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
- Katolian

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

Pitch Class Set | {0,1,2,3,5,6,10} |

Forte Number | 7-11 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3781 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 3 |

Modes | 6 |

Prime? | no prime: 379 |

Deep Scale | no |

Interval Vector | 444441 |

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

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

Spectra Variation | 3.143 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1135 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 2615 | Thoptian | ||||

3rd mode: Scale 3355 | Bagian | ||||

4th mode: Scale 3725 | Kyrian | ||||

5th mode: Scale 1955 | Sonian | ||||

6th mode: Scale 3025 | Epycrian | ||||

7th mode: Scale 445 | Gocrian |

The prime form of this scale is Scale 379

Scale 379 | Aeragian |

The heptatonic modal family [1135, 2615, 3355, 3725, 1955, 3025, 445] (Forte: 7-11) is the complement of the pentatonic modal family [157, 929, 1063, 2579, 3337] (Forte: 5-11)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1135 is 3781

Scale 3781 | Gyphian |

Only scales that are chiral will have an enantiomorph. Scale 1135 is chiral, and its enantiomorph is scale 3781

Scale 3781 | Gyphian |

T_{0} | 1135 | T_{0}I | 3781 | |||||

T_{1} | 2270 | T_{1}I | 3467 | |||||

T_{2} | 445 | T_{2}I | 2839 | |||||

T_{3} | 890 | T_{3}I | 1583 | |||||

T_{4} | 1780 | T_{4}I | 3166 | |||||

T_{5} | 3560 | T_{5}I | 2237 | |||||

T_{6} | 3025 | T_{6}I | 379 | |||||

T_{7} | 1955 | T_{7}I | 758 | |||||

T_{8} | 3910 | T_{8}I | 1516 | |||||

T_{9} | 3725 | T_{9}I | 3032 | |||||

T_{10} | 3355 | T_{10}I | 1969 | |||||

T_{11} | 2615 | T_{11}I | 3938 |

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 1133 | Stycrimic | |||

Scale 1131 | Honchoshi Plagal Form | |||

Scale 1127 | Eparimic | |||

Scale 1143 | Styrian | |||

Scale 1151 | Mythyllic | |||

Scale 1103 | Lynimic | |||

Scale 1119 | Rarian | |||

Scale 1071 | ||||

Scale 1199 | Magian | |||

Scale 1263 | Stynyllic | |||

Scale 1391 | Aeradyllic | |||

Scale 1647 | Polyllic | |||

Scale 111 | ||||

Scale 623 | Sycrian | |||

Scale 2159 | ||||

Scale 3183 | Mixonyllic |

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.