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Scale 3219: "Ionaphimic"

Scale 3219: Ionaphimic, 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
Ionaphimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,4,7,10,11}
Forte Number6-Z42
Rotational Symmetrynone
Reflection Axes5.5
Palindromicno
Chiralityno
Hemitonia3 (trihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections4
Modes5
Prime?no
prime: 591
Deep Scaleno
Interval Vector324222
Interval Spectrump2m2n4s2d3t2
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {3,5,7,9}
<4> = {6,8,10}
<5> = {9,11}
Spectra Variation3
Maximally Evenno
Maximal Area Setno
Interior Area2.25
Myhill Propertyno
Balancedno
Ridge Tones[11]
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{0,4,7}231.5
Minor Triadsem{4,7,11}231.5
Diminished Triadsc♯°{1,4,7}231.5
{4,7,10}231.5
{7,10,1}231.5
a♯°{10,1,4}231.5
Parsimonious Voice Leading Between Common Triads of Scale 3219. Created by Ian Ring ©2019 C C c#° c#° C->c#° em em C->em a#° a#° c#°->a#° e°->em e°->g° g°->a#°

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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3219 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3657
Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
3rd mode:
Scale 969
Scale 969: Ionogimic, Ian Ring Music TheoryIonogimic
4th mode:
Scale 633
Scale 633: Kydimic, Ian Ring Music TheoryKydimic
5th mode:
Scale 591
Scale 591: Gaptimic, Ian Ring Music TheoryGaptimicThis is the prime mode
6th mode:
Scale 2343
Scale 2343: Tharimic, Ian Ring Music TheoryTharimic

Prime

The prime form of this scale is Scale 591

Scale 591Scale 591: Gaptimic, Ian Ring Music TheoryGaptimic

Complement

The hexatonic modal family [3219, 3657, 969, 633, 591, 2343] (Forte: 6-Z42) is the complement of the hexatonic modal family [219, 1563, 1731, 2157, 2829, 2913] (Forte: 6-Z13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3219 is 2343

Scale 2343Scale 2343: Tharimic, Ian Ring Music TheoryTharimic

Transformations:

T0 3219  T0I 2343
T1 2343  T1I 591
T2 591  T2I 1182
T3 1182  T3I 2364
T4 2364  T4I 633
T5 633  T5I 1266
T6 1266  T6I 2532
T7 2532  T7I 969
T8 969  T8I 1938
T9 1938  T9I 3876
T10 3876  T10I 3657
T11 3657  T11I 3219

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 3217Scale 3217: Molitonic, Ian Ring Music TheoryMolitonic
Scale 3221Scale 3221: Bycrimic, Ian Ring Music TheoryBycrimic
Scale 3223Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3203Scale 3203, Ian Ring Music Theory
Scale 3211Scale 3211: Epacrimic, Ian Ring Music TheoryEpacrimic
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
Scale 3283Scale 3283: Mela Visvambhari, Ian Ring Music TheoryMela Visvambhari
Scale 3091Scale 3091, Ian Ring Music Theory
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 3347Scale 3347: Synimic, Ian Ring Music TheorySynimic
Scale 3475Scale 3475: Kylian, Ian Ring Music TheoryKylian
Scale 3731Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
Scale 2195Scale 2195: Zalitonic, Ian Ring Music TheoryZalitonic
Scale 2707Scale 2707: Banimic, Ian Ring Music TheoryBanimic
Scale 1171Scale 1171: Raga Manaranjani I, Ian Ring Music TheoryRaga Manaranjani I

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.