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Scale 3327: "Madyllian"

Scale 3327: Madyllian, 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
Madyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,4,5,6,7,10,11}
Forte Number10-1
Rotational Symmetrynone
Reflection Axes2.5
Palindromicno
Chiralityno
Hemitonia9 (multihemitonic)
Cohemitonia8 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1023
Deep Scaleno
Interval Vector988884
Interval Spectrump8m8n8s8d9t4
Distribution Spectra<1> = {1,3}
<2> = {2,4}
<3> = {3,5}
<4> = {4,6}
<5> = {5,7}
<6> = {6,8}
<7> = {7,9}
<8> = {8,10}
<9> = {9,11}
Spectra Variation1.8
Maximally Evenno
Maximal Area Setno
Interior Area2.75
Myhill Propertyyes
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{0,4,7}352.9
D♯{3,7,10}452.4
F♯{6,10,1}352.7
G{7,11,2}352.4
A♯{10,2,5}352.7
B{11,3,6}452.4
Minor Triadscm{0,3,7}352.7
d♯m{3,6,10}352.4
em{4,7,11}352.7
gm{7,10,2}452.4
a♯m{10,1,5}352.9
bm{11,2,6}452.4
Augmented TriadsD+{2,6,10}552.3
D♯+{3,7,11}552.3
Diminished Triads{0,3,6}252.9
c♯°{1,4,7}253.1
{4,7,10}252.9
{7,10,1}252.9
a♯°{10,1,4}253.1
{11,2,5}252.9
Parsimonious Voice Leading Between Common Triads of Scale 3327. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em a#° a#° c#°->a#° D+ D+ d#m d#m D+->d#m F# F# D+->F# gm gm D+->gm A# A# D+->A# bm bm D+->bm D# D# d#m->D# d#m->B D#->D#+ D#->e° D#->gm D#+->em Parsimonious Voice Leading Between Common Triads of Scale 3327. Created by Ian Ring ©2019 G D#+->G D#+->B e°->em F#->g° a#m a#m F#->a#m g°->gm gm->G G->bm a#°->a#m a#m->A# A#->b° b°->bm bm->B

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 3327 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 3711
Scale 3711: Dycryllian, Ian Ring Music TheoryDycryllian
3rd mode:
Scale 3903
Scale 3903: Aeogyllian, Ian Ring Music TheoryAeogyllian
4th mode:
Scale 3999
Scale 3999: Dydyllian, Ian Ring Music TheoryDydyllian
5th mode:
Scale 4047
Scale 4047: Thogyllian, Ian Ring Music TheoryThogyllian
6th mode:
Scale 4071
Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian
7th mode:
Scale 4083
Scale 4083: Bathyllian, Ian Ring Music TheoryBathyllian
8th mode:
Scale 4089
Scale 4089: Katoryllian, Ian Ring Music TheoryKatoryllian
9th mode:
Scale 1023
Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllianThis is the prime mode
10th mode:
Scale 2559
Scale 2559: Zogyllian, Ian Ring Music TheoryZogyllian

Prime

The prime form of this scale is Scale 1023

Scale 1023Scale 1023: Dodyllian, Ian Ring Music TheoryDodyllian

Complement

The decatonic modal family [3327, 3711, 3903, 3999, 4047, 4071, 4083, 4089, 1023, 2559] (Forte: 10-1) is the complement of the modal family [3, 2049] (Forte: 2-1)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3327 is 4071

Scale 4071Scale 4071: Rygyllian, Ian Ring Music TheoryRygyllian

Transformations:

T0 3327  T0I 4071
T1 2559  T1I 4047
T2 1023  T2I 3999
T3 2046  T3I 3903
T4 4092  T4I 3711
T5 4089  T5I 3327
T6 4083  T6I 2559
T7 4071  T7I 1023
T8 4047  T8I 2046
T9 3999  T9I 4092
T10 3903  T10I 4089
T11 3711  T11I 4083

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 3325Scale 3325: Mixolygic, Ian Ring Music TheoryMixolygic
Scale 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic
Scale 3319Scale 3319: Tholygic, Ian Ring Music TheoryTholygic
Scale 3311Scale 3311: Mixodygic, Ian Ring Music TheoryMixodygic
Scale 3295Scale 3295: Phroptygic, Ian Ring Music TheoryPhroptygic
Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
Scale 3199Scale 3199: Thaptygic, Ian Ring Music TheoryThaptygic
Scale 3455Scale 3455: Ryptyllian, Ian Ring Music TheoryRyptyllian
Scale 3583Scale 3583: Zylatic, Ian Ring Music TheoryZylatic
Scale 3839Scale 3839: Mixolatic, Ian Ring Music TheoryMixolatic
Scale 2303Scale 2303: Stanygic, Ian Ring Music TheoryStanygic
Scale 2815Scale 2815: Aeradyllian, Ian Ring Music TheoryAeradyllian
Scale 1279Scale 1279: Sarygic, Ian Ring Music TheorySarygic

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.