The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2985: "Epacrian"

Scale 2985: Epacrian, 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

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
Epacrian

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,3,5,7,8,9,11}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-26

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 699

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

3 (trihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

1 (uncohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

4

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 699

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[3, 2, 2, 1, 1, 2, 1]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<3, 4, 4, 5, 3, 2>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p3m5n4s4d3t2

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.286

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.549

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

5.967

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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 TriadsF{5,9,0}242
G♯{8,0,3}421.25
Minor Triadscm{0,3,7}231.75
fm{5,8,0}331.5
g♯m{8,11,3}331.5
Augmented TriadsD♯+{3,7,11}242
Diminished Triads{5,8,11}231.75
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 2985. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ G# G# cm->G# g#m g#m D#+->g#m fm fm f°->fm f°->g#m F F fm->F fm->G# F->a° g#m->G# G#->a°

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.

Diameter4
Radius2
Self-Centeredno
Central VerticesG♯
Peripheral VerticesD♯+, F

Modes

Modes are the rotational transformation of this scale. Scale 2985 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 885
Scale 885: Sathian, Ian Ring Music TheorySathian
3rd mode:
Scale 1245
Scale 1245: Lathian, Ian Ring Music TheoryLathian
4th mode:
Scale 1335
Scale 1335: Elephant Scale, Ian Ring Music TheoryElephant Scale
5th mode:
Scale 2715
Scale 2715: Kynian, Ian Ring Music TheoryKynian
6th mode:
Scale 3405
Scale 3405: Stynian, Ian Ring Music TheoryStynian
7th mode:
Scale 1875
Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale

Prime

The prime form of this scale is Scale 699

Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian

Complement

The heptatonic modal family [2985, 885, 1245, 1335, 2715, 3405, 1875] (Forte: 7-26) is the complement of the pentatonic modal family [309, 849, 1101, 1299, 2697] (Forte: 5-26)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2985 is 699

Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2985 is chiral, and its enantiomorph is scale 699

Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian

Transformations:

T0 2985  T0I 699
T1 1875  T1I 1398
T2 3750  T2I 2796
T3 3405  T3I 1497
T4 2715  T4I 2994
T5 1335  T5I 1893
T6 2670  T6I 3786
T7 1245  T7I 3477
T8 2490  T8I 2859
T9 885  T9I 1623
T10 1770  T10I 3246
T11 3540  T11I 2397

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 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 2977Scale 2977, Ian Ring Music Theory
Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
Scale 2993Scale 2993: Stythian, Ian Ring Music TheoryStythian
Scale 3001Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
Scale 2953Scale 2953: Ionylimic, Ian Ring Music TheoryIonylimic
Scale 2969Scale 2969: Tholian, Ian Ring Music TheoryTholian
Scale 3017Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
Scale 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 2857Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
Scale 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian
Scale 2729Scale 2729: Aeragimic, Ian Ring Music TheoryAeragimic
Scale 2473Scale 2473: Raga Takka, Ian Ring Music TheoryRaga Takka
Scale 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
Scale 4009Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
Scale 937Scale 937: Stothimic, Ian Ring Music TheoryStothimic
Scale 1961Scale 1961: Soptian, Ian Ring Music TheorySoptian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. 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.