The Exciting Universe Of Music Theory

presents

more than you ever wanted to know about...

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).

- Western
- Whole Tone

- Messiaen
- Messiaen Mode 1

- Carnatic Raga
- Raga Gopriya

- Western Modern
- Anhemitonic Hexatonic
- Anhemic Hexatonic
- Auxiliary Augmented

- Zeitler
- Kylimic

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

Pitch Class Set | {0,2,4,6,8,10} |

Forte Number | 6-35 |

Rotational Symmetry | 2, 4, 6, 8, 10 semitones |

Reflection Axes | 0, 1, 2, 3, 4, 5 |

Palindromic | yes |

Chirality | no |

Hemitonia | 0 (anhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 6 |

Modes | 0 |

Prime? | yes |

Deep Scale | no |

Interval Vector | 060603 |

Interval Spectrum | m^{6}s^{6}t^{3} |

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

Spectra Variation | 0 |

Maximally Even | yes |

Maximal Area Set | yes |

Interior Area | 2.598 |

Myhill Property | no |

Balanced | yes |

Ridge Tones | [0,2,4,6,8,10] |

Propriety | Strictly Proper |

Heliotonic | no |

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

** Pitches are shown with C as the root*

Triad Type | Triad^{*} | Pitch Classes | Degree | Eccentricity | Closeness Centrality |
---|---|---|---|---|---|

Augmented Triads | C+ | {0,4,8} | 0 | n/a | n/a |

D+ | {2,6,10} | 0 | n/a | n/a |

Above is a graph showing opportunities for parsimonious voice leading between triads^{*}. There are no lines connecting nodes in the graph, because the chords are not adjacent with common tones.

Diameter | n/a |
---|---|

Radius | n/a |

Self-Centered | yes |

Modes are the rotational transformation of this scale. This scale has no modes, becaue any rotation of this scale will produce another copy of itself.

This is the prime form of this scale.

The hexatonic modal family [1365] (Forte: 6-35) is the complement of the hexatonic modal family [1365] (Forte: 6-35)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1365 is itself, because it is a palindromic scale!

Scale 1365 | Whole Tone |

T_{0} | 1365 | T_{0}I | 1365 | |||||

T_{1} | 2730 | T_{1}I | 2730 | |||||

T_{2} | 1365 | T_{2}I | 1365 | |||||

T_{3} | 2730 | T_{3}I | 2730 | |||||

T_{4} | 1365 | T_{4}I | 1365 | |||||

T_{5} | 2730 | T_{5}I | 2730 | |||||

T_{6} | 1365 | T_{6}I | 1365 | |||||

T_{7} | 2730 | T_{7}I | 2730 | |||||

T_{8} | 1365 | T_{8}I | 1365 | |||||

T_{9} | 2730 | T_{9}I | 2730 | |||||

T_{10} | 1365 | T_{10}I | 1365 | |||||

T_{11} | 2730 | T_{11}I | 2730 |

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 1367 | Leading Whole-Tone Inverse | |||

Scale 1361 | Bolitonic | |||

Scale 1363 | Gygimic | |||

Scale 1369 | Boptimic | |||

Scale 1373 | Storian | |||

Scale 1349 | Tholitonic | |||

Scale 1357 | Takemitsu Linea Mode 2 | |||

Scale 1381 | Padimic | |||

Scale 1397 | Major Locrian | |||

Scale 1301 | Koditonic | |||

Scale 1333 | Lyptimic | |||

Scale 1429 | Bythimic | |||

Scale 1493 | Lydian Minor | |||

Scale 1109 | Kataditonic | |||

Scale 1237 | Salimic | |||

Scale 1621 | Scriabin's Prometheus | |||

Scale 1877 | Aeroptian | |||

Scale 341 | Bothitonic | |||

Scale 853 | Epothimic | |||

Scale 2389 | Eskimo Hexatonic 2 | |||

Scale 3413 | Leading Whole-tone |

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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.