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
- Stalian

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

Pitch Class Set | {0,3,6,7,8,10,11} |

Forte Number | 7-Z17 |

Rotational Symmetry | none |

Reflection Axes | 3 |

Palindromic | no |

Chirality | no |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 631 |

Deep Scale | no |

Interval Vector | 434541 |

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

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

Spectra Variation | 2.571 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [6] |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3529 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 953 | Mela Yagapriya | ||||

3rd mode: Scale 631 | Zygian | This is the prime mode | |||

4th mode: Scale 2363 | Kataptian | ||||

5th mode: Scale 3229 | Aeolaptian | ||||

6th mode: Scale 1831 | Pothian | ||||

7th mode: Scale 2963 | Bygian |

The prime form of this scale is Scale 631

Scale 631 | Zygian |

The heptatonic modal family [3529, 953, 631, 2363, 3229, 1831, 2963] (Forte: 7-Z17) is the complement of the pentatonic modal family [283, 433, 1571, 2189, 2833] (Forte: 5-Z17)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3529 is 631

Scale 631 | Zygian |

T_{0} | 3529 | T_{0}I | 631 | |||||

T_{1} | 2963 | T_{1}I | 1262 | |||||

T_{2} | 1831 | T_{2}I | 2524 | |||||

T_{3} | 3662 | T_{3}I | 953 | |||||

T_{4} | 3229 | T_{4}I | 1906 | |||||

T_{5} | 2363 | T_{5}I | 3812 | |||||

T_{6} | 631 | T_{6}I | 3529 | |||||

T_{7} | 1262 | T_{7}I | 2963 | |||||

T_{8} | 2524 | T_{8}I | 1831 | |||||

T_{9} | 953 | T_{9}I | 3662 | |||||

T_{10} | 1906 | T_{10}I | 3229 | |||||

T_{11} | 3812 | T_{11}I | 2363 |

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 3531 | Neveseri | |||

Scale 3533 | Thadyllic | |||

Scale 3521 | ||||

Scale 3525 | Zocrian | |||

Scale 3537 | Katogian | |||

Scale 3545 | Thyptyllic | |||

Scale 3561 | Pothyllic | |||

Scale 3465 | Katathimic | |||

Scale 3497 | Phrolian | |||

Scale 3401 | Palimic | |||

Scale 3273 | Raga Jivantini | |||

Scale 3785 | Epagian | |||

Scale 4041 | Zaryllic | |||

Scale 2505 | Mydimic | |||

Scale 3017 | Gacrian | |||

Scale 1481 | Zagimic |

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.