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Scale 3293: "Saryllic"

Scale 3293: Saryllic, 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
Saryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,4,6,7,10,11}
Forte Number8-19
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1895
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 887
Deep Scaleno
Interval Vector545752
Interval Spectrump5m7n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5,6}
<4> = {5,6,7}
<5> = {6,7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.75
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{0,4,7}252.62
D♯{3,7,10}431.77
G{7,11,2}331.92
B{11,3,6}431.77
Minor Triadscm{0,3,7}342.08
d♯m{3,6,10}342
em{4,7,11}342.08
gm{7,10,2}342.15
bm{11,2,6}342.15
Augmented TriadsD+{2,6,10}352.38
D♯+{3,7,11}531.54
Diminished Triads{0,3,6}242.31
{4,7,10}242.31
Parsimonious Voice Leading Between Common Triads of Scale 3293. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ em em C->em D+ D+ d#m d#m D+->d#m gm gm D+->gm bm bm D+->bm D# D# d#m->D# d#m->B D#->D#+ D#->e° D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3293. Created by Ian Ring ©2019 G D#+->G D#+->B e°->em gm->G G->bm bm->B

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.

Diameter5
Radius3
Self-Centeredno
Central VerticesD♯, D♯+, G, B
Peripheral VerticesC, D+

Modes

Modes are the rotational transformation of this scale. Scale 3293 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1847
Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
3rd mode:
Scale 2971
Scale 2971: Aeolynyllic, Ian Ring Music TheoryAeolynyllic
4th mode:
Scale 3533
Scale 3533: Thadyllic, Ian Ring Music TheoryThadyllic
5th mode:
Scale 1907
Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic
6th mode:
Scale 3001
Scale 3001: Lonyllic, Ian Ring Music TheoryLonyllic
7th mode:
Scale 887
Scale 887: Sathyllic, Ian Ring Music TheorySathyllicThis is the prime mode
8th mode:
Scale 2491
Scale 2491: Layllic, Ian Ring Music TheoryLayllic

Prime

The prime form of this scale is Scale 887

Scale 887Scale 887: Sathyllic, Ian Ring Music TheorySathyllic

Complement

The octatonic modal family [3293, 1847, 2971, 3533, 1907, 3001, 887, 2491] (Forte: 8-19) is the complement of the tetratonic modal family [275, 305, 785, 2185] (Forte: 4-19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3293 is 1895

Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3293 is chiral, and its enantiomorph is scale 1895

Scale 1895Scale 1895: Salyllic, Ian Ring Music TheorySalyllic

Transformations:

T0 3293  T0I 1895
T1 2491  T1I 3790
T2 887  T2I 3485
T3 1774  T3I 2875
T4 3548  T4I 1655
T5 3001  T5I 3310
T6 1907  T6I 2525
T7 3814  T7I 955
T8 3533  T8I 1910
T9 2971  T9I 3820
T10 1847  T10I 3545
T11 3694  T11I 2995

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 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6
Scale 3291Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic
Scale 3285Scale 3285: Mela Citrambari, Ian Ring Music TheoryMela Citrambari
Scale 3277Scale 3277: Mela Nitimati, Ian Ring Music TheoryMela Nitimati
Scale 3309Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
Scale 3325Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
Scale 3229Scale 3229: Aeolaptian, Ian Ring Music TheoryAeolaptian
Scale 3261Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
Scale 3165Scale 3165: Mylian, Ian Ring Music TheoryMylian
Scale 3421Scale 3421: Aerothyllic, Ian Ring Music TheoryAerothyllic
Scale 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 3805Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic
Scale 2269Scale 2269: Pygian, Ian Ring Music TheoryPygian
Scale 2781Scale 2781: Gycryllic, Ian Ring Music TheoryGycryllic
Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian

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.