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Scale 2427: "Katoryllic"

Scale 2427: Katoryllic, 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
Katoryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,5,6,8,11}
Forte Number8-14
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3027
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes7
Prime?no
prime: 759
Deep Scaleno
Interval Vector555562
Interval Spectrump6m5n5s5d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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♯{1,5,8}252.5
E{4,8,11}331.7
G♯{8,0,3}331.7
B{11,3,6}252.5
Minor Triadsc♯m{1,4,8}242.1
fm{5,8,0}341.9
g♯m{8,11,3}341.9
Augmented TriadsC+{0,4,8}431.5
Diminished Triads{0,3,6}242.3
{5,8,11}242.1
Parsimonious Voice Leading Between Common Triads of Scale 2427. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# C# C# c#m->C# C#->fm E->f° g#m g#m E->g#m f°->fm g#m->G# g#m->B

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesC+, E, G♯
Peripheral VerticesC♯, B

Modes

Modes are the rotational transformation of this scale. Scale 2427 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3261
Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
3rd mode:
Scale 1839
Scale 1839: Zogyllic, Ian Ring Music TheoryZogyllic
4th mode:
Scale 2967
Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
5th mode:
Scale 3531
Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
6th mode:
Scale 3813
Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
7th mode:
Scale 1977
Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic
8th mode:
Scale 759
Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllicThis is the prime mode

Prime

The prime form of this scale is Scale 759

Scale 759Scale 759: Katalyllic, Ian Ring Music TheoryKatalyllic

Complement

The octatonic modal family [2427, 3261, 1839, 2967, 3531, 3813, 1977, 759] (Forte: 8-14) is the complement of the tetratonic modal family [141, 417, 1059, 2577] (Forte: 4-14)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2427 is 3027

Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2427 is chiral, and its enantiomorph is scale 3027

Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic

Transformations:

T0 2427  T0I 3027
T1 759  T1I 1959
T2 1518  T2I 3918
T3 3036  T3I 3741
T4 1977  T4I 3387
T5 3954  T5I 2679
T6 3813  T6I 1263
T7 3531  T7I 2526
T8 2967  T8I 957
T9 1839  T9I 1914
T10 3678  T10I 3828
T11 3261  T11I 3561

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 2425Scale 2425: Rorian, Ian Ring Music TheoryRorian
Scale 2429Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
Scale 2419Scale 2419: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 2423Scale 2423, Ian Ring Music Theory
Scale 2411Scale 2411: Aeolorian, Ian Ring Music TheoryAeolorian
Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian
Scale 2363Scale 2363: Kataptian, Ian Ring Music TheoryKataptian
Scale 2491Scale 2491: Layllic, Ian Ring Music TheoryLayllic
Scale 2555Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
Scale 2171Scale 2171, Ian Ring Music Theory
Scale 2299Scale 2299: Phraptyllic, Ian Ring Music TheoryPhraptyllic
Scale 2683Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 3451Scale 3451: Garygic, Ian Ring Music TheoryGarygic
Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian
Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale

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. Special thanks to Richard Repp for helping with technical accuracy.