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
- Bolitonic

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

Pitch Class Set | {0,4,6,8,10} |

Forte Number | 5-33 |

Rotational Symmetry | none |

Reflection Axes | 2 |

Palindromic | no |

Chirality | no |

Hemitonia | 0 (anhemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 5 |

Modes | 4 |

Prime? | no prime: 341 |

Deep Scale | no |

Interval Vector | 040402 |

Interval Spectrum | m^{4}s^{4}t^{2} |

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

Spectra Variation | 1.6 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.165 |

Myhill Property | yes |

Balanced | no |

Ridge Tones | [4] |

Propriety | Proper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1361 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode: Scale 341 | Bothitonic | This is the prime mode | |||

3rd mode: Scale 1109 | Kataditonic | ||||

4th mode: Scale 1301 | Koditonic | ||||

5th mode: Scale 1349 | Tholitonic |

The prime form of this scale is Scale 341

Scale 341 | Bothitonic |

The pentatonic modal family [1361, 341, 1109, 1301, 1349] (Forte: 5-33) is the complement of the heptatonic modal family [1367, 1373, 1397, 1493, 1877, 2731, 3413] (Forte: 7-33)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1361 is 341

Scale 341 | Bothitonic |

T_{0} | 1361 | T_{0}I | 341 | |||||

T_{1} | 2722 | T_{1}I | 682 | |||||

T_{2} | 1349 | T_{2}I | 1364 | |||||

T_{3} | 2698 | T_{3}I | 2728 | |||||

T_{4} | 1301 | T_{4}I | 1361 | |||||

T_{5} | 2602 | T_{5}I | 2722 | |||||

T_{6} | 1109 | T_{6}I | 1349 | |||||

T_{7} | 2218 | T_{7}I | 2698 | |||||

T_{8} | 341 | T_{8}I | 1301 | |||||

T_{9} | 682 | T_{9}I | 2602 | |||||

T_{10} | 1364 | T_{10}I | 1109 | |||||

T_{11} | 2728 | T_{11}I | 2218 |

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 1363 | Gygimic | |||

Scale 1365 | Whole Tone | |||

Scale 1369 | Boptimic | |||

Scale 1345 | ||||

Scale 1353 | Raga Harikauns | |||

Scale 1377 | ||||

Scale 1393 | Mycrimic | |||

Scale 1297 | Aeolic | |||

Scale 1329 | Epygitonic | |||

Scale 1425 | Ryphitonic | |||

Scale 1489 | Raga Jyoti | |||

Scale 1105 | Messiaen Truncated Mode 6 Inverse | |||

Scale 1233 | Ionoditonic | |||

Scale 1617 | Phronitonic | |||

Scale 1873 | Dathimic | |||

Scale 337 | Koptic | |||

Scale 849 | Aerynitonic | |||

Scale 2385 | Aeolanitonic | |||

Scale 3409 | Katanimic |

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.