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.

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
- Aeraphitonic

Cardinality | 5 (pentatonic) |
---|---|

Pitch Class Set | {0,3,7,10,11} |

Forte Number | 5-Z37 |

Rotational Symmetry | none |

Reflection Axes | 5 |

Palindromic | no |

Chirality | no |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 3 |

Modes | 4 |

Prime? | no prime: 313 |

Deep Scale | no |

Interval Vector | 212320 |

Interval Spectrum | p^{2}m^{3}n^{2}sd^{2} |

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

Spectra Variation | 3.2 |

Maximally Even | no |

Myhill Property | no |

Balanced | no |

Ridge Tones | [10] |

Coherence | no |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 3209 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode: Scale 913 | Aeolyritonic | ||||

3rd mode: Scale 313 | Goritonic | This is the prime mode | |||

4th mode: Scale 551 | Aeoloditonic | ||||

5th mode: Scale 2323 | Doptitonic |

The prime form of this scale is Scale 313

Scale 313 | Goritonic |

The pentatonic modal family [3209, 913, 313, 551, 2323] (Forte: 5-Z37) is the complement of the heptatonic modal family [443, 1591, 1891, 2269, 2843, 2993, 3469] (Forte: 7-Z37)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3209 is 551

Scale 551 | Aeoloditonic |

T_{0} | 3209 | T_{0}I | 551 | |||||

T_{1} | 2323 | T_{1}I | 1102 | |||||

T_{2} | 551 | T_{2}I | 2204 | |||||

T_{3} | 1102 | T_{3}I | 313 | |||||

T_{4} | 2204 | T_{4}I | 626 | |||||

T_{5} | 313 | T_{5}I | 1252 | |||||

T_{6} | 626 | T_{6}I | 2504 | |||||

T_{7} | 1252 | T_{7}I | 913 | |||||

T_{8} | 2504 | T_{8}I | 1826 | |||||

T_{9} | 913 | T_{9}I | 3652 | |||||

T_{10} | 1826 | T_{10}I | 3209 | |||||

T_{11} | 3652 | T_{11}I | 2323 |

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 3211 | Epacrimic | |||

Scale 3213 | Eponimic | |||

Scale 3201 | ||||

Scale 3205 | ||||

Scale 3217 | Molitonic | |||

Scale 3225 | Ionalimic | |||

Scale 3241 | Dalimic | |||

Scale 3273 | Raga Jivantini | |||

Scale 3081 | ||||

Scale 3145 | Stolitonic | |||

Scale 3337 | ||||

Scale 3465 | Katathimic | |||

Scale 3721 | Phragimic | |||

Scale 2185 | Dygic | |||

Scale 2697 | Katagitonic | |||

Scale 1161 | Bi Yu |

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. Bibliography