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Scale 3933: "Ionidygic"

Scale 3933: Ionidygic, 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
Ionidygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,4,6,8,9,10,11}
Forte Number9-8
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1887
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1503
Deep Scaleno
Interval Vector676764
Interval Spectrump6m7n6s7d6t4
Distribution Spectra<1> = {1,2}
<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> = {10,11}
Spectra Variation1.556
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
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}342.47
E{4,8,11}242.47
G♯{8,0,3}442.2
B{11,3,6}442.07
Minor Triadsd♯m{3,6,10}342.33
g♯m{8,11,3}442.07
am{9,0,4}342.47
bm{11,2,6}342.33
Augmented TriadsC+{0,4,8}342.4
D+{2,6,10}342.4
Diminished Triads{0,3,6}242.33
d♯°{3,6,9}242.67
f♯°{6,9,0}242.53
g♯°{8,11,2}242.47
{9,0,3}242.53
Parsimonious Voice Leading Between Common Triads of Scale 3933. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ E E C+->E C+->G# am am C+->am D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m bm bm D+->bm d#°->d#m d#m->B g#m g#m E->g#m f#°->am g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B G#->a° a°->am bm->B

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 3933 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2007
Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
3rd mode:
Scale 3051
Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
4th mode:
Scale 3573
Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
5th mode:
Scale 1917
Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic
6th mode:
Scale 1503
Scale 1503: Padygic, Ian Ring Music TheoryPadygicThis is the prime mode
7th mode:
Scale 2799
Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
8th mode:
Scale 3447
Scale 3447: Kynygic, Ian Ring Music TheoryKynygic
9th mode:
Scale 3771
Scale 3771: Stophygic, Ian Ring Music TheoryStophygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Complement

The nonatonic modal family [3933, 2007, 3051, 3573, 1917, 1503, 2799, 3447, 3771] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3933 is 1887

Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3933 is chiral, and its enantiomorph is scale 1887

Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic

Transformations:

T0 3933  T0I 1887
T1 3771  T1I 3774
T2 3447  T2I 3453
T3 2799  T3I 2811
T4 1503  T4I 1527
T5 3006  T5I 3054
T6 1917  T6I 2013
T7 3834  T7I 4026
T8 3573  T8I 3957
T9 3051  T9I 3819
T10 2007  T10I 3543
T11 4014  T11I 2991

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 3935Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 3965Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse
Scale 3869Scale 3869: Bygyllic, Ian Ring Music TheoryBygyllic
Scale 3901Scale 3901: Bycrygic, Ian Ring Music TheoryBycrygic
Scale 3997Scale 3997: Dogygic, Ian Ring Music TheoryDogygic
Scale 4061Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
Scale 3677Scale 3677, Ian Ring Music Theory
Scale 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 2909Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
Scale 1885Scale 1885: Saptyllic, Ian Ring Music TheorySaptyllic

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.