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).

- Carnatic Raga
- Raga Mukhari

- Hindustani
- Anandabhairavi

- Unknown / Unsorted
- Deshi
- Manji

- Gregorian Numbered
- Gregorian Number 1

- Western Mixed
- Dorian/Aeolian Mixed

- Zeitler
- Gadyllic

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

Pitch Class Set | {0,2,3,5,7,8,9,10} |

Forte Number | 8-23 |

Rotational Symmetry | none |

Reflection Axes | 2.5 |

Palindromic | no |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 1 |

Modes | 7 |

Prime? | no prime: 1455 |

Deep Scale | no |

Interval Vector | 465472 |

Interval Spectrum | p^{7}m^{4}n^{5}s^{6}d^{4}t^{2} |

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

Spectra Variation | 1.5 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [5] |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1965 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode: Scale 1515 | Phrygian/Locrian Mixed | ||||

3rd mode: Scale 2805 | Ishikotsucho | ||||

4th mode: Scale 1725 | Minor Bebop | ||||

5th mode: Scale 1455 | Phrygiolian | This is the prime mode | |||

6th mode: Scale 2775 | Godyllic | ||||

7th mode: Scale 3435 | Prokofiev | ||||

8th mode: Scale 3765 | Dominant Bebop |

The prime form of this scale is Scale 1455

Scale 1455 | Phrygiolian |

The octatonic modal family [1965, 1515, 2805, 1725, 1455, 2775, 3435, 3765] (Forte: 8-23) is the complement of the tetratonic modal family [165, 645, 1065, 1185] (Forte: 4-23)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1965 is 1725

Scale 1725 | Minor Bebop |

T_{0} | 1965 | T_{0}I | 1725 | |||||

T_{1} | 3930 | T_{1}I | 3450 | |||||

T_{2} | 3765 | T_{2}I | 2805 | |||||

T_{3} | 3435 | T_{3}I | 1515 | |||||

T_{4} | 2775 | T_{4}I | 3030 | |||||

T_{5} | 1455 | T_{5}I | 1965 | |||||

T_{6} | 2910 | T_{6}I | 3930 | |||||

T_{7} | 1725 | T_{7}I | 3765 | |||||

T_{8} | 3450 | T_{8}I | 3435 | |||||

T_{9} | 2805 | T_{9}I | 2775 | |||||

T_{10} | 1515 | T_{10}I | 1455 | |||||

T_{11} | 3030 | T_{11}I | 2910 |

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 1967 | Diatonic Dorian Mixed | |||

Scale 1961 | Soptian | |||

Scale 1963 | Epocryllic | |||

Scale 1957 | Pyrian | |||

Scale 1973 | Zyryllic | |||

Scale 1981 | Houseini | |||

Scale 1933 | Mocrian | |||

Scale 1949 | Mathyllic | |||

Scale 1997 | Raga Cintamani | |||

Scale 2029 | Kiourdi | |||

Scale 1837 | Dalian | |||

Scale 1901 | Ionidyllic | |||

Scale 1709 | Dorian | |||

Scale 1453 | Aeolian | |||

Scale 941 | Mela Jhankaradhvani | |||

Scale 2989 | Bebop Minor | |||

Scale 4013 | Raga Pilu |

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