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Scale 3693: "Stadyllic"

Scale 3693: Stadyllic, 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
Stadyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,5,6,9,10,11}
Forte Number8-18
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1743
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 879
Deep Scaleno
Interval Vector546553
Interval Spectrump5m5n6s4d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2
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}441.92
F{5,9,0}342.23
A♯{10,2,5}342.08
B{11,3,6}342.15
Minor Triadsdm{2,5,9}342
d♯m{3,6,10}342.08
bm{11,2,6}342.08
Augmented TriadsD+{2,6,10}441.85
Diminished Triads{0,3,6}242.38
d♯°{3,6,9}242.31
f♯°{6,9,0}242.31
{9,0,3}242.46
{11,2,5}242.46
Parsimonious Voice Leading Between Common Triads of Scale 3693. Created by Ian Ring ©2019 c°->a° B B c°->B dm dm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° d#m d#m D+->d#m D+->A# bm bm D+->bm d#°->d#m d#m->B F->f#° F->a° A#->b° b°->bm 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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3693 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1947
Scale 1947: Byptyllic, Ian Ring Music TheoryByptyllic
3rd mode:
Scale 3021
Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
4th mode:
Scale 1779
Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
5th mode:
Scale 2937
Scale 2937: Phragyllic, Ian Ring Music TheoryPhragyllic
6th mode:
Scale 879
Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllicThis is the prime mode
7th mode:
Scale 2487
Scale 2487: Dothyllic, Ian Ring Music TheoryDothyllic
8th mode:
Scale 3291
Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic

Prime

The prime form of this scale is Scale 879

Scale 879Scale 879: Aeranyllic, Ian Ring Music TheoryAeranyllic

Complement

The octatonic modal family [3693, 1947, 3021, 1779, 2937, 879, 2487, 3291] (Forte: 8-18) is the complement of the tetratonic modal family [147, 609, 777, 2121] (Forte: 4-18)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3693 is 1743

Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3693 is chiral, and its enantiomorph is scale 1743

Scale 1743Scale 1743: Epigyllic, Ian Ring Music TheoryEpigyllic

Transformations:

T0 3693  T0I 1743
T1 3291  T1I 3486
T2 2487  T2I 2877
T3 879  T3I 1659
T4 1758  T4I 3318
T5 3516  T5I 2541
T6 2937  T6I 987
T7 1779  T7I 1974
T8 3558  T8I 3948
T9 3021  T9I 3801
T10 1947  T10I 3507
T11 3894  T11I 2919

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 3695Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
Scale 3689Scale 3689: Katocrian, Ian Ring Music TheoryKatocrian
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 3701Scale 3701: Bagyllic, Ian Ring Music TheoryBagyllic
Scale 3709Scale 3709: Katynygic, Ian Ring Music TheoryKatynygic
Scale 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
Scale 3677Scale 3677, Ian Ring Music Theory
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 3181Scale 3181: Rolian, Ian Ring Music TheoryRolian
Scale 3437Scale 3437, Ian Ring Music Theory
Scale 2669Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode
Scale 1645Scale 1645: Dorian Flat 5, Ian Ring Music TheoryDorian Flat 5

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.