The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 2467: "Raga Padi"

Scale 2467: Raga Padi, 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 Padi
Zeitler
Morimic
Dozenal
PEXIAN

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

{0,1,5,7,8,11}

Forte Number

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

6-Z43

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: 2227

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.

1 (uncohemitonic)

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.

3

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: 359

Deep Scale

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

no

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, 2, 2, 3, 3, 2]

Interval Spectrum

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

p3m3n2s2d3t2

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

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.

2.116

Polygon Perimeter

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

5.699

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

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♯{1,5,8}121
Minor Triadsfm{5,8,0}210.67
Diminished Triads{5,8,11}121

The following pitch classes are not present in any of the common triads: {7}

Parsimonious Voice Leading Between Common Triads of Scale 2467. Created by Ian Ring ©2019 C# C# fm fm C#->fm f°->fm

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.

Diameter2
Radius1
Self-Centeredno
Central Verticesfm
Peripheral VerticesC♯, f°

Modes

Modes are the rotational transformation of this scale. Scale 2467 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 3281
Scale 3281: Raga Vijayavasanta, Ian Ring Music TheoryRaga Vijayavasanta
3rd mode:
Scale 461
Scale 461: Raga Syamalam, Ian Ring Music TheoryRaga Syamalam
4th mode:
Scale 1139
Scale 1139: Aerygimic, Ian Ring Music TheoryAerygimic
5th mode:
Scale 2617
Scale 2617: Pylimic, Ian Ring Music TheoryPylimic
6th mode:
Scale 839
Scale 839: Ionathimic, Ian Ring Music TheoryIonathimic

Prime

The prime form of this scale is Scale 359

Scale 359Scale 359: Bothimic, Ian Ring Music TheoryBothimic

Complement

The hexatonic modal family [2467, 3281, 461, 1139, 2617, 839] (Forte: 6-Z43) is the complement of the hexatonic modal family [407, 739, 1817, 2251, 2417, 3173] (Forte: 6-Z17)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2467 is 2227

Scale 2227Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2467 is chiral, and its enantiomorph is scale 2227

Scale 2227Scale 2227: Raga Gaula, Ian Ring Music TheoryRaga Gaula

Transformations:

T0 2467  T0I 2227
T1 839  T1I 359
T2 1678  T2I 718
T3 3356  T3I 1436
T4 2617  T4I 2872
T5 1139  T5I 1649
T6 2278  T6I 3298
T7 461  T7I 2501
T8 922  T8I 907
T9 1844  T9I 1814
T10 3688  T10I 3628
T11 3281  T11I 3161

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 2465Scale 2465: Raga Devaranjani, Ian Ring Music TheoryRaga Devaranjani
Scale 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
Scale 2471Scale 2471: Mela Ganamurti, Ian Ring Music TheoryMela Ganamurti
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 2483Scale 2483: Double Harmonic, Ian Ring Music TheoryDouble Harmonic
Scale 2435Scale 2435: Raga Deshgaur, Ian Ring Music TheoryRaga Deshgaur
Scale 2451Scale 2451: Raga Bauli, Ian Ring Music TheoryRaga Bauli
Scale 2499Scale 2499: PIRIAN, Ian Ring Music TheoryPIRIAN
Scale 2531Scale 2531: Danian, Ian Ring Music TheoryDanian
Scale 2339Scale 2339: Raga Kshanika, Ian Ring Music TheoryRaga Kshanika
Scale 2403Scale 2403: Lycrimic, Ian Ring Music TheoryLycrimic
Scale 2211Scale 2211: Raga Gauri, Ian Ring Music TheoryRaga Gauri
Scale 2723Scale 2723: Raga Jivantika, Ian Ring Music TheoryRaga Jivantika
Scale 2979Scale 2979: Gyptian, Ian Ring Music TheoryGyptian
Scale 3491Scale 3491: Tharian, Ian Ring Music TheoryTharian
Scale 419Scale 419: Hon-kumoi-joshi, Ian Ring Music TheoryHon-kumoi-joshi
Scale 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti

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.

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.