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Scale 1943

Scale 1943, 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).

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,4,7,8,9,10}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3389
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 751
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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 TriadsC{0,4,7}341.9
A{9,1,4}341.9
Minor Triadsc♯m{1,4,8}341.9
gm{7,10,2}242.3
am{9,0,4}242.1
Augmented TriadsC+{0,4,8}341.9
Diminished Triadsc♯°{1,4,7}242.1
{4,7,10}242.1
{7,10,1}242.3
a♯°{10,1,4}242.1
Parsimonious Voice Leading Between Common Triads of Scale 1943. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m am am C+->am c#°->c#m A A c#m->A gm gm e°->gm g°->gm a#° a#° g°->a#° am->A A->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
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1943 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3019
Scale 3019, Ian Ring Music Theory
3rd mode:
Scale 3557
Scale 3557, Ian Ring Music Theory
4th mode:
Scale 1913
Scale 1913, Ian Ring Music Theory
5th mode:
Scale 751
Scale 751, Ian Ring Music TheoryThis is the prime mode
6th mode:
Scale 2423
Scale 2423, Ian Ring Music Theory
7th mode:
Scale 3259
Scale 3259, Ian Ring Music Theory
8th mode:
Scale 3677
Scale 3677, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [1943, 3019, 3557, 1913, 751, 2423, 3259, 3677] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1943 is 3389

Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1943 is chiral, and its enantiomorph is scale 3389

Scale 3389Scale 3389: Socryllic, Ian Ring Music TheorySocryllic

Transformations:

T0 1943  T0I 3389
T1 3886  T1I 2683
T2 3677  T2I 1271
T3 3259  T3I 2542
T4 2423  T4I 989
T5 751  T5I 1978
T6 1502  T6I 3956
T7 3004  T7I 3817
T8 1913  T8I 3539
T9 3826  T9I 2983
T10 3557  T10I 1871
T11 3019  T11I 3742

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 1941Scale 1941: Aeranian, Ian Ring Music TheoryAeranian
Scale 1939Scale 1939: Dathian, Ian Ring Music TheoryDathian
Scale 1947Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic
Scale 1951Scale 1951: Marygic, Ian Ring Music TheoryMarygic
Scale 1927Scale 1927, Ian Ring Music Theory
Scale 1935Scale 1935: Mycryllic, Ian Ring Music TheoryMycryllic
Scale 1959Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
Scale 1975Scale 1975: Ionocrygic, Ian Ring Music TheoryIonocrygic
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 1815Scale 1815: Godian, Ian Ring Music TheoryGodian
Scale 1879Scale 1879: Mixoryllic, Ian Ring Music TheoryMixoryllic
Scale 1687Scale 1687: Phralian, Ian Ring Music TheoryPhralian
Scale 1431Scale 1431: Phragian, Ian Ring Music TheoryPhragian
Scale 919Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 3991Scale 3991: Badygic, Ian Ring Music TheoryBadygic

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.