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
- Zolimic

Cardinality | 6 (hexatonic) |
---|---|

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

Forte Number | 6-Z48 |

Rotational Symmetry | none |

Reflection Axes | 0 |

Palindromic | yes |

Chirality | no |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 2 |

Modes | 5 |

Prime? | no prime: 679 |

Deep Scale | no |

Interval Vector | 232341 |

Interval Spectrum | p^{4}m^{3}n^{2}s^{3}d^{2}t |

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

Spectra Variation | 2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [0] |

Propriety | Improper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1253 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 1337 | Epogimic | ||||

3rd mode: Scale 679 | Lanimic | This is the prime mode | |||

4th mode: Scale 2387 | Paptimic | ||||

5th mode: Scale 3241 | Dalimic | ||||

6th mode: Scale 917 | Dygimic |

The prime form of this scale is Scale 679

Scale 679 | Lanimic |

The hexatonic modal family [1253, 1337, 679, 2387, 3241, 917] (Forte: 6-Z48) is the complement of the hexatonic modal family [427, 1379, 1421, 1589, 2261, 2737] (Forte: 6-Z26)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1253 is itself, because it is a palindromic scale!

Scale 1253 | Zolimic |

T_{0} | 1253 | T_{0}I | 1253 | |||||

T_{1} | 2506 | T_{1}I | 2506 | |||||

T_{2} | 917 | T_{2}I | 917 | |||||

T_{3} | 1834 | T_{3}I | 1834 | |||||

T_{4} | 3668 | T_{4}I | 3668 | |||||

T_{5} | 3241 | T_{5}I | 3241 | |||||

T_{6} | 2387 | T_{6}I | 2387 | |||||

T_{7} | 679 | T_{7}I | 679 | |||||

T_{8} | 1358 | T_{8}I | 1358 | |||||

T_{9} | 2716 | T_{9}I | 2716 | |||||

T_{10} | 1337 | T_{10}I | 1337 | |||||

T_{11} | 2674 | T_{11}I | 2674 |

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 1255 | Chromatic Mixolydian | |||

Scale 1249 | ||||

Scale 1251 | Sylimic | |||

Scale 1257 | Blues Scale | |||

Scale 1261 | Modified Blues | |||

Scale 1269 | Katythian | |||

Scale 1221 | Epyritonic | |||

Scale 1237 | Salimic | |||

Scale 1189 | Suspended Pentatonic | |||

Scale 1125 | Ionaritonic | |||

Scale 1381 | Padimic | |||

Scale 1509 | Ragian | |||

Scale 1765 | Lonian | |||

Scale 229 | ||||

Scale 741 | Gathimic | |||

Scale 2277 | Kagimic | |||

Scale 3301 | Chromatic Mixolydian Inverse |

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.