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
- Ionocrygic

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

Pitch Class Set | {0,1,2,4,5,7,8,9,10} |

Forte Number | 9-11 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3517 |

Hemitonia | 6 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 2 |

Modes | 8 |

Prime? | no prime: 1775 |

Deep Scale | no |

Interval Vector | 667773 |

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

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

Spectra Variation | 1.111 |

Maximally Even | no |

Maximal Area Set | yes |

Interior Area | 2.799 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Proper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1975 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode: Scale 3035 | Gocrygic | ||||

3rd mode: Scale 3565 | Aeolorygic | ||||

4th mode: Scale 1915 | Thydygic | ||||

5th mode: Scale 3005 | Gycrygic | ||||

6th mode: Scale 1775 | Lyrygic | This is the prime mode | |||

7th mode: Scale 2935 | Modygic | ||||

8th mode: Scale 3515 | Moorish Phrygian | ||||

9th mode: Scale 3805 | Moptygic |

The prime form of this scale is Scale 1775

Scale 1775 | Lyrygic |

The nonatonic modal family [1975, 3035, 3565, 1915, 3005, 1775, 2935, 3515, 3805] (Forte: 9-11) is the complement of the tritonic modal family [137, 289, 529] (Forte: 3-11)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1975 is 3517

Scale 3517 | Epocrygic |

Only scales that are chiral will have an enantiomorph. Scale 1975 is chiral, and its enantiomorph is scale 3517

Scale 3517 | Epocrygic |

T_{0} | 1975 | T_{0}I | 3517 | |||||

T_{1} | 3950 | T_{1}I | 2939 | |||||

T_{2} | 3805 | T_{2}I | 1783 | |||||

T_{3} | 3515 | T_{3}I | 3566 | |||||

T_{4} | 2935 | T_{4}I | 3037 | |||||

T_{5} | 1775 | T_{5}I | 1979 | |||||

T_{6} | 3550 | T_{6}I | 3958 | |||||

T_{7} | 3005 | T_{7}I | 3821 | |||||

T_{8} | 1915 | T_{8}I | 3547 | |||||

T_{9} | 3830 | T_{9}I | 2999 | |||||

T_{10} | 3565 | T_{10}I | 1903 | |||||

T_{11} | 3035 | T_{11}I | 3806 |

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 1973 | Zyryllic | |||

Scale 1971 | Aerynyllic | |||

Scale 1979 | Aeradygic | |||

Scale 1983 | Soryllian | |||

Scale 1959 | Katolyllic | |||

Scale 1967 | Diatonic Dorian Mixed | |||

Scale 1943 | ||||

Scale 2007 | Stonygic | |||

Scale 2039 | Danyllian | |||

Scale 1847 | Thacryllic | |||

Scale 1911 | Messiaen Mode 3 | |||

Scale 1719 | Lyryllic | |||

Scale 1463 | ||||

Scale 951 | Thogyllic | |||

Scale 2999 | Chromatic and Permuted Diatonic Dorian Mixed | |||

Scale 4023 | Styptyllian |

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.