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Scale 3509: "Stogyllic"

Scale 3509: Stogyllic, 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

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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
Stogyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,4,5,7,8,10,11}
Forte Number8-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1463
Hemitonia4 (multihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes7
Prime?no
prime: 1463
Deep Scaleno
Interval Vector456553
Interval Spectrump5m5n6s5d4t3
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.25
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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}242.23
E{4,8,11}441.92
G{7,11,2}441.92
A♯{10,2,5}342.23
Minor Triadsem{4,7,11}441.85
fm{5,8,0}342.23
gm{7,10,2}342.15
Augmented TriadsC+{0,4,8}342.15
Diminished Triads{2,5,8}242.31
{4,7,10}242.23
{5,8,11}242.31
g♯°{8,11,2}242.15
{11,2,5}242.31
Parsimonious Voice Leading Between Common Triads of Scale 3509. Created by Ian Ring ©2019 C C C+ C+ C->C+ em em C->em E E C+->E fm fm C+->fm d°->fm A# A# d°->A# e°->em gm gm e°->gm em->E Parsimonious Voice Leading Between Common Triads of Scale 3509. Created by Ian Ring ©2019 G em->G E->f° g#° g#° E->g#° f°->fm gm->G gm->A# G->g#° G->b° A#->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3509 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1901
Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
3rd mode:
Scale 1499
Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
4th mode:
Scale 2797
Scale 2797: Stalyllic, Ian Ring Music TheoryStalyllic
5th mode:
Scale 1723
Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
6th mode:
Scale 2909
Scale 2909: Mocryllic, Ian Ring Music TheoryMocryllic
7th mode:
Scale 1751
Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic
8th mode:
Scale 2923
Scale 2923: Baryllic, Ian Ring Music TheoryBaryllic

Prime

The prime form of this scale is Scale 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Complement

The octatonic modal family [3509, 1901, 1499, 2797, 1723, 2909, 1751, 2923] (Forte: 8-27) is the complement of the tetratonic modal family [293, 593, 649, 1097] (Forte: 4-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3509 is 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3509 is chiral, and its enantiomorph is scale 1463

Scale 1463Scale 1463, Ian Ring Music Theory

Transformations:

T0 3509  T0I 1463
T1 2923  T1I 2926
T2 1751  T2I 1757
T3 3502  T3I 3514
T4 2909  T4I 2933
T5 1723  T5I 1771
T6 3446  T6I 3542
T7 2797  T7I 2989
T8 1499  T8I 1883
T9 2998  T9I 3766
T10 1901  T10I 3437
T11 3802  T11I 2779

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 3511Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
Scale 3505Scale 3505: Stygian, Ian Ring Music TheoryStygian
Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
Scale 3513Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
Scale 3517Scale 3517: Epocrygic, Ian Ring Music TheoryEpocrygic
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 3477Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
Scale 3541Scale 3541: Racryllic, Ian Ring Music TheoryRacryllic
Scale 3573Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
Scale 3381Scale 3381: Katanian, Ian Ring Music TheoryKatanian
Scale 3445Scale 3445: Messiaen Mode 6 Inverse, Ian Ring Music TheoryMessiaen Mode 6 Inverse
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 4021Scale 4021: Raga Pahadi, Ian Ring Music TheoryRaga Pahadi
Scale 2485Scale 2485: Harmonic Major, Ian Ring Music TheoryHarmonic Major
Scale 2997Scale 2997: Major Bebop, Ian Ring Music TheoryMajor Bebop
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor

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.