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
- Starygic

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

Pitch Class Set | {0,2,5,6,7,8,9,10,11} |

Forte Number | 9-2 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1279 |

Hemitonia | 7 (multihemitonic) |

Cohemitonia | 6 (multicohemitonic) |

Imperfections | 3 |

Modes | 8 |

Prime? | no prime: 767 |

Deep Scale | no |

Interval Vector | 777663 |

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

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

Spectra Variation | 2.444 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 4069 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode: Scale 2041 | Aeolacrygic | ||||

3rd mode: Scale 767 | Raptygic | This is the prime mode | |||

4th mode: Scale 2431 | Gythygic | ||||

5th mode: Scale 3263 | Pyrygic | ||||

6th mode: Scale 3679 | Rycrygic | ||||

7th mode: Scale 3887 | Phrathygic | ||||

8th mode: Scale 3991 | Badygic | ||||

9th mode: Scale 4043 | Phrocrygic |

The prime form of this scale is Scale 767

Scale 767 | Raptygic |

The nonatonic modal family [4069, 2041, 767, 2431, 3263, 3679, 3887, 3991, 4043] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

The inverse of a scale is a reflection using the root as its axis. The inverse of 4069 is 1279

Scale 1279 | Sarygic |

Only scales that are chiral will have an enantiomorph. Scale 4069 is chiral, and its enantiomorph is scale 1279

Scale 1279 | Sarygic |

T_{0} | 4069 | T_{0}I | 1279 | |||||

T_{1} | 4043 | T_{1}I | 2558 | |||||

T_{2} | 3991 | T_{2}I | 1021 | |||||

T_{3} | 3887 | T_{3}I | 2042 | |||||

T_{4} | 3679 | T_{4}I | 4084 | |||||

T_{5} | 3263 | T_{5}I | 4073 | |||||

T_{6} | 2431 | T_{6}I | 4051 | |||||

T_{7} | 767 | T_{7}I | 4007 | |||||

T_{8} | 1534 | T_{8}I | 3919 | |||||

T_{9} | 3068 | T_{9}I | 3743 | |||||

T_{10} | 2041 | T_{10}I | 3391 | |||||

T_{11} | 4082 | T_{11}I | 2687 |

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 4071 | Rygyllian | |||

Scale 4065 | ||||

Scale 4067 | Aeolarygic | |||

Scale 4073 | Sathygic | |||

Scale 4077 | Gothyllian | |||

Scale 4085 | Sydyllian | |||

Scale 4037 | Ionyllic | |||

Scale 4053 | Kyrygic | |||

Scale 4005 | ||||

Scale 3941 | Stathyllic | |||

Scale 3813 | Aeologyllic | |||

Scale 3557 | ||||

Scale 3045 | Raptyllic | |||

Scale 2021 | Katycryllic |

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.