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
- Malian

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

Pitch Class Set | {0,2,4,5,6,8,11} |

Forte Number | 7-28 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1491 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 1 (uncohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 747 |

Deep Scale | no |

Interval Vector | 344433 |

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

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

Spectra Variation | 2 |

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 2421 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1629 | Synian | ||||

3rd mode: Scale 1431 | Phragian | ||||

4th mode: Scale 2763 | Mela Suvarnangi | ||||

5th mode: Scale 3429 | Marian | ||||

6th mode: Scale 1881 | Katorian | ||||

7th mode: Scale 747 | Lynian | This is the prime mode |

The prime form of this scale is Scale 747

Scale 747 | Lynian |

The heptatonic modal family [2421, 1629, 1431, 2763, 3429, 1881, 747] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

The inverse of a scale is a reflection using the root as its axis. The inverse of 2421 is 1491

Scale 1491 | Mela Namanarayani |

Only scales that are chiral will have an enantiomorph. Scale 2421 is chiral, and its enantiomorph is scale 1491

Scale 1491 | Mela Namanarayani |

T_{0} | 2421 | T_{0}I | 1491 | |||||

T_{1} | 747 | T_{1}I | 2982 | |||||

T_{2} | 1494 | T_{2}I | 1869 | |||||

T_{3} | 2988 | T_{3}I | 3738 | |||||

T_{4} | 1881 | T_{4}I | 3381 | |||||

T_{5} | 3762 | T_{5}I | 2667 | |||||

T_{6} | 3429 | T_{6}I | 1239 | |||||

T_{7} | 2763 | T_{7}I | 2478 | |||||

T_{8} | 1431 | T_{8}I | 861 | |||||

T_{9} | 2862 | T_{9}I | 1722 | |||||

T_{10} | 1629 | T_{10}I | 3444 | |||||

T_{11} | 3258 | T_{11}I | 2793 |

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 2423 | ||||

Scale 2417 | Kanimic | |||

Scale 2419 | Raga Lalita | |||

Scale 2425 | Rorian | |||

Scale 2429 | Kadyllic | |||

Scale 2405 | Katalimic | |||

Scale 2413 | Locrian Natural 2 | |||

Scale 2389 | Eskimo Hexatonic 2 | |||

Scale 2357 | Raga Sarasanana | |||

Scale 2485 | Harmonic Major | |||

Scale 2549 | Rydyllic | |||

Scale 2165 | ||||

Scale 2293 | Gorian | |||

Scale 2677 | Thodian | |||

Scale 2933 | ||||

Scale 3445 | Messiaen Mode 6 Inverse | |||

Scale 373 | Epagimic | |||

Scale 1397 | Major Locrian |

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.