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Scale 3019

Scale 3019, 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{0,1,3,6,7,8,9,11}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2683
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 TriadsG♯{8,0,3}341.9
B{11,3,6}341.9
Minor Triadscm{0,3,7}341.9
f♯m{6,9,1}242.3
g♯m{8,11,3}242.1
Augmented TriadsD♯+{3,7,11}341.9
Diminished Triads{0,3,6}242.1
d♯°{3,6,9}242.1
f♯°{6,9,0}242.3
{9,0,3}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3019. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# d#° d#° f#m f#m d#°->f#m d#°->B g#m g#m D#+->g#m D#+->B f#° f#° f#°->f#m f#°->a° g#m->G# 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 3019 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3557
Scale 3557, Ian Ring Music Theory
3rd mode:
Scale 1913
Scale 1913, Ian Ring Music Theory
4th mode:
Scale 751
Scale 751, Ian Ring Music TheoryThis is the prime mode
5th mode:
Scale 2423
Scale 2423, Ian Ring Music Theory
6th mode:
Scale 3259
Scale 3259, Ian Ring Music Theory
7th mode:
Scale 3677
Scale 3677, Ian Ring Music Theory
8th mode:
Scale 1943
Scale 1943, 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 [3019, 3557, 1913, 751, 2423, 3259, 3677, 1943] (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 3019 is 2683

Scale 2683Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3019 is chiral, and its enantiomorph is scale 2683

Scale 2683Scale 2683: Thodyllic, Ian Ring Music TheoryThodyllic

Transformations:

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

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 3017Scale 3017: Gacrian, Ian Ring Music TheoryGacrian
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 3023Scale 3023: Mothygic, Ian Ring Music TheoryMothygic
Scale 3011Scale 3011, Ian Ring Music Theory
Scale 3015Scale 3015: Laptyllic, Ian Ring Music TheoryLaptyllic
Scale 3027Scale 3027: Rythyllic, Ian Ring Music TheoryRythyllic
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 3051Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
Scale 2955Scale 2955: Thorian, Ian Ring Music TheoryThorian
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 2891Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 2507Scale 2507: Todi That, Ian Ring Music TheoryTodi That
Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
Scale 4043Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
Scale 971Scale 971: Mela Gavambodhi, Ian Ring Music TheoryMela Gavambodhi
Scale 1995Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic

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.