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Scale 1535: "Mixodyllian"

Scale 1535: Mixodyllian, 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
Mixodyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,5,6,7,8,10}
Forte Number10-2
Rotational Symmetrynone
Reflection Axes4
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia7 (multicohemitonic)
Imperfections2
Modes9
Prime?yes
Deep Scaleno
Interval Vector898884
Interval Spectrump8m8n8s9d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {8,9,10}
<9> = {10,11}
Spectra Variation1.6
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[8]
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{0,4,7}452.6
C♯{1,5,8}452.6
D♯{3,7,10}452.6
F♯{6,10,1}352.7
G♯{8,0,3}252.8
A♯{10,2,5}352.7
Minor Triadscm{0,3,7}452.6
c♯m{1,4,8}452.6
d♯m{3,6,10}352.7
fm{5,8,0}252.8
gm{7,10,2}352.7
a♯m{10,1,5}452.6
Augmented TriadsC+{0,4,8}452.6
D+{2,6,10}452.6
Diminished Triads{0,3,6}252.9
c♯°{1,4,7}252.8
{2,5,8}252.9
{4,7,10}252.8
{7,10,1}253
a♯°{10,1,4}252.8
Parsimonious Voice Leading Between Common Triads of Scale 1535. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m fm fm C+->fm C+->G# c#°->c#m C# C# c#m->C# a#° a#° c#m->a#° C#->d° C#->fm a#m a#m C#->a#m A# A# d°->A# D+ D+ D+->d#m F# F# D+->F# gm gm D+->gm D+->A# d#m->D# D#->e° D#->gm F#->g° F#->a#m g°->gm a#°->a#m a#m->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
Radius5
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1535 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 2815
Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
3rd mode:
Scale 3455
Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
4th mode:
Scale 3775
Scale 3775: Loptyllian, Ian Ring Music TheoryLoptyllian
5th mode:
Scale 3935
Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
6th mode:
Scale 4015
Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
7th mode:
Scale 4055
Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
8th mode:
Scale 4075
Scale 4075: Katyllian, Ian Ring Music TheoryKatyllian
9th mode:
Scale 4085
Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian
10th mode:
Scale 2045
Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian

Prime

This is the prime form of this scale.

Complement

The decatonic modal family [1535, 2815, 3455, 3775, 3935, 4015, 4055, 4075, 4085, 2045] (Forte: 10-2) is the complement of the modal family [5, 1025] (Forte: 2-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1535 is 4085

Scale 4085Scale 4085: Sydyllian, Ian Ring Music TheorySydyllian

Transformations:

T0 1535  T0I 4085
T1 3070  T1I 4075
T2 2045  T2I 4055
T3 4090  T3I 4015
T4 4085  T4I 3935
T5 4075  T5I 3775
T6 4055  T6I 3455
T7 4015  T7I 2815
T8 3935  T8I 1535
T9 3775  T9I 3070
T10 3455  T10I 2045
T11 2815  T11I 4090

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 1533Scale 1533: Katycrygic, Ian Ring Music TheoryKatycrygic
Scale 1531Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic
Scale 1527Scale 1527: Aeolyrigic, Ian Ring Music TheoryAeolyrigic
Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed
Scale 1503Scale 1503: Epiryllian, Ian Ring Music TheoryEpiryllian
Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic
Scale 1407Scale 1407: Tharygic, Ian Ring Music TheoryTharygic
Scale 1279Scale 1279: Sarygic, Ian Ring Music TheorySarygic
Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian
Scale 2047Scale 2047: Monatic, Ian Ring Music TheoryMonatic
Scale 511Scale 511: Polygic, Ian Ring Music TheoryPolygic
Scale 1023Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllian
Scale 2559Scale 2559: Zogyllian, Ian Ring Music TheoryZogyllian
Scale 3583Scale 3583: Zylatic, Ian Ring Music TheoryZylatic

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.