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).

- Zeitler
- Zonian

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

Pitch Class Set | {0,1,2,6,8,10,11} |

Forte Number | 7-9 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 3159 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 351 |

Deep Scale | no |

Interval Vector | 453432 |

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

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

Spectra Variation | 3.429 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.299 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 3399 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 3747 | Myrian | ||||

3rd mode: Scale 3921 | Pythian | ||||

4th mode: Scale 501 | Katylian | ||||

5th mode: Scale 1149 | Bydian | ||||

6th mode: Scale 1311 | Bynian | ||||

7th mode: Scale 2703 | Galian |

The prime form of this scale is Scale 351

Scale 351 | Epanian |

The heptatonic modal family [3399, 3747, 3921, 501, 1149, 1311, 2703] (Forte: 7-9) is the complement of the pentatonic modal family [87, 1473, 1797, 2091, 3093] (Forte: 5-9)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3399 is 3159

Scale 3159 | Stocrian |

Only scales that are chiral will have an enantiomorph. Scale 3399 is chiral, and its enantiomorph is scale 3159

Scale 3159 | Stocrian |

T_{0} | 3399 | T_{0}I | 3159 | |||||

T_{1} | 2703 | T_{1}I | 2223 | |||||

T_{2} | 1311 | T_{2}I | 351 | |||||

T_{3} | 2622 | T_{3}I | 702 | |||||

T_{4} | 1149 | T_{4}I | 1404 | |||||

T_{5} | 2298 | T_{5}I | 2808 | |||||

T_{6} | 501 | T_{6}I | 1521 | |||||

T_{7} | 1002 | T_{7}I | 3042 | |||||

T_{8} | 2004 | T_{8}I | 1989 | |||||

T_{9} | 4008 | T_{9}I | 3978 | |||||

T_{10} | 3921 | T_{10}I | 3861 | |||||

T_{11} | 3747 | T_{11}I | 3627 |

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 3397 | Sydimic | |||

Scale 3395 | ||||

Scale 3403 | Bylian | |||

Scale 3407 | Katocryllic | |||

Scale 3415 | Ionaptyllic | |||

Scale 3431 | Zyptyllic | |||

Scale 3335 | ||||

Scale 3367 | Moptian | |||

Scale 3463 | ||||

Scale 3527 | Ronyllic | |||

Scale 3143 | Polimic | |||

Scale 3271 | Mela Raghupriya | |||

Scale 3655 | Mathian | |||

Scale 3911 | Katyryllic | |||

Scale 2375 | Aeolaptimic | |||

Scale 2887 | Gaptian | |||

Scale 1351 | Aeraptimic |

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.