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Scale 3913: "Bonian"

Scale 3913: Bonian, 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
Bonian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,3,6,8,9,10,11}
Forte Number7-10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 607
Hemitonia4 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections4
Modes6
Prime?no
prime: 607
Deep Scaleno
Interval Vector445332
Interval Spectrump3m3n5s4d4t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5,6}
<3> = {3,4,5,6,7,8}
<4> = {4,5,6,7,8,9}
<5> = {6,7,8,9,10}
<6> = {9,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.433
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 TriadsG♯{8,0,3}331.63
B{11,3,6}331.63
Minor Triadsd♯m{3,6,10}231.75
g♯m{8,11,3}231.75
Diminished Triads{0,3,6}231.75
d♯°{3,6,9}231.88
f♯°{6,9,0}231.88
{9,0,3}231.75
Parsimonious Voice Leading Between Common Triads of Scale 3913. Created by Ian Ring ©2019 G# G# c°->G# B B c°->B d#° d#° d#m d#m d#°->d#m f#° f#° d#°->f#° d#m->B f#°->a° g#m g#m g#m->G# g#m->B G#->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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3913 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1001
Scale 1001: Badian, Ian Ring Music TheoryBadian
3rd mode:
Scale 637
Scale 637: Debussy's Heptatonic, Ian Ring Music TheoryDebussy's Heptatonic
4th mode:
Scale 1183
Scale 1183: Sadian, Ian Ring Music TheorySadian
5th mode:
Scale 2639
Scale 2639: Dothian, Ian Ring Music TheoryDothian
6th mode:
Scale 3367
Scale 3367: Moptian, Ian Ring Music TheoryMoptian
7th mode:
Scale 3731
Scale 3731: Aeryrian, Ian Ring Music TheoryAeryrian

Prime

The prime form of this scale is Scale 607

Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian

Complement

The heptatonic modal family [3913, 1001, 637, 1183, 2639, 3367, 3731] (Forte: 7-10) is the complement of the pentatonic modal family [91, 1547, 1729, 2093, 2821] (Forte: 5-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3913 is 607

Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3913 is chiral, and its enantiomorph is scale 607

Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian

Transformations:

T0 3913  T0I 607
T1 3731  T1I 1214
T2 3367  T2I 2428
T3 2639  T3I 761
T4 1183  T4I 1522
T5 2366  T5I 3044
T6 637  T6I 1993
T7 1274  T7I 3986
T8 2548  T8I 3877
T9 1001  T9I 3659
T10 2002  T10I 3223
T11 4004  T11I 2351

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 3915Scale 3915, Ian Ring Music Theory
Scale 3917Scale 3917: Katoptyllic, Ian Ring Music TheoryKatoptyllic
Scale 3905Scale 3905, Ian Ring Music Theory
Scale 3909Scale 3909: Rydian, Ian Ring Music TheoryRydian
Scale 3921Scale 3921: Pythian, Ian Ring Music TheoryPythian
Scale 3929Scale 3929: Aeolothyllic, Ian Ring Music TheoryAeolothyllic
Scale 3945Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
Scale 3849Scale 3849, Ian Ring Music Theory
Scale 3881Scale 3881: Morian, Ian Ring Music TheoryMorian
Scale 3977Scale 3977: Kythian, Ian Ring Music TheoryKythian
Scale 4041Scale 4041: Zaryllic, Ian Ring Music TheoryZaryllic
Scale 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian
Scale 3401Scale 3401: Palimic, Ian Ring Music TheoryPalimic
Scale 2889Scale 2889: Thoptimic, Ian Ring Music TheoryThoptimic
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic

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.