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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

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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

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,5,8,9}
Forte Number8-7
Rotational Symmetrynone
Reflection Axes2.5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?yes
Deep Scaleno
Interval Vector645652
Interval Spectrump5m6n5s4d6t2
Distribution Spectra<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 Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.5
Myhill Propertyno
Balancedno
Ridge Tones[5]
ProprietyImproper
Heliotonicno

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: Gaptygic, Ian Ring Music TheoryGaptygic
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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.