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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

Cardinality

Cardinality is the count of how many pitches are in the scale.

8 (octatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,1,4,6,8,9,10,11}

Forte Number

A code assigned by theorist Alan Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

8-11

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 2399

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

5 (multihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

4 (multicohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

3

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

7

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 703

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Formula

Defines the scale as the sequence of intervals between one tone and the next.

[1, 3, 2, 2, 1, 1, 1, 1]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<5, 6, 5, 5, 5, 2>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hansen.

p5m5n5s6d5t2

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<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 Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.75

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.616

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

6.002

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

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. 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.