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Scale 3791: "Stodygic"

Scale 3791: Stodygic, 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).

Common Names

Zeitler
Stodygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,6,7,9,10,11}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3695
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 895
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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 TriadsD{2,6,9}342.35
D♯{3,7,10}342.24
F♯{6,10,1}342.35
G{7,11,2}342.35
B{11,3,6}442.24
Minor Triadscm{0,3,7}342.53
d♯m{3,6,10}442.12
f♯m{6,9,1}342.53
gm{7,10,2}442.24
bm{11,2,6}342.24
Augmented TriadsD+{2,6,10}542
D♯+{3,7,11}442.24
Diminished Triads{0,3,6}252.71
d♯°{3,6,9}242.59
f♯°{6,9,0}242.76
{7,10,1}252.71
{9,0,3}242.76
Parsimonious Voice Leading Between Common Triads of Scale 3791. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° D D D+ D+ D->D+ d#° d#° D->d#° f#m f#m D->f#m d#m d#m D+->d#m F# F# D+->F# gm gm D+->gm bm bm D+->bm d#°->d#m D# D# d#m->D# d#m->B D#->D#+ D#->gm Parsimonious Voice Leading Between Common Triads of Scale 3791. Created by Ian Ring ©2019 G D#+->G D#+->B f#° f#° f#°->f#m f#°->a° f#m->F# F#->g° g°->gm gm->G G->bm bm->B

view full size

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.

Diameter5
Radius4
Self-Centeredno
Central Verticescm, D, D+, d♯°, d♯m, D♯, D♯+, f♯°, f♯m, F♯, gm, G, a°, bm, B
Peripheral Verticesc°, g°

Modes

Modes are the rotational transformation of this scale. Scale 3791 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3943
Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
3rd mode:
Scale 4019
Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
4th mode:
Scale 4057
Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
5th mode:
Scale 1019
Scale 1019: Aeranygic, Ian Ring Music TheoryAeranygic
6th mode:
Scale 2557
Scale 2557: Dothygic, Ian Ring Music TheoryDothygic
7th mode:
Scale 1663
Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
8th mode:
Scale 2879
Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
9th mode:
Scale 3487
Scale 3487: Byptygic, Ian Ring Music TheoryByptygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [3791, 3943, 4019, 4057, 1019, 2557, 1663, 2879, 3487] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3791 is 3695

Scale 3695Scale 3695: Kodygic, Ian Ring Music TheoryKodygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3791 is chiral, and its enantiomorph is scale 3695

Scale 3695Scale 3695: Kodygic, Ian Ring Music TheoryKodygic

Transformations:

T0 3791  T0I 3695
T1 3487  T1I 3295
T2 2879  T2I 2495
T3 1663  T3I 895
T4 3326  T4I 1790
T5 2557  T5I 3580
T6 1019  T6I 3065
T7 2038  T7I 2035
T8 4076  T8I 4070
T9 4057  T9I 4045
T10 4019  T10I 3995
T11 3943  T11I 3895

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 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
Scale 3783Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
Scale 3799Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
Scale 3807Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian
Scale 3823Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian
Scale 3727Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
Scale 3759Scale 3759: Darygic, Ian Ring Music TheoryDarygic
Scale 3663Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
Scale 3919Scale 3919: Lynygic, Ian Ring Music TheoryLynygic
Scale 4047Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
Scale 3279Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
Scale 3535Scale 3535: Mylygic, Ian Ring Music TheoryMylygic
Scale 2767Scale 2767: Katydyllic, Ian Ring Music TheoryKatydyllic
Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic

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.