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Scale 1445: "Raga Navamanohari"

Scale 1445: Raga Navamanohari, 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 Navamanohari
Dozenal
Jadian
Zeitler
Byptimic

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

{0,2,5,7,8,10}

Forte Number

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

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: 1205

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 Structure

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

[2, 3, 2, 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.

<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 TriadsA♯{10,2,5}221
Minor Triadsfm{5,8,0}131.5
gm{7,10,2}131.5
Diminished Triads{2,5,8}221
Parsimonious Voice Leading Between Common Triads of Scale 1445. Created by Ian Ring ©2019 fm fm d°->fm A# A# d°->A# gm gm 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 Verticesd°, A♯
Peripheral Verticesfm, gm

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.


Minor: {5, 8, 0}
Minor: {7, 10, 2}

Modes

Modes are the rotational transformation of this scale. Scale 1445 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 1385
Scale 1385: Phracrimic, Ian Ring Music TheoryPhracrimic
3rd mode:
Scale 685
Scale 685: Raga Suddha Bangala, Ian Ring Music TheoryRaga Suddha BangalaThis is the prime mode
4th mode:
Scale 1195
Scale 1195: Raga Gandharavam, Ian Ring Music TheoryRaga Gandharavam
5th mode:
Scale 2645
Scale 2645: Raga Mruganandana, Ian Ring Music TheoryRaga Mruganandana
6th mode:
Scale 1685
Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic

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 [1445, 1385, 685, 1195, 2645, 1685] (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 1445 is 1205

Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji

Enantiomorph

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

Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji

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

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 1447Scale 1447: Mela Ratnangi, Ian Ring Music TheoryMela Ratnangi
Scale 1441Scale 1441: Jabian, Ian Ring Music TheoryJabian
Scale 1443Scale 1443: Raga Phenadyuti, Ian Ring Music TheoryRaga Phenadyuti
Scale 1449Scale 1449: Raga Gopikavasantam, Ian Ring Music TheoryRaga Gopikavasantam
Scale 1453Scale 1453: Aeolian, Ian Ring Music TheoryAeolian
Scale 1461Scale 1461: Major-Minor, Ian Ring Music TheoryMajor-Minor
Scale 1413Scale 1413: Iruian, Ian Ring Music TheoryIruian
Scale 1429Scale 1429: Bythimic, Ian Ring Music TheoryBythimic
Scale 1477Scale 1477: Raga Jaganmohanam, Ian Ring Music TheoryRaga Jaganmohanam
Scale 1509Scale 1509: Ragian, Ian Ring Music TheoryRagian
Scale 1317Scale 1317: Chaio, Ian Ring Music TheoryChaio
Scale 1381Scale 1381: Padimic, Ian Ring Music TheoryPadimic
Scale 1189Scale 1189: Suspended Pentatonic, Ian Ring Music TheorySuspended Pentatonic
Scale 1701Scale 1701: Dominant Seventh, Ian Ring Music TheoryDominant Seventh
Scale 1957Scale 1957: Pyrian, Ian Ring Music TheoryPyrian
Scale 421Scale 421: Han-kumoi, Ian Ring Music TheoryHan-kumoi
Scale 933Scale 933: Dadimic, Ian Ring Music TheoryDadimic
Scale 2469Scale 2469: Raga Bhinna Pancama, Ian Ring Music TheoryRaga Bhinna Pancama
Scale 3493Scale 3493: Rathian, Ian Ring Music TheoryRathian

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.