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Scale 3259

Scale 3259, 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).

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,1,3,4,5,7,10,11}
Forte Number8-Z29
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2983
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 751
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {7,8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
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{0,4,7}341.9
D♯{3,7,10}341.9
Minor Triadscm{0,3,7}242.1
em{4,7,11}341.9
a♯m{10,1,5}242.3
Augmented TriadsD♯+{3,7,11}341.9
Diminished Triadsc♯°{1,4,7}242.1
{4,7,10}242.1
{7,10,1}242.1
a♯°{10,1,4}242.3
Parsimonious Voice Leading Between Common Triads of Scale 3259. Created by Ian Ring ©2019 cm cm C C cm->C D#+ D#+ cm->D#+ c#° c#° C->c#° em em C->em a#° a#° c#°->a#° D# D# D#->D#+ D#->e° D#->g° D#+->em e°->em a#m a#m g°->a#m a#°->a#m

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3259 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 3677
Scale 3677, Ian Ring Music Theory
3rd mode:
Scale 1943
Scale 1943, Ian Ring Music Theory
4th mode:
Scale 3019
Scale 3019, Ian Ring Music Theory
5th mode:
Scale 3557
Scale 3557, Ian Ring Music Theory
6th mode:
Scale 1913
Scale 1913, Ian Ring Music Theory
7th mode:
Scale 751
Scale 751, Ian Ring Music TheoryThis is the prime mode
8th mode:
Scale 2423
Scale 2423, Ian Ring Music Theory

Prime

The prime form of this scale is Scale 751

Scale 751Scale 751, Ian Ring Music Theory

Complement

The octatonic modal family [3259, 3677, 1943, 3019, 3557, 1913, 751, 2423] (Forte: 8-Z29) is the complement of the tetratonic modal family [139, 353, 1553, 2117] (Forte: 4-Z29)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3259 is 2983

Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3259 is chiral, and its enantiomorph is scale 2983

Scale 2983Scale 2983: Zythyllic, Ian Ring Music TheoryZythyllic

Transformations:

T0 3259  T0I 2983
T1 2423  T1I 1871
T2 751  T2I 3742
T3 1502  T3I 3389
T4 3004  T4I 2683
T5 1913  T5I 1271
T6 3826  T6I 2542
T7 3557  T7I 989
T8 3019  T8I 1978
T9 1943  T9I 3956
T10 3886  T10I 3817
T11 3677  T11I 3539

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 3257Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata
Scale 3261Scale 3261: Dodyllic, Ian Ring Music TheoryDodyllic
Scale 3263Scale 3263: Pyrygic, Ian Ring Music TheoryPyrygic
Scale 3251Scale 3251: Mela Hatakambari, Ian Ring Music TheoryMela Hatakambari
Scale 3255Scale 3255: Daryllic, Ian Ring Music TheoryDaryllic
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati
Scale 3227Scale 3227: Aeolocrian, Ian Ring Music TheoryAeolocrian
Scale 3291Scale 3291: Lygyllic, Ian Ring Music TheoryLygyllic
Scale 3323Scale 3323: Lacrygic, Ian Ring Music TheoryLacrygic
Scale 3131Scale 3131, Ian Ring Music Theory
Scale 3195Scale 3195: Raryllic, Ian Ring Music TheoryRaryllic
Scale 3387Scale 3387: Aeryptyllic, Ian Ring Music TheoryAeryptyllic
Scale 3515Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
Scale 3771Scale 3771: Katodyllian, Ian Ring Music TheoryKatodyllian
Scale 2235Scale 2235: Bathian, Ian Ring Music TheoryBathian
Scale 2747Scale 2747: Stythyllic, Ian Ring Music TheoryStythyllic
Scale 1211Scale 1211: Zadian, Ian Ring Music TheoryZadian

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.