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Scale 3667: "Kaptian"

Scale 3667: Kaptian, 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
Kaptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,4,6,9,10,11}
Forte Number7-Z12
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes6
Prime?no
prime: 671
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,4,5}
<3> = {3,5,6,8}
<4> = {4,6,7,9}
<5> = {7,8,10}
<6> = {9,10,11}
Spectra Variation2.857
Maximally Evenno
Maximal Area Setno
Interior Area2.433
Myhill Propertyno
Balancedno
Ridge Tones[10]
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 TriadsF♯{6,10,1}231.5
A{9,1,4}321.17
Minor Triadsf♯m{6,9,1}321.17
am{9,0,4}231.5
Diminished Triadsf♯°{6,9,0}231.5
a♯°{10,1,4}231.5
Parsimonious Voice Leading Between Common Triads of Scale 3667. Created by Ian Ring ©2019 f#° f#° f#m f#m f#°->f#m am am f#°->am F# F# f#m->F# A A f#m->A a#° a#° F#->a#° am->A A->a#°

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.

Diameter3
Radius2
Self-Centeredno
Central Verticesf♯m, A
Peripheral Verticesf♯°, F♯, am, a♯°

Modes

Modes are the rotational transformation of this scale. Scale 3667 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3881
Scale 3881: Morian, Ian Ring Music TheoryMorian
3rd mode:
Scale 997
Scale 997: Rycrian, Ian Ring Music TheoryRycrian
4th mode:
Scale 1273
Scale 1273: Ronian, Ian Ring Music TheoryRonian
5th mode:
Scale 671
Scale 671: Stycrian, Ian Ring Music TheoryStycrianThis is the prime mode
6th mode:
Scale 2383
Scale 2383: Katorian, Ian Ring Music TheoryKatorian
7th mode:
Scale 3239
Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi

Prime

The prime form of this scale is Scale 671

Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian

Complement

The heptatonic modal family [3667, 3881, 997, 1273, 671, 2383, 3239] (Forte: 7-Z12) is the complement of the pentatonic modal family [107, 1411, 1549, 2101, 2753] (Forte: 5-Z12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3667 is 2383

Scale 2383Scale 2383: Katorian, Ian Ring Music TheoryKatorian

Transformations:

T0 3667  T0I 2383
T1 3239  T1I 671
T2 2383  T2I 1342
T3 671  T3I 2684
T4 1342  T4I 1273
T5 2684  T5I 2546
T6 1273  T6I 997
T7 2546  T7I 1994
T8 997  T8I 3988
T9 1994  T9I 3881
T10 3988  T10I 3667
T11 3881  T11I 3239

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 3665Scale 3665: Stalimic, Ian Ring Music TheoryStalimic
Scale 3669Scale 3669: Mothian, Ian Ring Music TheoryMothian
Scale 3671Scale 3671: Aeonyllic, Ian Ring Music TheoryAeonyllic
Scale 3675Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
Scale 3651Scale 3651, Ian Ring Music Theory
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 3683Scale 3683: Dycrian, Ian Ring Music TheoryDycrian
Scale 3699Scale 3699: Galyllic, Ian Ring Music TheoryGalyllic
Scale 3603Scale 3603, Ian Ring Music Theory
Scale 3635Scale 3635: Katygian, Ian Ring Music TheoryKatygian
Scale 3731Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3923Scale 3923: Stoptyllic, Ian Ring Music TheoryStoptyllic
Scale 3155Scale 3155: Ladimic, Ian Ring Music TheoryLadimic
Scale 3411Scale 3411: Enigmatic, Ian Ring Music TheoryEnigmatic
Scale 2643Scale 2643: Raga Hamsanandi, Ian Ring Music TheoryRaga Hamsanandi
Scale 1619Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan

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.