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Scale 3495: "Banyllic"

Scale 3495: Banyllic, 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
Banyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,2,5,7,8,10,11}
Forte Number8-13
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3255
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 735
Deep Scaleno
Interval Vector556453
Interval Spectrump5m4n6s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.5
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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♯{1,5,8}342
G{7,11,2}342
A♯{10,2,5}441.82
Minor Triadsfm{5,8,0}242.27
gm{7,10,2}341.91
a♯m{10,1,5}341.91
Diminished Triads{2,5,8}242.09
{5,8,11}242.36
{7,10,1}242.18
g♯°{8,11,2}242.27
{11,2,5}242.09
Parsimonious Voice Leading Between Common Triads of Scale 3495. Created by Ian Ring ©2019 C# C# C#->d° fm fm C#->fm a#m a#m C#->a#m A# A# d°->A# f°->fm g#° g#° f°->g#° gm gm g°->gm g°->a#m Parsimonious Voice Leading Between Common Triads of Scale 3495. Created by Ian Ring ©2019 G gm->G gm->A# G->g#° G->b° a#m->A# A#->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3495 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3795
Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic
3rd mode:
Scale 3945
Scale 3945: Lydyllic, Ian Ring Music TheoryLydyllic
4th mode:
Scale 1005
Scale 1005: Radyllic, Ian Ring Music TheoryRadyllic
5th mode:
Scale 1275
Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic
6th mode:
Scale 2685
Scale 2685: Ionoryllic, Ian Ring Music TheoryIonoryllic
7th mode:
Scale 1695
Scale 1695: Phrodyllic, Ian Ring Music TheoryPhrodyllic
8th mode:
Scale 2895
Scale 2895: Aeoryllic, Ian Ring Music TheoryAeoryllic

Prime

The prime form of this scale is Scale 735

Scale 735Scale 735: Sylyllic, Ian Ring Music TheorySylyllic

Complement

The octatonic modal family [3495, 3795, 3945, 1005, 1275, 2685, 1695, 2895] (Forte: 8-13) is the complement of the tetratonic modal family [75, 705, 1545, 2085] (Forte: 4-13)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3495 is 3255

Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3495 is chiral, and its enantiomorph is scale 3255

Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic

Transformations:

T0 3495  T0I 3255
T1 2895  T1I 2415
T2 1695  T2I 735
T3 3390  T3I 1470
T4 2685  T4I 2940
T5 1275  T5I 1785
T6 2550  T6I 3570
T7 1005  T7I 3045
T8 2010  T8I 1995
T9 4020  T9I 3990
T10 3945  T10I 3885
T11 3795  T11I 3675

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 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 3503Scale 3503: Zyphygic, Ian Ring Music TheoryZyphygic
Scale 3511Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
Scale 3463Scale 3463, Ian Ring Music Theory
Scale 3479Scale 3479: Rothyllic, Ian Ring Music TheoryRothyllic
Scale 3527Scale 3527: Ronyllic, Ian Ring Music TheoryRonyllic
Scale 3559Scale 3559: Thophygic, Ian Ring Music TheoryThophygic
Scale 3367Scale 3367: Moptian, Ian Ring Music TheoryMoptian
Scale 3431Scale 3431: Zyptyllic, Ian Ring Music TheoryZyptyllic
Scale 3239Scale 3239: Mela Tanarupi, Ian Ring Music TheoryMela Tanarupi
Scale 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 4007Scale 4007: Doptygic, Ian Ring Music TheoryDoptygic
Scale 2471Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti
Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic
Scale 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi

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.