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Scale 3907

Scale 3907, Ian Ring Music Theory

Bracelet Diagram

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 Diagram

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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).

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,6,8,9,10,11}
Forte Number7-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2143
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 191
Deep Scaleno
Interval Vector554331
Interval Spectrump3m3n4s5d5t
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6,7}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {5,6,9,10}
<6> = {7,10,11}
Spectra Variation4
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

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 TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsF♯{6,10,1}121
Minor Triadsf♯m{6,9,1}210.67
Diminished Triadsf♯°{6,9,0}121
Parsimonious Voice Leading Between Common Triads of Scale 3907. Created by Ian Ring ©2019 f#° f#° f#m f#m f#°->f#m F# F# f#m->F#

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.

Diameter2
Radius1
Self-Centeredno
Central Verticesf♯m
Peripheral Verticesf♯°, F♯

Modes

Modes are the rotational transformation of this scale. Scale 3907 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 4001
Scale 4001, Ian Ring Music Theory
3rd mode:
Scale 253
Scale 253, Ian Ring Music Theory
4th mode:
Scale 1087
Scale 1087, Ian Ring Music Theory
5th mode:
Scale 2591
Scale 2591, Ian Ring Music Theory
6th mode:
Scale 3343
Scale 3343, Ian Ring Music Theory
7th mode:
Scale 3719
Scale 3719, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 191

Scale 191Scale 191, Ian Ring Music Theory

Complement

The heptatonic modal family [3907, 4001, 253, 1087, 2591, 3343, 3719] (Forte: 7-2) is the complement of the pentatonic modal family [47, 1921, 2071, 3083, 3589] (Forte: 5-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3907 is 2143

Scale 2143Scale 2143, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3907 is chiral, and its enantiomorph is scale 2143

Scale 2143Scale 2143, Ian Ring Music Theory

Transformations:

T0 3907  T0I 2143
T1 3719  T1I 191
T2 3343  T2I 382
T3 2591  T3I 764
T4 1087  T4I 1528
T5 2174  T5I 3056
T6 253  T6I 2017
T7 506  T7I 4034
T8 1012  T8I 3973
T9 2024  T9I 3851
T10 4048  T10I 3607
T11 4001  T11I 3119

Nearby Scales:

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 3905Scale 3905, Ian Ring Music Theory
Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian
Scale 3911Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic
Scale 3915Scale 3915, Ian Ring Music Theory
Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 3843Scale 3843, Ian Ring Music Theory
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 3971Scale 3971, Ian Ring Music Theory
Scale 4035Scale 4035, Ian Ring Music Theory
Scale 3651Scale 3651, Ian Ring Music Theory
Scale 3779Scale 3779, Ian Ring Music Theory
Scale 3395Scale 3395, Ian Ring Music Theory
Scale 2883Scale 2883, Ian Ring Music Theory
Scale 1859Scale 1859, Ian Ring Music Theory

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.