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Scale 3789: "Eporyllic"

Scale 3789: Eporyllic, 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
Eporyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,6,7,9,10,11}
Forte Number8-17
Rotational Symmetrynone
Reflection Axes4.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 891
Deep Scaleno
Interval Vector546652
Interval Spectrump5m6n6s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[9]
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 TriadsD{2,6,9}342.21
D♯{3,7,10}342.07
G{7,11,2}342.21
B{11,3,6}441.93
Minor Triadscm{0,3,7}342.21
d♯m{3,6,10}441.93
gm{7,10,2}342.21
bm{11,2,6}342.07
Augmented TriadsD+{2,6,10}441.93
D♯+{3,7,11}441.93
Diminished Triads{0,3,6}242.36
d♯°{3,6,9}242.36
f♯°{6,9,0}242.5
{9,0,3}242.5
Parsimonious Voice Leading Between Common Triads of Scale 3789. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ cm->a° D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m gm gm D+->gm 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 3789. Created by Ian Ring ©2019 G D#+->G D#+->B f#°->a° gm->G G->bm bm->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 3789 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1971
Scale 1971: Aerynyllic, Ian Ring Music TheoryAerynyllic
3rd mode:
Scale 3033
Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
4th mode:
Scale 891
Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllicThis is the prime mode
5th mode:
Scale 2493
Scale 2493: Manyllic, Ian Ring Music TheoryManyllic
6th mode:
Scale 1647
Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
7th mode:
Scale 2871
Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
8th mode:
Scale 3483
Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic

Prime

The prime form of this scale is Scale 891

Scale 891Scale 891: Ionilyllic, Ian Ring Music TheoryIonilyllic

Complement

The octatonic modal family [3789, 1971, 3033, 891, 2493, 1647, 2871, 3483] (Forte: 8-17) is the complement of the tetratonic modal family [153, 531, 801, 2313] (Forte: 4-17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3789 is 1647

Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic

Transformations:

T0 3789  T0I 1647
T1 3483  T1I 3294
T2 2871  T2I 2493
T3 1647  T3I 891
T4 3294  T4I 1782
T5 2493  T5I 3564
T6 891  T6I 3033
T7 1782  T7I 1971
T8 3564  T8I 3942
T9 3033  T9I 3789
T10 1971  T10I 3483
T11 3942  T11I 2871

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 3791Scale 3791: Stodygic, Ian Ring Music TheoryStodygic
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3797Scale 3797: Rocryllic, Ian Ring Music TheoryRocryllic
Scale 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
Scale 3277Scale 3277: Mela Nitimati, Ian Ring Music TheoryMela Nitimati
Scale 3533Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
Scale 2765Scale 2765: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished

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.