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Scale 2855: "Epocrain"

Scale 2855: Epocrain, 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
Epocrain

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,5,8,9,11}
Forte Number7-16
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3227
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes6
Prime?no
prime: 623
Deep Scaleno
Interval Vector435432
Interval Spectrump3m4n5s3d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,8,9,10}
<6> = {9,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.433
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}331.67
F{5,9,0}231.89
Minor Triadsdm{2,5,9}331.67
fm{5,8,0}331.67
Augmented TriadsC♯+{1,5,9}331.67
Diminished Triads{2,5,8}231.89
{5,8,11}231.89
g♯°{8,11,2}232
{11,2,5}231.89
Parsimonious Voice Leading Between Common Triads of Scale 2855. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F d°->dm dm->b° f°->fm g#° g#° f°->g#° fm->F g#°->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2855 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3475
Scale 3475: Kylian, Ian Ring Music TheoryKylian
3rd mode:
Scale 3785
Scale 3785: Epagian, Ian Ring Music TheoryEpagian
4th mode:
Scale 985
Scale 985: Mela Sucaritra, Ian Ring Music TheoryMela Sucaritra
5th mode:
Scale 635
Scale 635: Epolian, Ian Ring Music TheoryEpolian
6th mode:
Scale 2365
Scale 2365: Sythian, Ian Ring Music TheorySythian
7th mode:
Scale 1615
Scale 1615: Sydian, Ian Ring Music TheorySydian

Prime

The prime form of this scale is Scale 623

Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian

Complement

The heptatonic modal family [2855, 3475, 3785, 985, 635, 2365, 1615] (Forte: 7-16) is the complement of the pentatonic modal family [155, 865, 1555, 2125, 2825] (Forte: 5-16)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2855 is 3227

Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2855 is chiral, and its enantiomorph is scale 3227

Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian

Transformations:

T0 2855  T0I 3227
T1 1615  T1I 2359
T2 3230  T2I 623
T3 2365  T3I 1246
T4 635  T4I 2492
T5 1270  T5I 889
T6 2540  T6I 1778
T7 985  T7I 3556
T8 1970  T8I 3017
T9 3940  T9I 1939
T10 3785  T10I 3878
T11 3475  T11I 3661

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 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 2851Scale 2851: Katoptimic, Ian Ring Music TheoryKatoptimic
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2863Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic
Scale 2871Scale 2871: Stanyllic, Ian Ring Music TheoryStanyllic
Scale 2823Scale 2823, Ian Ring Music Theory
Scale 2839Scale 2839: Lyptian, Ian Ring Music TheoryLyptian
Scale 2887Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 2599Scale 2599: Malimic, Ian Ring Music TheoryMalimic
Scale 2727Scale 2727: Mela Manavati, Ian Ring Music TheoryMela Manavati
Scale 2343Scale 2343: Tharimic, Ian Ring Music TheoryTharimic
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3879Scale 3879: Pathyllic, Ian Ring Music TheoryPathyllic
Scale 807Scale 807: Raga Suddha Mukhari, Ian Ring Music TheoryRaga Suddha Mukhari
Scale 1831Scale 1831: Pothian, Ian Ring Music TheoryPothian

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.