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
- Kaptygic

Cardinality | 9 (nonatonic) |
---|---|

Pitch Class Set | {0,2,4,5,6,7,8,10,11} |

Forte Number | 9-8 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1527 |

Hemitonia | 6 (multihemitonic) |

Cohemitonia | 4 (multicohemitonic) |

Imperfections | 3 |

Modes | 8 |

Prime? | no prime: 1503 |

Deep Scale | no |

Interval Vector | 676764 |

Interval Spectrum | p^{6}m^{7}n^{6}s^{7}d^{6}t^{4} |

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

Spectra Variation | 1.556 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3573 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode: Scale 1917 | Thydyllian | ||||

3rd mode: Scale 1503 | Epiryllian | This is the prime mode | |||

4th mode: Scale 2799 | Lyryllian | ||||

5th mode: Scale 3447 | Mogyllian | ||||

6th mode: Scale 3771 | Katodyllian | ||||

7th mode: Scale 3933 | Ionidygic | ||||

8th mode: Scale 2007 | Stonygic | ||||

9th mode: Scale 3051 | Stalygic |

The prime form of this scale is Scale 1503

Scale 1503 | Epiryllian |

The nonatonic modal family [3573, 1917, 1503, 2799, 3447, 3771, 3933, 2007, 3051] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3573 is 1527

Scale 1527 | Aeolyrigic |

Only scales that are chiral will have an enantiomorph. Scale 3573 is chiral, and its enantiomorph is scale 1527

Scale 1527 | Aeolyrigic |

T_{0} | 3573 | T_{0}I | 1527 | |||||

T_{1} | 3051 | T_{1}I | 3054 | |||||

T_{2} | 2007 | T_{2}I | 2013 | |||||

T_{3} | 4014 | T_{3}I | 4026 | |||||

T_{4} | 3933 | T_{4}I | 3957 | |||||

T_{5} | 3771 | T_{5}I | 3819 | |||||

T_{6} | 3447 | T_{6}I | 3543 | |||||

T_{7} | 2799 | T_{7}I | 2991 | |||||

T_{8} | 1503 | T_{8}I | 1887 | |||||

T_{9} | 3006 | T_{9}I | 3774 | |||||

T_{10} | 1917 | T_{10}I | 3453 | |||||

T_{11} | 3834 | T_{11}I | 2811 |

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 3575 | Symmetrical Decatonic | |||

Scale 3569 | Aeoladyllic | |||

Scale 3571 | Dyrygic | |||

Scale 3577 | Loptygic | |||

Scale 3581 | Epocryllian | |||

Scale 3557 | ||||

Scale 3565 | Aeolorygic | |||

Scale 3541 | Racryllic | |||

Scale 3509 | Stogyllic | |||

Scale 3445 | Messiaen Mode 6 Inverse | |||

Scale 3317 | Katynyllic | |||

Scale 3829 | Taishikicho | |||

Scale 4085 | Sydyllian | |||

Scale 2549 | Rydyllic | |||

Scale 3061 | Apinygic | |||

Scale 1525 | Sodyllic |

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.