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Scale 2021: "Katycryllic"

Scale 2021: Katycryllic, 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

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



Cardinality8 (octatonic)
Pitch Class Set{0,2,5,6,7,8,9,10}
Forte Number8-11
Rotational Symmetrynone
Reflection Axesnone
enantiomorph: 1277
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
prime: 703
Deep Scaleno
Interval Vector565552
Interval Spectrump5m5n5s6d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {4,5,6,7,8}
<5> = {5,6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.75
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Ridge Tonesnone

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 TriadsD{2,6,9}331.56
Minor Triadsdm{2,5,9}431.44
Augmented TriadsD+{2,6,10}341.89
Diminished Triads{2,5,8}242
Parsimonious Voice Leading Between Common Triads of Scale 2021. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° gm gm D+->gm D+->A# fm->F F->f#°

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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.

Central Verticesdm, D, f♯°, A♯
Peripheral Verticesfm, gm


Modes are the rotational transformation of this scale. Scale 2021 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1529
Scale 1529: Kataryllic, Ian Ring Music TheoryKataryllic
3rd mode:
Scale 703
Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllicThis is the prime mode
4th mode:
Scale 2399
Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
5th mode:
Scale 3247
Scale 3247: Aeolonyllic, Ian Ring Music TheoryAeolonyllic
6th mode:
Scale 3671
Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
7th mode:
Scale 3883
Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
8th mode:
Scale 3989
Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic


The prime form of this scale is Scale 703

Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic


The octatonic modal family [2021, 1529, 703, 2399, 3247, 3671, 3883, 3989] (Forte: 8-11) is the complement of the tetratonic modal family [43, 1409, 1541, 2069] (Forte: 4-11)


The inverse of a scale is a reflection using the root as its axis. The inverse of 2021 is 1277

Scale 1277Scale 1277: Zadyllic, Ian Ring Music TheoryZadyllic


Only scales that are chiral will have an enantiomorph. Scale 2021 is chiral, and its enantiomorph is scale 1277

Scale 1277Scale 1277: Zadyllic, Ian Ring Music TheoryZadyllic


T0 2021  T0I 1277
T1 4042  T1I 2554
T2 3989  T2I 1013
T3 3883  T3I 2026
T4 3671  T4I 4052
T5 3247  T5I 4009
T6 2399  T6I 3923
T7 703  T7I 3751
T8 1406  T8I 3407
T9 2812  T9I 2719
T10 1529  T10I 1343
T11 3058  T11I 2686

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 2023Scale 2023: Zodygic, Ian Ring Music TheoryZodygic
Scale 2017Scale 2017, Ian Ring Music Theory
Scale 2019Scale 2019: Palyllic, Ian Ring Music TheoryPalyllic
Scale 2025Scale 2025, Ian Ring Music Theory
Scale 2029Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
Scale 2037Scale 2037: Sythygic, Ian Ring Music TheorySythygic
Scale 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
Scale 1957Scale 1957: Pyrian, Ian Ring Music TheoryPyrian
Scale 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian
Scale 1765Scale 1765: Lonian, Ian Ring Music TheoryLonian
Scale 1509Scale 1509: Ragian, Ian Ring Music TheoryRagian
Scale 997Scale 997: Rycrian, Ian Ring Music TheoryRycrian
Scale 3045Scale 3045: Raptyllic, Ian Ring Music TheoryRaptyllic
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic

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 ( 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.