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Scale 2981: "Ionolian"

Scale 2981: Ionolian, 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
Ionolian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,5,7,8,9,11}
Forte Number7-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1211
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 733
Deep Scaleno
Interval Vector345342
Interval Spectrump4m3n5s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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}231.75
G{7,11,2}231.88
Minor Triadsdm{2,5,9}331.63
fm{5,8,0}331.63
Diminished Triads{2,5,8}231.75
{5,8,11}231.75
g♯°{8,11,2}231.88
{11,2,5}231.75
Parsimonious Voice Leading Between Common Triads of Scale 2981. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm F F dm->F dm->b° f°->fm g#° g#° f°->g#° fm->F Parsimonious Voice Leading Between Common Triads of Scale 2981. Created by Ian Ring ©2019 G G->g#° G->b°

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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 2981 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1769
Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
3rd mode:
Scale 733
Scale 733: Donian, Ian Ring Music TheoryDonianThis is the prime mode
4th mode:
Scale 1207
Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
5th mode:
Scale 2651
Scale 2651: Panian, Ian Ring Music TheoryPanian
6th mode:
Scale 3373
Scale 3373: Lodian, Ian Ring Music TheoryLodian
7th mode:
Scale 1867
Scale 1867: Solian, Ian Ring Music TheorySolian

Prime

The prime form of this scale is Scale 733

Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian

Complement

The heptatonic modal family [2981, 1769, 733, 1207, 2651, 3373, 1867] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2981 is 1211

Scale 1211Scale 1211: Zadian, Ian Ring Music TheoryZadian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2981 is chiral, and its enantiomorph is scale 1211

Scale 1211Scale 1211: Zadian, Ian Ring Music TheoryZadian

Transformations:

T0 2981  T0I 1211
T1 1867  T1I 2422
T2 3734  T2I 749
T3 3373  T3I 1498
T4 2651  T4I 2996
T5 1207  T5I 1897
T6 2414  T6I 3794
T7 733  T7I 3493
T8 1466  T8I 2891
T9 2932  T9I 1687
T10 1769  T10I 3374
T11 3538  T11I 2653

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 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 2977Scale 2977, Ian Ring Music Theory
Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
Scale 2985Scale 2985: Epacrian, Ian Ring Music TheoryEpacrian
Scale 2989Scale 2989: Bebop Minor, Ian Ring Music TheoryBebop Minor
Scale 2997Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop
Scale 2949Scale 2949, Ian Ring Music Theory
Scale 2965Scale 2965: Darian, Ian Ring Music TheoryDarian
Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian
Scale 3045Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
Scale 2853Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
Scale 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 4005Scale 4005, Ian Ring Music Theory
Scale 933Scale 933: Dadimic, Ian Ring Music TheoryDadimic
Scale 1957Scale 1957: Pyrian, Ian Ring Music TheoryPyrian

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.