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
- Thacrimic

Cardinality | 6 (hexatonic) |
---|---|

Pitch Class Set | {0,1,3,6,7,10} |

Forte Number | 6-Z50 |

Rotational Symmetry | none |

Reflection Axes | 0.5 |

Palindromic | no |

Chirality | no |

Hemitonia | 2 (dihemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 3 |

Modes | 5 |

Prime? | no prime: 723 |

Deep Scale | no |

Interval Vector | 224232 |

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

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

Spectra Variation | 1.667 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.366 |

Myhill Property | no |

Balanced | no |

Ridge Tones | [1] |

Propriety | Proper |

Heliotonic | no |

Modes are the rotational transformation of this scale. Scale 1227 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 2661 | Stydimic | ||||

3rd mode: Scale 1689 | Lorimic | ||||

4th mode: Scale 723 | Ionadimic | This is the prime mode | |||

5th mode: Scale 2409 | Zacrimic | ||||

6th mode: Scale 813 | Larimic |

The prime form of this scale is Scale 723

Scale 723 | Ionadimic |

The hexatonic modal family [1227, 2661, 1689, 723, 2409, 813] (Forte: 6-Z50) is the complement of the hexatonic modal family [717, 843, 1203, 1641, 2469, 2649] (Forte: 6-Z29)

The inverse of a scale is a reflection using the root as its axis. The inverse of 1227 is 2661

Scale 2661 | Stydimic |

T_{0} | 1227 | T_{0}I | 2661 | |||||

T_{1} | 2454 | T_{1}I | 1227 | |||||

T_{2} | 813 | T_{2}I | 2454 | |||||

T_{3} | 1626 | T_{3}I | 813 | |||||

T_{4} | 3252 | T_{4}I | 1626 | |||||

T_{5} | 2409 | T_{5}I | 3252 | |||||

T_{6} | 723 | T_{6}I | 2409 | |||||

T_{7} | 1446 | T_{7}I | 723 | |||||

T_{8} | 2892 | T_{8}I | 1446 | |||||

T_{9} | 1689 | T_{9}I | 2892 | |||||

T_{10} | 3378 | T_{10}I | 1689 | |||||

T_{11} | 2661 | T_{11}I | 3378 |

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 1225 | Raga Samudhra Priya | |||

Scale 1229 | Raga Simharava | |||

Scale 1231 | Logian | |||

Scale 1219 | ||||

Scale 1223 | Phryptimic | |||

Scale 1235 | Messiaen Truncated Mode 2 | |||

Scale 1243 | Epylian | |||

Scale 1259 | Stadian | |||

Scale 1163 | Raga Rukmangi | |||

Scale 1195 | Raga Gandharavam | |||

Scale 1099 | Dyritonic | |||

Scale 1355 | Raga Bhavani | |||

Scale 1483 | Mela Bhavapriya | |||

Scale 1739 | Mela Sadvidhamargini | |||

Scale 203 | ||||

Scale 715 | Messiaen Truncated Mode 2 | |||

Scale 2251 | Zodimic | |||

Scale 3275 | Mela Divyamani |

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.