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
- Stynian

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

Pitch Class Set | {0,2,3,6,8,10,11} |

Forte Number | 7-26 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1623 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 699 |

Deep Scale | no |

Interval Vector | 344532 |

Interval Spectrum | p^{3}m^{5}n^{4}s^{4}d^{3}t^{2} |

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

Spectra Variation | 2.286 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.549 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3405 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1875 | Persichetti Scale | ||||

3rd mode: Scale 2985 | Epacrian | ||||

4th mode: Scale 885 | Sathian | ||||

5th mode: Scale 1245 | Lathian | ||||

6th mode: Scale 1335 | Elephant Scale | ||||

7th mode: Scale 2715 | Kynian |

The prime form of this scale is Scale 699

Scale 699 | Aerothian |

The heptatonic modal family [3405, 1875, 2985, 885, 1245, 1335, 2715] (Forte: 7-26) is the complement of the pentatonic modal family [309, 849, 1101, 1299, 2697] (Forte: 5-26)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3405 is 1623

Scale 1623 | Lothian |

Only scales that are chiral will have an enantiomorph. Scale 3405 is chiral, and its enantiomorph is scale 1623

Scale 1623 | Lothian |

T_{0} | 3405 | T_{0}I | 1623 | |||||

T_{1} | 2715 | T_{1}I | 3246 | |||||

T_{2} | 1335 | T_{2}I | 2397 | |||||

T_{3} | 2670 | T_{3}I | 699 | |||||

T_{4} | 1245 | T_{4}I | 1398 | |||||

T_{5} | 2490 | T_{5}I | 2796 | |||||

T_{6} | 885 | T_{6}I | 1497 | |||||

T_{7} | 1770 | T_{7}I | 2994 | |||||

T_{8} | 3540 | T_{8}I | 1893 | |||||

T_{9} | 2985 | T_{9}I | 3786 | |||||

T_{10} | 1875 | T_{10}I | 3477 | |||||

T_{11} | 3750 | T_{11}I | 2859 |

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 3407 | Katocryllic | |||

Scale 3401 | Palimic | |||

Scale 3403 | Bylian | |||

Scale 3397 | Sydimic | |||

Scale 3413 | Leading Whole-tone | |||

Scale 3421 | Aerothyllic | |||

Scale 3437 | ||||

Scale 3341 | ||||

Scale 3373 | Lodian | |||

Scale 3469 | Monian | |||

Scale 3533 | Thadyllic | |||

Scale 3149 | Phrycrimic | |||

Scale 3277 | Mela Nitimati | |||

Scale 3661 | Mixodorian | |||

Scale 3917 | Katoptyllic | |||

Scale 2381 | Takemitsu Linea Mode 1 | |||

Scale 2893 | Lylian | |||

Scale 1357 | Takemitsu Linea Mode 2 |

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.