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Scale 3891: "Ryryllic"

Scale 3891: Ryryllic, 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
Ryryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,4,5,8,9,10,11}
Forte Number8-7
Rotational Symmetrynone
Reflection Axes4.5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 831
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[9]
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}331.83
E{4,8,11}252.5
F{5,9,0}331.83
A{9,1,4}441.83
Minor Triadsc♯m{1,4,8}331.83
fm{5,8,0}441.83
am{9,0,4}331.83
a♯m{10,1,5}252.5
Augmented TriadsC+{0,4,8}441.83
C♯+{1,5,9}441.83
Diminished Triads{5,8,11}252.5
a♯°{10,1,4}252.5
Parsimonious Voice Leading Between Common Triads of Scale 3891. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->fm F F C#+->F C#+->A a#m a#m C#+->a#m E->f° f°->fm fm->F F->am am->A a#° a#° A->a#° a#°->a#m

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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, C♯, F, am
Peripheral VerticesE, f°, a♯°, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3891 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3993
Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
3rd mode:
Scale 1011
Scale 1011: Kycryllic, Ian Ring Music TheoryKycryllic
4th mode:
Scale 2553
Scale 2553: Aeolaptyllic, Ian Ring Music TheoryAeolaptyllic
5th mode:
Scale 831
Scale 831: Rodyllic, Ian Ring Music TheoryRodyllicThis is the prime mode
6th mode:
Scale 2463
Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
7th mode:
Scale 3279
Scale 3279: Pythyllic, Ian Ring Music TheoryPythyllic
8th mode:
Scale 3687
Scale 3687: Zonyllic, Ian Ring Music TheoryZonyllic

Prime

The prime form of this scale is Scale 831

Scale 831Scale 831: Rodyllic, Ian Ring Music TheoryRodyllic

Complement

The octatonic modal family [3891, 3993, 1011, 2553, 831, 2463, 3279, 3687] (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 3891 is 2463

Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic

Transformations:

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

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 3889Scale 3889: Parian, Ian Ring Music TheoryParian
Scale 3893Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic
Scale 3895Scale 3895: Eparygic, Ian Ring Music TheoryEparygic
Scale 3899Scale 3899: Katorygic, Ian Ring Music TheoryKatorygic
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 3859Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 4019Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
Scale 3635Scale 3635: Katygian, Ian Ring Music TheoryKatygian
Scale 3763Scale 3763: Modyllic, Ian Ring Music TheoryModyllic
Scale 3379Scale 3379: Verdi's Scala Enigmatica Descending, Ian Ring Music TheoryVerdi's Scala Enigmatica Descending
Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian
Scale 1843Scale 1843: Ionygian, Ian Ring Music TheoryIonygian

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.