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Scale 4003: "Sadyllic"

Scale 4003: Sadyllic, 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
Sadyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,5,7,8,9,10,11}
Forte Number8-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2239
Hemitonia6 (multihemitonic)
Cohemitonia5 (multicohemitonic)
Imperfections4
Modes7
Prime?no
prime: 383
Deep Scaleno
Interval Vector665542
Interval Spectrump4m5n5s6d6t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,6,7}
<4> = {4,5,7,8}
<5> = {5,6,8,9}
<6> = {6,7,9,10}
<7> = {8,10,11}
Spectra Variation3.25
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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 TriadsC♯{1,5,8}231.57
F{5,9,0}231.57
Minor Triadsfm{5,8,0}341.71
a♯m{10,1,5}241.86
Augmented TriadsC♯+{1,5,9}331.43
Diminished Triadsf°{5,8,11}152.43
g°{7,10,1}152.57
Parsimonious Voice Leading Between Common Triads of Scale 4003. Created by Ian Ring ©2019 C# C# C#+ C#+ C#->C#+ fm fm C#->fm F F C#+->F a#m a#m C#+->a#m f° f° f°->fm fm->F g° g° g°->a#m

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♯, C♯+, F
Peripheral Verticesf°, g°

Modes

Modes are the rotational transformation of this scale. Scale 4003 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 4049		Scale 4049: Stycryllic, Ian Ring Music TheoryStycryllic
3rd mode:
Scale 509		Scale 509: Ionothyllic, Ian Ring Music TheoryIonothyllic
4th mode:
Scale 1151		Scale 1151: Mythyllic, Ian Ring Music TheoryMythyllic
5th mode:
Scale 2623		Scale 2623: Aerylyllic, Ian Ring Music TheoryAerylyllic
6th mode:
Scale 3359		Scale 3359: Bonyllic, Ian Ring Music TheoryBonyllic
7th mode:
Scale 3727		Scale 3727: Tholyllic, Ian Ring Music TheoryTholyllic
8th mode:
Scale 3911		Scale 3911: Katyryllic, Ian Ring Music TheoryKatyryllic

Prime

The prime form of this scale is Scale 383

Scale 383Scale 383: Logyllic, Ian Ring Music TheoryLogyllic

Complement

The octatonic modal family [4003, 4049, 509, 1151, 2623, 3359, 3727, 3911] (Forte: 8-2) is the complement of the tetratonic modal family [23, 1793, 2059, 3077] (Forte: 4-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 4003 is 2239

Scale 2239Scale 2239: Dacryllic, Ian Ring Music TheoryDacryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 4003 is chiral, and its enantiomorph is scale 2239

Scale 2239Scale 2239: Dacryllic, Ian Ring Music TheoryDacryllic

Transformations:

T0 4003  T0I 2239
T1 3911  T1I 383
T2 3727  T2I 766
T3 3359  T3I 1532
T4 2623  T4I 3064
T5 1151  T5I 2033
T6 2302  T6I 4066
T7 509  T7I 4037
T8 1018  T8I 3979
T9 2036  T9I 3863
T10 4072  T10I 3631
T11 4049  T11I 3167

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 4001Scale 4001, Ian Ring Music Theory
Scale 4005Scale 4005, Ian Ring Music Theory
Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
Scale 4011Scale 4011: Styrygic, Ian Ring Music TheoryStyrygic
Scale 4019Scale 4019: Lonygic, Ian Ring Music TheoryLonygic
Scale 3971Scale 3971, Ian Ring Music Theory
Scale 3987Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
Scale 4035Scale 4035, Ian Ring Music Theory
Scale 4067Scale 4067: Aeolarygic, Ian Ring Music TheoryAeolarygic
Scale 3875Scale 3875: Aeryptian, Ian Ring Music TheoryAeryptian
Scale 3939Scale 3939: Dogyllic, Ian Ring Music TheoryDogyllic
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
Scale 1955Scale 1955: Sonian, Ian Ring Music TheorySonian

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.