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Scale 3493: "Rathian"

Scale 3493: Rathian, 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
Rathian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,2,5,7,8,10,11}
Forte Number7-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1207
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes6
Prime?no
prime: 733
Deep Scaleno
Interval Vector345342
Interval Spectrump4m3n5s4d3t2
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,5}
<3> = {4,5,6,7}
<4> = {5,6,7,8}
<5> = {7,9,10}
<6> = {9,10,11}
Spectra Variation2.286
Maximally Evenno
Maximal Area Setno
Interior Area2.549
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 TriadsG{7,11,2}331.63
A♯{10,2,5}331.63
Minor Triadsfm{5,8,0}231.88
gm{7,10,2}231.75
Diminished Triads{2,5,8}231.75
{5,8,11}231.88
g♯°{8,11,2}231.75
{11,2,5}231.75
Parsimonious Voice Leading Between Common Triads of Scale 3493. Created by Ian Ring ©2019 fm fm d°->fm A# A# d°->A# f°->fm g#° g#° f°->g#° gm gm Parsimonious Voice Leading Between Common Triads of Scale 3493. Created by Ian Ring ©2019 G gm->G gm->A# G->g#° G->b° 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.

Diameter3
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3493 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1897
Scale 1897: Ionopian, Ian Ring Music TheoryIonopian
3rd mode:
Scale 749
Scale 749: Aeologian, Ian Ring Music TheoryAeologian
4th mode:
Scale 1211
Scale 1211: Zadian, Ian Ring Music TheoryZadian
5th mode:
Scale 2653
Scale 2653: Sygian, Ian Ring Music TheorySygian
6th mode:
Scale 1687
Scale 1687: Phralian, Ian Ring Music TheoryPhralian
7th mode:
Scale 2891
Scale 2891: Phrogian, Ian Ring Music TheoryPhrogian

Prime

The prime form of this scale is Scale 733

Scale 733Scale 733: Donian, Ian Ring Music TheoryDonian

Complement

The heptatonic modal family [3493, 1897, 749, 1211, 2653, 1687, 2891] (Forte: 7-25) is the complement of the pentatonic modal family [301, 721, 1099, 1673, 2597] (Forte: 5-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3493 is 1207

Scale 1207Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3493 is chiral, and its enantiomorph is scale 1207

Scale 1207Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian

Transformations:

T0 3493  T0I 1207
T1 2891  T1I 2414
T2 1687  T2I 733
T3 3374  T3I 1466
T4 2653  T4I 2932
T5 1211  T5I 1769
T6 2422  T6I 3538
T7 749  T7I 2981
T8 1498  T8I 1867
T9 2996  T9I 3734
T10 1897  T10I 3373
T11 3794  T11I 2651

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 3495Scale 3495: Banyllic, Ian Ring Music TheoryBanyllic
Scale 3489Scale 3489, Ian Ring Music Theory
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 3497Scale 3497: Phrolian, Ian Ring Music TheoryPhrolian
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 3509Scale 3509: Stogyllic, Ian Ring Music TheoryStogyllic
Scale 3461Scale 3461, Ian Ring Music Theory
Scale 3477Scale 3477: Kyptian, Ian Ring Music TheoryKyptian
Scale 3525Scale 3525: Zocrian, Ian Ring Music TheoryZocrian
Scale 3557Scale 3557, Ian Ring Music Theory
Scale 3365Scale 3365: Katolimic, Ian Ring Music TheoryKatolimic
Scale 3429Scale 3429: Marian, Ian Ring Music TheoryMarian
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 4005Scale 4005, Ian Ring Music Theory
Scale 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
Scale 2981Scale 2981: Ionolian, Ian Ring Music TheoryIonolian
Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari

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.