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Scale 2299: "Phraptyllic"

Scale 2299: Phraptyllic, 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
Phraptyllic

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

{0,1,3,4,5,6,7,11}

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: 3043

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 Formula

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

[1, 2, 1, 1, 1, 1, 4, 1] 9

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 TriadsC{0,4,7}331.43
B{11,3,6}241.86
Minor Triadscm{0,3,7}321.29
em{4,7,11}231.57
Augmented TriadsD♯+{3,7,11}331.43
Diminished Triads{0,3,6}231.71
c♯°{1,4,7}142.14

The following pitch classes are not present in any of the common triads: {5}

Parsimonious Voice Leading Between Common Triads of Scale 2299. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em D#+->em D#+->B

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 Verticescm
Peripheral Verticesc♯°, B

Modes

Modes are the rotational transformation of this scale. Scale 2299 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3197
Scale 3197: Gylyllic, Ian Ring Music TheoryGylyllic
3rd mode:
Scale 1823
Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
4th mode:
Scale 2959
Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
5th mode:
Scale 3527
Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
6th mode:
Scale 3811
Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
7th mode:
Scale 3953
Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
8th mode:
Scale 503
Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [2299, 3197, 1823, 2959, 3527, 3811, 3953, 503] (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 2299 is 3043

Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2299 is chiral, and its enantiomorph is scale 3043

Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic

Transformations:

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

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 2297Scale 2297: Thylian, Ian Ring Music TheoryThylian
Scale 2301Scale 2301: Bydyllic, Ian Ring Music TheoryBydyllic
Scale 2303Scale 2303: Stanygic, Ian Ring Music TheoryStanygic
Scale 2291Scale 2291: Zydian, Ian Ring Music TheoryZydian
Scale 2295Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
Scale 2283Scale 2283: Aeolyptian, Ian Ring Music TheoryAeolyptian
Scale 2267Scale 2267: Padian, Ian Ring Music TheoryPadian
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 2171Scale 2171, Ian Ring Music Theory
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 2555Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
Scale 2811Scale 2811: Barygic, Ian Ring Music TheoryBarygic
Scale 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic
Scale 251Scale 251, Ian Ring Music Theory
Scale 1275Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic

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.