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).

Cardinality | 4 (tetratonic) |
---|---|

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

Forte Number | 4-25 |

Rotational Symmetry | 6 semitones |

Reflection Axes | 1, 4 |

Palindromic | no |

Chirality | no |

Hemitonia | 0 (anhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 4 |

Modes | 1 |

Prime? | yes |

Deep Scale | no |

Interval Vector | 020202 |

Interval Spectrum | m^{2}s^{2}t^{2} |

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

Spectra Variation | 1 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 1.732 |

Myhill Property | no |

Balanced | yes |

Ridge Tones | [2,8] |

Propriety | Strictly Proper |

Heliotonic | no |

There are no common triads (major, minor, augmented and diminished) that can be formed using notes in this scale.

Modes are the rotational transformation of this scale. Scale 325 can be rotated to make 1 other scales. The 1st mode is itself.

2nd mode: Scale 1105 | Messiaen Truncated Mode 6 Inverse |

This is the prime form of this scale.

The tetratonic modal family [325, 1105] (Forte: 4-25) is the complement of the octatonic modal family [1495, 1885, 2795, 3445] (Forte: 8-25)

The inverse of a scale is a reflection using the root as its axis. The inverse of 325 is 1105

Scale 1105 | Messiaen Truncated Mode 6 Inverse |

T_{0} | 325 | T_{0}I | 1105 | |||||

T_{1} | 650 | T_{1}I | 2210 | |||||

T_{2} | 1300 | T_{2}I | 325 | |||||

T_{3} | 2600 | T_{3}I | 650 | |||||

T_{4} | 1105 | T_{4}I | 1300 | |||||

T_{5} | 2210 | T_{5}I | 2600 | |||||

T_{6} | 325 | T_{6}I | 1105 | |||||

T_{7} | 650 | T_{7}I | 2210 | |||||

T_{8} | 1300 | T_{8}I | 325 | |||||

T_{9} | 2600 | T_{9}I | 650 | |||||

T_{10} | 1105 | T_{10}I | 1300 | |||||

T_{11} | 2210 | T_{11}I | 2600 |

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 327 | Syptitonic | |||

Scale 321 | ||||

Scale 323 | ||||

Scale 329 | Mynic | |||

Scale 333 | Bogitonic | |||

Scale 341 | Bothitonic | |||

Scale 357 | Banitonic | |||

Scale 261 | ||||

Scale 293 | Raga Haripriya | |||

Scale 389 | ||||

Scale 453 | Raditonic | |||

Scale 69 | ||||

Scale 197 | ||||

Scale 581 | Eporic | |||

Scale 837 | Epaditonic | |||

Scale 1349 | Tholitonic | |||

Scale 2373 | Dyptitonic |

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.