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Scale 3779

Scale 3779, 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{0,1,6,7,9,10,11}
Forte Number7-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2159
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 223
Deep Scaleno
Interval Vector544332
Interval Spectrump3m3n4s4d5t2
Distribution Spectra<1> = {1,2,5}
<2> = {2,3,6}
<3> = {3,4,7,8}
<4> = {4,5,8,9}
<5> = {6,9,10}
<6> = {7,10,11}
Spectra Variation3.714
Maximally Evenno
Maximal Area Setno
Interior Area1.933
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}221
Minor Triadsf♯m{6,9,1}221
Diminished Triadsf♯°{6,9,0}131.5
{7,10,1}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3779. Created by Ian Ring ©2019 f#° f#° f#m f#m f#°->f#m F# F# f#m->F# F#->g°

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesf♯m, F♯
Peripheral Verticesf♯°, g°

Modes

Modes are the rotational transformation of this scale. Scale 3779 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3937
Scale 3937, Ian Ring Music Theory
3rd mode:
Scale 251
Scale 251, Ian Ring Music Theory
4th mode:
Scale 2173
Scale 2173, Ian Ring Music Theory
5th mode:
Scale 1567
Scale 1567, Ian Ring Music Theory
6th mode:
Scale 2831
Scale 2831, Ian Ring Music Theory
7th mode:
Scale 3463
Scale 3463, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 223

Scale 223Scale 223, Ian Ring Music Theory

Complement

The heptatonic modal family [3779, 3937, 251, 2173, 1567, 2831, 3463] (Forte: 7-4) is the complement of the pentatonic modal family [79, 961, 2087, 3091, 3593] (Forte: 5-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3779 is 2159

Scale 2159Scale 2159, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3779 is chiral, and its enantiomorph is scale 2159

Scale 2159Scale 2159, Ian Ring Music Theory

Transformations:

T0 3779  T0I 2159
T1 3463  T1I 223
T2 2831  T2I 446
T3 1567  T3I 892
T4 3134  T4I 1784
T5 2173  T5I 3568
T6 251  T6I 3041
T7 502  T7I 1987
T8 1004  T8I 3974
T9 2008  T9I 3853
T10 4016  T10I 3611
T11 3937  T11I 3127

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 3777Scale 3777, Ian Ring Music Theory
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3783Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
Scale 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3811Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
Scale 3715Scale 3715, Ian Ring Music Theory
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 3651Scale 3651, Ian Ring Music Theory
Scale 3907Scale 3907, Ian Ring Music Theory
Scale 4035Scale 4035, Ian Ring Music Theory
Scale 3267Scale 3267, Ian Ring Music Theory
Scale 3523Scale 3523, Ian Ring Music Theory
Scale 2755Scale 2755, Ian Ring Music Theory
Scale 1731Scale 1731, 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.