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
- Katylygic

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

Pitch Class Set | {0,1,2,3,4,5,7,8,9} |

Forte Number | 9-4 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 4025 |

Hemitonia | 7 (multihemitonic) |

Cohemitonia | 5 (multicohemitonic) |

Imperfections | 2 |

Modes | 8 |

Prime? | yes |

Deep Scale | no |

Interval Vector | 766773 |

Interval Spectrum | p^{7}m^{7}n^{6}s^{6}d^{7}t^{3} |

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

Spectra Variation | 2 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.683 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 959 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode: Scale 2527 | Phradygic | ||||

3rd mode: Scale 3311 | Mixodygic | ||||

4th mode: Scale 3703 | Katalygic | ||||

5th mode: Scale 3899 | Katorygic | ||||

6th mode: Scale 3997 | Dogygic | ||||

7th mode: Scale 2023 | Zodygic | ||||

8th mode: Scale 3059 | Madygic | ||||

9th mode: Scale 3577 | Loptygic |

This is the prime form of this scale.

The nonatonic modal family [959, 2527, 3311, 3703, 3899, 3997, 2023, 3059, 3577] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

The inverse of a scale is a reflection using the root as its axis. The inverse of 959 is 4025

Scale 4025 | Kalygic |

Only scales that are chiral will have an enantiomorph. Scale 959 is chiral, and its enantiomorph is scale 4025

Scale 4025 | Kalygic |

T_{0} | 959 | T_{0}I | 4025 | |||||

T_{1} | 1918 | T_{1}I | 3955 | |||||

T_{2} | 3836 | T_{2}I | 3815 | |||||

T_{3} | 3577 | T_{3}I | 3535 | |||||

T_{4} | 3059 | T_{4}I | 2975 | |||||

T_{5} | 2023 | T_{5}I | 1855 | |||||

T_{6} | 4046 | T_{6}I | 3710 | |||||

T_{7} | 3997 | T_{7}I | 3325 | |||||

T_{8} | 3899 | T_{8}I | 2555 | |||||

T_{9} | 3703 | T_{9}I | 1015 | |||||

T_{10} | 3311 | T_{10}I | 2030 | |||||

T_{11} | 2527 | T_{11}I | 4060 |

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 957 | Phronyllic | |||

Scale 955 | Ionogyllic | |||

Scale 951 | Thogyllic | |||

Scale 943 | Aerygyllic | |||

Scale 927 | Gaptyllic | |||

Scale 991 | Aeolygic | |||

Scale 1023 | Dodyllian | |||

Scale 831 | Rodyllic | |||

Scale 895 | Aeolathygic | |||

Scale 703 | Aerocryllic | |||

Scale 447 | Thyphyllic | |||

Scale 1471 | Radygic | |||

Scale 1983 | Soryllian | |||

Scale 3007 | Zyryllian |

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.