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
- Phroptian

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

Pitch Class Set | {0,2,4,8,9,10,11} |

Forte Number | 7-9 |

Rotational Symmetry | none |

Reflection Axes | none |

Palindromic | no |

Chirality | yes enantiomorph: 1311 |

Hemitonia | 4 (multihemitonic) |

Cohemitonia | 3 (tricohemitonic) |

Imperfections | 4 |

Modes | 6 |

Prime? | no prime: 351 |

Deep Scale | no |

Interval Vector | 453432 |

Interval Spectrum | p^{3}m^{4}n^{3}s^{5}d^{4}t^{2} |

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

Spectra Variation | 3.429 |

Maximally Even | no |

Maximal Area Set | no |

Interior Area | 2.299 |

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 | E | {4,8,11} | 2 | 2 | 1 |

Minor Triads | am | {9,0,4} | 1 | 3 | 1.5 |

Augmented Triads | C+ | {0,4,8} | 2 | 2 | 1 |

Diminished Triads | g♯° | {8,11,2} | 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 | C+, E |

Peripheral Vertices | g♯°, am |

Modes are the rotational transformation of this scale. Scale 3861 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode: Scale 1989 | Dydian | ||||

3rd mode: Scale 1521 | Stanian | ||||

4th mode: Scale 351 | Epanian | This is the prime mode | |||

5th mode: Scale 2223 | Konian | ||||

6th mode: Scale 3159 | Stocrian | ||||

7th mode: Scale 3627 | Kalian |

The prime form of this scale is Scale 351

Scale 351 | Epanian |

The heptatonic modal family [3861, 1989, 1521, 351, 2223, 3159, 3627] (Forte: 7-9) is the complement of the pentatonic modal family [87, 1473, 1797, 2091, 3093] (Forte: 5-9)

The inverse of a scale is a reflection using the root as its axis. The inverse of 3861 is 1311

Scale 1311 | Bynian |

Only scales that are chiral will have an enantiomorph. Scale 3861 is chiral, and its enantiomorph is scale 1311

Scale 1311 | Bynian |

T_{0} | 3861 | T_{0}I | 1311 | |||||

T_{1} | 3627 | T_{1}I | 2622 | |||||

T_{2} | 3159 | T_{2}I | 1149 | |||||

T_{3} | 2223 | T_{3}I | 2298 | |||||

T_{4} | 351 | T_{4}I | 501 | |||||

T_{5} | 702 | T_{5}I | 1002 | |||||

T_{6} | 1404 | T_{6}I | 2004 | |||||

T_{7} | 2808 | T_{7}I | 4008 | |||||

T_{8} | 1521 | T_{8}I | 3921 | |||||

T_{9} | 3042 | T_{9}I | 3747 | |||||

T_{10} | 1989 | T_{10}I | 3399 | |||||

T_{11} | 3978 | T_{11}I | 2703 |

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 3863 | Eparyllic | |||

Scale 3857 | Ponimic | |||

Scale 3859 | Aeolarian | |||

Scale 3865 | Starian | |||

Scale 3869 | Bygyllic | |||

Scale 3845 | ||||

Scale 3853 | ||||

Scale 3877 | Thanian | |||

Scale 3893 | Phrocryllic | |||

Scale 3925 | Thyryllic | |||

Scale 3989 | Sythyllic | |||

Scale 3605 | ||||

Scale 3733 | Gycrian | |||

Scale 3349 | Aeolocrimic | |||

Scale 2837 | Aelothimic | |||

Scale 1813 | Katothimic |

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.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.