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
- Phragimic

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

Pitch Class Set | {0,3,7,9,10,11} |

Forte Number | 6-Z39 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 559 |

Hemitonia | 3 (trihemitonic) |

Cohemitonia | 2 (dicohemitonic) |

Imperfections | 4 |

Modes | 5 |

Prime? | no prime: 317 |

Deep Scale | no |

Interval Vector | 333321 |

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

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

Spectra Variation | 3.667 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.116 |

Myhill Property | no |

Balanced | no |

Ridge Tones | none |

Propriety | Improper |

Heliotonic | no |

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

** Pitches are shown with C as the root*

Triad Type | Triad^{*} | Pitch Classes | Degree | Eccentricity | Closeness Centrality |
---|---|---|---|---|---|

Major Triads | D♯ | {3,7,10} | 1 | 3 | 1.5 |

Minor Triads | cm | {0,3,7} | 2 | 2 | 1 |

Augmented Triads | D♯+ | {3,7,11} | 2 | 2 | 1 |

Diminished Triads | a° | {9,0,3} | 1 | 3 | 1.5 |

Above is a graph showing opportunities for parsimonious voice leading between triads^{*}. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter | 3 |
---|---|

Radius | 2 |

Self-Centered | no |

Central Vertices | cm, D♯+ |

Peripheral Vertices | D♯, a° |

Modes are the rotational transformation of this scale. Scale 3721 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode: Scale 977 | Kocrimic | ||||

3rd mode: Scale 317 | Korimic | This is the prime mode | |||

4th mode: Scale 1103 | Lynimic | ||||

5th mode: Scale 2599 | Malimic | ||||

6th mode: Scale 3347 | Synimic |

The prime form of this scale is Scale 317

Scale 317 | Korimic |

The hexatonic modal family [3721, 977, 317, 1103, 2599, 3347] (Forte: 6-Z39) is the complement of the hexatonic modal family [187, 1559, 1889, 2141, 2827, 3461] (Forte: 6-Z10)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3721 is 559

Scale 559 | Lylimic |

Only scales that are chiral will have an enantiomorph. Scale 3721 is chiral, and its enantiomorph is scale 559

Scale 559 | Lylimic |

T_{0} | 3721 | T_{0}I | 559 | |||||

T_{1} | 3347 | T_{1}I | 1118 | |||||

T_{2} | 2599 | T_{2}I | 2236 | |||||

T_{3} | 1103 | T_{3}I | 377 | |||||

T_{4} | 2206 | T_{4}I | 754 | |||||

T_{5} | 317 | T_{5}I | 1508 | |||||

T_{6} | 634 | T_{6}I | 3016 | |||||

T_{7} | 1268 | T_{7}I | 1937 | |||||

T_{8} | 2536 | T_{8}I | 3874 | |||||

T_{9} | 977 | T_{9}I | 3653 | |||||

T_{10} | 1954 | T_{10}I | 3211 | |||||

T_{11} | 3908 | T_{11}I | 2327 |

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 3723 | Myptian | |||

Scale 3725 | Kyrian | |||

Scale 3713 | ||||

Scale 3717 | ||||

Scale 3729 | Starimic | |||

Scale 3737 | Phrocrian | |||

Scale 3753 | Phraptian | |||

Scale 3785 | Epagian | |||

Scale 3593 | ||||

Scale 3657 | Epynimic | |||

Scale 3849 | ||||

Scale 3977 | Kythian | |||

Scale 3209 | Aeraphitonic | |||

Scale 3465 | Katathimic | |||

Scale 2697 | Katagitonic | |||

Scale 1673 | Thocritonic |

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, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.