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Scale 1997: "Raga Cintamani"

Scale 1997: Raga Cintamani, 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 Cintamani
Zeitler
Staryllic

Analysis

Cardinality8 (octatonic)
Pitch Class Set{0,2,3,6,7,8,9,10}
Forte Number8-Z15
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 1661
Hemitonia5 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes7
Prime?no
prime: 863
Deep Scaleno
Interval Vector555553
Interval Spectrump5m5n5s5d5t3
Distribution Spectra<1> = {1,2,3}
<2> = {2,3,4}
<3> = {3,4,5,6}
<4> = {4,5,6,7,8}
<5> = {6,7,8,9}
<6> = {8,9,10}
<7> = {9,10,11}
Spectra Variation2.25
Maximally Evenno
Maximal Area Setno
Interior Area2.616
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{2,6,9}342
D♯{3,7,10}341.91
G♯{8,0,3}242.27
Minor Triadscm{0,3,7}342
d♯m{3,6,10}441.82
gm{7,10,2}242.18
Augmented TriadsD+{2,6,10}341.91
Diminished Triads{0,3,6}242.09
d♯°{3,6,9}242.09
f♯°{6,9,0}242.27
{9,0,3}242.36
Parsimonious Voice Leading Between Common Triads of Scale 1997. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m D# D# cm->D# G# G# cm->G# D D D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° D+->d#m gm gm D+->gm d#°->d#m d#m->D# D#->gm f#°->a° G#->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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1997 can be rotated to make 7 other scales. The 1st mode is itself.

2nd mode:
Scale 1523
Scale 1523: Zothyllic, Ian Ring Music TheoryZothyllic
3rd mode:
Scale 2809
Scale 2809: Gythyllic, Ian Ring Music TheoryGythyllic
4th mode:
Scale 863
Scale 863: Pyryllic, Ian Ring Music TheoryPyryllicThis is the prime mode
5th mode:
Scale 2479
Scale 2479: Harmonic and Neapolitan Minor Mixed, Ian Ring Music TheoryHarmonic and Neapolitan Minor Mixed
6th mode:
Scale 3287
Scale 3287: Phrathyllic, Ian Ring Music TheoryPhrathyllic
7th mode:
Scale 3691
Scale 3691: Badyllic, Ian Ring Music TheoryBadyllic
8th mode:
Scale 3893
Scale 3893: Phrocryllic, Ian Ring Music TheoryPhrocryllic

Prime

The prime form of this scale is Scale 863

Scale 863Scale 863: Pyryllic, Ian Ring Music TheoryPyryllic

Complement

The octatonic modal family [1997, 1523, 2809, 863, 2479, 3287, 3691, 3893] (Forte: 8-Z15) is the complement of the tetratonic modal family [83, 773, 1217, 2089] (Forte: 4-Z15)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1997 is 1661

Scale 1661Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1997 is chiral, and its enantiomorph is scale 1661

Scale 1661Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic

Transformations:

T0 1997  T0I 1661
T1 3994  T1I 3322
T2 3893  T2I 2549
T3 3691  T3I 1003
T4 3287  T4I 2006
T5 2479  T5I 4012
T6 863  T6I 3929
T7 1726  T7I 3763
T8 3452  T8I 3431
T9 2809  T9I 2767
T10 1523  T10I 1439
T11 3046  T11I 2878

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 1999Scale 1999: Zacrygic, Ian Ring Music TheoryZacrygic
Scale 1993Scale 1993: Katoptian, Ian Ring Music TheoryKatoptian
Scale 1995Scale 1995: Aeolacryllic, Ian Ring Music TheoryAeolacryllic
Scale 1989Scale 1989: Dydian, Ian Ring Music TheoryDydian
Scale 2005Scale 2005: Gygyllic, Ian Ring Music TheoryGygyllic
Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic
Scale 2029Scale 2029: Kiourdi, Ian Ring Music TheoryKiourdi
Scale 1933Scale 1933: Mocrian, Ian Ring Music TheoryMocrian
Scale 1965Scale 1965: Raga Mukhari, Ian Ring Music TheoryRaga Mukhari
Scale 1869Scale 1869: Katyrian, Ian Ring Music TheoryKatyrian
Scale 1741Scale 1741: Lydian Diminished, Ian Ring Music TheoryLydian Diminished
Scale 1485Scale 1485: Minor Romani, Ian Ring Music TheoryMinor Romani
Scale 973Scale 973: Mela Syamalangi, Ian Ring Music TheoryMela Syamalangi
Scale 3021Scale 3021: Stodyllic, Ian Ring Music TheoryStodyllic
Scale 4045Scale 4045: Gyptygic, Ian Ring Music TheoryGyptygic

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.