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Scale 2899: "Kagian"

Scale 2899: Kagian, 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
Kagian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,4,6,8,9,11}
Forte Number7-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2395
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections2
Modes6
Prime?no
prime: 695
Deep Scaleno
Interval Vector344451
Interval Spectrump5m4n4s4d3t
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,8,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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 TriadsE{4,8,11}142.14
A{9,1,4}331.43
Minor Triadsc♯m{1,4,8}231.57
f♯m{6,9,1}241.86
am{9,0,4}321.29
Augmented TriadsC+{0,4,8}331.43
Diminished Triadsf♯°{6,9,0}231.71
Parsimonious Voice Leading Between Common Triads of Scale 2899. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E am am C+->am A A c#m->A f#° f#° f#m f#m f#°->f#m f#°->am f#m->A am->A

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
Radius2
Self-Centeredno
Central Verticesam
Peripheral VerticesE, f♯m

Modes

Modes are the rotational transformation of this scale. Scale 2899 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3497		Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
3rd mode:
Scale 949		Scale 949: Mela Mararanjani, Ian Ring Music TheoryMela Mararanjani
4th mode:
Scale 1261		Scale 1261: Modified Blues, Ian Ring Music TheoryModified Blues
5th mode:
Scale 1339		Scale 1339: Kycrian, Ian Ring Music TheoryKycrian
6th mode:
Scale 2717		Scale 2717: Epygian, Ian Ring Music TheoryEpygian
7th mode:
Scale 1703		Scale 1703: Mela Vanaspati, Ian Ring Music TheoryMela Vanaspati

Prime

The prime form of this scale is Scale 695

Scale 695Scale 695: Sarian, Ian Ring Music TheorySarian

Complement

The heptatonic modal family [2899, 3497, 949, 1261, 1339, 2717, 1703] (Forte: 7-27) is the complement of the pentatonic modal family [299, 689, 1417, 1573, 2197] (Forte: 5-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2899 is 2395

Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2899 is chiral, and its enantiomorph is scale 2395

Scale 2395Scale 2395: Zoptian, Ian Ring Music TheoryZoptian

Transformations:

T0 2899  T0I 2395
T1 1703  T1I 695
T2 3406  T2I 1390
T3 2717  T3I 2780
T4 1339  T4I 1465
T5 2678  T5I 2930
T6 1261  T6I 1765
T7 2522  T7I 3530
T8 949  T8I 2965
T9 1898  T9I 1835
T10 3796  T10I 3670
T11 3497  T11I 3245

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 2897Scale 2897: Rycrimic, Ian Ring Music TheoryRycrimic
Scale 2901Scale 2901: Lydian Augmented, Ian Ring Music TheoryLydian Augmented
Scale 2903Scale 2903: Gothyllic, Ian Ring Music TheoryGothyllic
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
Scale 2883Scale 2883, Ian Ring Music Theory
Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
Scale 2915Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian
Scale 2931Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
Scale 2835Scale 2835: Ionygimic, Ian Ring Music TheoryIonygimic
Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian
Scale 2963Scale 2963: Bygian, Ian Ring Music TheoryBygian
Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
Scale 2643Scale 2643: Raga Hamsanandi, Ian Ring Music TheoryRaga Hamsanandi
Scale 2771Scale 2771: Marva That, Ian Ring Music TheoryMarva That
Scale 2387Scale 2387: Paptimic, Ian Ring Music TheoryPaptimic
Scale 3411Scale 3411: Enigmatic, Ian Ring Music TheoryEnigmatic
Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
Scale 851Scale 851: Raga Hejjajji, Ian Ring Music TheoryRaga Hejjajji
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti 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.