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Scale 2459: "Ionocrian"

Scale 2459: Ionocrian, 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
Ionocrian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,7,8,11}
Forte Number7-21
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2867
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 823
Deep Scaleno
Interval Vector424641
Interval Spectrump4m6n4s2d4t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {8,9,10}
<6> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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 TriadsC{0,4,7}431.5
E{4,8,11}331.7
G♯{8,0,3}331.7
Minor Triadscm{0,3,7}331.7
c♯m{1,4,8}242.1
em{4,7,11}331.7
g♯m{8,11,3}341.9
Augmented TriadsC+{0,4,8}431.5
D♯+{3,7,11}341.9
Diminished Triadsc♯°{1,4,7}242.1
Parsimonious Voice Leading Between Common Triads of Scale 2459. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# c#°->c#m D#+->em g#m g#m D#+->g#m em->E E->g#m g#m->G#

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
Radius3
Self-Centeredno
Central Verticescm, C, C+, em, E, G♯
Peripheral Verticesc♯°, c♯m, D♯+, g♯m

Modes

Modes are the rotational transformation of this scale. Scale 2459 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3277
Scale 3277: Mela Nitimati, Ian Ring Music TheoryMela Nitimati
3rd mode:
Scale 1843
Scale 1843: Ionygian, Ian Ring Music TheoryIonygian
4th mode:
Scale 2969
Scale 2969: Tholian, Ian Ring Music TheoryTholian
5th mode:
Scale 883
Scale 883: Ralian, Ian Ring Music TheoryRalian
6th mode:
Scale 2489
Scale 2489: Mela Gangeyabhusani, Ian Ring Music TheoryMela Gangeyabhusani
7th mode:
Scale 823
Scale 823: Stodian, Ian Ring Music TheoryStodianThis is the prime mode

Prime

The prime form of this scale is Scale 823

Scale 823Scale 823: Stodian, Ian Ring Music TheoryStodian

Complement

The heptatonic modal family [2459, 3277, 1843, 2969, 883, 2489, 823] (Forte: 7-21) is the complement of the pentatonic modal family [307, 787, 817, 2201, 2441] (Forte: 5-21)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2459 is 2867

Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2459 is chiral, and its enantiomorph is scale 2867

Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian

Transformations:

T0 2459  T0I 2867
T1 823  T1I 1639
T2 1646  T2I 3278
T3 3292  T3I 2461
T4 2489  T4I 827
T5 883  T5I 1654
T6 1766  T6I 3308
T7 3532  T7I 2521
T8 2969  T8I 947
T9 1843  T9I 1894
T10 3686  T10I 3788
T11 3277  T11I 3481

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 2457Scale 2457: Major Augmented, Ian Ring Music TheoryMajor Augmented
Scale 2461Scale 2461: Sagian, Ian Ring Music TheorySagian
Scale 2463Scale 2463: Ionathyllic, Ian Ring Music TheoryIonathyllic
Scale 2451Scale 2451: Raga Bauli, Ian Ring Music TheoryRaga Bauli
Scale 2455Scale 2455: Bothian, Ian Ring Music TheoryBothian
Scale 2443Scale 2443: Panimic, Ian Ring Music TheoryPanimic
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 2491Scale 2491: Layllic, Ian Ring Music TheoryLayllic
Scale 2523Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
Scale 2331Scale 2331: Dylimic, Ian Ring Music TheoryDylimic
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
Scale 2203Scale 2203: Dorimic, Ian Ring Music TheoryDorimic
Scale 2715Scale 2715: Kynian, Ian Ring Music TheoryKynian
Scale 2971Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
Scale 3483Scale 3483: Mixotharyllic, Ian Ring Music TheoryMixotharyllic
Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic
Scale 1435Scale 1435: Makam Huzzam, Ian Ring Music TheoryMakam Huzzam

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.