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Scale 1195: "Raga Gandharavam"

Scale 1195: Raga Gandharavam, 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 Gandharavam
Ethiopian
Sabai Silt
Zeitler
Sarimic

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

{0,1,3,5,7,10}

Forte Number

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

6-33

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: 2725

Hemitonia

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

1 (unhemitonic)

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.

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.

5

Prime Form

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

no
prime: 685

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.

[1, 2, 2, 2, 3, 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.

<1, 4, 3, 2, 4, 1>

Interval Spectrum

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

p4m2n3s4dt

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

Spectra Variation

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

1.667

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.

2.482

Polygon Perimeter

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

5.932

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".

Proper

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 TriadsD♯{3,7,10}221
Minor Triadscm{0,3,7}131.5
a♯m{10,1,5}131.5
Diminished Triads{7,10,1}221
Parsimonious Voice Leading Between Common Triads of Scale 1195. Created by Ian Ring ©2019 cm cm D# D# cm->D# D#->g° a#m a#m g°->a#m

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 VerticesD♯, g°
Peripheral Verticescm, a♯m

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.


Minor: {0, 3, 7}
Minor: {10, 1, 5}

Modes

Modes are the rotational transformation of this scale. Scale 1195 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2645
Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana
3rd mode:
Scale 1685
Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
4th mode:
Scale 1445
Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari
5th mode:
Scale 1385
Scale 1385: Phracrimic, Ian Ring Music TheoryPhracrimic
6th mode:
Scale 685
Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha BangalaThis is the prime mode

Prime

The prime form of this scale is Scale 685

Scale 685Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha Bangala

Complement

The hexatonic modal family [1195, 2645, 1685, 1445, 1385, 685] (Forte: 6-33) is the complement of the hexatonic modal family [685, 1195, 1385, 1445, 1685, 2645] (Forte: 6-33)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1195 is 2725

Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1195 is chiral, and its enantiomorph is scale 2725

Scale 2725Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari

Transformations:

T0 1195  T0I 2725
T1 2390  T1I 1355
T2 685  T2I 2710
T3 1370  T3I 1325
T4 2740  T4I 2650
T5 1385  T5I 1205
T6 2770  T6I 2410
T7 1445  T7I 725
T8 2890  T8I 1450
T9 1685  T9I 2900
T10 3370  T10I 1705
T11 2645  T11I 3410

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 1193Scale 1193: Minor Pentatonic, Ian Ring Music TheoryMinor Pentatonic
Scale 1197Scale 1197: Minor Hexatonic, Ian Ring Music TheoryMinor Hexatonic
Scale 1199Scale 1199: Magian, Ian Ring Music TheoryMagian
Scale 1187Scale 1187: Kokin-joshi, Ian Ring Music TheoryKokin-joshi
Scale 1191Scale 1191: Pyrimic, Ian Ring Music TheoryPyrimic
Scale 1203Scale 1203: Pagimic, Ian Ring Music TheoryPagimic
Scale 1211Scale 1211: Zadian, Ian Ring Music TheoryZadian
Scale 1163Scale 1163: Raga Rukmangi, Ian Ring Music TheoryRaga Rukmangi
Scale 1179Scale 1179: Sonimic, Ian Ring Music TheorySonimic
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic
Scale 1259Scale 1259: Stadian, Ian Ring Music TheoryStadian
Scale 1067Scale 1067, Ian Ring Music Theory
Scale 1131Scale 1131: Honchoshi Plagal Form, Ian Ring Music TheoryHonchoshi Plagal Form
Scale 1323Scale 1323: Ritsu, Ian Ring Music TheoryRitsu
Scale 1451Scale 1451: Phrygian, Ian Ring Music TheoryPhrygian
Scale 1707Scale 1707: Dorian Flat 2, Ian Ring Music TheoryDorian Flat 2
Scale 171Scale 171, Ian Ring Music Theory
Scale 683Scale 683: Stogimic, Ian Ring Music TheoryStogimic
Scale 2219Scale 2219: Phrydimic, Ian Ring Music TheoryPhrydimic
Scale 3243Scale 3243: Mela Rupavati, Ian Ring Music TheoryMela Rupavati

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. 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.