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Scale 2423

Scale 2423, 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{0,1,2,4,5,6,8,11}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3539
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♯{1,5,8}341.9
E{4,8,11}341.9
Minor Triadsc♯m{1,4,8}242.1
fm{5,8,0}341.9
bm{11,2,6}242.3
Augmented TriadsC+{0,4,8}341.9
Diminished Triads{2,5,8}242.1
{5,8,11}242.1
g♯°{8,11,2}242.1
{11,2,5}242.3
Parsimonious Voice Leading Between Common Triads of Scale 2423. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C# C# c#m->C# C#->d° C#->fm d°->b° E->f° g#° g#° E->g#° f°->fm bm bm g#°->bm b°->bm

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 2423 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3259
Scale 3259, Ian Ring Music Theory
3rd mode:
Scale 3677
Scale 3677, Ian Ring Music Theory
4th mode:
Scale 1943
Scale 1943, Ian Ring Music Theory
5th mode:
Scale 3019
Scale 3019, Ian Ring Music Theory
6th mode:
Scale 3557
Scale 3557, Ian Ring Music Theory
7th mode:
Scale 1913
Scale 1913, Ian Ring Music Theory
8th mode:
Scale 751
Scale 751, Ian Ring Music TheoryThis is the prime mode

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [2423, 3259, 3677, 1943, 3019, 3557, 1913, 751] (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 2423 is 3539

Scale 3539Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2423 is chiral, and its enantiomorph is scale 3539

Scale 3539Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic

Transformations:

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

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 2421Scale 2421: Malian, Ian Ring Music TheoryMalian
Scale 2419Scale 2419: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 2431Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
Scale 2407Scale 2407: Zylian, Ian Ring Music TheoryZylian
Scale 2415Scale 2415: Lothyllic, Ian Ring Music TheoryLothyllic
Scale 2391Scale 2391: Molian, Ian Ring Music TheoryMolian
Scale 2359Scale 2359: Gadian, Ian Ring Music TheoryGadian
Scale 2487Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
Scale 2551Scale 2551: Thocrygic, Ian Ring Music TheoryThocrygic
Scale 2167Scale 2167, Ian Ring Music Theory
Scale 2295Scale 2295: Kogyllic, Ian Ring Music TheoryKogyllic
Scale 2679Scale 2679: Rathyllic, Ian Ring Music TheoryRathyllic
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic
Scale 3447Scale 3447: Mogyllian, Ian Ring Music TheoryMogyllian
Scale 375Scale 375: Sodian, Ian Ring Music TheorySodian
Scale 1399Scale 1399: Syryllic, Ian Ring Music TheorySyryllic

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.