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Scale 383: "Logyllic"

Scale 383: Logyllic, 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
Logyllic

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

{0,1,2,3,4,5,6,8}

Forte Number

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

8-2

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: 4049

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.

5 (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.

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.

yes

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, 6, 5, 5, 4, 2]

Interval Spectrum

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

p4m5n5s6d6t2

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

3.25

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♯{1,5,8}341.71
G♯{8,0,3}241.86
Minor Triadsc♯m{1,4,8}231.57
fm{5,8,0}231.57
Augmented TriadsC+{0,4,8}331.43
Diminished Triads{0,3,6}152.57
{2,5,8}152.43
Parsimonious Voice Leading Between Common Triads of Scale 383. Created by Ian Ring ©2019 G# G# c°->G# C+ C+ c#m c#m C+->c#m fm fm C+->fm C+->G# C# C# c#m->C# C#->d° C#->fm

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+, c♯m, fm
Peripheral Verticesc°, d°

Modes

Modes are the rotational transformation of this scale. Scale 383 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2239
Scale 2239: Dacryllic, Ian Ring Music TheoryDacryllic
3rd mode:
Scale 3167
Scale 3167: Thynyllic, Ian Ring Music TheoryThynyllic
4th mode:
Scale 3631
Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic
5th mode:
Scale 3863
Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
6th mode:
Scale 3979
Scale 3979: Dynyllic, Ian Ring Music TheoryDynyllic
7th mode:
Scale 4037
Scale 4037: Ionyllic, Ian Ring Music TheoryIonyllic
8th mode:
Scale 2033
Scale 2033: Stolyllic, Ian Ring Music TheoryStolyllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [383, 2239, 3167, 3631, 3863, 3979, 4037, 2033] (Forte: 8-2) is the complement of the tetratonic modal family [23, 1793, 2059, 3077] (Forte: 4-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 383 is 4049

Scale 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 383 is chiral, and its enantiomorph is scale 4049

Scale 4049Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic

Transformations:

T0 383  T0I 4049
T1 766  T1I 4003
T2 1532  T2I 3911
T3 3064  T3I 3727
T4 2033  T4I 3359
T5 4066  T5I 2623
T6 4037  T6I 1151
T7 3979  T7I 2302
T8 3863  T8I 509
T9 3631  T9I 1018
T10 3167  T10I 2036
T11 2239  T11I 4072

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 381Scale 381: Kogian, Ian Ring Music TheoryKogian
Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic
Scale 511Scale 511: Chromatic Nonamode, Ian Ring Music TheoryChromatic Nonamode
Scale 127Scale 127, Ian Ring Music Theory
Scale 255Scale 255: Chromatic Octamode, Ian Ring Music TheoryChromatic Octamode
Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic

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.