The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2867: "Socrian"

Scale 2867: Socrian, 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

41161837294116105072918310504116183
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
Socrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,4,5,8,9,11}
Forte Number7-21
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2459
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 823
Deep Scaleno
Interval Vector424641
Interval Spectrump4m6n4s2d4t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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 TriadsC♯{1,5,8}331.7
E{4,8,11}242.1
F{5,9,0}331.7
A{9,1,4}341.9
Minor Triadsc♯m{1,4,8}331.7
fm{5,8,0}431.5
am{9,0,4}331.7
Augmented TriadsC+{0,4,8}431.5
C♯+{1,5,9}341.9
Diminished Triads{5,8,11}242.1
Parsimonious Voice Leading Between Common Triads of Scale 2867. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->fm F F C#+->F C#+->A E->f° f°->fm fm->F F->am am->A

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.

Diameter4
Radius3
Self-Centeredno
Central VerticesC+, c♯m, C♯, fm, F, am
Peripheral VerticesC♯+, E, f°, A

Modes

Modes are the rotational transformation of this scale. Scale 2867 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3481
Scale 3481: Katathian, Ian Ring Music TheoryKatathian
3rd mode:
Scale 947
Scale 947: Mela Gayakapriya, Ian Ring Music TheoryMela Gayakapriya
4th mode:
Scale 2521
Scale 2521: Mela Dhatuvardhani, Ian Ring Music TheoryMela Dhatuvardhani
5th mode:
Scale 827
Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
6th mode:
Scale 2461
Scale 2461: Sagian, Ian Ring Music TheorySagian
7th mode:
Scale 1639
Scale 1639: Aeolothian, Ian Ring Music TheoryAeolothian

Prime

The prime form of this scale is Scale 823

Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian

Complement

The heptatonic modal family [2867, 3481, 947, 2521, 827, 2461, 1639] (Forte: 7-21) is the complement of the pentatonic modal family [307, 787, 817, 2201, 2441] (Forte: 5-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2867 is 2459

Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2867 is chiral, and its enantiomorph is scale 2459

Scale 2459Scale 2459: Ionocrian, Ian Ring Music TheoryIonocrian

Transformations:

T0 2867  T0I 2459
T1 1639  T1I 823
T2 3278  T2I 1646
T3 2461  T3I 3292
T4 827  T4I 2489
T5 1654  T5I 883
T6 3308  T6I 1766
T7 2521  T7I 3532
T8 947  T8I 2969
T9 1894  T9I 1843
T10 3788  T10I 3686
T11 3481  T11I 3277

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 2865Scale 2865: Solimic, Ian Ring Music TheorySolimic
Scale 2869Scale 2869: Major Augmented, Ian Ring Music TheoryMajor Augmented
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 2875Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2835Scale 2835: Ionygimic, Ian Ring Music TheoryIonygimic
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 2931Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
Scale 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
Scale 2611Scale 2611: Raga Vasanta, Ian Ring Music TheoryRaga Vasanta
Scale 2739Scale 2739: Mela Suryakanta, Ian Ring Music TheoryMela Suryakanta
Scale 2355Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 819Scale 819: Augmented Inverse, Ian Ring Music TheoryAugmented Inverse
Scale 1843Scale 1843: Ionygian, Ian Ring Music TheoryIonygian

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.