Friday, 7 February 2020

Musical Scales: Thāṭ and Rāga - I



Musical Scales: Thāṭ  and Rāga - I

Shrikant G. Talageri


[This article is a short(!) tribute to the incomparable greatness of Indian music.
A few points:
1. If the article contains ambiguities or errors, I beg not only the indulgence of the readers but also that the reader should point out these errors in comments. If necessary, they will be corrected.
2. The reader must excuse my arbitrariness or idiosyncracy in the use of general spellings versus phonetic or strictly Sanskritic spellings: thus, I have used rāga rather than rāg, but tāl rather than tāla.
3. In the few places where I have given the URLs of youtube videos, the reader must be prepared for the peculiar habit of the youtube site of often arbitrarily deleting videos from their site - in which case some particular video may not be available]. 

The two basic components of music are melody and rhythm (or, in common Indian parlance sur and tāl). Here in this article we will only discuss some of the basic aspects of the melody or sur aspect of music.

Pitch is the highness or lowness of any sound. Now this is not a technical scientific article in that sense, so it will be assumed that the reader understands what is "high" and "low" in pitch without any scientific explanations provided for understanding the terms, and we will not discuss the scientific technicalities and physics of sound relationships and production, but only the actual notes.

If pitch is represented on a long vertical line so that various points higher or lower on that line depict higher and lower pitches respectively, then there is a certain fixed distance/length on that line which represents what is known as an "octave": if we start with a sound at a certain pitch and mark it as a point on that line, and then keep taking the voice higher and higher, we will reach another point further up where we find what is clearly the same sound at a higher pitch: (technically this is because the second sound is formed out of twice the number of wave cycles per second, measured in hertz, as the first sound, but we will not concern ourselves with these technicalities). This length, or distance between the two points, is what is called an "octave". An octave is a natural division of sound, and a natural phenomenon which is discovered in every civilization which develops a musical culture.

This "octave" can be illustrated with a musical instrument. Take for example the easiest instrument to illustrate the octave: a harmonium. We will find that the keys on a harmonium are in two rows, a lower row of white keys and a higher row of black keys, in the following form:



As we can see, the pattern of keys (taking both rows) is as follows:
white-black-white-black-white,
white-black-white-black-white-black-white.
Let us number the keys 1 to 12. Each key one after the other produces a sound which keeps rising by one note over the previous key.
In the above picture, the first 12 keys represent (at least on the harmonium) what we call the mandra saptak (low octave), the next 12 keys represent the madhya saptak (middle octave) and the last 12 keys represent the tār saptak (high octave).

If we press any two keys at the same time, we will generally hear a discordant medley of two sounds. But if we press key 1 and key 13 (i.e. the first key in the first series of 12, and the first key in the second series of 12) together, we will hear a composite sound in what is called "absolute harmony" because it is actually the same sound at two different pitches: it will be as if we are hearing the same sound moving like a wave between a high pitch and a low pitch. Similarly, if we press any other two keys which are at a distance of 12 (or multiples of the same) from each other (2 and 14, 3 and 15, or even 1 and 25, 2 and 26, etc), the same effect of "one sound at two pitches" will be produced.
The octave is the length or distance, on the "pitch" line, between a given sound and the same sound at a (i.e. at the next) higher pitch, and this distance has been theoretically divided by musicologists into fixed smaller divisions known as "cents", where one octave is 1200 cents.

In ancient India with its unique oral tradition (as shown in the oral transmission of the Rigveda in oral form for millenniums without the slightest change), the various notes were distinguished on the basis of the performer's highly-trained voice and ears, and passed on from guru to śiṣya in that form, and musical instruments were also tuned on that basis, and the notes and the natural scale were based on pure acoustics, leading to very subtle nuances in sounds. In Western music, the octave is divided into 12 equal notes of 100 cents each. This is known as the "tempered scale" because of this uniform equal division into 100 cents. Because of the dominant use of the harmonium in learning Indian classical music, and consequent laxity, modern day Indian music has also generally leveled out the notes into equal divisions.

Apart from the octave, there is another very important distance between two sounds: the fifth. The different notes of the scale within an octave are in fact possible on the basis of this relationship between two sounds: just as we get one sound in the form of an undulating wave between two pitches when we press two keys at a distance of 12 (i.e. at 1200 cents) from one another, and this distance is called an "octave" with the resulting composite sound producing "absolute harmony"; similarly we get another combined sound which is extremely musical when we press two keys at a distance of 7 (i.e. 700 cents) from one another (e.g. key 1 and key 8, key 2 and key 9, etc.), and this distance is known as a "fifth", and the resulting composite sound produces what is described as two different sounds in "perfect harmony".
In the above picture of the harmonium keys, if the first white key represents the starting note called ṣaḍja or SA, the eighth white key represents the ṣaḍja or SA in the higher octave, and the fifth white key represents the pañcam or PA. These two notes SA and PA are considered the two basic and unalterable pillars of the octave or saptak. From these two are produced the other notes.

