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).

- Named After Composers
- Jeths' Mode

- Zeitler
- Gamian

Cardinality | 7 (heptatonic) |
---|---|

Pitch Class Set | {0,2,3,5,6,9,11} |

Forte Number | 7-31 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1739 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 0 (ancohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 731 |

Deep Scale | no |

Interval Vector | 336333 |

Interval Spectrum | p^{3}m^{3}n^{6}s^{3}d^{3}t^{3} |

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

Spectra Variation | 1.714 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.549 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | yes |

Modes are the rotational transformation of this scale. Scale 2669 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1691 | Kathian | ||||

3rd mode: Scale 2893 | Lylian | ||||

4th mode: Scale 1747 | Mela Ramapriya | ||||

5th mode: Scale 2921 | Pogian | ||||

6th mode: Scale 877 | Moravian Pistalkova | ||||

7th mode: Scale 1243 | Epylian |

The prime form of this scale is Scale 731

Scale 731 | Ionorian |

The heptatonic modal family [2669, 1691, 2893, 1747, 2921, 877, 1243] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2669 is 1739

Scale 1739 | Mela Sadvidhamargini |

Only scales that are chiral will have an enantiomorph. Scale 2669 is chiral, and its enantiomorph is scale 1739

Scale 1739 | Mela Sadvidhamargini |

T_{0} | 2669 | T_{0}I | 1739 | |||||

T_{1} | 1243 | T_{1}I | 3478 | |||||

T_{2} | 2486 | T_{2}I | 2861 | |||||

T_{3} | 877 | T_{3}I | 1627 | |||||

T_{4} | 1754 | T_{4}I | 3254 | |||||

T_{5} | 3508 | T_{5}I | 2413 | |||||

T_{6} | 2921 | T_{6}I | 731 | |||||

T_{7} | 1747 | T_{7}I | 1462 | |||||

T_{8} | 3494 | T_{8}I | 2924 | |||||

T_{9} | 2893 | T_{9}I | 1753 | |||||

T_{10} | 1691 | T_{10}I | 3506 | |||||

T_{11} | 3382 | T_{11}I | 2917 |

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 2671 | Aerolyllic | |||

Scale 2665 | Aeradimic | |||

Scale 2667 | Byrian | |||

Scale 2661 | Stydimic | |||

Scale 2677 | Thodian | |||

Scale 2685 | Ionoryllic | |||

Scale 2637 | Raga Ranjani | |||

Scale 2653 | Sygian | |||

Scale 2605 | Rylimic | |||

Scale 2733 | Melodic Minor Ascending | |||

Scale 2797 | Stalyllic | |||

Scale 2925 | Diminished | |||

Scale 2157 | ||||

Scale 2413 | Locrian Natural 2 | |||

Scale 3181 | Rolian | |||

Scale 3693 | Stadyllic | |||

Scale 621 | Pyramid Hexatonic | |||

Scale 1645 | Dorian Flat 5 |

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.