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Scale 3923: "Stoptyllic"

Scale 3923: Stoptyllic, 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
Stoptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,4,6,8,9,10,11}
Forte Number8-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2399
Hemitonia5 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes7
Prime?no
prime: 703
Deep Scaleno
Interval Vector565552
Interval Spectrump5m5n5s6d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {4,5,6,7,8}
<5> = {5,6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.75
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 TriadsE{4,8,11}152.67
F♯{6,10,1}252.33
A{9,1,4}431.44
Minor Triadsc♯m{1,4,8}231.78
f♯m{6,9,1}341.78
am{9,0,4}331.56
Augmented TriadsC+{0,4,8}341.89
Diminished Triadsf♯°{6,9,0}231.89
a♯°{10,1,4}242
Parsimonious Voice Leading Between Common Triads of Scale 3923. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E am am C+->am A A c#m->A f#° f#° f#m f#m f#°->f#m f#°->am F# F# f#m->F# f#m->A a#° a#° F#->a#° am->A A->a#°

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 Verticesc♯m, f♯°, am, A
Peripheral VerticesE, F♯

Modes

Modes are the rotational transformation of this scale. Scale 3923 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 4009
Scale 4009: Phranyllic, Ian Ring Music TheoryPhranyllic
3rd mode:
Scale 1013
Scale 1013: Stydyllic, Ian Ring Music TheoryStydyllic
4th mode:
Scale 1277
Scale 1277: Zadyllic, Ian Ring Music TheoryZadyllic
5th mode:
Scale 1343
Scale 1343: Zalyllic, Ian Ring Music TheoryZalyllic
6th mode:
Scale 2719
Scale 2719: Zocryllic, Ian Ring Music TheoryZocryllic
7th mode:
Scale 3407
Scale 3407: Katocryllic, Ian Ring Music TheoryKatocryllic
8th mode:
Scale 3751
Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic

Prime

The prime form of this scale is Scale 703

Scale 703Scale 703: Aerocryllic, Ian Ring Music TheoryAerocryllic

Complement

The octatonic modal family [3923, 4009, 1013, 1277, 1343, 2719, 3407, 3751] (Forte: 8-11) is the complement of the tetratonic modal family [43, 1409, 1541, 2069] (Forte: 4-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3923 is 2399

Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3923 is chiral, and its enantiomorph is scale 2399

Scale 2399Scale 2399: Zanyllic, Ian Ring Music TheoryZanyllic

Transformations:

T0 3923  T0I 2399
T1 3751  T1I 703
T2 3407  T2I 1406
T3 2719  T3I 2812
T4 1343  T4I 1529
T5 2686  T5I 3058
T6 1277  T6I 2021
T7 2554  T7I 4042
T8 1013  T8I 3989
T9 2026  T9I 3883
T10 4052  T10I 3671
T11 4009  T11I 3247

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 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian
Scale 3925Scale 3925: Thyryllic, Ian Ring Music TheoryThyryllic
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic
Scale 3931Scale 3931: Aerygic, Ian Ring Music TheoryAerygic
Scale 3907Scale 3907, Ian Ring Music Theory
Scale 3915Scale 3915, Ian Ring Music Theory
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 3859Scale 3859: Aeolarian, Ian Ring Music TheoryAeolarian
Scale 3891Scale 3891: Ryryllic, Ian Ring Music TheoryRyryllic
Scale 3987Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
Scale 4051Scale 4051: Ionilygic, Ian Ring Music TheoryIonilygic
Scale 3667Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
Scale 3411Scale 3411: Enigmatic, Ian Ring Music TheoryEnigmatic
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale

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.