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Scale 311: "Stagimic"

Scale 311: Stagimic, 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
Stagimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,4,5,8}
Forte Number6-15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3473
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections4
Modes5
Prime?yes
Deep Scaleno
Interval Vector323421
Interval Spectrump2m4n3s2d3t
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5,7}
<3> = {4,6,8}
<4> = {5,7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation3.333
Maximally Evenno
Maximal Area Setno
Interior Area2.116
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 TriadsC♯{1,5,8}321
Minor Triadsc♯m{1,4,8}221.2
fm{5,8,0}221.2
Augmented TriadsC+{0,4,8}231.4
Diminished Triads{2,5,8}131.6
Parsimonious Voice Leading Between Common Triads of Scale 311. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm C# C# c#m->C# C#->d° C#->fm

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesc♯m, C♯, fm
Peripheral VerticesC+, d°

Modes

Modes are the rotational transformation of this scale. Scale 311 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2203
Scale 2203: Dorimic, Ian Ring Music TheoryDorimic
3rd mode:
Scale 3149
Scale 3149: Phrycrimic, Ian Ring Music TheoryPhrycrimic
4th mode:
Scale 1811
Scale 1811: Kyptimic, Ian Ring Music TheoryKyptimic
5th mode:
Scale 2953
Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
6th mode:
Scale 881
Scale 881: Aerothimic, Ian Ring Music TheoryAerothimic

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [311, 2203, 3149, 1811, 2953, 881] (Forte: 6-15) is the complement of the hexatonic modal family [311, 881, 1811, 2203, 2953, 3149] (Forte: 6-15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 311 is 3473

Scale 3473Scale 3473: Lathimic, Ian Ring Music TheoryLathimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 311 is chiral, and its enantiomorph is scale 3473

Scale 3473Scale 3473: Lathimic, Ian Ring Music TheoryLathimic

Transformations:

T0 311  T0I 3473
T1 622  T1I 2851
T2 1244  T2I 1607
T3 2488  T3I 3214
T4 881  T4I 2333
T5 1762  T5I 571
T6 3524  T6I 1142
T7 2953  T7I 2284
T8 1811  T8I 473
T9 3622  T9I 946
T10 3149  T10I 1892
T11 2203  T11I 3784

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 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 307Scale 307: Raga Megharanjani, Ian Ring Music TheoryRaga Megharanjani
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 295Scale 295: Gyritonic, Ian Ring Music TheoryGyritonic
Scale 303Scale 303: Golimic, Ian Ring Music TheoryGolimic
Scale 279Scale 279: Poditonic, Ian Ring Music TheoryPoditonic
Scale 343Scale 343: Ionorimic, Ian Ring Music TheoryIonorimic
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 55Scale 55, Ian Ring Music Theory
Scale 183Scale 183, Ian Ring Music Theory
Scale 567Scale 567: Aeoladimic, Ian Ring Music TheoryAeoladimic
Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 1335Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale
Scale 2359Scale 2359: Gadian, Ian Ring Music TheoryGadian

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.