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Scale 1205: "Raga Siva Kambhoji"

Scale 1205: Raga Siva Kambhoji, 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 Siva Kambhoji
Vivardhini
Hindustani
Andhali
Zeitler
Ionycrimic

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

{0,2,4,5,7,10}

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: 1445

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

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.

[2, 2, 1, 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

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.

(0, 12, 54)

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}131.5
A♯{10,2,5}131.5
Minor Triadsgm{7,10,2}221
Diminished Triads{4,7,10}221
Parsimonious Voice Leading Between Common Triads of Scale 1205. Created by Ian Ring ©2019 C C C->e° gm gm e°->gm A# A# gm->A#

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 Verticese°, gm
Peripheral VerticesC, A♯

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.


Major: {0, 4, 7}
Major: {10, 2, 5}

Modes

Modes are the rotational transformation of this scale. Scale 1205 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1325
Scale 1325: Phradimic, Ian Ring Music TheoryPhradimic
3rd mode:
Scale 1355
Scale 1355: Raga Bhavani, Ian Ring Music TheoryRaga Bhavani
4th mode:
Scale 2725
Scale 2725: Raga Nagagandhari, Ian Ring Music TheoryRaga Nagagandhari
5th mode:
Scale 1705
Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
6th mode:
Scale 725
Scale 725: Raga Yamuna Kalyani, Ian Ring Music TheoryRaga Yamuna Kalyani

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 [1205, 1325, 1355, 2725, 1705, 725] (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 1205 is 1445

Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1205 is chiral, and its enantiomorph is scale 1445

Scale 1445Scale 1445: Raga Navamanohari, Ian Ring Music TheoryRaga Navamanohari

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> 1205       T0I <11,0> 1445
T1 <1,1> 2410      T1I <11,1> 2890
T2 <1,2> 725      T2I <11,2> 1685
T3 <1,3> 1450      T3I <11,3> 3370
T4 <1,4> 2900      T4I <11,4> 2645
T5 <1,5> 1705      T5I <11,5> 1195
T6 <1,6> 3410      T6I <11,6> 2390
T7 <1,7> 2725      T7I <11,7> 685
T8 <1,8> 1355      T8I <11,8> 1370
T9 <1,9> 2710      T9I <11,9> 2740
T10 <1,10> 1325      T10I <11,10> 1385
T11 <1,11> 2650      T11I <11,11> 2770
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 3335      T0MI <7,0> 3095
T1M <5,1> 2575      T1MI <7,1> 2095
T2M <5,2> 1055      T2MI <7,2> 95
T3M <5,3> 2110      T3MI <7,3> 190
T4M <5,4> 125      T4MI <7,4> 380
T5M <5,5> 250      T5MI <7,5> 760
T6M <5,6> 500      T6MI <7,6> 1520
T7M <5,7> 1000      T7MI <7,7> 3040
T8M <5,8> 2000      T8MI <7,8> 1985
T9M <5,9> 4000      T9MI <7,9> 3970
T10M <5,10> 3905      T10MI <7,10> 3845
T11M <5,11> 3715      T11MI <7,11> 3595

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 1207Scale 1207: Aeoloptian, Ian Ring Music TheoryAeoloptian
Scale 1201Scale 1201: Mixolydian Pentatonic, Ian Ring Music TheoryMixolydian Pentatonic
Scale 1203Scale 1203: Pagimic, Ian Ring Music TheoryPagimic
Scale 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 1213Scale 1213: Gyrian, Ian Ring Music TheoryGyrian
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 1197Scale 1197: Minor Hexatonic, Ian Ring Music TheoryMinor Hexatonic
Scale 1173Scale 1173: Dominant Pentatonic, Ian Ring Music TheoryDominant Pentatonic
Scale 1237Scale 1237: Salimic, Ian Ring Music TheorySalimic
Scale 1269Scale 1269: Katythian, Ian Ring Music TheoryKatythian
Scale 1077Scale 1077, Ian Ring Music Theory
Scale 1141Scale 1141: Rynimic, Ian Ring Music TheoryRynimic
Scale 1333Scale 1333: Lyptimic, Ian Ring Music TheoryLyptimic
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 181Scale 181: Raga Budhamanohari, Ian Ring Music TheoryRaga Budhamanohari
Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 2229Scale 2229: Raga Nalinakanti, Ian Ring Music TheoryRaga Nalinakanti
Scale 3253Scale 3253: Mela Naganandini, Ian Ring Music TheoryMela Naganandini

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.