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Scale 2911: "Katygic"

Scale 2911: Katygic, 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
Katygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,6,8,9,11}
Forte Number9-7
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3931
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1471
Deep Scaleno
Interval Vector677673
Interval Spectrump7m6n7s7d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.778
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
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 TriadsD{2,6,9}342.44
E{4,8,11}242.38
G♯{8,0,3}442.13
A{9,1,4}342.44
B{11,3,6}442.31
Minor Triadsc♯m{1,4,8}242.56
f♯m{6,9,1}342.44
g♯m{8,11,3}442.19
am{9,0,4}442.31
bm{11,2,6}342.44
Augmented TriadsC+{0,4,8}442.19
Diminished Triads{0,3,6}242.44
d♯°{3,6,9}242.56
f♯°{6,9,0}242.56
g♯°{8,11,2}242.56
{9,0,3}242.44
Parsimonious Voice Leading Between Common Triads of Scale 2911. 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 C+->G# am am C+->am A A c#m->A D D d#° d#° D->d#° f#m f#m D->f#m bm bm D->bm d#°->B g#m g#m E->g#m f#° f#° f#°->f#m f#°->am f#m->A g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B G#->a° a°->am am->A bm->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 2911 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3503
Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
3rd mode:
Scale 3799
Scale 3799: Aeralygic, Ian Ring Music TheoryAeralygic
4th mode:
Scale 3947
Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
5th mode:
Scale 4021
Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
6th mode:
Scale 2029
Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
7th mode:
Scale 1531
Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic
8th mode:
Scale 2813
Scale 2813: Zolygic, Ian Ring Music TheoryZolygic
9th mode:
Scale 1727
Scale 1727: Sydygic, Ian Ring Music TheorySydygic

Prime

The prime form of this scale is Scale 1471

Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic

Complement

The nonatonic modal family [2911, 3503, 3799, 3947, 4021, 2029, 1531, 2813, 1727] (Forte: 9-7) is the complement of the tritonic modal family [37, 641, 1033] (Forte: 3-7)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2911 is 3931

Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2911 is chiral, and its enantiomorph is scale 3931

Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic

Transformations:

T0 2911  T0I 3931
T1 1727  T1I 3767
T2 3454  T2I 3439
T3 2813  T3I 2783
T4 1531  T4I 1471
T5 3062  T5I 2942
T6 2029  T6I 1789
T7 4058  T7I 3578
T8 4021  T8I 3061
T9 3947  T9I 2027
T10 3799  T10I 4054
T11 3503  T11I 4013

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 2909Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 2895Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic
Scale 2927Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
Scale 2943Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
Scale 2847Scale 2847: Phracryllic, Ian Ring Music TheoryPhracryllic
Scale 2879Scale 2879: Stadygic, Ian Ring Music TheoryStadygic
Scale 2975Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
Scale 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
Scale 2655Scale 2655, Ian Ring Music Theory
Scale 2783Scale 2783: Gothygic, Ian Ring Music TheoryGothygic
Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3935Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 1887Scale 1887: Aerocrygic, Ian Ring Music TheoryAerocrygic

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.