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Scale 4025: "Kalygic"

Scale 4025: Kalygic, 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
Kalygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,3,4,5,7,8,9,10,11}
Forte Number9-4
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 959
Hemitonia7 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections2
Modes8
Prime?no
prime: 959
Deep Scaleno
Interval Vector766773
Interval Spectrump7m7n6s6d7t3
Distribution Spectra<1> = {1,2,3}
<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> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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}332
D♯{3,7,10}263
E{4,8,11}431.87
F{5,9,0}263
G♯{8,0,3}442
Minor Triadscm{0,3,7}342.2
em{4,7,11}442.07
fm{5,8,0}352.4
g♯m{8,11,3}342.07
am{9,0,4}352.4
Augmented TriadsC+{0,4,8}541.8
D♯+{3,7,11}452.27
Diminished Triads{4,7,10}252.8
{5,8,11}242.47
{9,0,3}252.6
Parsimonious Voice Leading Between Common Triads of Scale 4025. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm C+->G# am am C+->am D# D# D#->D#+ D#->e° D#+->em g#m g#m D#+->g#m e°->em em->E E->f° E->g#m f°->fm F F fm->F F->am g#m->G# G#->a° a°->am

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.

Diameter6
Radius3
Self-Centeredno
Central VerticesC, E
Peripheral VerticesD♯, F

Modes

Modes are the rotational transformation of this scale. Scale 4025 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1015
Scale 1015: Ionodygic, Ian Ring Music TheoryIonodygic
3rd mode:
Scale 2555
Scale 2555: Bythygic, Ian Ring Music TheoryBythygic
4th mode:
Scale 3325
Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
5th mode:
Scale 1855
Scale 1855: Gaptygic, Ian Ring Music TheoryGaptygic
6th mode:
Scale 2975
Scale 2975: Aeroptygic, Ian Ring Music TheoryAeroptygic
7th mode:
Scale 3535
Scale 3535: Mylygic, Ian Ring Music TheoryMylygic
8th mode:
Scale 3815
Scale 3815: Galygic, Ian Ring Music TheoryGalygic
9th mode:
Scale 3955
Scale 3955: Pothygic, Ian Ring Music TheoryPothygic

Prime

The prime form of this scale is Scale 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Complement

The nonatonic modal family [4025, 1015, 2555, 3325, 1855, 2975, 3535, 3815, 3955] (Forte: 9-4) is the complement of the tritonic modal family [35, 385, 2065] (Forte: 3-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4025 is 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 4025 is chiral, and its enantiomorph is scale 959

Scale 959Scale 959: Katylygic, Ian Ring Music TheoryKatylygic

Transformations:

T0 4025  T0I 959
T1 3955  T1I 1918
T2 3815  T2I 3836
T3 3535  T3I 3577
T4 2975  T4I 3059
T5 1855  T5I 2023
T6 3710  T6I 4046
T7 3325  T7I 3997
T8 2555  T8I 3899
T9 1015  T9I 3703
T10 2030  T10I 3311
T11 4060  T11I 2527

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 4027Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
Scale 4029Scale 4029: Major/Minor Mixed, Ian Ring Music TheoryMajor/Minor Mixed
Scale 4017Scale 4017: Dolyllic, Ian Ring Music TheoryDolyllic
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 4009Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
Scale 3993Scale 3993: Ioniptyllic, Ian Ring Music TheoryIoniptyllic
Scale 4057Scale 4057: Phrygic, Ian Ring Music TheoryPhrygic
Scale 4089Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
Scale 3897Scale 3897: Kalyllic, Ian Ring Music TheoryKalyllic
Scale 3961Scale 3961: Zathygic, Ian Ring Music TheoryZathygic
Scale 3769Scale 3769: Eponyllic, Ian Ring Music TheoryEponyllic
Scale 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
Scale 3001Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
Scale 1977Scale 1977: Dagyllic, Ian Ring Music TheoryDagyllic

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.