We will examine this subject under the following heads:
I. The Formation of the Notes of the Octave.
II. The Classification of Parent-Scales or Thāṭs and Meḷas.
III. The Rāgas of Indian Music.
IV. India's Unparalleled Musical Wealth and Contribution to World Music.



I. The Formation of the Notes of the Octave

As we saw:
1. Once the starting-point pitch is chosen, it becomes the note SA, and a sound which is 1200 cents higher than this SA becomes the next SA in a higher pitch, and the distance (of absolute harmony) between the two sounds produces the octave of 1200 cents.
2. The next note, produced by perfect harmony within the octave, is 700 cents higher than SA, and this is called PA.

How do the other sounds of the scale arise?

1. Just as any note is in absolute harmony with the note 1200 cents higher than it, it is therefore also in absolute harmony with the note 1200 cents lower than it. All the three notes are the same note, e.g. SA, in three different octaves (and of course also in all other octaves extending further into higher pitches as well as into lower pitches), since they all represent the starting points of the respective octaves. In the above picture of the keyboard of a harmonium, the first, the eighth and the fifteenth white keys represent SA in the three octaves.
SA is in perfect harmony with PA which is 700 cents higher within the octave: so the fifth, twelfth and nineteenth white keys represent PA in the three octaves.
But if SA is in perfect harmony with the note 700 cents above it, it is also in perfect harmony with the note 700 cents below it. In the above diagram, this note would be represented by the fourth, eleventh and eighteenth white keys (the eighteenth key being 700 cents below the next SA, not shown in the picture). Now, since all the three octaves already have notes named PA, this note, which is 500 cents above the lower SA, has to be given another name: madhyam or MA.
So each SA is in perfect harmony with the PA higher than it, and with the MA lower than it.
So now, within each octave, we have three notes in harmony with each other: SA, MA and PA.

2. In each octave, the MA is in perfect harmony with the higher SA (700 cents above it), and the PA is in perfect harmony with the lower SA (700 cents below it). Therefore MA and PA also are in harmony with each other. The distance between MA and the PA above it is 200 cents: this distance is called a tone (or a second, but this word used here would be confusing, so let us just call it a tone here).
From this, we get the remaining notes within the octave, each separated from the note below it by a tone or 200 cents: 200 cents above SA is ṛṣabh (RE or RI), 200 cents above RE is gāndhār (GA), 200 cents above PA is dhaivat (DHA), and 200 cents above DHA is niṣād (NI).

Thus we get the seven "primary" or shuddh (pure) notes: SA, RE, GA, MA, PA, DHA, and NI, representing the seven white keys (in the above picture of the keyboard) in an octave.
These seven shuddh notes with SA as the starting point (and therefore counted as 0 cents) are SA (0 cents), RE (200 cents), GA (400 cents), MA (500 cents), PA (700 cents), DHA (900 cents), NI (1100 cents). The next higher SA is at 1200 cents.

3. Then what notes do the seven black keys represent?
As we saw, the distance between GA and the MA above it, as well as between NI and the SA above it, is only 100 cents. This distance, half of the tone, is known as a semi-tone.
At the distance of a 100 cents below RE, GA, DHA and NI, we get the four flat (komal) forms of these four sounds: re, ga, dha and ni, represented by the first, second, fourth and fifth black keys in the octave.
At a distance of a 100 cents above MA (and a 100 cents below PA), we get the sharp (tīvra) form of the former sound, i.e. ma, represented by the third black key. [Logically, this could also be called pa, the komal form of PA, but since SA and PA are considered as the two original fixed (acal) notes which have only one form each, this note is called ma].

