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Scale 1991: "Phryptyllic"

Scale 1991: Phryptyllic, 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
Phryptyllic

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

{0,1,2,6,7,8,9,10}

Forte Number

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

8-5

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: 3197

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: 479

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, 4, 5, 5, 3]

Interval Spectrum

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

p5m5n4s5d6t3

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}
<4> = {4,5,7,8}
<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.

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.

2.366

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 TriadsD{2,6,9}231.57
F♯{6,10,1}321.29
Minor Triadsf♯m{6,9,1}331.43
gm{7,10,2}241.86
Augmented TriadsD+{2,6,10}331.43
Diminished Triadsf♯°{6,9,0}142.14
{7,10,1}231.71

The following pitch classes are not present in any of the common triads: {8}

Parsimonious Voice Leading Between Common Triads of Scale 1991. Created by Ian Ring ©2019 D D D+ D+ D->D+ f#m f#m D->f#m F# F# D+->F# gm gm D+->gm f#° f#° f#°->f#m f#m->F# F#->g° g°->gm

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 VerticesF♯
Peripheral Verticesf♯°, gm

Modes

Modes are the rotational transformation of this scale. Scale 1991 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3043
Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
3rd mode:
Scale 3569
Scale 3569: Aeoladyllic, Ian Ring Music TheoryAeoladyllic
4th mode:
Scale 479
Scale 479: Kocryllic, Ian Ring Music TheoryKocryllicThis is the prime mode
5th mode:
Scale 2287
Scale 2287: Lodyllic, Ian Ring Music TheoryLodyllic
6th mode:
Scale 3191
Scale 3191: Bynyllic, Ian Ring Music TheoryBynyllic
7th mode:
Scale 3643
Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
8th mode:
Scale 3869
Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [1991, 3043, 3569, 479, 2287, 3191, 3643, 3869] (Forte: 8-5) is the complement of the tetratonic modal family [71, 449, 2083, 3089] (Forte: 4-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1991 is 3197

Scale 3197Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1991 is chiral, and its enantiomorph is scale 3197

Scale 3197Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic

Transformations:

T0 1991  T0I 3197
T1 3982  T1I 2299
T2 3869  T2I 503
T3 3643  T3I 1006
T4 3191  T4I 2012
T5 2287  T5I 4024
T6 479  T6I 3953
T7 958  T7I 3811
T8 1916  T8I 3527
T9 3832  T9I 2959
T10 3569  T10I 1823
T11 3043  T11I 3646

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 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 1987Scale 1987, Ian Ring Music Theory
Scale 1995Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
Scale 1999Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 2023Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
Scale 1927Scale 1927, Ian Ring Music Theory
Scale 1959Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
Scale 1863Scale 1863: Pycrian, Ian Ring Music TheoryPycrian
Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam
Scale 1479Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava
Scale 967Scale 967: Mela Salaga, Ian Ring Music TheoryMela Salaga
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 4039Scale 4039: Ionogygic, Ian Ring Music TheoryIonogygic

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.