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Scale 3991: "Badygic"

Scale 3991: Badygic, 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
Badygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,4,7,8,9,10,11}
Forte Number9-2
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3391
Hemitonia7 (multihemitonic)
Cohemitonia6 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 767
Deep Scaleno
Interval Vector777663
Interval Spectrump6m6n7s7d7t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7}
<5> = {5,6,7,8}
<6> = {6,7,8,9}
<7> = {7,8,9,10}
<8> = {9,10,11}
Spectra Variation2.444
Maximally Evenno
Maximal Area Setno
Interior Area2.683
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{0,4,7}342.14
E{4,8,11}342.14
G{7,11,2}342.29
A{9,1,4}342.43
Minor Triadsc♯m{1,4,8}342.29
em{4,7,11}442.07
gm{7,10,2}342.43
am{9,0,4}242.43
Augmented TriadsC+{0,4,8}442.07
Diminished Triadsc♯°{1,4,7}242.5
{4,7,10}242.43
{7,10,1}242.57
g♯°{8,11,2}242.5
a♯°{10,1,4}242.57
Parsimonious Voice Leading Between Common Triads of Scale 3991. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° em em C->em c#m c#m C+->c#m E E C+->E am am C+->am c#°->c#m A A c#m->A e°->em gm gm e°->gm em->E Parsimonious Voice Leading Between Common Triads of Scale 3991. Created by Ian Ring ©2019 G em->G g#° g#° E->g#° g°->gm a#° a#° g°->a#° gm->G G->g#° am->A A->a#°

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3991 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 4043
Scale 4043: Phrocrygic, Ian Ring Music TheoryPhrocrygic
3rd mode:
Scale 4069
Scale 4069: Starygic, Ian Ring Music TheoryStarygic
4th mode:
Scale 2041
Scale 2041: Aeolacrygic, Ian Ring Music TheoryAeolacrygic
5th mode:
Scale 767
Scale 767: Raptygic, Ian Ring Music TheoryRaptygicThis is the prime mode
6th mode:
Scale 2431
Scale 2431: Gythygic, Ian Ring Music TheoryGythygic
7th mode:
Scale 3263
Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
8th mode:
Scale 3679
Scale 3679: Rycrygic, Ian Ring Music TheoryRycrygic
9th mode:
Scale 3887
Scale 3887: Phrathygic, Ian Ring Music TheoryPhrathygic

Prime

The prime form of this scale is Scale 767

Scale 767Scale 767: Raptygic, Ian Ring Music TheoryRaptygic

Complement

The nonatonic modal family [3991, 4043, 4069, 2041, 767, 2431, 3263, 3679, 3887] (Forte: 9-2) is the complement of the tritonic modal family [11, 1537, 2053] (Forte: 3-2)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3991 is 3391

Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3991 is chiral, and its enantiomorph is scale 3391

Scale 3391Scale 3391: Aeolynygic, Ian Ring Music TheoryAeolynygic

Transformations:

T0 3991  T0I 3391
T1 3887  T1I 2687
T2 3679  T2I 1279
T3 3263  T3I 2558
T4 2431  T4I 1021
T5 767  T5I 2042
T6 1534  T6I 4084
T7 3068  T7I 4073
T8 2041  T8I 4051
T9 4082  T9I 4007
T10 4069  T10I 3919
T11 4043  T11I 3743

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 3989Scale 3989: Sythyllic, Ian Ring Music TheorySythyllic
Scale 3987Scale 3987: Loryllic, Ian Ring Music TheoryLoryllic
Scale 3995Scale 3995: Ionygic, Ian Ring Music TheoryIonygic
Scale 3999Scale 3999: Dydyllian, Ian Ring Music TheoryDydyllian
Scale 3975Scale 3975, Ian Ring Music Theory
Scale 3983Scale 3983: Thyptygic, Ian Ring Music TheoryThyptygic
Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
Scale 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian
Scale 4055Scale 4055: Dagyllian, Ian Ring Music TheoryDagyllian
Scale 3863Scale 3863: Eparyllic, Ian Ring Music TheoryEparyllic
Scale 3927Scale 3927: Monygic, Ian Ring Music TheoryMonygic
Scale 3735Scale 3735, Ian Ring Music Theory
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 2967Scale 2967: Madyllic, Ian Ring Music TheoryMadyllic
Scale 1943Scale 1943, Ian Ring Music Theory

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.