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Scale 3387: "Aeryptyllic"

Scale 3387: Aeryptyllic, 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
Aeryptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,5,8,10,11}
Forte Number8-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2967
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes7
Prime?no
prime: 759
Deep Scaleno
Interval Vector555562
Interval Spectrump6m5n5s5d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tonesnone
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♯{1,5,8}341.9
E{4,8,11}341.9
G♯{8,0,3}242.1
Minor Triadsc♯m{1,4,8}331.7
fm{5,8,0}331.7
g♯m{8,11,3}252.5
a♯m{10,1,5}252.5
Augmented TriadsC+{0,4,8}431.5
Diminished Triads{5,8,11}242.1
a♯°{10,1,4}242.3
Parsimonious Voice Leading Between Common Triads of Scale 3387. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm G# G# C+->G# C# C# c#m->C# a#° a#° c#m->a#° C#->fm a#m a#m C#->a#m E->f° g#m g#m E->g#m f°->fm g#m->G# a#°->a#m

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC+, c♯m, fm
Peripheral Verticesg♯m, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3387 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3741
Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
3rd mode:
Scale 1959
Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
4th mode:
Scale 3027
Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
5th mode:
Scale 3561
Scale 3561: Pothyllic, Ian Ring Music TheoryPothyllic
6th mode:
Scale 957
Scale 957: Phronyllic, Ian Ring Music TheoryPhronyllic
7th mode:
Scale 1263
Scale 1263: Stynyllic, Ian Ring Music TheoryStynyllic
8th mode:
Scale 2679
Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [3387, 3741, 1959, 3027, 3561, 957, 1263, 2679] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3387 is 2967

Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3387 is chiral, and its enantiomorph is scale 2967

Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic

Transformations:

T0 3387  T0I 2967
T1 2679  T1I 1839
T2 1263  T2I 3678
T3 2526  T3I 3261
T4 957  T4I 2427
T5 1914  T5I 759
T6 3828  T6I 1518
T7 3561  T7I 3036
T8 3027  T8I 1977
T9 1959  T9I 3954
T10 3918  T10I 3813
T11 3741  T11I 3531

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 3385Scale 3385: Chromatic Phrygian, Ian Ring Music TheoryChromatic Phrygian
Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic
Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic
Scale 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
Scale 3355Scale 3355: Bagian, Ian Ring Music TheoryBagian
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic
Scale 3515Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
Scale 3131Scale 3131, Ian Ring Music Theory
Scale 3259Scale 3259, Ian Ring Music Theory
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2875Scale 2875: Ganyllic, Ian Ring Music TheoryGanyllic
Scale 1339Scale 1339: Kycrian, Ian Ring Music TheoryKycrian

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.