presents more than you ever wanted to know about...

*i* = imperfections

Tones | 8 (octatonic) |
---|---|

Pitch Class Set | {0,1,4,5,6,7,10,11} |

Forte Number | 8-9 |

Rotational Symmetry | 6 semitones |

Palindromic | no |

Hemitonia | 6 (multihemitonic) |

Cohemitonia | 4 (multicohemitonic) |

Imperfections | 2 |

Modes | 3 |

Prime? | no prime: 975 |

Chirality | no |

Deep Scale | no |

Interval Vector | 644464 |

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

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

Spectra Variation | 1.5 |

Myhill Property | no |

Balanced | yes |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3315 can be rotated to make 3 other scales. The 1st mode is itself.

2nd mode: Scale 3705 | Messiaen mode 4 inverse | ||||

3rd mode: Scale 975 | Messiaen mode 4 | This is the prime mode | |||

4th mode: Scale 2535 | Messiaen mode 4 |

The prime form of this scale is Scale 975

Scale 975 | Messiaen mode 4 |

The octatonic modal family [3315, 3705, 975, 2535] is the negative of the tetratonic modal family [195, 2145]

The inverse of a scale is a reflection using the root as its axis. The inverse of 3315 is 2535

Scale 2535 | Messiaen mode 4 |

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 3313 | ||||

Scale 3317 | ||||

Scale 3319 | ||||

Scale 3323 | ||||

Scale 3299 | ||||

Scale 3307 | ||||

Scale 3283 | Mela Visvambhari | |||

Scale 3251 | Mela Hatakambari | |||

Scale 3187 | ||||

Scale 3443 | Verdi's Scala enigmatica | |||

Scale 3571 | ||||

Scale 3827 | ||||

Scale 2291 | ||||

Scale 2803 | Raga Bhatiyar | |||

Scale 1267 |

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