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Scale 3511: "Epolygic"

Scale 3511: Epolygic, 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
Epolygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,4,5,7,8,10,11}
Forte Number9-10
Rotational Symmetrynone
Reflection Axes0
Palindromicyes
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1759
Deep Scaleno
Interval Vector668664
Interval Spectrump6m6n8s6d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[0]
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{0,4,7}342.47
C♯{1,5,8}442.32
E{4,8,11}442.37
G{7,11,2}442.37
A♯{10,2,5}442.42
Minor Triadsc♯m{1,4,8}442.37
em{4,7,11}442.32
fm{5,8,0}342.47
gm{7,10,2}442.42
a♯m{10,1,5}442.37
Augmented TriadsC+{0,4,8}442.32
Diminished Triadsc♯°{1,4,7}242.74
{2,5,8}242.58
{4,7,10}242.58
{5,8,11}242.74
{7,10,1}242.63
g♯°{8,11,2}242.63
a♯°{10,1,4}242.63
{11,2,5}242.63
Parsimonious Voice Leading Between Common Triads of Scale 3511. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E fm fm C+->fm c#°->c#m C# C# c#m->C# a#° a#° c#m->a#° C#->d° C#->fm a#m a#m C#->a#m A# A# d°->A# e°->em gm gm e°->gm em->E Parsimonious Voice Leading Between Common Triads of Scale 3511. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm g°->gm g°->a#m gm->G gm->A# G->g#° G->b° a#°->a#m a#m->A# A#->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3511 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3803
Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
3rd mode:
Scale 3949
Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
4th mode:
Scale 2011
Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
5th mode:
Scale 3053
Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
6th mode:
Scale 1787
Scale 1787: Mycrygic, Ian Ring Music TheoryMycrygic
7th mode:
Scale 2941
Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
8th mode:
Scale 1759
Scale 1759: Pylygic, Ian Ring Music TheoryPylygicThis is the prime mode
9th mode:
Scale 2927
Scale 2927: Rodygic, Ian Ring Music TheoryRodygic

Prime

The prime form of this scale is Scale 1759

Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic

Complement

The nonatonic modal family [3511, 3803, 3949, 2011, 3053, 1787, 2941, 1759, 2927] (Forte: 9-10) is the complement of the tritonic modal family [73, 521, 577] (Forte: 3-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3511 is itself, because it is a palindromic scale!

Scale 3511Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic

Transformations:

T0 3511  T0I 3511
T1 2927  T1I 2927
T2 1759  T2I 1759
T3 3518  T3I 3518
T4 2941  T4I 2941
T5 1787  T5I 1787
T6 3574  T6I 3574
T7 3053  T7I 3053
T8 2011  T8I 2011
T9 4022  T9I 4022
T10 3949  T10I 3949
T11 3803  T11I 3803

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 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
Scale 3515Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
Scale 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3575Scale 3575: Symmetrical Decatonic, Ian Ring Music TheorySymmetrical Decatonic
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 3447Scale 3447: Mogyllian, Ian Ring Music TheoryMogyllian
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 1463Scale 1463, 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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.