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Scale 3491: "Tharian"

Scale 3491: Tharian, 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
Tharian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,5,7,8,10,11}
Forte Number7-Z36
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2231
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections3
Modes6
Prime?no
prime: 367
Deep Scaleno
Interval Vector444342
Interval Spectrump4m3n4s4d4t2
Distribution Spectra<1> = {1,2,4}
<2> = {2,3,5,6}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {6,7,9,10}
<6> = {8,10,11}
Spectra Variation3.143
Maximally Evenno
Maximal Area Setno
Interior Area2.299
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 TriadsC♯{1,5,8}221.2
Minor Triadsfm{5,8,0}231.4
a♯m{10,1,5}231.4
Diminished Triads{5,8,11}142
{7,10,1}142
Parsimonious Voice Leading Between Common Triads of Scale 3491. Created by Ian Ring ©2019 C# C# fm fm C#->fm a#m a#m C#->a#m f°->fm g°->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
Radius2
Self-Centeredno
Central VerticesC♯
Peripheral Verticesf°, g°

Modes

Modes are the rotational transformation of this scale. Scale 3491 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3793
Scale 3793: Aeopian, Ian Ring Music TheoryAeopian
3rd mode:
Scale 493
Scale 493: Rygian, Ian Ring Music TheoryRygian
4th mode:
Scale 1147
Scale 1147: Epynian, Ian Ring Music TheoryEpynian
5th mode:
Scale 2621
Scale 2621: Ionogian, Ian Ring Music TheoryIonogian
6th mode:
Scale 1679
Scale 1679: Kydian, Ian Ring Music TheoryKydian
7th mode:
Scale 2887
Scale 2887: Gaptian, Ian Ring Music TheoryGaptian

Prime

The prime form of this scale is Scale 367

Scale 367Scale 367: Aerodian, Ian Ring Music TheoryAerodian

Complement

The heptatonic modal family [3491, 3793, 493, 1147, 2621, 1679, 2887] (Forte: 7-Z36) is the complement of the pentatonic modal family [151, 737, 1801, 2123, 3109] (Forte: 5-Z36)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3491 is 2231

Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3491 is chiral, and its enantiomorph is scale 2231

Scale 2231Scale 2231: Macrian, Ian Ring Music TheoryMacrian

Transformations:

T0 3491  T0I 2231
T1 2887  T1I 367
T2 1679  T2I 734
T3 3358  T3I 1468
T4 2621  T4I 2936
T5 1147  T5I 1777
T6 2294  T6I 3554
T7 493  T7I 3013
T8 986  T8I 1931
T9 1972  T9I 3862
T10 3944  T10I 3629
T11 3793  T11I 3163

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 3489Scale 3489, Ian Ring Music Theory
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 3499Scale 3499: Hamel, Ian Ring Music TheoryHamel
Scale 3507Scale 3507: Maqam Hijaz, Ian Ring Music TheoryMaqam Hijaz
Scale 3459Scale 3459, Ian Ring Music Theory
Scale 3475Scale 3475: Kylian, Ian Ring Music TheoryKylian
Scale 3523Scale 3523, Ian Ring Music Theory
Scale 3555Scale 3555: Pylyllic, Ian Ring Music TheoryPylyllic
Scale 3363Scale 3363: Rogimic, Ian Ring Music TheoryRogimic
Scale 3427Scale 3427: Zacrian, Ian Ring Music TheoryZacrian
Scale 3235Scale 3235: Pothimic, Ian Ring Music TheoryPothimic
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 4003Scale 4003: Sadyllic, Ian Ring Music TheorySadyllic
Scale 2467Scale 2467: Raga Padi, Ian Ring Music TheoryRaga Padi
Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
Scale 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti

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.