The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 3659: "Polian"

Scale 3659: Polian, 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
Polian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,6,9,10,11}
Forte Number7-10
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2639
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
Heliotonicyes

Harmonic Chords

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 TriadsF♯{6,10,1}231.75
B{11,3,6}231.75
Minor Triadsd♯m{3,6,10}331.63
f♯m{6,9,1}331.63
Diminished Triads{0,3,6}231.88
d♯°{3,6,9}231.75
f♯°{6,9,0}231.75
{9,0,3}231.88
Parsimonious Voice Leading Between Common Triads of Scale 3659. Created by Ian Ring ©2019 c°->a° B B c°->B d#° d#° d#m d#m d#°->d#m f#m f#m d#°->f#m F# F# d#m->F# d#m->B f#° f#° f#°->f#m f#°->a° f#m->F#

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 3659 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3877
Scale 3877: Thanian, Ian Ring Music TheoryThanian
3rd mode:
Scale 1993
Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
4th mode:
Scale 761
Scale 761: Ponian, Ian Ring Music TheoryPonian
5th mode:
Scale 607
Scale 607: Kadian, Ian Ring Music TheoryKadianThis is the prime mode
6th mode:
Scale 2351
Scale 2351: Gynian, Ian Ring Music TheoryGynian
7th mode:
Scale 3223
Scale 3223: Thyphian, Ian Ring Music TheoryThyphian

Prime

The prime form of this scale is Scale 607

Scale 607Scale 607: Kadian, Ian Ring Music TheoryKadian

Complement

The heptatonic modal family [3659, 3877, 1993, 761, 607, 2351, 3223] (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 3659 is 2639

Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3659 is chiral, and its enantiomorph is scale 2639

Scale 2639Scale 2639: Dothian, Ian Ring Music TheoryDothian

Transformations:

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

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 3657Scale 3657: Epynimic, Ian Ring Music TheoryEpynimic
Scale 3661Scale 3661: Mixodorian, Ian Ring Music TheoryMixodorian
Scale 3663Scale 3663: Sonyllic, Ian Ring Music TheorySonyllic
Scale 3651Scale 3651, Ian Ring Music Theory
Scale 3655Scale 3655: Mathian, Ian Ring Music TheoryMathian
Scale 3667Scale 3667: Kaptian, Ian Ring Music TheoryKaptian
Scale 3675Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic
Scale 3691Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
Scale 3595Scale 3595, Ian Ring Music Theory
Scale 3627Scale 3627: Kalian, Ian Ring Music TheoryKalian
Scale 3723Scale 3723: Myptian, Ian Ring Music TheoryMyptian
Scale 3787Scale 3787: Kagyllic, Ian Ring Music TheoryKagyllic
Scale 3915Scale 3915, Ian Ring Music Theory
Scale 3147Scale 3147: Ryrimic, Ian Ring Music TheoryRyrimic
Scale 3403Scale 3403: Bylian, Ian Ring Music TheoryBylian
Scale 2635Scale 2635: Gocrimic, Ian Ring Music TheoryGocrimic
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic

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.