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Scale 443: "Kothian"

Scale 443: Kothian, 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
Kothian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,5,7,8}
Forte Number7-Z37
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?yes
Deep Scaleno
Interval Vector434541
Interval Spectrump4m5n4s3d4t
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5}
<3> = {4,6,7}
<4> = {5,6,8}
<5> = {7,9,10}
<6> = {8,10,11}
Spectra Variation2.571
Maximally Evenno
Maximal Area Setno
Interior Area2.299
Myhill Propertyno
Balancedno
Ridge Tones[8]
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}331.5
C♯{1,5,8}242
G♯{8,0,3}231.75
Minor Triadscm{0,3,7}242
c♯m{1,4,8}331.5
fm{5,8,0}231.75
Augmented TriadsC+{0,4,8}421.25
Diminished Triadsc♯°{1,4,7}231.75
Parsimonious Voice Leading Between Common Triads of Scale 443. Created by Ian Ring ©2019 cm cm C C cm->C G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° c#m c#m C+->c#m fm fm C+->fm C+->G# c#°->c#m C# C# c#m->C# C#->fm

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 VerticesC+
Peripheral Verticescm, C♯

Modes

Modes are the rotational transformation of this scale. Scale 443 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2269
Scale 2269: Pygian, Ian Ring Music TheoryPygian
3rd mode:
Scale 1591
Scale 1591: Rodian, Ian Ring Music TheoryRodian
4th mode:
Scale 2843
Scale 2843: Sorian, Ian Ring Music TheorySorian
5th mode:
Scale 3469
Scale 3469: Monian, Ian Ring Music TheoryMonian
6th mode:
Scale 1891
Scale 1891: Thalian, Ian Ring Music TheoryThalian
7th mode:
Scale 2993
Scale 2993: Stythian, Ian Ring Music TheoryStythian

Prime

This is the prime form of this scale.

Complement

The heptatonic modal family [443, 2269, 1591, 2843, 3469, 1891, 2993] (Forte: 7-Z37) is the complement of the pentatonic modal family [313, 551, 913, 2323, 3209] (Forte: 5-Z37)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 443 is 2993

Scale 2993Scale 2993: Stythian, Ian Ring Music TheoryStythian

Transformations:

T0 443  T0I 2993
T1 886  T1I 1891
T2 1772  T2I 3782
T3 3544  T3I 3469
T4 2993  T4I 2843
T5 1891  T5I 1591
T6 3782  T6I 3182
T7 3469  T7I 2269
T8 2843  T8I 443
T9 1591  T9I 886
T10 3182  T10I 1772
T11 2269  T11I 3544

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 441Scale 441: Thycrimic, Ian Ring Music TheoryThycrimic
Scale 445Scale 445: Gocrian, Ian Ring Music TheoryGocrian
Scale 447Scale 447: Thyphyllic, Ian Ring Music TheoryThyphyllic
Scale 435Scale 435: Raga Purna Pancama, Ian Ring Music TheoryRaga Purna Pancama
Scale 439Scale 439: Bythian, Ian Ring Music TheoryBythian
Scale 427Scale 427: Raga Suddha Simantini, Ian Ring Music TheoryRaga Suddha Simantini
Scale 411Scale 411: Lygimic, Ian Ring Music TheoryLygimic
Scale 475Scale 475: Aeolygian, Ian Ring Music TheoryAeolygian
Scale 507Scale 507: Moryllic, Ian Ring Music TheoryMoryllic
Scale 315Scale 315: Stodimic, Ian Ring Music TheoryStodimic
Scale 379Scale 379: Aeragian, Ian Ring Music TheoryAeragian
Scale 187Scale 187, Ian Ring Music Theory
Scale 699Scale 699: Aerothian, Ian Ring Music TheoryAerothian
Scale 955Scale 955: Ionogyllic, Ian Ring Music TheoryIonogyllic
Scale 1467Scale 1467: Spanish Phrygian, Ian Ring Music TheorySpanish Phrygian
Scale 2491Scale 2491: Layllic, Ian Ring Music TheoryLayllic

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.