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Scale 3757: "Raga Mian Ki Malhar"

Scale 3757: Raga Mian Ki Malhar, 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 Mian Ki Malhar
Unknown / Unsorted
Bahar
Sindhura
Zeitler
Goptyllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,5,7,9,10,11}
Forte Number8-22
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1711
Hemitonia4 (multihemitonic)
Cohemitonia2 (dicohemitonic)
Imperfections2
Modes7
Prime?no
prime: 1391
Deep Scaleno
Interval Vector465562
Interval Spectrump6m5n5s6d4t2
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {5,6,7}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {10,11}
Spectra Variation1.75
Maximally Evenno
Maximal Area Setyes
Interior Area2.732
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 TriadsD♯{3,7,10}242.1
F{5,9,0}242.3
G{7,11,2}341.9
A♯{10,2,5}341.9
Minor Triadscm{0,3,7}242.1
dm{2,5,9}242.1
gm{7,10,2}341.9
Augmented TriadsD♯+{3,7,11}341.9
Diminished Triads{9,0,3}242.3
{11,2,5}242.1
Parsimonious Voice Leading Between Common Triads of Scale 3757. Created by Ian Ring ©2019 cm cm D#+ D#+ cm->D#+ cm->a° dm dm F F dm->F A# A# dm->A# D# D# D#->D#+ gm gm D#->gm Parsimonious Voice Leading Between Common Triads of Scale 3757. Created by Ian Ring ©2019 G D#+->G F->a° gm->G gm->A# G->b° A#->b°

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 3757 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1963
Scale 1963: Epocryllic, Ian Ring Music TheoryEpocryllic
3rd mode:
Scale 3029
Scale 3029: Ionocryllic, Ian Ring Music TheoryIonocryllic
4th mode:
Scale 1781
Scale 1781: Gocryllic, Ian Ring Music TheoryGocryllic
5th mode:
Scale 1469
Scale 1469: Epiryllic, Ian Ring Music TheoryEpiryllic
6th mode:
Scale 1391
Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllicThis is the prime mode
7th mode:
Scale 2743
Scale 2743: Staptyllic, Ian Ring Music TheoryStaptyllic
8th mode:
Scale 3419
Scale 3419: Magen Abot 1, Ian Ring Music TheoryMagen Abot 1

Prime

The prime form of this scale is Scale 1391

Scale 1391Scale 1391: Aeradyllic, Ian Ring Music TheoryAeradyllic

Complement

The octatonic modal family [3757, 1963, 3029, 1781, 1469, 1391, 2743, 3419] (Forte: 8-22) is the complement of the tetratonic modal family [149, 673, 1061, 1289] (Forte: 4-22)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 3757 is 1711

Scale 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 3757 is chiral, and its enantiomorph is scale 1711

Scale 1711Scale 1711: Adonai Malakh, Ian Ring Music TheoryAdonai Malakh

Transformations:

T0 3757  T0I 1711
T1 3419  T1I 3422
T2 2743  T2I 2749
T3 1391  T3I 1403
T4 2782  T4I 2806
T5 1469  T5I 1517
T6 2938  T6I 3034
T7 1781  T7I 1973
T8 3562  T8I 3946
T9 3029  T9I 3797
T10 1963  T10I 3499
T11 3926  T11I 2903

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 3759Scale 3759: Darygic, Ian Ring Music TheoryDarygic
Scale 3753Scale 3753: Phraptian, Ian Ring Music TheoryPhraptian
Scale 3755Scale 3755: Phryryllic, Ian Ring Music TheoryPhryryllic
Scale 3749Scale 3749: Raga Sorati, Ian Ring Music TheoryRaga Sorati
Scale 3765Scale 3765: Dominant Bebop, Ian Ring Music TheoryDominant Bebop
Scale 3773Scale 3773: Raga Malgunji, Ian Ring Music TheoryRaga Malgunji
Scale 3725Scale 3725: Kyrian, Ian Ring Music TheoryKyrian
Scale 3741Scale 3741: Zydyllic, Ian Ring Music TheoryZydyllic
Scale 3789Scale 3789: Eporyllic, Ian Ring Music TheoryEporyllic
Scale 3821Scale 3821: Epyrygic, Ian Ring Music TheoryEpyrygic
Scale 3629Scale 3629: Boptian, Ian Ring Music TheoryBoptian
Scale 3693Scale 3693: Stadyllic, Ian Ring Music TheoryStadyllic
Scale 3885Scale 3885: Styryllic, Ian Ring Music TheoryStyryllic
Scale 4013Scale 4013: Raga Pilu, Ian Ring Music TheoryRaga Pilu
Scale 3245Scale 3245: Mela Varunapriya, Ian Ring Music TheoryMela Varunapriya
Scale 3501Scale 3501: Maqam Nahawand, Ian Ring Music TheoryMaqam Nahawand
Scale 2733Scale 2733: Melodic Minor Ascending, Ian Ring Music TheoryMelodic Minor Ascending
Scale 1709Scale 1709: Dorian, Ian Ring Music TheoryDorian

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.