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Scale 1631: "Rynyllic"

Scale 1631: Rynyllic, 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
Rynyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,3,4,6,9,10}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3917
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 763
Deep Scaleno
Interval Vector556543
Interval Spectrump4m5n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tonesnone
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 TriadsD{2,6,9}342
F♯{6,10,1}342
A{9,1,4}342
Minor Triadsd♯m{3,6,10}342.17
f♯m{6,9,1}441.83
am{9,0,4}342.17
Augmented TriadsD+{2,6,10}342
Diminished Triads{0,3,6}242.33
d♯°{3,6,9}242.33
f♯°{6,9,0}242.17
{9,0,3}242.33
a♯°{10,1,4}242.33
Parsimonious Voice Leading Between Common Triads of Scale 1631. Created by Ian Ring ©2019 d#m d#m c°->d#m c°->a° D D D+ D+ D->D+ d#° d#° D->d#° f#m f#m D->f#m D+->d#m F# F# D+->F# d#°->d#m f#° f#° f#°->f#m am am f#°->am f#m->F# A A f#m->A a#° a#° F#->a#° a°->am am->A A->a#°

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1631 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2863
Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic
3rd mode:
Scale 3479
Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
4th mode:
Scale 3787
Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
5th mode:
Scale 3941
Scale 3941: Stathyllic, Ian Ring Music TheoryStathyllic
6th mode:
Scale 2009
Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
7th mode:
Scale 763
Scale 763: Doryllic, Ian Ring Music TheoryDoryllicThis is the prime mode
8th mode:
Scale 2429
Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [1631, 2863, 3479, 3787, 3941, 2009, 763, 2429] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1631 is 3917

Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1631 is chiral, and its enantiomorph is scale 3917

Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic

Transformations:

T0 1631  T0I 3917
T1 3262  T1I 3739
T2 2429  T2I 3383
T3 763  T3I 2671
T4 1526  T4I 1247
T5 3052  T5I 2494
T6 2009  T6I 893
T7 4018  T7I 1786
T8 3941  T8I 3572
T9 3787  T9I 3049
T10 3479  T10I 2003
T11 2863  T11I 4006

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 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1627Scale 1627: Zyptian, Ian Ring Music TheoryZyptian
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1615Scale 1615: Sydian, Ian Ring Music TheorySydian
Scale 1647Scale 1647: Polyllic, Ian Ring Music TheoryPolyllic
Scale 1663Scale 1663: Lydygic, Ian Ring Music TheoryLydygic
Scale 1567Scale 1567, Ian Ring Music Theory
Scale 1599Scale 1599: Pocryllic, Ian Ring Music TheoryPocryllic
Scale 1695Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic
Scale 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic
Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 3679Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic

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.