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Scale 607: "Kadian"

Scale 607: Kadian, 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
Kadian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,2,3,4,6,9}
Forte Number7-10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3913
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?yes
Deep Scaleno
Interval Vector445332
Interval Spectrump3m3n5s4d4t2
Distribution Spectra<1> = {1,2,3}
<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> = {9,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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}231.75
A{9,1,4}231.75
Minor Triadsf♯m{6,9,1}331.63
am{9,0,4}331.63
Diminished Triads{0,3,6}231.88
d♯°{3,6,9}231.88
f♯°{6,9,0}231.75
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 607. Created by Ian Ring ©2019 d#° d#° c°->d#° c°->a° D D D->d#° f#m f#m D->f#m f#° f#° f#°->f#m am am f#°->am A A f#m->A a°->am 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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 607 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2351
Scale 2351: Gynian, Ian Ring Music TheoryGynian
3rd mode:
Scale 3223
Scale 3223: Thyphian, Ian Ring Music TheoryThyphian
4th mode:
Scale 3659
Scale 3659: Polian, Ian Ring Music TheoryPolian
5th mode:
Scale 3877
Scale 3877: Thanian, Ian Ring Music TheoryThanian
6th mode:
Scale 1993
Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
7th mode:
Scale 761
Scale 761: Ponian, Ian Ring Music TheoryPonian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [607, 2351, 3223, 3659, 3877, 1993, 761] (Forte: 7-10) is the complement of the pentatonic modal family [91, 1547, 1729, 2093, 2821] (Forte: 5-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 607 is 3913

Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 607 is chiral, and its enantiomorph is scale 3913

Scale 3913Scale 3913: Bonian, Ian Ring Music TheoryBonian

Transformations:

T0 607  T0I 3913
T1 1214  T1I 3731
T2 2428  T2I 3367
T3 761  T3I 2639
T4 1522  T4I 1183
T5 3044  T5I 2366
T6 1993  T6I 637
T7 3986  T7I 1274
T8 3877  T8I 2548
T9 3659  T9I 1001
T10 3223  T10I 2002
T11 2351  T11I 4004

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 605Scale 605: Dycrimic, Ian Ring Music TheoryDycrimic
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 599Scale 599: Thyrimic, Ian Ring Music TheoryThyrimic
Scale 591Scale 591: Gaptimic, Ian Ring Music TheoryGaptimic
Scale 623Scale 623: Sycrian, Ian Ring Music TheorySycrian
Scale 639Scale 639: Ionaryllic, Ian Ring Music TheoryIonaryllic
Scale 543Scale 543, Ian Ring Music Theory
Scale 575Scale 575: Ionydian, Ian Ring Music TheoryIonydian
Scale 671Scale 671: Stycrian, Ian Ring Music TheoryStycrian
Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic
Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic
Scale 95Scale 95, Ian Ring Music Theory
Scale 351Scale 351: Epanian, Ian Ring Music TheoryEpanian
Scale 1119Scale 1119: Rarian, Ian Ring Music TheoryRarian
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 2655Scale 2655, Ian Ring Music Theory

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.