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Scale 3941: "Stathyllic"

Scale 3941: Stathyllic, 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
Stathyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,5,6,8,9,10,11}
Forte Number8-12
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1247
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes7
Prime?no
prime: 763
Deep Scaleno
Interval Vector556543
Interval Spectrump4m5n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,6}
<4> = {4,5,7,8}
<5> = {6,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
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 TriadsD{2,6,9}342
F{5,9,0}342
A♯{10,2,5}342
Minor Triadsdm{2,5,9}441.83
fm{5,8,0}342.17
bm{11,2,6}342.17
Augmented TriadsD+{2,6,10}342
Diminished Triads{2,5,8}242.17
{5,8,11}242.33
f♯°{6,9,0}242.33
g♯°{8,11,2}242.33
{11,2,5}242.33
Parsimonious Voice Leading Between Common Triads of Scale 3941. Created by Ian Ring ©2019 dm dm d°->dm fm fm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ f#° f#° D->f#° D+->A# bm bm D+->bm f°->fm g#° g#° f°->g#° fm->F F->f#° g#°->bm A#->b° b°->bm

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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 3941 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 2009
Scale 2009: Stacryllic, Ian Ring Music TheoryStacryllic
3rd mode:
Scale 763
Scale 763: Doryllic, Ian Ring Music TheoryDoryllicThis is the prime mode
4th mode:
Scale 2429
Scale 2429: Kadyllic, Ian Ring Music TheoryKadyllic
5th mode:
Scale 1631
Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
6th mode:
Scale 2863
Scale 2863: Aerogyllic, Ian Ring Music TheoryAerogyllic
7th mode:
Scale 3479
Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
8th mode:
Scale 3787
Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic

Prime

The prime form of this scale is Scale 763

Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic

Complement

The octatonic modal family [3941, 2009, 763, 2429, 1631, 2863, 3479, 3787] (Forte: 8-12) is the complement of the tetratonic modal family [77, 833, 1043, 2569] (Forte: 4-12)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3941 is 1247

Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3941 is chiral, and its enantiomorph is scale 1247

Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic

Transformations:

T0 3941  T0I 1247
T1 3787  T1I 2494
T2 3479  T2I 893
T3 2863  T3I 1786
T4 1631  T4I 3572
T5 3262  T5I 3049
T6 2429  T6I 2003
T7 763  T7I 4006
T8 1526  T8I 3917
T9 3052  T9I 3739
T10 2009  T10I 3383
T11 4018  T11I 2671

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 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 3937Scale 3937, Ian Ring Music Theory
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic
Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 4005Scale 4005, Ian Ring Music Theory
Scale 4069Scale 4069: Starygic, Ian Ring Music TheoryStarygic
Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 2917Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
Scale 1893Scale 1893: Ionylian, Ian Ring Music TheoryIonylian

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. Special thanks to Richard Repp for helping with technical accuracy.