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Scale 3749: "Raga Sorati"

Scale 3749: Raga Sorati, 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

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

Carnatic
Raga Sorati
Unknown / Unsorted
Sur Malhar
Zeitler
Zothian
Dozenal
Xuxian

Analysis

Cardinality

Cardinality is the count of how many pitches are in the scale.

7 (heptatonic)

Pitch Class Set

The tones in this scale, expressed as numbers from 0 to 11

{0,2,5,7,9,10,11}

Forte Number

A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

7-23

Rotational Symmetry

Some scales have rotational symmetry, sometimes known as "limited transposition". If there are any rotational symmetries, these are the intervals of periodicity.

none

Reflection Axes

If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. It also implies that the scale has Ridge Tones. Notably an axis of reflection can occur directly on a tone or half way between two tones.

none

Palindromicity

A palindromic scale has the same pattern of intervals both ascending and descending.

no

Chirality

A chiral scale can not be transformed into its inverse by rotation. If a scale is chiral, then it has an enantiomorph.

yes
enantiomorph: 1199

Hemitonia

A hemitone is two tones separated by a semitone interval. Hemitonia describes how many such hemitones exist.

3 (trihemitonic)

Cohemitonia

A cohemitone is an instance of two adjacent hemitones. Cohemitonia describes how many such cohemitones exist.

2 (dicohemitonic)

Imperfections

An imperfection is a tone which does not have a perfect fifth above it in the scale. This value is the quantity of imperfections in this scale.

2

Modes

Modes are the rotational transformations of this scale. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes.

6

Prime Form

Describes if this scale is in prime form, using the Rahn/Ring formula.

no
prime: 701

Generator

Indicates if the scale can be constructed using a generator, and an origin.

none

Deep Scale

A deep scale is one where the interval vector has 6 different digits.

no

Interval Structure

Defines the scale as the sequence of intervals between one tone and the next.

[2, 3, 2, 2, 1, 1, 1]

Interval Vector

Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones.

<3, 5, 4, 3, 5, 1>

Interval Spectrum

The same as the Interval Vector, but expressed in a syntax used by Howard Hanson.

p5m3n4s5d3t

Distribution Spectra

Describes the specific interval sizes that exist for each generic interval size. Each generic <g> has a spectrum {n,...}. The Spectrum Width is the difference between the highest and lowest values in each spectrum.

<1> = {1,2,3}
<2> = {2,3,4,5}
<3> = {3,4,5,6,7}
<4> = {5,6,7,8,9}
<5> = {7,8,9,10}
<6> = {9,10,11}

Spectra Variation

Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality.

2.571

Maximally Even

A scale is maximally even if the tones are optimally spaced apart from each other.

no

Maximal Area Set

A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. All maximally even sets have maximal area, but not all maximal area sets are maximally even.

no

Interior Area

Area of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle, ie a circle with radius of 1.

2.549

Polygon Perimeter

Perimeter of the polygon described by vertices placed for each tone of the scale dodecimetrically around a unit circle.

5.967

Myhill Property

A scale has Myhill Property if the Interval Spectra has exactly two specific intervals for every generic interval.

no

Balanced

A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point.

no

Ridge Tones

Ridge Tones are those that appear in all transpositions of a scale upon the members of that scale. Ridge Tones correspond directly with axes of reflective symmetry.

none

Propriety

Also known as Rothenberg Propriety, named after its inventor. Propriety describes whether every specific interval is uniquely mapped to a generic interval. A scale is either "Proper", "Strictly Proper", or "Improper".

Improper

Heteromorphic Profile

Defined by Norman Carey (2002), the heteromorphic profile is an ordered triple of (c, a, d) where c is the number of contradictions, a is the number of ambiguities, and d is the number of differences. When c is zero, the scale is Proper. When a is also zero, the scale is Strictly Proper.