So the 12 final notes (semi-tones) of the tempered scale octave, as normally used at present, are:

ṣaḍja (SA) -  0 cents.
komal ṛṣabh (re) - 100 cents.
ṛṣabh (RE) - 200 cents.
komal gāndhār (ga) - 300 cents.
gāndhār (GA) - 400 cents.
madhyam (MA) - 500 cents
tīvra madhyam (ma) - 600 cents.
pañcam (PA) - 700 cents
komal dhaivat (dha) - 800 cents.
dhaivat (DHA) - 900 cents.
komal niṣād (ni) - 1000 cents.
niṣād (NI) - 1100 cents.
(upper) ṣaḍja (SA) -  1200 cents.
[Henceforward, for brevity, the notes will be written as S r R g G M m P d D n N S. The notes in the upper octave will be marked with an accent, e.g. Ś, and in the lower octave, if it becomes necessary to specify it, will be underlined, e.g. N.]

The original form of Indian classical music, however, was based on actual acoustics. Hence, the distances between the notes were not "tempered" and equal. The actual distance between a starting note (S) and the note which is in perfect harmony with it (P) is actually 702 cents (if the octave is divided into 1200 cents) rather than 700 cents. This is too extremely tiny a difference for the normal human ear to hear, which is why there is little apparent difference between ancient Indian classical music and its present-day form. But perhaps the (although exaggerated in myths and tales) almost magical effect that music was supposed to produce must have been due to the scale and notes used in ancient music, based on purely natural acoustic relationship between sounds, producing pure acoustic vibrations in the air. The ancient Indian scale had 22 śrutis, also called micro-tones or (less correctly) quarter-tones, a more minute division of sounds within the scale than the 12 semi-tones. Other than the two fixed or acal (अचल) sounds S and P, all the other 10 semi-tones had two subtle variations each, one slightly higher than the other. The use of these subtle variations in different rāgas, or melodies, passed on vocally and orally down the ages, was the secret of the almost magical effect of music.      
   
These 22 śrutis were derived on the basis of the continuing application of the perfect harmony principle, as follows: the starting point S was, of course, at 0 cents. The note higher than S which is in perfect harmony with it is at 702 cents. The next note above this which is in perfect harmony with this note is at 1404 cents, i.e. in the next octave: but this is actually the same note as the note in the earlier octave at 204 cents (i.e. 1200 cents below 1404). The next note above this in perfect harmony with this note is at 906 cents. The next note above this which is in perfect harmony with this note is at 1608 cents, i.e. in the next octave: but this is actually the same note as the note in the earlier octave at 408 cents (i.e. 1200 cents below 1608). Continuing with this pattern, we get the following 22 śrutis:
ṣaḍja (S) -  0 cents.
lower komal ṛṣabh (r1) - 90 cents.
upper komal ṛṣabh (r2) - 114 cents.
lower ṛṣabh (R1) - 180 cents.
upper ṛṣabh (R2) - 204 cents.
lower komal gāndhār (g1) - 294 cents.
upper komal gāndhār (g2) - 318 cents.
lower gāndhār (G1) - 384 cents.
upper gāndhār (G2) - 408 cents.
lower madhyam (M1) - 498 cents.
upper madhyam (M2) - 522 cents.
lower tīvra madhyam (m1) - 588 cents.
upper tīvra madhyam (m2) - 612 cents.
pañcam (P) - 702 cents
lower komal dhaivat (d1) - 792 cents.
upper komal dhaivat (d2) - 816 cents.
lower dhaivat (D1) - 882 cents.
upper dhaivat (D2) - 906 cents.
lower komal niṣād (n1) - 996 cents.
upper komal niṣād (n2) - 1020 cents.
lower niṣād (N1) - 1086 cents.
upper niṣād (N2) - 1110 cents.
(upper) ṣaḍja (Ś) -  1200 cents.

It will be noticed that a full tone (the distance between M1 and P) is actually 204 cents, which is also the distance between S and R2, R2 and G2, G2 and m2, P and D2, and D2 and N2. And likewise between r2 and g2, and so on. The distance between 2 forms of the same note (r1 and r2, etc.) is 24 cents. And between the two closest forms of two distinct notes (S and r1, R2 and g1, etc.) is 90 cents.

As we can see, each of the notes (except S and P, which were fixed), had 2 varieties each, one low (flat) and the other high (sharp), at a distance of 24 cents from each other. Each rāga must have used one particular form of a note, and the different śrutis must also have been used as extra notes to add beauty to each melody. Which of the two varieties to use depended on the rāga: the difference was too subtle for the untrained ear to detect the difference, but the acoustic effect of the two varieties must obviously have been different. Even today, using the tempered scale, the magical effect of the different rāgas on the mood, the intellect, the health and the environment is phenomenal: one can imagine what the effect of the śruti-based rāgas must have been!

