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).

- Zeitler
- Donian

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

Pitch Class Set | {0,2,3,4,6,7,9} |

Forte Number | 7-25 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1897 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | yes |

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 |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 733 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1207 | Aeoloptian | ||||

3rd mode: Scale 2651 | Panian | ||||

4th mode: Scale 3373 | Lodian | ||||

5th mode: Scale 1867 | Solian | ||||

6th mode: Scale 2981 | Ionolian | ||||

7th mode: Scale 1769 | Blues Heptatonic II |

This is the prime form of this scale.

The heptatonic modal family [733, 1207, 2651, 3373, 1867, 2981, 1769] (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 733 is 1897

Scale 1897 | Ionopian |

Only scales that are chiral will have an enantiomorph. Scale 733 is chiral, and its enantiomorph is scale 1897

Scale 1897 | Ionopian |

T_{0} | 733 | T_{0}I | 1897 | |||||

T_{1} | 1466 | T_{1}I | 3794 | |||||

T_{2} | 2932 | T_{2}I | 3493 | |||||

T_{3} | 1769 | T_{3}I | 2891 | |||||

T_{4} | 3538 | T_{4}I | 1687 | |||||

T_{5} | 2981 | T_{5}I | 3374 | |||||

T_{6} | 1867 | T_{6}I | 2653 | |||||

T_{7} | 3734 | T_{7}I | 1211 | |||||

T_{8} | 3373 | T_{8}I | 2422 | |||||

T_{9} | 2651 | T_{9}I | 749 | |||||

T_{10} | 1207 | T_{10}I | 1498 | |||||

T_{11} | 2414 | T_{11}I | 2996 |

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 735 | Sylyllic | |||

Scale 729 | Stygimic | |||

Scale 731 | Ionorian | |||

Scale 725 | Raga Yamuna Kalyani | |||

Scale 717 | Raga Vijayanagari | |||

Scale 749 | Aeologian | |||

Scale 765 | ||||

Scale 669 | Gycrimic | |||

Scale 701 | Mixonyphian | |||

Scale 605 | Dycrimic | |||

Scale 861 | Rylian | |||

Scale 989 | Phrolyllic | |||

Scale 221 | ||||

Scale 477 | Stacrian | |||

Scale 1245 | Lathian | |||

Scale 1757 | ||||

Scale 2781 | Gycryllic |

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.