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Scale 3029: "Ionocryllic"

Scale 3029: Ionocryllic, 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
Ionocryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,4,6,7,8,9,11}
Forte Number8-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1403
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 1391
Deep Scaleno
Interval Vector465562
Interval Spectrump6m5n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.75
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
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 TriadsC{0,4,7}242.1
D{2,6,9}242.3
E{4,8,11}341.9
G{7,11,2}341.9
Minor Triadsem{4,7,11}341.9
am{9,0,4}242.1
bm{11,2,6}242.1
Augmented TriadsC+{0,4,8}341.9
Diminished Triadsf♯°{6,9,0}242.3
g♯°{8,11,2}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3029. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E am am C+->am D D f#° f#° D->f#° bm bm D->bm em->E Parsimonious Voice Leading Between Common Triads of Scale 3029. Created by Ian Ring ©2019 G em->G g#° g#° E->g#° f#°->am G->g#° G->bm

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3029 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1781
Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
3rd mode:
Scale 1469
Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic
4th mode:
Scale 1391
Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllicThis is the prime mode
5th mode:
Scale 2743
Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
6th mode:
Scale 3419
Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
7th mode:
Scale 3757
Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
8th mode:
Scale 1963
Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic

Prime

The prime form of this scale is Scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Complement

The octatonic modal family [3029, 1781, 1469, 1391, 2743, 3419, 3757, 1963] (Forte: 8-22) is the complement of the tetratonic modal family [149, 673, 1061, 1289] (Forte: 4-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3029 is 1403

Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3029 is chiral, and its enantiomorph is scale 1403

Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale

Transformations:

T0 3029  T0I 1403
T1 1963  T1I 2806
T2 3926  T2I 1517
T3 3757  T3I 3034
T4 3419  T4I 1973
T5 2743  T5I 3946
T6 1391  T6I 3797
T7 2782  T7I 3499
T8 1469  T8I 2903
T9 2938  T9I 1711
T10 1781  T10I 3422
T11 3562  T11I 2749

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 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
Scale 3025Scale 3025: Epycrian, Ian Ring Music TheoryEpycrian
Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
Scale 3033Scale 3033: Doptyllic, Ian Ring Music TheoryDoptyllic
Scale 3037Scale 3037: Nine Tone Scale, Ian Ring Music TheoryNine Tone Scale
Scale 3013Scale 3013: Thynian, Ian Ring Music TheoryThynian
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 3045Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
Scale 3061Scale 3061: Apinygic, Ian Ring Music TheoryApinygic
Scale 2965Scale 2965: Darian, Ian Ring Music TheoryDarian
Scale 2997Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop
Scale 2901Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
Scale 2773Scale 2773: Lydian, Ian Ring Music TheoryLydian
Scale 2517Scale 2517: Harmonic Lydian, Ian Ring Music TheoryHarmonic Lydian
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 4053Scale 4053: Kyrygic, Ian Ring Music TheoryKyrygic
Scale 981Scale 981: Mela Kantamani, Ian Ring Music TheoryMela Kantamani
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic

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.