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- Zeitler
- Phrodian

Cardinality | 7 (heptatonic) |
---|---|

Pitch Class Set | {0,2,3,4,8,10,11} |

Forte Number | 7-13 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1815 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 375 |

Deep Scale | no |

Interval Vector | 443532 |

Interval Spectrum | p^{3}m^{5}n^{3}s^{4}d^{4}t^{2} |

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

Spectra Variation | 2.857 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3357 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1863 | Pycrian | ||||

3rd mode: Scale 2979 | Gyptian | ||||

4th mode: Scale 3537 | Katogian | ||||

5th mode: Scale 477 | Stacrian | ||||

6th mode: Scale 1143 | Styrian | ||||

7th mode: Scale 2619 | Ionyrian |

The prime form of this scale is Scale 375

Scale 375 | Sodian |

The heptatonic modal family [3357, 1863, 2979, 3537, 477, 1143, 2619] (Forte: 7-13) is the complement of the pentatonic modal family [279, 369, 1809, 2187, 3141] (Forte: 5-13)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3357 is 1815

Scale 1815 | Godian |

Only scales that are chiral will have an enantiomorph. Scale 3357 is chiral, and its enantiomorph is scale 1815

Scale 1815 | Godian |

T_{0} | 3357 | T_{0}I | 1815 | |||||

T_{1} | 2619 | T_{1}I | 3630 | |||||

T_{2} | 1143 | T_{2}I | 3165 | |||||

T_{3} | 2286 | T_{3}I | 2235 | |||||

T_{4} | 477 | T_{4}I | 375 | |||||

T_{5} | 954 | T_{5}I | 750 | |||||

T_{6} | 1908 | T_{6}I | 1500 | |||||

T_{7} | 3816 | T_{7}I | 3000 | |||||

T_{8} | 3537 | T_{8}I | 1905 | |||||

T_{9} | 2979 | T_{9}I | 3810 | |||||

T_{10} | 1863 | T_{10}I | 3525 | |||||

T_{11} | 3726 | T_{11}I | 2955 |

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 3359 | Bonyllic | |||

Scale 3353 | Phraptimic | |||

Scale 3355 | Bagian | |||

Scale 3349 | Aeolocrimic | |||

Scale 3341 | ||||

Scale 3373 | Lodian | |||

Scale 3389 | Socryllic | |||

Scale 3421 | Aerothyllic | |||

Scale 3485 | Sabach | |||

Scale 3101 | ||||

Scale 3229 | Aeolaptian | |||

Scale 3613 | ||||

Scale 3869 | Bygyllic | |||

Scale 2333 | Stynimic | |||

Scale 2845 | Baptian | |||

Scale 1309 | Pogimic |

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