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Scale 181: "Raga Budhamanohari"

Scale 181: Raga Budhamanohari, 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 Budhamanohari

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,2,4,5,7}
Forte Number5-23
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1441
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections2
Modes4
Prime?no
prime: 173
Deep Scaleno
Interval Vector132130
Interval Spectrump3mn2s3d
Distribution Spectra<1> = {1,2,5}
<2> = {3,4,7}
<3> = {5,8,9}
<4> = {7,10,11}
Spectra Variation3.2
Maximally Evenno
Maximal Area Setno
Interior Area1.799
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}000

Since there is only one common triad in this scale, there are no opportunities for parsimonious voice leading between triads.

Modes

Modes are the rotational transformation of this scale. Scale 181 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 1069
Scale 1069, Ian Ring Music Theory
3rd mode:
Scale 1291
Scale 1291, Ian Ring Music Theory
4th mode:
Scale 2693
Scale 2693, Ian Ring Music Theory
5th mode:
Scale 1697
Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali

Prime

The prime form of this scale is Scale 173

Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita

Complement

The pentatonic modal family [181, 1069, 1291, 2693, 1697] (Forte: 5-23) is the complement of the heptatonic modal family [701, 1199, 1513, 1957, 2647, 3371, 3733] (Forte: 7-23)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 181 is 1441

Scale 1441Scale 1441, Ian Ring Music Theory

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 181 is chiral, and its enantiomorph is scale 1441

Scale 1441Scale 1441, Ian Ring Music Theory

Transformations:

T0 181  T0I 1441
T1 362  T1I 2882
T2 724  T2I 1669
T3 1448  T3I 3338
T4 2896  T4I 2581
T5 1697  T5I 1067
T6 3394  T6I 2134
T7 2693  T7I 173
T8 1291  T8I 346
T9 2582  T9I 692
T10 1069  T10I 1384
T11 2138  T11I 2768

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 183Scale 183, Ian Ring Music Theory
Scale 177Scale 177, Ian Ring Music Theory
Scale 179Scale 179, Ian Ring Music Theory
Scale 185Scale 185, Ian Ring Music Theory
Scale 189Scale 189, Ian Ring Music Theory
Scale 165Scale 165: Genus Primum, Ian Ring Music TheoryGenus Primum
Scale 173Scale 173: Raga Purnalalita, Ian Ring Music TheoryRaga Purnalalita
Scale 149Scale 149: Eskimo Tetratonic, Ian Ring Music TheoryEskimo Tetratonic
Scale 213Scale 213, Ian Ring Music Theory
Scale 245Scale 245: Raga Dipak, Ian Ring Music TheoryRaga Dipak
Scale 53Scale 53, Ian Ring Music Theory
Scale 117Scale 117, Ian Ring Music Theory
Scale 309Scale 309: Palitonic, Ian Ring Music TheoryPalitonic
Scale 437Scale 437: Ronimic, Ian Ring Music TheoryRonimic
Scale 693Scale 693: Arezzo Major Diatonic Hexachord, Ian Ring Music TheoryArezzo Major Diatonic Hexachord
Scale 1205Scale 1205: Raga Siva Kambhoji, Ian Ring Music TheoryRaga Siva Kambhoji
Scale 2229Scale 2229: Raga Nalinakanti, Ian Ring Music TheoryRaga Nalinakanti

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.