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Scale 1713: "Raga Khamas"

Scale 1713: Raga Khamas, 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

Carnatic Raga
Raga Khamas
Unknown / Unsorted
Desya Khamas
Bahudari
Zeitler
Garimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,4,5,7,9,10}
Forte Number6-Z25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 429
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes5
Prime?no
prime: 363
Deep Scaleno
Interval Vector233241
Interval Spectrump4m2n3s3d2t
Distribution Spectra<1> = {1,2,4}
<2> = {3,4,5,6}
<3> = {5,7}
<4> = {6,7,8,9}
<5> = {8,10,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.232
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

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}221
F{5,9,0}131.5
Minor Triadsam{9,0,4}221
Diminished Triads{4,7,10}131.5
Parsimonious Voice Leading Between Common Triads of Scale 1713. Created by Ian Ring ©2019 C C C->e° am am C->am F F F->am

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 VerticesC, am
Peripheral Verticese°, F

Modes

Modes are the rotational transformation of this scale. Scale 1713 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 363
Scale 363: Soptimic, Ian Ring Music TheorySoptimicThis is the prime mode
3rd mode:
Scale 2229
Scale 2229: Raga Nalinakanti, Ian Ring Music TheoryRaga Nalinakanti
4th mode:
Scale 1581
Scale 1581: Raga Bagesri, Ian Ring Music TheoryRaga Bagesri
5th mode:
Scale 1419
Scale 1419: Raga Kashyapi, Ian Ring Music TheoryRaga Kashyapi
6th mode:
Scale 2757
Scale 2757: Raga Nishadi, Ian Ring Music TheoryRaga Nishadi

Prime

The prime form of this scale is Scale 363

Scale 363Scale 363: Soptimic, Ian Ring Music TheorySoptimic

Complement

The hexatonic modal family [1713, 363, 2229, 1581, 1419, 2757] (Forte: 6-Z25) is the complement of the hexatonic modal family [663, 741, 1209, 1833, 2379, 3237] (Forte: 6-Z47)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1713 is 429

Scale 429Scale 429: Koptimic, Ian Ring Music TheoryKoptimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1713 is chiral, and its enantiomorph is scale 429

Scale 429Scale 429: Koptimic, Ian Ring Music TheoryKoptimic

Transformations:

T0 1713  T0I 429
T1 3426  T1I 858
T2 2757  T2I 1716
T3 1419  T3I 3432
T4 2838  T4I 2769
T5 1581  T5I 1443
T6 3162  T6I 2886
T7 2229  T7I 1677
T8 363  T8I 3354
T9 726  T9I 2613
T10 1452  T10I 1131
T11 2904  T11I 2262

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 1715Scale 1715: Harmonic Minor Inverse, Ian Ring Music TheoryHarmonic Minor Inverse
Scale 1717Scale 1717: Mixolydian, Ian Ring Music TheoryMixolydian
Scale 1721Scale 1721: Mela Vagadhisvari, Ian Ring Music TheoryMela Vagadhisvari
Scale 1697Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali
Scale 1705Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
Scale 1681Scale 1681: Raga Valaji, Ian Ring Music TheoryRaga Valaji
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1777Scale 1777: Saptian, Ian Ring Music TheorySaptian
Scale 1585Scale 1585: Raga Khamaji Durga, Ian Ring Music TheoryRaga Khamaji Durga
Scale 1649Scale 1649: Bolimic, Ian Ring Music TheoryBolimic
Scale 1841Scale 1841: Thogimic, Ian Ring Music TheoryThogimic
Scale 1969Scale 1969: Stylian, Ian Ring Music TheoryStylian
Scale 1201Scale 1201: Mixolydian Pentatonic, Ian Ring Music TheoryMixolydian Pentatonic
Scale 1457Scale 1457: Raga Kamalamanohari, Ian Ring Music TheoryRaga Kamalamanohari
Scale 689Scale 689: Raga Nagasvaravali, Ian Ring Music TheoryRaga Nagasvaravali
Scale 2737Scale 2737: Raga Hari Nata, Ian Ring Music TheoryRaga Hari Nata
Scale 3761Scale 3761: Raga Madhuri, Ian Ring Music TheoryRaga Madhuri

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.