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Scale 315: "Stodimic"

Scale 315: Stodimic, 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
Stodimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,3,4,5,8}
Forte Number6-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2961
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?yes
Deep Scaleno
Interval Vector323430
Interval Spectrump3m4n3s2d3
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5,7}
<3> = {4,5,7,8}
<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}231.4
G♯{8,0,3}131.6
Minor Triadsc♯m{1,4,8}221.2
fm{5,8,0}221.2
Augmented TriadsC+{0,4,8}321
Parsimonious Voice Leading Between Common Triads of Scale 315. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm G# G# C+->G# C# C# c#m->C# 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+, c♯m, fm
Peripheral VerticesC♯, G♯

Modes

Modes are the rotational transformation of this scale. Scale 315 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2205
Scale 2205: Ionocrimic, Ian Ring Music TheoryIonocrimic
3rd mode:
Scale 1575
Scale 1575: Zycrimic, Ian Ring Music TheoryZycrimic
4th mode:
Scale 2835
Scale 2835: Ionygimic, Ian Ring Music TheoryIonygimic
5th mode:
Scale 3465
Scale 3465: Katathimic, Ian Ring Music TheoryKatathimic
6th mode:
Scale 945
Scale 945: Raga Saravati, Ian Ring Music TheoryRaga Saravati

Prime

This is the prime form of this scale.

Complement

The hexatonic modal family [315, 2205, 1575, 2835, 3465, 945] (Forte: 6-14) is the complement of the hexatonic modal family [315, 945, 1575, 2205, 2835, 3465] (Forte: 6-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 315 is 2961

Scale 2961Scale 2961: Bygimic, Ian Ring Music TheoryBygimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 315 is chiral, and its enantiomorph is scale 2961

Scale 2961Scale 2961: Bygimic, Ian Ring Music TheoryBygimic

Transformations:

T0 315  T0I 2961
T1 630  T1I 1827
T2 1260  T2I 3654
T3 2520  T3I 3213
T4 945  T4I 2331
T5 1890  T5I 567
T6 3780  T6I 1134
T7 3465  T7I 2268
T8 2835  T8I 441
T9 1575  T9I 882
T10 3150  T10I 1764
T11 2205  T11I 3528

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 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic
Scale 317Scale 317: Korimic, Ian Ring Music TheoryKorimic
Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 307Scale 307: Raga Megharanjani, Ian Ring Music TheoryRaga Megharanjani
Scale 311Scale 311: Stagimic, Ian Ring Music TheoryStagimic
Scale 299Scale 299: Raga Chitthakarshini, Ian Ring Music TheoryRaga Chitthakarshini
Scale 283Scale 283: Aerylitonic, Ian Ring Music TheoryAerylitonic
Scale 347Scale 347: Barimic, Ian Ring Music TheoryBarimic
Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian
Scale 443Scale 443: Kothian, Ian Ring Music TheoryKothian
Scale 59Scale 59, Ian Ring Music Theory
Scale 187Scale 187, Ian Ring Music Theory
Scale 571Scale 571: Kynimic, Ian Ring Music TheoryKynimic
Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 1339Scale 1339: Kycrian, Ian Ring Music TheoryKycrian
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian

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.