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Scale 831: "Rodyllic"

Scale 831: Rodyllic, 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

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
Rodyllic
Dozenal
FEZIAN

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

{0,1,2,3,4,5,8,9}

Forte Number

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

8-7

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.

[2.5]

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.

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.

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, 4, 5, 6, 5, 2]

Interval Spectrum

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

p5m6n5s4d6t2

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> = {1,3}
<2> = {2,4}
<3> = {3,5,7}
<4> = {4,6,8}
<5> = {5,7,9}
<6> = {8,10}
<7> = {9,11}

Spectra Variation

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

2.5

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.

2.5

Polygon Perimeter

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

5.934

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.

[5]

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}441.83
F{5,9,0}331.83
G♯{8,0,3}252.5
A{9,1,4}331.83
Minor Triadsc♯m{1,4,8}331.83
dm{2,5,9}252.5
fm{5,8,0}331.83
am{9,0,4}441.83
Augmented TriadsC+{0,4,8}441.83
C♯+{1,5,9}441.83
Diminished Triads{2,5,8}252.5
{9,0,3}252.5
Parsimonious Voice Leading Between Common Triads of Scale 831. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m fm fm C+->fm G# G# C+->G# am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F C#+->A d°->dm fm->F F->am G#->a° a°->am am->A

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♯m, fm, F, A
Peripheral Verticesd°, dm, G♯, a°

Modes

Modes are the rotational transformation of this scale. Scale 831 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2463
Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
3rd mode:
Scale 3279
Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
4th mode:
Scale 3687
Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic
5th mode:
Scale 3891
Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
6th mode:
Scale 3993
Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
7th mode:
Scale 1011
Scale 1011: Kycryllic, Ian Ring Music TheoryKycryllic
8th mode:
Scale 2553
Scale 2553: Aeolaptyllic, Ian Ring Music TheoryAeolaptyllic

Prime

This is the prime form of this scale.

Complement

The octatonic modal family [831, 2463, 3279, 3687, 3891, 3993, 1011, 2553] (Forte: 8-7) is the complement of the tetratonic modal family [51, 771, 2073, 2433] (Forte: 4-7)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 831 is 3993

Scale 3993Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic

Transformations:

T0 831  T0I 3993
T1 1662  T1I 3891
T2 3324  T2I 3687
T3 2553  T3I 3279
T4 1011  T4I 2463
T5 2022  T5I 831
T6 4044  T6I 1662
T7 3993  T7I 3324
T8 3891  T8I 2553
T9 3687  T9I 1011
T10 3279  T10I 2022
T11 2463  T11I 4044

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 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian
Scale 815Scale 815: Bolian, Ian Ring Music TheoryBolian
Scale 799Scale 799: Lolian, Ian Ring Music TheoryLolian
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 895Scale 895: Aeolathygic, Ian Ring Music TheoryAeolathygic
Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic
Scale 575Scale 575: Ionydian, Ian Ring Music TheoryIonydian
Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic
Scale 319Scale 319: Epodian, Ian Ring Music TheoryEpodian
Scale 1343Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic
Scale 1855Scale 1855: Marygic, Ian Ring Music TheoryMarygic
Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic

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.