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Scale 1737: "Raga Madhukauns"

Scale 1737: Raga Madhukauns, 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 Madhukauns
Zeitler
Thalimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,6,7,9,10}
Forte Number6-27
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 621
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 603
Deep Scaleno
Interval Vector225222
Interval Spectrump2m2n5s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5,6}
<3> = {4,5,6,7,8}
<4> = {6,7,8,9}
<5> = {9,10,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.366
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}231.57
Minor Triadscm{0,3,7}331.43
d♯m{3,6,10}331.43
Diminished Triads{0,3,6}231.57
d♯°{3,6,9}231.57
f♯°{6,9,0}231.71
{9,0,3}231.57
Parsimonious Voice Leading Between Common Triads of Scale 1737. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# cm->a° d#° d#° d#°->d#m f#° f#° d#°->f#° d#m->D# 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 1737 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 729
Scale 729: Stygimic, Ian Ring Music TheoryStygimic
3rd mode:
Scale 603
Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimicThis is the prime mode
4th mode:
Scale 2349
Scale 2349: Raga Ghantana, Ian Ring Music TheoryRaga Ghantana
5th mode:
Scale 1611
Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
6th mode:
Scale 2853
Scale 2853: Baptimic, Ian Ring Music TheoryBaptimic

Prime

The prime form of this scale is Scale 603

Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic

Complement

The hexatonic modal family [1737, 729, 603, 2349, 1611, 2853] (Forte: 6-27) is the complement of the hexatonic modal family [603, 729, 1611, 1737, 2349, 2853] (Forte: 6-27)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1737 is 621

Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1737 is chiral, and its enantiomorph is scale 621

Scale 621Scale 621: Pyramid Hexatonic, Ian Ring Music TheoryPyramid Hexatonic

Transformations:

T0 1737  T0I 621
T1 3474  T1I 1242
T2 2853  T2I 2484
T3 1611  T3I 873
T4 3222  T4I 1746
T5 2349  T5I 3492
T6 603  T6I 2889
T7 1206  T7I 1683
T8 2412  T8I 3366
T9 729  T9I 2637
T10 1458  T10I 1179
T11 2916  T11I 2358

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 1739Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1729Scale 1729, Ian Ring Music Theory
Scale 1733Scale 1733: Raga Sarasvati, Ian Ring Music TheoryRaga Sarasvati
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 1769Scale 1769: Blues Heptatonic II, Ian Ring Music TheoryBlues Heptatonic II
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
Scale 1705Scale 1705: Raga Manohari, Ian Ring Music TheoryRaga Manohari
Scale 1609Scale 1609: Thyritonic, Ian Ring Music TheoryThyritonic
Scale 1865Scale 1865: Thagimic, Ian Ring Music TheoryThagimic
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 1225Scale 1225: Raga Samudhra Priya, Ian Ring Music TheoryRaga Samudhra Priya
Scale 1481Scale 1481: Zagimic, Ian Ring Music TheoryZagimic
Scale 713Scale 713: Thoptitonic, Ian Ring Music TheoryThoptitonic
Scale 2761Scale 2761: Dagimic, Ian Ring Music TheoryDagimic
Scale 3785Scale 3785: Epagian, Ian Ring Music TheoryEpagian

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.