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Scale 2923: "Baryllic"

Scale 2923: Baryllic, 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
Baryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,5,6,8,9,11}
Forte Number8-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2779
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes7
Prime?no
prime: 1463
Deep Scaleno
Interval Vector456553
Interval Spectrump5m5n6s5d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.25
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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}242.23
F{5,9,0}441.92
G♯{8,0,3}441.92
B{11,3,6}342.23
Minor Triadsfm{5,8,0}441.85
f♯m{6,9,1}342.23
g♯m{8,11,3}342.15
Augmented TriadsC♯+{1,5,9}342.15
Diminished Triads{0,3,6}242.31
d♯°{3,6,9}242.31
{5,8,11}242.23
f♯°{6,9,0}242.31
{9,0,3}242.15
Parsimonious Voice Leading Between Common Triads of Scale 2923. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F f#m f#m C#+->f#m d#° d#° d#°->f#m d#°->B f°->fm g#m g#m f°->g#m fm->F fm->G# f#° f#° F->f#° F->a° f#°->f#m g#m->G# g#m->B G#->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 2923 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3509
Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
3rd mode:
Scale 1901
Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
4th mode:
Scale 1499
Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
5th mode:
Scale 2797
Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
6th mode:
Scale 1723
Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
7th mode:
Scale 2909
Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
8th mode:
Scale 1751
Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic

Prime

The prime form of this scale is Scale 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Complement

The octatonic modal family [2923, 3509, 1901, 1499, 2797, 1723, 2909, 1751] (Forte: 8-27) is the complement of the tetratonic modal family [293, 593, 649, 1097] (Forte: 4-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2923 is 2779

Scale 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2923 is chiral, and its enantiomorph is scale 2779

Scale 2779Scale 2779: Shostakovich, Ian Ring Music TheoryShostakovich

Transformations:

T0 2923  T0I 2779
T1 1751  T1I 1463
T2 3502  T2I 2926
T3 2909  T3I 1757
T4 1723  T4I 3514
T5 3446  T5I 2933
T6 2797  T6I 1771
T7 1499  T7I 3542
T8 2998  T8I 2989
T9 1901  T9I 1883
T10 3802  T10I 3766
T11 3509  T11I 3437

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 2921Scale 2921: Pogian, Ian Ring Music TheoryPogian
Scale 2925Scale 2925: Diminished, Ian Ring Music TheoryDiminished
Scale 2927Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
Scale 2915Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian
Scale 2919Scale 2919: Molyllic, Ian Ring Music TheoryMolyllic
Scale 2931Scale 2931: Zathyllic, Ian Ring Music TheoryZathyllic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
Scale 2907Scale 2907: Magen Abot 2, Ian Ring Music TheoryMagen Abot 2
Scale 2859Scale 2859: Phrycrian, Ian Ring Music TheoryPhrycrian
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 2667Scale 2667: Byrian, Ian Ring Music TheoryByrian
Scale 2795Scale 2795: Van der Horst Octatonic, Ian Ring Music TheoryVan der Horst Octatonic
Scale 2411Scale 2411: Aeolorian, Ian Ring Music TheoryAeolorian
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 875Scale 875: Locrian Double-flat 7, Ian Ring Music TheoryLocrian Double-flat 7
Scale 1899Scale 1899: Moptyllic, Ian Ring Music TheoryMoptyllic

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.