The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1681: "Raga Valaji"

Scale 1681: Raga Valaji, 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 Valaji
Zeitler
Ionaditonic

Analysis

Cardinality5 (pentatonic)
Pitch Class Set{0,4,7,9,10}
Forte Number5-25
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 301
Hemitonia1 (unhemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections3
Modes4
Prime?no
prime: 301
Deep Scaleno
Interval Vector123121
Interval Spectrump2mn3s2dt
Distribution Spectra<1> = {1,2,3,4}
<2> = {3,5,6,7}
<3> = {5,6,7,9}
<4> = {8,9,10,11}
Spectra Variation2.8
Maximally Evenno
Maximal Area Setno
Interior Area2.049
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}210.67
Minor Triadsam{9,0,4}121
Diminished Triads{4,7,10}121
Parsimonious Voice Leading Between Common Triads of Scale 1681. Created by Ian Ring ©2019 C C C->e° am am C->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.

Diameter2
Radius1
Self-Centeredno
Central VerticesC
Peripheral Verticese°, am

Modes

Modes are the rotational transformation of this scale. Scale 1681 can be rotated to make 4 other scales. The 1st mode is itself.

2nd mode:
Scale 361
Scale 361: Bocritonic, Ian Ring Music TheoryBocritonic
3rd mode:
Scale 557
Scale 557: Raga Abhogi, Ian Ring Music TheoryRaga Abhogi
4th mode:
Scale 1163
Scale 1163: Raga Rukmangi, Ian Ring Music TheoryRaga Rukmangi
5th mode:
Scale 2629
Scale 2629: Raga Shubravarni, Ian Ring Music TheoryRaga Shubravarni

Prime

The prime form of this scale is Scale 301

Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari

Complement

The pentatonic modal family [1681, 361, 557, 1163, 2629] (Forte: 5-25) is the complement of the heptatonic modal family [733, 1207, 1769, 1867, 2651, 2981, 3373] (Forte: 7-25)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1681 is 301

Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1681 is chiral, and its enantiomorph is scale 301

Scale 301Scale 301: Raga Audav Tukhari, Ian Ring Music TheoryRaga Audav Tukhari

Transformations:

T0 1681  T0I 301
T1 3362  T1I 602
T2 2629  T2I 1204
T3 1163  T3I 2408
T4 2326  T4I 721
T5 557  T5I 1442
T6 1114  T6I 2884
T7 2228  T7I 1673
T8 361  T8I 3346
T9 722  T9I 2597
T10 1444  T10I 1099
T11 2888  T11I 2198

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 1683Scale 1683: Raga Malayamarutam, Ian Ring Music TheoryRaga Malayamarutam
Scale 1685Scale 1685: Zeracrimic, Ian Ring Music TheoryZeracrimic
Scale 1689Scale 1689: Lorimic, Ian Ring Music TheoryLorimic
Scale 1665Scale 1665, Ian Ring Music Theory
Scale 1673Scale 1673: Thocritonic, Ian Ring Music TheoryThocritonic
Scale 1697Scale 1697: Raga Kuntvarali, Ian Ring Music TheoryRaga Kuntvarali
Scale 1713Scale 1713: Raga Khamas, Ian Ring Music TheoryRaga Khamas
Scale 1745Scale 1745: Raga Vutari, Ian Ring Music TheoryRaga Vutari
Scale 1553Scale 1553, Ian Ring Music Theory
Scale 1617Scale 1617: Phronitonic, Ian Ring Music TheoryPhronitonic
Scale 1809Scale 1809: Ranitonic, Ian Ring Music TheoryRanitonic
Scale 1937Scale 1937: Galimic, Ian Ring Music TheoryGalimic
Scale 1169Scale 1169: Raga Mahathi, Ian Ring Music TheoryRaga Mahathi
Scale 1425Scale 1425: Ryphitonic, Ian Ring Music TheoryRyphitonic
Scale 657Scale 657: Epathic, Ian Ring Music TheoryEpathic
Scale 2705Scale 2705: Raga Mamata, Ian Ring Music TheoryRaga Mamata
Scale 3729Scale 3729: Starimic, Ian Ring Music TheoryStarimic

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.