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).

- Messiaen
- Messiaen Truncated Mode 6 Inverse

- Zeitler
- Stathic

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

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

Forte Number | 4-25 |

Rotational Symmetry | 6 semitones |

Reflection Axes | 2, 5 |

Palindromic | no |

Chirality | no |

Hemitonia | 0 (anhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 4 |

Modes | 1 |

Prime? | no prime: 325 |

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 |

Myhill Property | no |

Balanced | yes |

Ridge Tones | [4,10] |

Propriety | Strictly Proper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1105 can be rotated to make 1 other scales. The 1st mode is itself.

2nd mode: Scale 325 | Messiaen Truncated Mode 6 | This is the prime mode |

The prime form of this scale is Scale 325

Scale 325 | Messiaen Truncated Mode 6 |

The tetratonic modal family [1105, 325] (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 1105 is 325

Scale 325 | Messiaen Truncated Mode 6 |

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

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

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

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

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

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

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

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

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

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

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

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

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 1107 | Mogitonic | |||

Scale 1109 | Kataditonic | |||

Scale 1113 | Locrian Pentatonic 2 | |||

Scale 1089 | ||||

Scale 1097 | Aeraphic | |||

Scale 1121 | ||||

Scale 1137 | Stonitonic | |||

Scale 1041 | ||||

Scale 1073 | ||||

Scale 1169 | Raga Mahathi | |||

Scale 1233 | Ionoditonic | |||

Scale 1361 | Bolitonic | |||

Scale 1617 | Phronitonic | |||

Scale 81 | ||||

Scale 593 | Saric | |||

Scale 2129 | Raga Nigamagamini | |||

Scale 3153 | Zathitonic |

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.