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Scale 3551: "Sagyllian"

Scale 3551: Sagyllian, 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
Sagyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,6,7,8,10,11}
Forte Number10-4
Rotational Symmetrynone
Reflection Axes1
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1919
Deep Scaleno
Interval Vector888984
Interval Spectrump8m9n8s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.2
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[2]
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}452.65
D♯{3,7,10}452.43
E{4,8,11}352.74
F♯{6,10,1}353
G{7,11,2}452.43
G♯{8,0,3}352.74
B{11,3,6}452.52
Minor Triadscm{0,3,7}452.43
c♯m{1,4,8}353
d♯m{3,6,10}352.74
em{4,7,11}452.43
gm{7,10,2}452.65
g♯m{8,11,3}452.52
bm{11,2,6}352.74
Augmented TriadsC+{0,4,8}452.78
D+{2,6,10}452.78
D♯+{3,7,11}652.13
Diminished Triads{0,3,6}252.91
c♯°{1,4,7}253.13
{4,7,10}252.83
{7,10,1}253.13
g♯°{8,11,2}252.91
a♯°{10,1,4}253.13
Parsimonious Voice Leading Between Common Triads of Scale 3551. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E C+->G# c#°->c#m a#° a#° c#m->a#° D+ D+ d#m d#m D+->d#m F# F# D+->F# 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 3551. Created by Ian Ring ©2019 G D#+->G g#m g#m D#+->g#m D#+->B e°->em em->E E->g#m F#->g° F#->a#° g°->gm gm->G g#° g#° G->g#° G->bm g#°->g#m g#m->G# bm->B

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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
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3551 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3823
Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian
3rd mode:
Scale 3959
Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
4th mode:
Scale 4027
Scale 4027: Ragyllian, Ian Ring Music TheoryRagyllian
5th mode:
Scale 4061
Scale 4061: Staptyllian, Ian Ring Music TheoryStaptyllian
6th mode:
Scale 2039
Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
7th mode:
Scale 3067
Scale 3067: Goptyllian, Ian Ring Music TheoryGoptyllian
8th mode:
Scale 3581
Scale 3581: Epocryllian, Ian Ring Music TheoryEpocryllian
9th mode:
Scale 1919
Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllianThis is the prime mode
10th mode:
Scale 3007
Scale 3007: Zyryllian, Ian Ring Music TheoryZyryllian

Prime

The prime form of this scale is Scale 1919

Scale 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian

Complement

The decatonic modal family [3551, 3823, 3959, 4027, 4061, 2039, 3067, 3581, 1919, 3007] (Forte: 10-4) is the complement of the modal family [17, 257] (Forte: 2-4)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3551 is 3959

Scale 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian

Transformations:

T0 3551  T0I 3959
T1 3007  T1I 3823
T2 1919  T2I 3551
T3 3838  T3I 3007
T4 3581  T4I 1919
T5 3067  T5I 3838
T6 2039  T6I 3581
T7 4078  T7I 3067
T8 4061  T8I 2039
T9 4027  T9I 4078
T10 3959  T10I 4061
T11 3823  T11I 4027

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 3549Scale 3549: Messiaen Mode 3 Inverse, Ian Ring Music TheoryMessiaen Mode 3 Inverse
Scale 3547Scale 3547: Sadygic, Ian Ring Music TheorySadygic
Scale 3543Scale 3543: Aeolonygic, Ian Ring Music TheoryAeolonygic
Scale 3535Scale 3535: Mylygic, Ian Ring Music TheoryMylygic
Scale 3567Scale 3567: Epityllian, Ian Ring Music TheoryEpityllian
Scale 3583Scale 3583: Zylatic, Ian Ring Music TheoryZylatic
Scale 3487Scale 3487: Byptygic, Ian Ring Music TheoryByptygic
Scale 3519Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
Scale 3423Scale 3423: Lothygic, Ian Ring Music TheoryLothygic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3807Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian
Scale 4063Scale 4063: Eptatic, Ian Ring Music TheoryEptatic
Scale 2527Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
Scale 3039Scale 3039: Godyllian, Ian Ring Music TheoryGodyllian
Scale 1503Scale 1503: Epiryllian, Ian Ring Music TheoryEpiryllian

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.