The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3451: "Garygic"

Scale 3451: Garygic, 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
Garygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,4,5,6,8,10,11}
Forte Number9-9
Rotational Symmetrynone
Reflection Axes2
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections1
Modes8
Prime?no
prime: 1519
Deep Scaleno
Interval Vector676683
Interval Spectrump8m6n6s7d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tones[4]
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}342.29
E{4,8,11}342.21
F♯{6,10,1}242.57
G♯{8,0,3}342.21
B{11,3,6}342.43
Minor Triadsc♯m{1,4,8}342.21
d♯m{3,6,10}242.57
fm{5,8,0}342.21
g♯m{8,11,3}342.29
a♯m{10,1,5}342.43
Augmented TriadsC+{0,4,8}442
Diminished Triads{0,3,6}242.57
{5,8,11}242.57
a♯°{10,1,4}242.57
Parsimonious Voice Leading Between Common Triads of Scale 3451. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm C+->G# C# C# c#m->C# a#° a#° c#m->a#° C#->fm a#m a#m C#->a#m d#m d#m F# F# d#m->F# d#m->B E->f° g#m g#m E->g#m f°->fm F#->a#m g#m->G# g#m->B a#°->a#m

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 3451 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3773
Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
3rd mode:
Scale 1967
Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed
4th mode:
Scale 3031
Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic
5th mode:
Scale 3563
Scale 3563: Ionoptygic, Ian Ring Music TheoryIonoptygic
6th mode:
Scale 3829
Scale 3829: Taishikicho, Ian Ring Music TheoryTaishikicho
7th mode:
Scale 1981
Scale 1981: Houseini, Ian Ring Music TheoryHouseini
8th mode:
Scale 1519
Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian MixedThis is the prime mode
9th mode:
Scale 2807
Scale 2807: Zylygic, Ian Ring Music TheoryZylygic

Prime

The prime form of this scale is Scale 1519

Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed

Complement

The nonatonic modal family [3451, 3773, 1967, 3031, 3563, 3829, 1981, 1519, 2807] (Forte: 9-9) is the complement of the tritonic modal family [133, 161, 1057] (Forte: 3-9)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3451 is 3031

Scale 3031Scale 3031: Epithygic, Ian Ring Music TheoryEpithygic

Transformations:

T0 3451  T0I 3031
T1 2807  T1I 1967
T2 1519  T2I 3934
T3 3038  T3I 3773
T4 1981  T4I 3451
T5 3962  T5I 2807
T6 3829  T6I 1519
T7 3563  T7I 3038
T8 3031  T8I 1981
T9 1967  T9I 3962
T10 3934  T10I 3829
T11 3773  T11I 3563

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 3449Scale 3449: Bacryllic, Ian Ring Music TheoryBacryllic
Scale 3453Scale 3453: Katarygic, Ian Ring Music TheoryKatarygic
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
Scale 3443Scale 3443: Verdi's Scala Enigmatica, Ian Ring Music TheoryVerdi's Scala Enigmatica
Scale 3447Scale 3447: Mogyllian, Ian Ring Music TheoryMogyllian
Scale 3435Scale 3435: Prokofiev, Ian Ring Music TheoryProkofiev
Scale 3419Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1
Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
Scale 3515Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
Scale 3579Scale 3579: Zyphyllian, Ian Ring Music TheoryZyphyllian
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic
Scale 3707Scale 3707: Rynygic, Ian Ring Music TheoryRynygic
Scale 3963Scale 3963: Aeoryllian, Ian Ring Music TheoryAeoryllian
Scale 2427Scale 2427: Katoryllic, Ian Ring Music TheoryKatoryllic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 1403Scale 1403: Espla's Scale, Ian Ring Music TheoryEspla's Scale

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.