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Scale 3951: "Mathyllian"

Scale 3951: Mathyllian, 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
Mathyllian

Analysis

Cardinality10 (decatonic)
Pitch Class Set{0,1,2,3,5,6,8,9,10,11}
Forte Number10-3
Rotational Symmetrynone
Reflection Axes5.5
Palindromicno
Chiralityno
Hemitonia8 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections2
Modes9
Prime?no
prime: 1791
Deep Scaleno
Interval Vector889884
Interval Spectrump8m8n9s8d8t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {5,6,7}
<6> = {6,7,8}
<7> = {7,8,9}
<8> = {9,10}
<9> = {10,11}
Spectra Variation1.4
Maximally Evenno
Maximal Area Setyes
Interior Area2.866
Myhill Propertyno
Balancedno
Ridge Tones[11]
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}352.75
D{2,6,9}452.58
F{5,9,0}452.67
F♯{6,10,1}352.75
G♯{8,0,3}452.83
A♯{10,2,5}452.67
B{11,3,6}452.75
Minor Triadsdm{2,5,9}452.58
d♯m{3,6,10}352.75
fm{5,8,0}452.75
f♯m{6,9,1}452.67
g♯m{8,11,3}452.83
a♯m{10,1,5}352.75
bm{11,2,6}452.67
Augmented TriadsC♯+{1,5,9}552.5
D+{2,6,10}552.5
Diminished Triads{0,3,6}253
{2,5,8}253
d♯°{3,6,9}253
{5,8,11}253
f♯°{6,9,0}253
g♯°{8,11,2}253
{9,0,3}253
{11,2,5}253
Parsimonious Voice Leading Between Common Triads of Scale 3951. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B C# C# C#+ C#+ C#->C#+ C#->d° fm fm C#->fm dm dm C#+->dm F F C#+->F f#m f#m C#+->f#m a#m a#m C#+->a#m d°->dm D D dm->D A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° D->f#m d#m d#m D+->d#m F# F# D+->F# D+->A# bm bm D+->bm d#°->d#m d#m->B f°->fm g#m g#m f°->g#m fm->F fm->G# f#° f#° F->f#° F->a° f#°->f#m f#m->F# F#->a#m g#° g#° g#°->g#m g#°->bm g#m->G# g#m->B G#->a° a#m->A# A#->b° b°->bm bm->B

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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 3951 can be rotated to make 9 other scales. The 1st mode is itself.

2nd mode:
Scale 4023
Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
3rd mode:
Scale 4059
Scale 4059: Zolyllian, Ian Ring Music TheoryZolyllian
4th mode:
Scale 4077
Scale 4077: Gothyllian, Ian Ring Music TheoryGothyllian
5th mode:
Scale 2043
Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn
6th mode:
Scale 3069
Scale 3069: Maqam Shawq Afza, Ian Ring Music TheoryMaqam Shawq Afza
7th mode:
Scale 1791
Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllianThis is the prime mode
8th mode:
Scale 2943
Scale 2943: Dathyllian, Ian Ring Music TheoryDathyllian
9th mode:
Scale 3519
Scale 3519: Raga Sindhi-Bhairavi, Ian Ring Music TheoryRaga Sindhi-Bhairavi
10th mode:
Scale 3807
Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian

Prime

The prime form of this scale is Scale 1791

Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian

Complement

The decatonic modal family [3951, 4023, 4059, 4077, 2043, 3069, 1791, 2943, 3519, 3807] (Forte: 10-3) is the complement of the modal family [9, 513] (Forte: 2-3)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3951 is 3807

Scale 3807Scale 3807: Bagyllian, Ian Ring Music TheoryBagyllian

Transformations:

T0 3951  T0I 3807
T1 3807  T1I 3519
T2 3519  T2I 2943
T3 2943  T3I 1791
T4 1791  T4I 3582
T5 3582  T5I 3069
T6 3069  T6I 2043
T7 2043  T7I 4086
T8 4086  T8I 4077
T9 4077  T9I 4059
T10 4059  T10I 4023
T11 4023  T11I 3951

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 3949Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
Scale 3947Scale 3947: Ryptygic, Ian Ring Music TheoryRyptygic
Scale 3943Scale 3943: Zynygic, Ian Ring Music TheoryZynygic
Scale 3959Scale 3959: Katagyllian, Ian Ring Music TheoryKatagyllian
Scale 3967Scale 3967: Soratic, Ian Ring Music TheorySoratic
Scale 3919Scale 3919: Lynygic, Ian Ring Music TheoryLynygic
Scale 3935Scale 3935: Kataphyllian, Ian Ring Music TheoryKataphyllian
Scale 3887Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic
Scale 4015Scale 4015: Phradyllian, Ian Ring Music TheoryPhradyllian
Scale 4079Scale 4079: Ionatic, Ian Ring Music TheoryIonatic
Scale 3695Scale 3695: Kodygic, Ian Ring Music TheoryKodygic
Scale 3823Scale 3823: Epinyllian, Ian Ring Music TheoryEpinyllian
Scale 3439Scale 3439: Lythygic, Ian Ring Music TheoryLythygic
Scale 2927Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
Scale 1903Scale 1903: Rocrygic, Ian Ring Music TheoryRocrygic

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.