The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2931: "Zathyllic"

Scale 2931: Zathyllic, 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
Zathyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,4,5,6,8,9,11}
Forte Number8-20
Rotational Symmetrynone
Reflection Axes2.5
Palindromicno
Chiralityno
Hemitonia5 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 951
Deep Scaleno
Interval Vector545662
Interval Spectrump6m6n5s4d5t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {4,5}
<4> = {5,6,7}
<5> = {7,8}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation1.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
Myhill Propertyno
Balancedno
Ridge Tones[5]
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}331.83
E{4,8,11}252.5
F{5,9,0}431.67
A{9,1,4}342
Minor Triadsc♯m{1,4,8}342
fm{5,8,0}431.67
f♯m{6,9,1}252.5
am{9,0,4}331.83
Augmented TriadsC+{0,4,8}441.83
C♯+{1,5,9}441.83
Diminished Triads{5,8,11}242.33
f♯°{6,9,0}242.33
Parsimonious Voice Leading Between Common Triads of Scale 2931. Created by Ian Ring ©2019 C+ C+ c#m c#m C+->c#m E E C+->E fm fm C+->fm am am C+->am C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->fm F F C#+->F f#m f#m C#+->f#m C#+->A E->f° f°->fm fm->F f#° f#° F->f#° F->am f#°->f#m am->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♯, fm, F, am
Peripheral VerticesE, f♯m

Modes

Modes are the rotational transformation of this scale. Scale 2931 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3513
Scale 3513: Dydyllic, Ian Ring Music TheoryDydyllic
3rd mode:
Scale 951
Scale 951: Thogyllic, Ian Ring Music TheoryThogyllicThis is the prime mode
4th mode:
Scale 2523
Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
5th mode:
Scale 3309
Scale 3309: Bycryllic, Ian Ring Music TheoryBycryllic
6th mode:
Scale 1851
Scale 1851: Zacryllic, Ian Ring Music TheoryZacryllic
7th mode:
Scale 2973
Scale 2973: Panyllic, Ian Ring Music TheoryPanyllic
8th mode:
Scale 1767
Scale 1767: Dyryllic, Ian Ring Music TheoryDyryllic

Prime

The prime form of this scale is Scale 951

Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic

Complement

The octatonic modal family [2931, 3513, 951, 2523, 3309, 1851, 2973, 1767] (Forte: 8-20) is the complement of the tetratonic modal family [291, 393, 561, 2193] (Forte: 4-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2931 is 2523

Scale 2523Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale

Transformations:

T0 2931  T0I 2523
T1 1767  T1I 951
T2 3534  T2I 1902
T3 2973  T3I 3804
T4 1851  T4I 3513
T5 3702  T5I 2931
T6 3309  T6I 1767
T7 2523  T7I 3534
T8 951  T8I 2973
T9 1902  T9I 1851
T10 3804  T10I 3702
T11 3513  T11I 3309

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 2929Scale 2929: Aeolathian, Ian Ring Music TheoryAeolathian
Scale 2933Scale 2933, Ian Ring Music Theory
Scale 2935Scale 2935: Modygic, Ian Ring Music TheoryModygic
Scale 2939Scale 2939: Goptygic, Ian Ring Music TheoryGoptygic
Scale 2915Scale 2915: Aeolydian, Ian Ring Music TheoryAeolydian
Scale 2923Scale 2923: Baryllic, Ian Ring Music TheoryBaryllic
Scale 2899Scale 2899: Kagian, Ian Ring Music TheoryKagian
Scale 2867Scale 2867: Socrian, Ian Ring Music TheorySocrian
Scale 2995Scale 2995: Raga Saurashtra, Ian Ring Music TheoryRaga Saurashtra
Scale 3059Scale 3059: Madygic, Ian Ring Music TheoryMadygic
Scale 2675Scale 2675: Chromatic Lydian, Ian Ring Music TheoryChromatic Lydian
Scale 2803Scale 2803: Raga Bhatiyar, Ian Ring Music TheoryRaga Bhatiyar
Scale 2419Scale 2419: Raga Lalita, Ian Ring Music TheoryRaga Lalita
Scale 3443Scale 3443: Verdi's Scala Enigmatica, Ian Ring Music TheoryVerdi's Scala Enigmatica
Scale 3955Scale 3955: Pothygic, Ian Ring Music TheoryPothygic
Scale 883Scale 883: Ralian, Ian Ring Music TheoryRalian
Scale 1907Scale 1907: Lynyllic, Ian Ring Music TheoryLynyllic

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.