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Scale 2507: "Todi That"

Scale 2507: Todi That, 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

41161837294116105072918310504116183
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

Hindustani
Todi That
Todi Theta
Carnatic Mela
Mela Shubhapantuvarali
Carnatic Raga
Raga Multani
Gamakasamantam
Western Modern
Harsh Minor
Western Chromatic
Chromatic Lydian Inverse
Arabic
Maqam Athar Kurd
Zeitler
Ionyphian

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

{0,1,3,6,7,8,11}

Forte Number

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

7-20

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: 2675

Hemitonia

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

4 (multihemitonic)

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: 743

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.

[4, 3, 3, 4, 5, 2]

Interval Spectrum

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

p5m4n3s3d4t2

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> = {4,5,6}
<4> = {6,7,8}
<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

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.

2.433

Polygon Perimeter

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

5.899

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

Harmonic Chords

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 TriadsG♯{8,0,3}231.5
B{11,3,6}231.5
Minor Triadscm{0,3,7}321.17
g♯m{8,11,3}231.5
Augmented TriadsD♯+{3,7,11}321.17
Diminished Triads{0,3,6}231.5

The following pitch classes are not present in any of the common triads: {1}

Parsimonious Voice Leading Between Common Triads of Scale 2507. Created by Ian Ring ©2019 cm cm c°->cm B B c°->B D#+ D#+ cm->D#+ G# G# cm->G# g#m g#m D#+->g#m D#+->B g#m->G#

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 Verticescm, D♯+
Peripheral Verticesc°, g♯m, G♯, B

Modes

Modes are the rotational transformation of this scale. Scale 2507 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 3301
Scale 3301: Chromatic Mixolydian Inverse, Ian Ring Music TheoryChromatic Mixolydian Inverse
3rd mode:
Scale 1849
Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
4th mode:
Scale 743
Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian InverseThis is the prime mode
5th mode:
Scale 2419
Scale 2419: Raga Lalita, Ian Ring Music TheoryRaga Lalita
6th mode:
Scale 3257
Scale 3257: Mela Calanata, Ian Ring Music TheoryMela Calanata
7th mode:
Scale 919
Scale 919: Chromatic Phrygian Inverse, Ian Ring Music TheoryChromatic Phrygian Inverse

Prime

The prime form of this scale is Scale 743

Scale 743Scale 743: Chromatic Hypophrygian Inverse, Ian Ring Music TheoryChromatic Hypophrygian Inverse

Complement

The heptatonic modal family [2507, 3301, 1849, 743, 2419, 3257, 919] (Forte: 7-20) is the complement of the pentatonic modal family [355, 395, 1585, 2225, 2245] (Forte: 5-20)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 2507 is 2675

Scale 2675Scale 2675: Chromatic Lydian, Ian Ring Music TheoryChromatic Lydian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 2507 is chiral, and its enantiomorph is scale 2675

Scale 2675Scale 2675: Chromatic Lydian, Ian Ring Music TheoryChromatic Lydian

Transformations:

T0 2507  T0I 2675
T1 919  T1I 1255
T2 1838  T2I 2510
T3 3676  T3I 925
T4 3257  T4I 1850
T5 2419  T5I 3700
T6 743  T6I 3305
T7 1486  T7I 2515
T8 2972  T8I 935
T9 1849  T9I 1870
T10 3698  T10I 3740
T11 3301  T11I 3385

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 2505Scale 2505: Mydimic, Ian Ring Music TheoryMydimic
Scale 2509Scale 2509: Double Harmonic Minor, Ian Ring Music TheoryDouble Harmonic Minor
Scale 2511Scale 2511: Aeroptyllic, Ian Ring Music TheoryAeroptyllic
Scale 2499Scale 2499, Ian Ring Music Theory
Scale 2503Scale 2503: Mela Jhalavarali, Ian Ring Music TheoryMela Jhalavarali
Scale 2515Scale 2515: Chromatic Hypolydian, Ian Ring Music TheoryChromatic Hypolydian
Scale 2523Scale 2523: Mirage Scale, Ian Ring Music TheoryMirage Scale
Scale 2539Scale 2539: Half-Diminished Bebop, Ian Ring Music TheoryHalf-Diminished Bebop
Scale 2443Scale 2443: Panimic, Ian Ring Music TheoryPanimic
Scale 2475Scale 2475: Neapolitan Minor, Ian Ring Music TheoryNeapolitan Minor
Scale 2379Scale 2379: Raga Gurjari Todi, Ian Ring Music TheoryRaga Gurjari Todi
Scale 2251Scale 2251: Zodimic, Ian Ring Music TheoryZodimic
Scale 2763Scale 2763: Mela Suvarnangi, Ian Ring Music TheoryMela Suvarnangi
Scale 3019Scale 3019, Ian Ring Music Theory
Scale 3531Scale 3531: Neveseri, Ian Ring Music TheoryNeveseri
Scale 459Scale 459: Zaptimic, Ian Ring Music TheoryZaptimic
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya

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.