The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3051: "Stalygic"

Scale 3051: Stalygic, 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
Stalygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,5,6,7,8,9,11}
Forte Number9-8
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2811
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1503
Deep Scaleno
Interval Vector676764
Interval Spectrump6m7n6s7d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.556
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
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}242.47
F{5,9,0}442.2
G♯{8,0,3}442.07
B{11,3,6}342.47
Minor Triadscm{0,3,7}342.33
fm{5,8,0}442.07
f♯m{6,9,1}342.47
g♯m{8,11,3}342.33
Augmented TriadsC♯+{1,5,9}342.4
D♯+{3,7,11}342.4
Diminished Triads{0,3,6}242.67
d♯°{3,6,9}242.53
{5,8,11}242.47
f♯°{6,9,0}242.53
{9,0,3}242.33
Parsimonious Voice Leading Between Common Triads of Scale 3051. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# 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 g#m g#m D#+->g#m D#+->B f°->fm f°->g#m fm->F fm->G# f#° f#° F->f#° F->a° f#°->f#m 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 3051 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3573
Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
3rd mode:
Scale 1917
Scale 1917: Thydyllian, Ian Ring Music TheoryThydyllian
4th mode:
Scale 1503
Scale 1503: Epiryllian, Ian Ring Music TheoryEpiryllianThis is the prime mode
5th mode:
Scale 2799
Scale 2799: Lyryllian, Ian Ring Music TheoryLyryllian
6th mode:
Scale 3447
Scale 3447: Mogyllian, Ian Ring Music TheoryMogyllian
7th mode:
Scale 3771
Scale 3771: Katodyllian, Ian Ring Music TheoryKatodyllian
8th mode:
Scale 3933
Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
9th mode:
Scale 2007
Scale 2007: Stonygic, Ian Ring Music TheoryStonygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Epiryllian, Ian Ring Music TheoryEpiryllian

Complement

The nonatonic modal family [3051, 3573, 1917, 1503, 2799, 3447, 3771, 3933, 2007] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3051 is 2811

Scale 2811Scale 2811: Barygic, Ian Ring Music TheoryBarygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3051 is chiral, and its enantiomorph is scale 2811

Scale 2811Scale 2811: Barygic, Ian Ring Music TheoryBarygic

Transformations:

T0 3051  T0I 2811
T1 2007  T1I 1527
T2 4014  T2I 3054
T3 3933  T3I 2013
T4 3771  T4I 4026
T5 3447  T5I 3957
T6 2799  T6I 3819
T7 1503  T7I 3543
T8 3006  T8I 2991
T9 1917  T9I 1887
T10 3834  T10I 3774
T11 3573  T11I 3453

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 3049Scale 3049: Phrydyllic, Ian Ring Music TheoryPhrydyllic
Scale 3053Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic
Scale 3055Scale 3055: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 3043Scale 3043: Ionayllic, Ian Ring Music TheoryIonayllic
Scale 3047Scale 3047: Panygic, Ian Ring Music TheoryPanygic
Scale 3059Scale 3059: Madygic, Ian Ring Music TheoryMadygic
Scale 3067Scale 3067: Goptyllian, Ian Ring Music TheoryGoptyllian
Scale 3019Scale 3019, Ian Ring Music Theory
Scale 3035Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
Scale 2987Scale 2987: Neapolitan Major and Minor Mixed, Ian Ring Music TheoryNeapolitan Major and Minor Mixed
Scale 2923Scale 2923: Baryllic, Ian Ring Music TheoryBaryllic
Scale 2795Scale 2795: Van der Horst Octatonic, Ian Ring Music TheoryVan der Horst Octatonic
Scale 2539Scale 2539: Half-Diminished Bebop, Ian Ring Music TheoryHalf-Diminished Bebop
Scale 3563Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic
Scale 4075Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
Scale 1003Scale 1003: Ionyryllic, Ian Ring Music TheoryIonyryllic
Scale 2027Scale 2027: Boptygic, Ian Ring Music TheoryBoptygic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.