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Scale 3627: "Kalian"

Scale 3627: Kalian, 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
Kalian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,5,9,10,11}
Forte Number7-9
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2703
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 351
Deep Scaleno
Interval Vector453432
Interval Spectrump3m4n3s5d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,4,5,6}
<3> = {3,4,5,6,7,8}
<4> = {4,5,6,7,8,9}
<5> = {6,7,8,9,10}
<6> = {8,10,11}
Spectra Variation3.429
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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 TriadsF{5,9,0}221
Minor Triadsa♯m{10,1,5}131.5
Augmented TriadsC♯+{1,5,9}221
Diminished Triads{9,0,3}131.5
Parsimonious Voice Leading Between Common Triads of Scale 3627. Created by Ian Ring ©2019 C#+ C#+ F F C#+->F a#m a#m C#+->a#m F->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 VerticesC♯+, F
Peripheral Verticesa°, a♯m

Modes

Modes are the rotational transformation of this scale. Scale 3627 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3861
Scale 3861: Phroptian, Ian Ring Music TheoryPhroptian
3rd mode:
Scale 1989
Scale 1989: Dydian, Ian Ring Music TheoryDydian
4th mode:
Scale 1521
Scale 1521: Stanian, Ian Ring Music TheoryStanian
5th mode:
Scale 351
Scale 351: Epanian, Ian Ring Music TheoryEpanianThis is the prime mode
6th mode:
Scale 2223
Scale 2223: Konian, Ian Ring Music TheoryKonian
7th mode:
Scale 3159
Scale 3159: Stocrian, Ian Ring Music TheoryStocrian

Prime

The prime form of this scale is Scale 351

Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian

Complement

The heptatonic modal family [3627, 3861, 1989, 1521, 351, 2223, 3159] (Forte: 7-9) is the complement of the pentatonic modal family [87, 1473, 1797, 2091, 3093] (Forte: 5-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3627 is 2703

Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3627 is chiral, and its enantiomorph is scale 2703

Scale 2703Scale 2703: Galian, Ian Ring Music TheoryGalian

Transformations:

T0 3627  T0I 2703
T1 3159  T1I 1311
T2 2223  T2I 2622
T3 351  T3I 1149
T4 702  T4I 2298
T5 1404  T5I 501
T6 2808  T6I 1002
T7 1521  T7I 2004
T8 3042  T8I 4008
T9 1989  T9I 3921
T10 3978  T10I 3747
T11 3861  T11I 3399

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 3625Scale 3625: Podimic, Ian Ring Music TheoryPodimic
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 3631Scale 3631: Gydyllic, Ian Ring Music TheoryGydyllic
Scale 3619Scale 3619: Thanimic, Ian Ring Music TheoryThanimic
Scale 3623Scale 3623: Aerocrian, Ian Ring Music TheoryAerocrian
Scale 3635Scale 3635: Katygian, Ian Ring Music TheoryKatygian
Scale 3643Scale 3643: Kydyllic, Ian Ring Music TheoryKydyllic
Scale 3595Scale 3595, Ian Ring Music Theory
Scale 3611Scale 3611, Ian Ring Music Theory
Scale 3659Scale 3659: Polian, Ian Ring Music TheoryPolian
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3883Scale 3883: Kyryllic, Ian Ring Music TheoryKyryllic
Scale 3115Scale 3115, Ian Ring Music Theory
Scale 3371Scale 3371: Aeolylian, Ian Ring Music TheoryAeolylian
Scale 2603Scale 2603: Gadimic, Ian Ring Music TheoryGadimic
Scale 1579Scale 1579: Sagimic, Ian Ring Music TheorySagimic

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.