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Scale 3821: "Epyrygic"

Scale 3821: Epyrygic, 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
Epyrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,5,6,7,9,10,11}
Forte Number9-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1775
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1775
Deep Scaleno
Interval Vector667773
Interval Spectrump7m7n7s6d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.111
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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}442.28
D♯{3,7,10}342.44
F{5,9,0}342.67
G{7,11,2}342.44
A♯{10,2,5}342.39
B{11,3,6}442.22
Minor Triadscm{0,3,7}342.56
dm{2,5,9}342.5
d♯m{3,6,10}442.17
gm{7,10,2}342.39
bm{11,2,6}442.17
Augmented TriadsD+{2,6,10}542
D♯+{3,7,11}442.33
Diminished Triads{0,3,6}242.67
d♯°{3,6,9}242.56
f♯°{6,9,0}242.72
{9,0,3}242.72
{11,2,5}242.67
Parsimonious Voice Leading Between Common Triads of Scale 3821. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m gm gm D+->gm D+->A# 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 3821. Created by Ian Ring ©2019 G D#+->G D#+->B F->f#° F->a° gm->G G->bm A#->b° b°->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3821 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1979
Scale 1979: Aeradygic, Ian Ring Music TheoryAeradygic
3rd mode:
Scale 3037
Scale 3037: Nine Tone Scale, Ian Ring Music TheoryNine Tone Scale
4th mode:
Scale 1783
Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
5th mode:
Scale 2939
Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
6th mode:
Scale 3517
Scale 3517: Epocrygic, Ian Ring Music TheoryEpocrygic
7th mode:
Scale 1903
Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
8th mode:
Scale 2999
Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
9th mode:
Scale 3547
Scale 3547: Sadygic, Ian Ring Music TheorySadygic

Prime

The prime form of this scale is Scale 1775

Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic

Complement

The nonatonic modal family [3821, 1979, 3037, 1783, 2939, 3517, 1903, 2999, 3547] (Forte: 9-11) is the complement of the tritonic modal family [137, 289, 529] (Forte: 3-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3821 is 1775

Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3821 is chiral, and its enantiomorph is scale 1775

Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic

Transformations:

T0 3821  T0I 1775
T1 3547  T1I 3550
T2 2999  T2I 3005
T3 1903  T3I 1915
T4 3806  T4I 3830
T5 3517  T5I 3565
T6 2939  T6I 3035
T7 1783  T7I 1975
T8 3566  T8I 3950
T9 3037  T9I 3805
T10 1979  T10I 3515
T11 3958  T11I 2935

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 3823Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian
Scale 3817Scale 3817: Zoryllic, Ian Ring Music TheoryZoryllic
Scale 3819Scale 3819: Aeolanygic, Ian Ring Music TheoryAeolanygic
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 3829Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
Scale 3837Scale 3837: Minor Pentatonic With Leading Tones, Ian Ring Music TheoryMinor Pentatonic With Leading Tones
Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 4077Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
Scale 3309Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
Scale 3565Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
Scale 2797Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
Scale 1773Scale 1773: Blues Scale II, Ian Ring Music TheoryBlues Scale II

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. Special thanks to Richard Repp for helping with technical accuracy.