The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1747: "Mela Ramapriya"

Scale 1747: Mela Ramapriya, 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
Mela Ramapriya
Raga Ramamanohari
Dozenal
Kuhian
Exoticisms
Romanian Major
Named After Composers
Petrushka
Zeitler
Epalian
Carnatic Melakarta
Ramapriya
Carnatic Numbered Melakarta
52nd Melakarta raga

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

{0,1,4,6,7,9,10}

Forte Number

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

7-31

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: 2413

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.

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.

6

Prime Form

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

no
prime: 731

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 Structure

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

[1, 3, 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.

<3, 3, 6, 3, 3, 3>

Interval Spectrum

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

p3m3n6s3d3t3

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

Spectra Variation

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

1.714

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.

2.549

Polygon Perimeter

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

5.967

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

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.

(4, 27, 84)

Tertian Harmonic Chords

Tertian chords are made from alternating members of the scale, ie built from "stacked thirds". Not all scales lend themselves well to tertian harmony.

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}331.8
F♯{6,10,1}331.8
A{9,1,4}431.6
Minor Triadsf♯m{6,9,1}331.7
am{9,0,4}331.7
Diminished Triadsc♯°{1,4,7}231.9
{4,7,10}232
f♯°{6,9,0}232
{7,10,1}232
a♯°{10,1,4}231.9
Parsimonious Voice Leading Between Common Triads of Scale 1747. Created by Ian Ring ©2019 C C c#° c#° C->c#° C->e° am am C->am A A c#°->A e°->g° f#° f#° f#m f#m f#°->f#m f#°->am F# F# f#m->F# f#m->A F#->g° a#° a#° F#->a#° am->A A->a#°

view full size

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
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1747 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2921
Scale 2921: Pogian, Ian Ring Music TheoryPogian
3rd mode:
Scale 877
Scale 877: Moravian Pistalkova, Ian Ring Music TheoryMoravian Pistalkova
4th mode:
Scale 1243
Scale 1243: Epylian, Ian Ring Music TheoryEpylian
5th mode:
Scale 2669
Scale 2669: Jeths' Mode, Ian Ring Music TheoryJeths' Mode
6th mode:
Scale 1691
Scale 1691: Kathian, Ian Ring Music TheoryKathian
7th mode:
Scale 2893
Scale 2893: Lylian, Ian Ring Music TheoryLylian

Prime

The prime form of this scale is Scale 731

Scale 731Scale 731: Alternating Heptamode, Ian Ring Music TheoryAlternating Heptamode

Complement

The heptatonic modal family [1747, 2921, 877, 1243, 2669, 1691, 2893] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1747 is 2413

Scale 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1747 is chiral, and its enantiomorph is scale 2413

Scale 2413Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2

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> 1747       T0I <11,0> 2413
T1 <1,1> 3494      T1I <11,1> 731
T2 <1,2> 2893      T2I <11,2> 1462
T3 <1,3> 1691      T3I <11,3> 2924
T4 <1,4> 3382      T4I <11,4> 1753
T5 <1,5> 2669      T5I <11,5> 3506
T6 <1,6> 1243      T6I <11,6> 2917
T7 <1,7> 2486      T7I <11,7> 1739
T8 <1,8> 877      T8I <11,8> 3478
T9 <1,9> 1754      T9I <11,9> 2861
T10 <1,10> 3508      T10I <11,10> 1627
T11 <1,11> 2921      T11I <11,11> 3254
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2917      T0MI <7,0> 1243
T1M <5,1> 1739      T1MI <7,1> 2486
T2M <5,2> 3478      T2MI <7,2> 877
T3M <5,3> 2861      T3MI <7,3> 1754
T4M <5,4> 1627      T4MI <7,4> 3508
T5M <5,5> 3254      T5MI <7,5> 2921
T6M <5,6> 2413      T6MI <7,6> 1747
T7M <5,7> 731      T7MI <7,7> 3494
T8M <5,8> 1462      T8MI <7,8> 2893
T9M <5,9> 2924      T9MI <7,9> 1691
T10M <5,10> 1753      T10MI <7,10> 3382
T11M <5,11> 3506      T11MI <7,11> 2669

The transformations that map this set to itself are: T0, 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 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1749Scale 1749: Acoustic, Ian Ring Music TheoryAcoustic
Scale 1751Scale 1751: Aeolyryllic, Ian Ring Music TheoryAeolyryllic
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1731Scale 1731: Koxian, Ian Ring Music TheoryKoxian
Scale 1739Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
Scale 1763Scale 1763: Katalian, Ian Ring Music TheoryKatalian
Scale 1779Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
Scale 1683Scale 1683: Raga Malayamarutam, Ian Ring Music TheoryRaga Malayamarutam
Scale 1715Scale 1715: Harmonic Minor Inverse, Ian Ring Music TheoryHarmonic Minor Inverse
Scale 1619Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan
Scale 1875Scale 1875: Persichetti Scale, Ian Ring Music TheoryPersichetti Scale
Scale 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
Scale 1235Scale 1235: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 1491Scale 1491: Namanarayani, Ian Ring Music TheoryNamanarayani
Scale 723Scale 723: Ionadimic, Ian Ring Music TheoryIonadimic
Scale 2771Scale 2771: Marva That, Ian Ring Music TheoryMarva That
Scale 3795Scale 3795: Epothyllic, Ian Ring Music TheoryEpothyllic

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, and George Howlett for assistance with the Carnatic ragas.