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Scale 2621: "Ionogian"

Scale 2621: Ionogian, 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
Ionogian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,3,4,5,9,11}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1931
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 367
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}221.2
Minor Triadsdm{2,5,9}231.4
am{9,0,4}231.4
Diminished Triads{9,0,3}142
{11,2,5}142
Parsimonious Voice Leading Between Common Triads of Scale 2621. Created by Ian Ring ©2019 dm dm F F dm->F dm->b° am am F->am a°->am

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
Radius2
Self-Centeredno
Central VerticesF
Peripheral Verticesa°, b°

Modes

Modes are the rotational transformation of this scale. Scale 2621 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1679
Scale 1679: Kydian, Ian Ring Music TheoryKydian
3rd mode:
Scale 2887
Scale 2887: Gaptian, Ian Ring Music TheoryGaptian
4th mode:
Scale 3491
Scale 3491: Tharian, Ian Ring Music TheoryTharian
5th mode:
Scale 3793
Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
6th mode:
Scale 493
Scale 493: Rygian, Ian Ring Music TheoryRygian
7th mode:
Scale 1147
Scale 1147: Epynian, Ian Ring Music TheoryEpynian

Prime

The prime form of this scale is Scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Complement

The heptatonic modal family [2621, 1679, 2887, 3491, 3793, 493, 1147] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2621 is 1931

Scale 1931Scale 1931: Stogian, Ian Ring Music TheoryStogian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2621 is chiral, and its enantiomorph is scale 1931

Scale 1931Scale 1931: Stogian, Ian Ring Music TheoryStogian

Transformations:

T0 2621  T0I 1931
T1 1147  T1I 3862
T2 2294  T2I 3629
T3 493  T3I 3163
T4 986  T4I 2231
T5 1972  T5I 367
T6 3944  T6I 734
T7 3793  T7I 1468
T8 3491  T8I 2936
T9 2887  T9I 1777
T10 1679  T10I 3554
T11 3358  T11I 3013

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 2623Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
Scale 2617Scale 2617: Pylimic, Ian Ring Music TheoryPylimic
Scale 2619Scale 2619: Ionyrian, Ian Ring Music TheoryIonyrian
Scale 2613Scale 2613: Raga Hamsa Vinodini, Ian Ring Music TheoryRaga Hamsa Vinodini
Scale 2605Scale 2605: Rylimic, Ian Ring Music TheoryRylimic
Scale 2589Scale 2589, Ian Ring Music Theory
Scale 2653Scale 2653: Sygian, Ian Ring Music TheorySygian
Scale 2685Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic
Scale 2749Scale 2749: Katagyllic, Ian Ring Music TheoryKatagyllic
Scale 2877Scale 2877: Phrylyllic, Ian Ring Music TheoryPhrylyllic
Scale 2109Scale 2109, Ian Ring Music Theory
Scale 2365Scale 2365: Sythian, Ian Ring Music TheorySythian
Scale 3133Scale 3133, Ian Ring Music Theory
Scale 3645Scale 3645: Zycryllic, Ian Ring Music TheoryZycryllic
Scale 573Scale 573: Saptimic, Ian Ring Music TheorySaptimic
Scale 1597Scale 1597: Aeolodian, Ian Ring Music TheoryAeolodian

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.