation | 2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3507 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 3801 | Maptyllic | ||||

3rd mode: Scale 987 | Aeraptyllic | ||||

4th mode: Scale 2541 | Algerian | ||||

5th mode: Scale 1659 | Maqam Shadd'araban | ||||

6th mode: Scale 2877 | Phrylyllic | ||||

7th mode: Scale 1743 | Epigyllic | ||||

8th mode: Scale 2919 | Molyllic |

The prime form of this scale is Scale 879

Scale 879 | Aeranyllic |

The octatonic modal family [3507, 3801, 987, 2541, 1659, 2877, 1743, 2919] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3507 is 2487

Scale 2487 | Dothyllic |

Only scales that are chiral will have an enantiomorph. Scale 3507 is chiral, and its enantiomorph is scale 2487

Scale 2487 | Dothyllic |

T_{0} | 3507 | T_{0}I | 2487 | |||||

T_{1} | 2919 | T_{1}I | 879 | |||||

T_{2} | 1743 | T_{2}I | 1758 | |||||

T_{3} | 3486 | T_{3}I | 3516 | |||||

T_{4} | 2877 | T_{4}I | 2937 | |||||

T_{5} | 1659 | T_{5}I | 1779 | |||||

T_{6} | 3318 | T_{6}I | 3558 | |||||

T_{7} | 2541 | T_{7}I | 3021 | |||||

T_{8} | 987 | T_{8}I | 1947 | |||||

T_{9} | 1974 | T_{9}I | 3894 | |||||

T_{10} | 3948 | T_{10}I | 3693 | |||||

T_{11} | 3801 | T_{11}I | 3291 |

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 3505 | Stygian | |||

Scale 3509 | Stogyllic | |||

Scale 3511 | Epolygic | |||

Scale 3515 | Moorish Phrygian | |||

Scale 3491 | Tharian | |||

Scale 3499 | Hamel | |||

Scale 3475 | Kylian | |||

Scale 3539 | Aeoryllic | |||

Scale 3571 | Dyrygic | |||

Scale 3379 | Verdi's Scala Enigmatica Descending | |||

Scale 3443 | Verdi's Scala Enigmatica | |||

Scale 3251 | Mela Hatakambari | |||

Scale 3763 | Modyllic | |||

Scale 4019 | Lonygic | |||

Scale 2483 | Double Harmonic | |||

Scale 2995 | Raga Saurashtra | |||

Scale 1459 | Phrygian Dominant |

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.