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Scale 1745: "Raga Vutari"

Scale 1745: Raga Vutari, 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
Raga Vutari
Zeitler
Manimic

Analysis

Cardinality

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

6 (hexatonic)

Pitch Class Set

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

{0,4,6,7,9,10}

Forte Number

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

6-Z23

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.

[2]

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.

no

Hemitonia

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

2 (dihemitonic)

Cohemitonia

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

0 (ancohemitonic)

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.

4

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.

5

Prime Form

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

no
prime: 365

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 Formula

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

[4, 2, 1, 2, 1, 2]

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.

<2, 3, 4, 2, 2, 2>

Interval Spectrum

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

p2m2n4s3d2t2

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

Spectra Variation

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

2.667

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.

2.232

Polygon Perimeter

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

5.767

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.

[4]

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.

(20, 6, 51)

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}221
Minor Triadsam{9,0,4}221
Diminished Triads{4,7,10}131.5
f♯°{6,9,0}131.5
Parsimonious Voice Leading Between Common Triads of Scale 1745. Created by Ian Ring ©2019 C C C->e° am am C->am f#° f#° f#°->am

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
Radius2
Self-Centeredno
Central VerticesC, am
Peripheral Verticese°, f♯°

Triad Polychords

Also known as Bi-Triadic Hexatonics (a term coined by mDecks), and related to Generic Modality Compression (a method for guitar by Mick Goodrick and Tim Miller), these are two common triads that when combined use all the tones in this scale.

There is 1 way that this hexatonic scale can be split into two common triads.


Diminished: {4, 7, 10}
Diminished: {6, 9, 0}

Modes

Modes are the rotational transformation of this scale. Scale 1745 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 365
Scale 365: Marimic, Ian Ring Music TheoryMarimicThis is the prime mode
3rd mode:
Scale 1115
Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
4th mode:
Scale 2605
Scale 2605: Rylimic, Ian Ring Music TheoryRylimic
5th mode:
Scale 1675
Scale 1675: Raga Salagavarali, Ian Ring Music TheoryRaga Salagavarali
6th mode:
Scale 2885
Scale 2885: Byrimic, Ian Ring Music TheoryByrimic

Prime

The prime form of this scale is Scale 365

Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic

Complement

The hexatonic modal family [1745, 365, 1115, 2605, 1675, 2885] (Forte: 6-Z23) is the complement of the hexatonic modal family [605, 745, 1175, 1865, 2635, 3365] (Forte: 6-Z45)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1745 is 365

Scale 365Scale 365: Marimic, Ian Ring Music TheoryMarimic

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> 1745       T0I <11,0> 365
T1 <1,1> 3490      T1I <11,1> 730
T2 <1,2> 2885      T2I <11,2> 1460
T3 <1,3> 1675      T3I <11,3> 2920
T4 <1,4> 3350      T4I <11,4> 1745
T5 <1,5> 2605      T5I <11,5> 3490
T6 <1,6> 1115      T6I <11,6> 2885
T7 <1,7> 2230      T7I <11,7> 1675
T8 <1,8> 365      T8I <11,8> 3350
T9 <1,9> 730      T9I <11,9> 2605
T10 <1,10> 1460      T10I <11,10> 1115
T11 <1,11> 2920      T11I <11,11> 2230
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2885      T0MI <7,0> 1115
T1M <5,1> 1675      T1MI <7,1> 2230
T2M <5,2> 3350      T2MI <7,2> 365
T3M <5,3> 2605      T3MI <7,3> 730
T4M <5,4> 1115      T4MI <7,4> 1460
T5M <5,5> 2230      T5MI <7,5> 2920
T6M <5,6> 365      T6MI <7,6> 1745
T7M <5,7> 730      T7MI <7,7> 3490
T8M <5,8> 1460      T8MI <7,8> 2885
T9M <5,9> 2920      T9MI <7,9> 1675
T10M <5,10> 1745       T10MI <7,10> 3350
T11M <5,11> 3490      T11MI <7,11> 2605

The transformations that map this set to itself are: T0, T4I, T10M, T6MI

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 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1729Scale 1729, Ian Ring Music Theory
Scale 1737Scale 1737: Raga Madhukauns, Ian Ring Music TheoryRaga Madhukauns
Scale 1761Scale 1761, Ian Ring Music Theory
Scale 1777Scale 1777: Saptian, Ian Ring Music TheorySaptian
Scale 1681Scale 1681: Raga Valaji, Ian Ring Music TheoryRaga Valaji
Scale 1713Scale 1713: Raga Khamas, Ian Ring Music TheoryRaga Khamas
Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic
Scale 1873Scale 1873: Dathimic, Ian Ring Music TheoryDathimic
Scale 2001Scale 2001: Gydian, Ian Ring Music TheoryGydian
Scale 1233Scale 1233: Ionoditonic, Ian Ring Music TheoryIonoditonic
Scale 1489Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
Scale 721Scale 721: Raga Dhavalashri, Ian Ring Music TheoryRaga Dhavalashri
Scale 2769Scale 2769: Dyrimic, Ian Ring Music TheoryDyrimic
Scale 3793Scale 3793: Aeopian, Ian Ring Music TheoryAeopian

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.