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
- Rathian

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

Pitch Class Set | {0,2,5,7,8,10,11} |

Forte Number | 7-25 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1207 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 733 |

Deep Scale | no |

Interval Vector | 345342 |

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

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

Spectra Variation | 2.286 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Coherence | no |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3493 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1897 | Ionopian | ||||

3rd mode: Scale 749 | Aeologian | ||||

4th mode: Scale 1211 | Zadian | ||||

5th mode: Scale 2653 | Sygian | ||||

6th mode: Scale 1687 | Phralian | ||||

7th mode: Scale 2891 | Phrogian |

The prime form of this scale is Scale 733

Scale 733 | Donian |

The heptatonic modal family [3493, 1897, 749, 1211, 2653, 1687, 2891] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3493 is 1207

Scale 1207 | Aeoloptian |

Only scales that are chiral will have an enantiomorph. Scale 3493 is chiral, and its enantiomorph is scale 1207

Scale 1207 | Aeoloptian |

T_{0} | 3493 | T_{0}I | 1207 | |||||

T_{1} | 2891 | T_{1}I | 2414 | |||||

T_{2} | 1687 | T_{2}I | 733 | |||||

T_{3} | 3374 | T_{3}I | 1466 | |||||

T_{4} | 2653 | T_{4}I | 2932 | |||||

T_{5} | 1211 | T_{5}I | 1769 | |||||

T_{6} | 2422 | T_{6}I | 3538 | |||||

T_{7} | 749 | T_{7}I | 2981 | |||||

T_{8} | 1498 | T_{8}I | 1867 | |||||

T_{9} | 2996 | T_{9}I | 3734 | |||||

T_{10} | 1897 | T_{10}I | 3373 | |||||

T_{11} | 3794 | T_{11}I | 2651 |

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 3495 | Banyllic | |||

Scale 3489 | ||||

Scale 3491 | Tharian | |||

Scale 3497 | Phrolian | |||

Scale 3501 | Maqam Nahawand | |||

Scale 3509 | Stogyllic | |||

Scale 3461 | ||||

Scale 3477 | Kyptian | |||

Scale 3525 | Zocrian | |||

Scale 3557 | ||||

Scale 3365 | Katolimic | |||

Scale 3429 | Marian | |||

Scale 3237 | Raga Brindabani Sarang | |||

Scale 3749 | Raga Sorati | |||

Scale 4005 | ||||

Scale 2469 | Raga Bhinna Pancama | |||

Scale 2981 | Ionolian | |||

Scale 1445 | Raga Navamanohari |

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