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Scale 3197: "Gylyllic"

Scale 3197: Gylyllic, 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
Gylyllic

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

{0,2,3,4,5,6,10,11}

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: 1991

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.

[2, 1, 1, 1, 1, 4, 1, 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.

<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 TriadsA♯{10,2,5}241.86
B{11,3,6}331.43
Minor Triadsd♯m{3,6,10}231.57
bm{11,2,6}321.29
Augmented TriadsD+{2,6,10}331.43
Diminished Triads{0,3,6}142.14
{11,2,5}231.71

The following pitch classes are not present in any of the common triads: {4}

Parsimonious Voice Leading Between Common Triads of Scale 3197. Created by Ian Ring ©2019 B B c°->B D+ D+ d#m d#m D+->d#m A# A# D+->A# bm bm D+->bm d#m->B A#->b° b°->bm bm->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 Verticesbm
Peripheral Verticesc°, A♯

Modes

Modes are the rotational transformation of this scale. Scale 3197 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1823
Scale 1823: Phralyllic, Ian Ring Music TheoryPhralyllic
3rd mode:
Scale 2959
Scale 2959: Dygyllic, Ian Ring Music TheoryDygyllic
4th mode:
Scale 3527
Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
5th mode:
Scale 3811
Scale 3811: Epogyllic, Ian Ring Music TheoryEpogyllic
6th mode:
Scale 3953
Scale 3953: Thagyllic, Ian Ring Music TheoryThagyllic
7th mode:
Scale 503
Scale 503: Thoptyllic, Ian Ring Music TheoryThoptyllic
8th mode:
Scale 2299
Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic

Prime

The prime form of this scale is Scale 479

Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic

Complement

The octatonic modal family [3197, 1823, 2959, 3527, 3811, 3953, 503, 2299] (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 3197 is 1991

Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic

Enantiomorph

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

Scale 1991Scale 1991: Phryptyllic, Ian Ring Music TheoryPhryptyllic

Transformations:

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

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 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
Scale 3193Scale 3193: Zathian, Ian Ring Music TheoryZathian
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3189Scale 3189: Aeolonian, Ian Ring Music TheoryAeolonian
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3261Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
Scale 3325Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic
Scale 2173Scale 2173, Ian Ring Music Theory
Scale 2685Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic
Scale 1149Scale 1149: Bydian, Ian Ring Music TheoryBydian

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.