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Scale 3895: "Eparygic"

Scale 3895: Eparygic, 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
Eparygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,4,5,8,9,10,11}
Forte Number9-3
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3487
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 895
Deep Scaleno
Interval Vector767763
Interval Spectrump6m7n7s6d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation2.222
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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}442.12
E{4,8,11}342.53
F{5,9,0}342.24
A{9,1,4}442.24
A♯{10,2,5}342.53
Minor Triadsc♯m{1,4,8}342.24
dm{2,5,9}342.35
fm{5,8,0}442.24
am{9,0,4}342.35
a♯m{10,1,5}342.35
Augmented TriadsC+{0,4,8}442.24
C♯+{1,5,9}542
Diminished Triads{2,5,8}242.59
{5,8,11}252.71
g♯°{8,11,2}242.76
a♯°{10,1,4}252.71
{11,2,5}242.76
Parsimonious Voice Leading Between Common Triads of Scale 3895. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F C#+->A a#m a#m C#+->a#m d°->dm A# A# dm->A# E->f° g#° g#° E->g#° f°->fm fm->F F->am g#°->b° am->A a#° a#° A->a#° 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.

Diameter5
Radius4
Self-Centeredno
Central VerticesC+, c♯m, C♯, C♯+, d°, dm, E, fm, F, g♯°, am, A, a♯m, A♯, b°
Peripheral Verticesf°, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 3895 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3995
Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
3rd mode:
Scale 4045
Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic
4th mode:
Scale 2035
Scale 2035: Aerythygic, Ian Ring Music TheoryAerythygic
5th mode:
Scale 3065
Scale 3065: Zothygic, Ian Ring Music TheoryZothygic
6th mode:
Scale 895
Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygicThis is the prime mode
7th mode:
Scale 2495
Scale 2495: Aeolocrygic, Ian Ring Music TheoryAeolocrygic
8th mode:
Scale 3295
Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
9th mode:
Scale 3695
Scale 3695: Kodygic, Ian Ring Music TheoryKodygic

Prime

The prime form of this scale is Scale 895

Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic

Complement

The nonatonic modal family [3895, 3995, 4045, 2035, 3065, 895, 2495, 3295, 3695] (Forte: 9-3) is the complement of the tritonic modal family [19, 769, 2057] (Forte: 3-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3895 is 3487

Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3895 is chiral, and its enantiomorph is scale 3487

Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic

Transformations:

T0 3895  T0I 3487
T1 3695  T1I 2879
T2 3295  T2I 1663
T3 2495  T3I 3326
T4 895  T4I 2557
T5 1790  T5I 1019
T6 3580  T6I 2038
T7 3065  T7I 4076
T8 2035  T8I 4057
T9 4070  T9I 4019
T10 4045  T10I 3943
T11 3995  T11I 3791

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 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
Scale 3903Scale 3903: Aeogyllian, Ian Ring Music TheoryAeogyllian
Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
Scale 3887Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
Scale 3863Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic
Scale 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
Scale 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
Scale 3639Scale 3639: Paptyllic, Ian Ring Music TheoryPaptyllic
Scale 3767Scale 3767: Chromatic Bebop, Ian Ring Music TheoryChromatic Bebop
Scale 3383Scale 3383: Zoptyllic, Ian Ring Music TheoryZoptyllic
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic

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.