(26, 43, 104)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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{5,9,0}142.17
G{7,11,2}241.83
A♯{10,2,5}321.17
Minor Triadsdm{2,5,9}231.5
gm{7,10,2}231.5
Diminished Triads{11,2,5}231.5
Parsimonious Voice Leading Between Common Triads of Scale 3749. Created by Ian Ring ©2019 dm dm F F dm->F A# A# dm->A# gm gm Parsimonious Voice Leading Between Common Triads of Scale 3749. Created by Ian Ring ©2019 G gm->G gm->A# G->b° A#->b°

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 VerticesA♯
Peripheral VerticesF, G

Modes

Modes are the rotational transformation of this scale. Scale 3749 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 1961
Scale 1961: Soptian, Ian Ring Music TheorySoptian
3rd mode:
Scale 757
Scale 757: Ionyptian, Ian Ring Music TheoryIonyptian
4th mode:
Scale 1213
Scale 1213: Gyrian, Ian Ring Music TheoryGyrian
5th mode:
Scale 1327
Scale 1327: Zalian, Ian Ring Music TheoryZalian
6th mode:
Scale 2711
Scale 2711: Stolian, Ian Ring Music TheoryStolian
7th mode:
Scale 3403
Scale 3403: Bylian, Ian Ring Music TheoryBylian

Prime

The prime form of this scale is Scale 701

Scale 701Scale 701: Mixonyphian, Ian Ring Music TheoryMixonyphian

Complement

The heptatonic modal family [3749, 1961, 757, 1213, 1327, 2711, 3403] (Forte: 7-23) is the complement of the pentatonic modal family [173, 1067, 1441, 1669, 2581] (Forte: 5-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3749 is 1199

Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3749 is chiral, and its enantiomorph is scale 1199

Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian

Transformations:

In the abbreviation, the subscript number after "T" is the number of semitones of tranposition, "M" means the pitch class is multiplied by 5, and "I" means the result is inverted. Operation is an identical way to express the same thing; the syntax is <a,b> where each tone of the set x is transformed by the equation y = ax + b

Abbrev Operation Result Abbrev Operation Result
T0 <1,0> 3749       T0I <11,0> 1199
T1 <1,1> 3403      T1I <11,1> 2398
T2 <1,2> 2711      T2I <11,2> 701
T3 <1,3> 1327      T3I <11,3> 1402
T4 <1,4> 2654      T4I <11,4> 2804
T5 <1,5> 1213      T5I <11,5> 1513
T6 <1,6> 2426      T6I <11,6> 3026
T7 <1,7> 757      T7I <11,7> 1957
T8 <1,8> 1514      T8I <11,8> 3914
T9 <1,9> 3028      T9I <11,9> 3733
T10 <1,10> 1961      T10I <11,10> 3371
T11 <1,11> 3922      T11I <11,11> 2647
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3719      T0MI <7,0> 3119
T1M <5,1> 3343      T1MI <7,1> 2143
T2M <5,2> 2591      T2MI <7,2> 191
T3M <5,3> 1087      T3MI <7,3> 382
T4M <5,4> 2174      T4MI <7,4> 764
T5M <5,5> 253      T5MI <7,5> 1528
T6M <5,6> 506      T6MI <7,6> 3056
T7M <5,7> 1012      T7MI <7,7> 2017
T8M <5,8> 2024      T8MI <7,8> 4034
T9M <5,9> 4048      T9MI <7,9> 3973
T10M <5,10> 4001      T10MI <7,10> 3851
T11M <5,11> 3907      T11MI <7,11> 3607

The transformations that map this set to itself are: T0

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 3751Scale 3751: Aerathyllic, Ian Ring Music TheoryAerathyllic
Scale 3745Scale 3745: Xuvian, Ian Ring Music TheoryXuvian
Scale 3747Scale 3747: Myrian, Ian Ring Music TheoryMyrian
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3757Scale 3757: Raga Mian Ki Malhar, Ian Ring Music TheoryRaga Mian Ki Malhar
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 3717Scale 3717: Xidian, Ian Ring Music TheoryXidian
Scale 3733Scale 3733: Gycrian, Ian Ring Music TheoryGycrian
Scale 3781Scale 3781: Gyphian, Ian Ring Music TheoryGyphian
Scale 3813Scale 3813: Aeologyllic, Ian Ring Music TheoryAeologyllic
Scale 3621Scale 3621: Gylimic, Ian Ring Music TheoryGylimic
Scale 3685Scale 3685: Kodian, Ian Ring Music TheoryKodian
Scale 3877Scale 3877: Thanian, Ian Ring Music TheoryThanian
Scale 4005Scale 4005: Zibian, Ian Ring Music TheoryZibian
Scale 3237Scale 3237: Raga Brindabani Sarang, Ian Ring Music TheoryRaga Brindabani Sarang
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian
Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
Scale 1701Scale 1701: Dominant Seventh, Ian Ring Music TheoryDominant Seventh

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. All other diagrams and visualizations are © Ian Ring. 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. Special thanks to Richard Repp for helping with technical accuracy, and George Howlett for assistance with the Carnatic ragas.