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Scale 3707: "Rynygic"

Scale 3707: Rynygic, 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
Rynygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,4,5,6,9,10,11}
Forte Number9-5
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3023
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 991
Deep Scaleno
Interval Vector766674
Interval Spectrump7m6n6s6d7t4
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {9,10,11}
Spectra Variation1.778
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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 TriadsF{5,9,0}342.21
F♯{6,10,1}342.14
A{9,1,4}342.21
B{11,3,6}242.64
Minor Triadsd♯m{3,6,10}342.36
f♯m{6,9,1}442.07
am{9,0,4}342.29
a♯m{10,1,5}342.21
Augmented TriadsC♯+{1,5,9}442
Diminished Triads{0,3,6}242.71
d♯°{3,6,9}242.43
f♯°{6,9,0}242.43
{9,0,3}242.57
a♯°{10,1,4}242.57
Parsimonious Voice Leading Between Common Triads of Scale 3707. Created by Ian Ring ©2019 c°->a° B B c°->B C#+ C#+ F F C#+->F f#m f#m C#+->f#m A A C#+->A a#m a#m C#+->a#m d#° d#° d#m d#m d#°->d#m d#°->f#m F# F# d#m->F# d#m->B f#° f#° F->f#° am am F->am f#°->f#m f#m->F# F#->a#m a°->am am->A a#° a#° A->a#° a#°->a#m

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3707 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3901
Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
3rd mode:
Scale 1999
Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
4th mode:
Scale 3047
Scale 3047: Panygic, Ian Ring Music TheoryPanygic
5th mode:
Scale 3571
Scale 3571: Dyrygic, Ian Ring Music TheoryDyrygic
6th mode:
Scale 3833
Scale 3833: Dycrygic, Ian Ring Music TheoryDycrygic
7th mode:
Scale 991
Scale 991: Aeolygic, Ian Ring Music TheoryAeolygicThis is the prime mode
8th mode:
Scale 2543
Scale 2543: Dydygic, Ian Ring Music TheoryDydygic
9th mode:
Scale 3319
Scale 3319: Tholygic, Ian Ring Music TheoryTholygic

Prime

The prime form of this scale is Scale 991

Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic

Complement

The nonatonic modal family [3707, 3901, 1999, 3047, 3571, 3833, 991, 2543, 3319] (Forte: 9-5) is the complement of the tritonic modal family [67, 193, 2081] (Forte: 3-5)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3707 is 3023

Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3707 is chiral, and its enantiomorph is scale 3023

Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic

Transformations:

T0 3707  T0I 3023
T1 3319  T1I 1951
T2 2543  T2I 3902
T3 991  T3I 3709
T4 1982  T4I 3323
T5 3964  T5I 2551
T6 3833  T6I 1007
T7 3571  T7I 2014
T8 3047  T8I 4028
T9 1999  T9I 3961
T10 3998  T10I 3827
T11 3901  T11I 3559

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 3705Scale 3705: Messiaen Mode 4 Inverse, Ian Ring Music TheoryMessiaen Mode 4 Inverse
Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic
Scale 3711Scale 3711: Dycryllian, Ian Ring Music TheoryDycryllian
Scale 3699Scale 3699: Galyllic, Ian Ring Music TheoryGalyllic
Scale 3703Scale 3703: Katalygic, Ian Ring Music TheoryKatalygic
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3675Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3771Scale 3771: Stophygic, Ian Ring Music TheoryStophygic
Scale 3835Scale 3835: Katodyllian, Ian Ring Music TheoryKatodyllian
Scale 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic
Scale 2683Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
Scale 1659Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban

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.