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Scale 1491: "Namanarayani"

Scale 1491: Namanarayani, 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 Melakarta
Namanarayani
Dozenal
Jegian
Carnatic
Mela Namanarayani
Raga Narmada
Unknown / Unsorted
Pratapa
Harsh Major-Minor
Zeitler
Rynian
Carnatic Numbered Melakarta
50th 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

{0,1,4,6,7,8,10}

Forte Number

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

7-28

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: 2421

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.

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: 747

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

Interval Spectrum

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

p3m4n4s4d3t3

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.

2.549

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.

(6, 33, 96)

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}331.63
F♯{6,10,1}231.88
Minor Triadsc♯m{1,4,8}331.63
Augmented TriadsC+{0,4,8}231.75
Diminished Triadsc♯°{1,4,7}231.75
{4,7,10}231.75
{7,10,1}231.88
a♯°{10,1,4}231.75
Parsimonious Voice Leading Between Common Triads of Scale 1491. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m c#°->c#m a#° a#° c#m->a#° e°->g° F# F# F#->g° F#->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 1491 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2793
Scale 2793: Eporian, Ian Ring Music TheoryEporian
3rd mode:
Scale 861
Scale 861: Rylian, Ian Ring Music TheoryRylian
4th mode:
Scale 1239
Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
5th mode:
Scale 2667
Scale 2667: Byrian, Ian Ring Music TheoryByrian
6th mode:
Scale 3381
Scale 3381: Katanian, Ian Ring Music TheoryKatanian
7th mode:
Scale 1869
Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian

Prime

The prime form of this scale is Scale 747

Scale 747Scale 747: Lynian, Ian Ring Music TheoryLynian

Complement

The heptatonic modal family [1491, 2793, 861, 1239, 2667, 3381, 1869] (Forte: 7-28) is the complement of the pentatonic modal family [333, 837, 1107, 1233, 2601] (Forte: 5-28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1491 is 2421

Scale 2421Scale 2421: Malian, Ian Ring Music TheoryMalian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1491 is chiral, and its enantiomorph is scale 2421

Scale 2421Scale 2421: Malian, Ian Ring Music TheoryMalian

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> 1491       T0I <11,0> 2421
T1 <1,1> 2982      T1I <11,1> 747
T2 <1,2> 1869      T2I <11,2> 1494
T3 <1,3> 3738      T3I <11,3> 2988
T4 <1,4> 3381      T4I <11,4> 1881
T5 <1,5> 2667      T5I <11,5> 3762
T6 <1,6> 1239      T6I <11,6> 3429
T7 <1,7> 2478      T7I <11,7> 2763
T8 <1,8> 861      T8I <11,8> 1431
T9 <1,9> 1722      T9I <11,9> 2862
T10 <1,10> 3444      T10I <11,10> 1629
T11 <1,11> 2793      T11I <11,11> 3258
Abbrev Operation Result Abbrev Operation Result
T0M <5,0> 2421      T0MI <7,0> 1491
T1M <5,1> 747      T1MI <7,1> 2982
T2M <5,2> 1494      T2MI <7,2> 1869
T3M <5,3> 2988      T3MI <7,3> 3738
T4M <5,4> 1881      T4MI <7,4> 3381
T5M <5,5> 3762      T5MI <7,5> 2667
T6M <5,6> 3429      T6MI <7,6> 1239
T7M <5,7> 2763      T7MI <7,7> 2478
T8M <5,8> 1431      T8MI <7,8> 861
T9M <5,9> 2862      T9MI <7,9> 1722
T10M <5,10> 1629      T10MI <7,10> 3444
T11M <5,11> 3258      T11MI <7,11> 2793

The transformations that map this set to itself are: T0, T0MI

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 1489Scale 1489: Raga Jyoti, Ian Ring Music TheoryRaga Jyoti
Scale 1493Scale 1493: Lydian Minor, Ian Ring Music TheoryLydian Minor
Scale 1495Scale 1495: Messiaen Mode 6, Ian Ring Music TheoryMessiaen Mode 6
Scale 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
Scale 1475Scale 1475: Uffian, Ian Ring Music TheoryUffian
Scale 1483Scale 1483: Mela Bhavapriya, Ian Ring Music TheoryMela Bhavapriya
Scale 1507Scale 1507: Zynian, Ian Ring Music TheoryZynian
Scale 1523Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
Scale 1427Scale 1427: Lolimic, Ian Ring Music TheoryLolimic
Scale 1459Scale 1459: Phrygian Dominant, Ian Ring Music TheoryPhrygian Dominant
Scale 1363Scale 1363: Gygimic, Ian Ring Music TheoryGygimic
Scale 1235Scale 1235: Messiaen Truncated Mode 2, Ian Ring Music TheoryMessiaen Truncated Mode 2
Scale 1747Scale 1747: Mela Ramapriya, Ian Ring Music TheoryMela Ramapriya
Scale 2003Scale 2003: Podyllic, Ian Ring Music TheoryPodyllic
Scale 467Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam
Scale 979Scale 979: Mela Dhavalambari, Ian Ring Music TheoryMela Dhavalambari
Scale 2515Scale 2515: Chromatic Hypolydian, Ian Ring Music TheoryChromatic Hypolydian
Scale 3539Scale 3539: Aeoryllic, Ian Ring Music TheoryAeoryllic

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.