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Scale 2719: "Zocryllic"

Scale 2719: Zocryllic, 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
Zocryllic

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

{0,1,2,3,4,7,9,11}

Forte Number

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

8-11

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: 3883

Hemitonia

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

5 (multihemitonic)

Cohemitonia

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

4 (multicohemitonic)

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.

3

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: 703

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.

[1, 1, 1, 1, 3, 2, 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.

<5, 6, 5, 5, 5, 2>

Interval Spectrum

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

p5m5n5s6d5t2

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

Spectra Variation

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

2.75

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.

2.616

Polygon Perimeter

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

6.002

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

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{0,4,7}431.44
G{7,11,2}152.67
A{9,1,4}252.33
Minor Triadscm{0,3,7}331.56
em{4,7,11}231.78
am{9,0,4}341.78
Augmented TriadsD♯+{3,7,11}341.89
Diminished Triadsc♯°{1,4,7}242
{9,0,3}231.89
Parsimonious Voice Leading Between Common Triads of Scale 2719. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ cm->a° c#° c#° C->c#° em em C->em am am C->am A A c#°->A D#+->em Parsimonious Voice Leading Between Common Triads of Scale 2719. Created by Ian Ring ©2019 G D#+->G a°->am am->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.

Diameter5
Radius3
Self-Centeredno
Central Verticescm, C, em, a°
Peripheral VerticesG, A

Modes

Modes are the rotational transformation of this scale. Scale 2719 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3407
Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
3rd mode:
Scale 3751
Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
4th mode:
Scale 3923
Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
5th mode:
Scale 4009
Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
6th mode:
Scale 1013
Scale 1013: Stydyllic, Ian Ring Music TheoryStydyllic
7th mode:
Scale 1277
Scale 1277: Zadyllic, Ian Ring Music TheoryZadyllic
8th mode:
Scale 1343
Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic

Prime

The prime form of this scale is Scale 703

Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic

Complement

The octatonic modal family [2719, 3407, 3751, 3923, 4009, 1013, 1277, 1343] (Forte: 8-11) is the complement of the tetratonic modal family [43, 1409, 1541, 2069] (Forte: 4-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2719 is 3883

Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2719 is chiral, and its enantiomorph is scale 3883

Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic

Transformations:

T0 2719  T0I 3883
T1 1343  T1I 3671
T2 2686  T2I 3247
T3 1277  T3I 2399
T4 2554  T4I 703
T5 1013  T5I 1406
T6 2026  T6I 2812
T7 4052  T7I 1529
T8 4009  T8I 3058
T9 3923  T9I 2021
T10 3751  T10I 4042
T11 3407  T11I 3989

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 2717Scale 2717: Epygian, Ian Ring Music TheoryEpygian
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 2711Scale 2711: Stolian, Ian Ring Music TheoryStolian
Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian
Scale 2735Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
Scale 2751Scale 2751: Sylygic, Ian Ring Music TheorySylygic
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 2591Scale 2591, Ian Ring Music Theory
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 2847Scale 2847: Phracryllic, Ian Ring Music TheoryPhracryllic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 2207Scale 2207: Mygian, Ian Ring Music TheoryMygian
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
Scale 3231Scale 3231: Kataptyllic, Ian Ring Music TheoryKataptyllic
Scale 3743Scale 3743: Thadygic, Ian Ring Music TheoryThadygic
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic

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.