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Scale 3517: "Epocrygic"

Scale 3517: Epocrygic, 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
Epocrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,4,5,7,8,10,11}
Forte Number9-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1975
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 TriadsC{0,4,7}342.44
D♯{3,7,10}342.39
E{4,8,11}442.22
G{7,11,2}442.28
G♯{8,0,3}342.44
A♯{10,2,5}342.67
Minor Triadscm{0,3,7}342.39
em{4,7,11}442.17
fm{5,8,0}342.56
gm{7,10,2}342.5
g♯m{8,11,3}442.17
Augmented TriadsC+{0,4,8}442.33
D♯+{3,7,11}542
Diminished Triads{2,5,8}242.72
{4,7,10}242.67
{5,8,11}242.67
g♯°{8,11,2}242.56
{11,2,5}242.72
Parsimonious Voice Leading Between Common Triads of Scale 3517. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm C+->G# d°->fm A# A# d°->A# D# D# D#->D#+ D#->e° gm gm D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3517. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m e°->em em->E E->f° E->g#m f°->fm gm->G gm->A# g#° g#° G->g#° G->b° g#°->g#m g#m->G# A#->b°

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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 3517 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1903
Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic
3rd mode:
Scale 2999
Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
4th mode:
Scale 3547
Scale 3547: Sadygic, Ian Ring Music TheorySadygic
5th mode:
Scale 3821
Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
6th mode:
Scale 1979
Scale 1979: Aeradygic, Ian Ring Music TheoryAeradygic
7th mode:
Scale 3037
Scale 3037: Nine Tone Scale, Ian Ring Music TheoryNine Tone Scale
8th mode:
Scale 1783
Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
9th mode:
Scale 2939
Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic

Prime

The prime form of this scale is Scale 1775

Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic

Complement

The nonatonic modal family [3517, 1903, 2999, 3547, 3821, 1979, 3037, 1783, 2939] (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 3517 is 1975

Scale 1975Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3517 is chiral, and its enantiomorph is scale 1975

Scale 1975Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic

Transformations:

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

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 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
Scale 3515Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 3485Scale 3485: Sabach, Ian Ring Music TheorySabach
Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 3581Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 3261Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
Scale 3773Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
Scale 4029Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
Scale 2493Scale 2493: Manyllic, Ian Ring Music TheoryManyllic
Scale 3005Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
Scale 1469Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic

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.