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Scale 2005: "Gygyllic"

Scale 2005: Gygyllic, 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
Gygyllic

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

{0,2,4,6,7,8,9,10}

Forte Number

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

8-21

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.

[2]

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.

no

Hemitonia

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

4 (multihemitonic)

Cohemitonia

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

3 (tricohemitonic)

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.

4

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: 1375

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.

[4, 7, 4, 6, 4, 3]

Interval Spectrum

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

p4m6n4s7d4t3

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

Spectra Variation

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

2

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.

yes

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.

2.732

Polygon Perimeter

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

6.071

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.

[4]

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}242
D{2,6,9}242
Minor Triadsgm{7,10,2}242
am{9,0,4}242
Augmented TriadsC+{0,4,8}242
D+{2,6,10}242
Diminished Triads{4,7,10}242
f♯°{6,9,0}242
Parsimonious Voice Leading Between Common Triads of Scale 2005. Created by Ian Ring ©2019 C C C+ C+ C->C+ C->e° am am C+->am D D D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm e°->gm f#°->am

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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2005 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1525
Scale 1525: Sodyllic, Ian Ring Music TheorySodyllic
3rd mode:
Scale 1405
Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
4th mode:
Scale 1375
Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllicThis is the prime mode
5th mode:
Scale 2735
Scale 2735: Gynyllic, Ian Ring Music TheoryGynyllic
6th mode:
Scale 3415
Scale 3415: Ionaptyllic, Ian Ring Music TheoryIonaptyllic
7th mode:
Scale 3755
Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
8th mode:
Scale 3925
Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic

Prime

The prime form of this scale is Scale 1375

Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic

Complement

The octatonic modal family [2005, 1525, 1405, 1375, 2735, 3415, 3755, 3925] (Forte: 8-21) is the complement of the tetratonic modal family [85, 1045, 1285, 1345] (Forte: 4-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2005 is 1405

Scale 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic

Transformations:

T0 2005  T0I 1405
T1 4010  T1I 2810
T2 3925  T2I 1525
T3 3755  T3I 3050
T4 3415  T4I 2005
T5 2735  T5I 4010
T6 1375  T6I 3925
T7 2750  T7I 3755
T8 1405  T8I 3415
T9 2810  T9I 2735
T10 1525  T10I 1375
T11 3050  T11I 2750

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 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 2001Scale 2001: Gydian, Ian Ring Music TheoryGydian
Scale 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
Scale 2009Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
Scale 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 1997Scale 1997: Raga Cintamani, Ian Ring Music TheoryRaga Cintamani
Scale 2021Scale 2021: Katycryllic, Ian Ring Music TheoryKatycryllic
Scale 2037Scale 2037: Sythygic, Ian Ring Music TheorySythygic
Scale 1941Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
Scale 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 1877Scale 1877: Aeroptian, Ian Ring Music TheoryAeroptian
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani
Scale 3029Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic

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.