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Scale 1909: "Epicryllic"

Scale 1909: Epicryllic, 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
Epicryllic

Analysis

Cardinality

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

8 (octatonic)

Pitch Class Set

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

{0,2,4,5,6,8,9,10}

Forte Number

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

8-24

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.

[1]

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.

no

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

2 (dicohemitonic)

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.

7

Prime Form

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

no
prime: 1399

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.

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

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.

<4, 6, 4, 7, 4, 3>

Interval Spectrum

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

p4m7n4s6d4t3

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

Spectra Variation

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

1.5

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.

yes

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.

2.732

Polygon Perimeter

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

6.071

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.

[2]

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

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}341.9
F{5,9,0}431.5
A♯{10,2,5}242.1
Minor Triadsdm{2,5,9}431.5
fm{5,8,0}341.9
am{9,0,4}242.1
Augmented TriadsC+{0,4,8}252.5
D+{2,6,10}252.5
Diminished Triads{2,5,8}231.9
f♯°{6,9,0}231.9
Parsimonious Voice Leading Between Common Triads of Scale 1909. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm am am C+->am dm dm d°->dm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° D+->A# fm->F F->f#° F->am

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 Verticesd°, dm, F, f♯°
Peripheral VerticesC+, D+

Modes

Modes are the rotational transformation of this scale. Scale 1909 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1501
Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
3rd mode:
Scale 1399
Scale 1399: Syryllic, Ian Ring Music TheorySyryllicThis is the prime mode
4th mode:
Scale 2747
Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
5th mode:
Scale 3421
Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
6th mode:
Scale 1879
Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
7th mode:
Scale 2987
Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
8th mode:
Scale 3541
Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic

Prime

The prime form of this scale is Scale 1399

Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic

Complement

The octatonic modal family [1909, 1501, 1399, 2747, 3421, 1879, 2987, 3541] (Forte: 8-24) is the complement of the tetratonic modal family [277, 337, 1093, 1297] (Forte: 4-24)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1909 is 1501

Scale 1501Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic

Transformations:

T0 1909  T0I 1501
T1 3818  T1I 3002
T2 3541  T2I 1909
T3 2987  T3I 3818
T4 1879  T4I 3541
T5 3758  T5I 2987
T6 3421  T6I 1879
T7 2747  T7I 3758
T8 1399  T8I 3421
T9 2798  T9I 2747
T10 1501  T10I 1399
T11 3002  T11I 2798

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 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3
Scale 1905Scale 1905: Katacrian, Ian Ring Music TheoryKatacrian
Scale 1907Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic
Scale 1913Scale 1913, Ian Ring Music Theory
Scale 1917Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic
Scale 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1845Scale 1845: Lagian, Ian Ring Music TheoryLagian
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 2037Scale 2037: Sythygic, Ian Ring Music TheorySythygic
Scale 1653Scale 1653: Minor Romani Inverse, Ian Ring Music TheoryMinor Romani Inverse
Scale 1781Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
Scale 1397Scale 1397: Major Locrian, Ian Ring Music TheoryMajor Locrian
Scale 885Scale 885: Sathian, Ian Ring Music TheorySathian
Scale 2933Scale 2933, Ian Ring Music Theory
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic

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.