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Scale 1599: "Pocryllic"

Scale 1599: Pocryllic, 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
Pocryllic

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

{0,1,2,3,4,5,9,10}

Forte Number

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

8-4

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: 3981

Hemitonia

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

6 (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: 447

Deep Scale

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

no

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.

[6, 5, 5, 5, 5, 2]

Interval Spectrum

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

p5m5n5s5d6t2

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

Spectra Variation

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

3

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.

2.366

Polygon Perimeter

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

5.838

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 TriadsF{5,9,0}231.78
A{9,1,4}331.56
A♯{10,2,5}252.33
Minor Triadsdm{2,5,9}242
am{9,0,4}341.89
a♯m{10,1,5}341.78
Augmented TriadsC♯+{1,5,9}431.44
Diminished Triads{9,0,3}152.67
a♯°{10,1,4}231.89
Parsimonious Voice Leading Between Common Triads of Scale 1599. Created by Ian Ring ©2019 C#+ C#+ dm dm C#+->dm F F C#+->F A A C#+->A a#m a#m C#+->a#m A# A# dm->A# am am F->am a°->am am->A a#° a#° A->a#° a#°->a#m a#m->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 VerticesC♯+, F, A, a♯°
Peripheral Verticesa°, A♯

Modes

Modes are the rotational transformation of this scale. Scale 1599 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2847
Scale 2847: Phracryllic, Ian Ring Music TheoryPhracryllic
3rd mode:
Scale 3471
Scale 3471: Gyryllic, Ian Ring Music TheoryGyryllic
4th mode:
Scale 3783
Scale 3783: Phrygyllic, Ian Ring Music TheoryPhrygyllic
5th mode:
Scale 3939
Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
6th mode:
Scale 4017
Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic
7th mode:
Scale 507
Scale 507: Moryllic, Ian Ring Music TheoryMoryllic
8th mode:
Scale 2301
Scale 2301: Bydyllic, Ian Ring Music TheoryBydyllic

Prime

The prime form of this scale is Scale 447

Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic

Complement

The octatonic modal family [1599, 2847, 3471, 3783, 3939, 4017, 507, 2301] (Forte: 8-4) is the complement of the tetratonic modal family [39, 897, 2067, 3081] (Forte: 4-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1599 is 3981

Scale 3981Scale 3981: Phrycryllic, Ian Ring Music TheoryPhrycryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1599 is chiral, and its enantiomorph is scale 3981

Scale 3981Scale 3981: Phrycryllic, Ian Ring Music TheoryPhrycryllic

Transformations:

T0 1599  T0I 3981
T1 3198  T1I 3867
T2 2301  T2I 3639
T3 507  T3I 3183
T4 1014  T4I 2271
T5 2028  T5I 447
T6 4056  T6I 894
T7 4017  T7I 1788
T8 3939  T8I 3576
T9 3783  T9I 3057
T10 3471  T10I 2019
T11 2847  T11I 4038

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 1597Scale 1597: Aeolodian, Ian Ring Music TheoryAeolodian
Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
Scale 1591Scale 1591: Rodian, Ian Ring Music TheoryRodian
Scale 1583Scale 1583: Salian, Ian Ring Music TheorySalian
Scale 1567Scale 1567, Ian Ring Music Theory
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
Scale 1727Scale 1727: Sydygic, Ian Ring Music TheorySydygic
Scale 1855Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic
Scale 1087Scale 1087, Ian Ring Music Theory
Scale 1343Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic
Scale 575Scale 575: Ionydian, Ian Ring Music TheoryIonydian
Scale 2623Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
Scale 3647Scale 3647: Eporygic, Ian Ring Music TheoryEporygic

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.