All this heritage is now extinct. But while it may not be possible to fully revive śruti-based rāgas, perhaps all may not be lost either. While details of the exact śrutis used in each rāga may not be available, nor the method of śruti-based teaching and singing (with the very subtly trained ears required to recognize such minute variations), some individuals have indeed made attempts to delve into this lost treasure-house: according to a report in the Indian Express (16/5/1999), Avinash Patwardhan, a nephew of the renowned social worker Baba Amte, created a flute which could play the 22 śrutis, and was in the process of developing a harmonium which could also play them. It is not clear what finally came out of all this, but the efforts of this great musicologist deserve general honor and recognition.



II. The Classification of Parent-Scales or Thāṭs and Meḷas

Different melodies use different (now, of course, tempered-scale) notes.

When a person starts learning music, the first thing he has to learn is to sing the scale of shuddh notes (S R G M P D N Ś - Ś N D P M G R S) in āroh (ascending) and avaroh (descending) orders in the correct pitch. This is known in Hindustani (North Indian Classical) music as the Bilāval thāṭ, in Carnatic (South Indian Classical) music as the Dhīraśaṅkarābharaṇam meḷa, and in western classical music as the Major Scale. Listening to this ascending-and-descending singing of the scale will give a familiar feel, since this is the common scale we hear when people learn music in real life or in films.

But there are other scales. To get an idea of the different atmospheres created by different scales, play this above scale 4-5 times continuously, in ascending and descending order, on a harmonium (with the first 8 white keys) to get into the atmosphere of it. Then play another scale, for example Bhairav thāṭ (replacing the second and sixth white keys with the black keys immediately preceding them): S r G M P d N Ś - Ś N d P M G r S. You will immediately notice the difference.
There is one more aspect of melody that is necessary to take note of  in understanding scales and melodies: the aspect of steps or intervals between the two consecutive notes within a scale, in terms of semi-tones. Just as the precise notes in a scale give the scale its special, unique and characteristic feel and atmosphere, the length of the interval between consecutive notes also gives (perhaps more sharply) the particular special atmosphere of a scale. This is particularly so in pentatonic scales, because there are only 5 notes, so the intervals between two consecutive notes can be of many kinds. The intervals are based on the number of semi-tones (each of 100 cents) between two consecutive notes, and are named as follows: 1 (semi-tone), 2 (tone), 3 (minor third), 4 (major third), 5 (fourth), 6 (augmented fourth), 7 (fifth), 8 (minor sixth), 9 (major sixth), 10 (minor seventh), 11 (major seventh), and 12 (octave).
Below, the lists of scales will show both the notes as well as the intervals (in terms of semi-tones) of each scale:


II.A. HEPTATONIC Scales (Thāṭs / Meḷas) of Indian Classical Music:

V. N. Bhatkhande (1875-1935), the great musicologist, in his seminal book "Śrīmallakṣya Saṅgītam" (1909), classified the heptatonic (7 note) scales of Hindustani music into 10 thāṭs: Bilāval, Khamāj, Kāfī, Āsāvarī, Bhairavī, Kalyāṇ, Mārvā, Pūrvī, Toḍī and Bhairav.
[Note: The above are the scales or thāṭs. Actually the rāga Mārvā has no P: rāga Pūriyā-Kalyāṇ has the full scale. Likewise, the rāga Pūrvī also has an additional M].

While Bhatkhande only named 10 thāṭs, actually we also get the following 10 out of 22 possible additional thāṭs: ĀnandBhairav, Paṭdīp, NaṭaBhairav, AhīrBhairav, Kiravāṇī, Cārukeśi, Basantamukhārī, Madhuvantī, Vācaspati, and SarasvatīRanjanī.

As we saw, P is in perfect harmony with the lower S, and M is in perfect harmony with the upper Ś: the note between M and P is conventionally taken to be m (i.e. M sharp or tīvra), but it could equally well be treated as p (P flat or komal): so that m = p.
We can get 16 thāṭs with the combination of notes MP, and 16 with the combination of notes mP. Theoretically, there could be another 16 thāṭs with the combination of notes Mp (i.e. Mm). Hindustani music actually does have at least 4 (out of 16 theoretically possible) such thāṭs: Lalat, AhīrLalat, Pañcam and Meladalan. These 24 scales or thāṭs are as follows:

[In the case of these scales, we will also list them on the basis of the aspect of steps or intervals between the two consecutive notes within a scale. Just as the precise notes in a scale give the scale its special, unique and characteristic feel and atmosphere, the length of the interval between consecutive notes also gives (perhaps more sharply) the particular special atmosphere of a scale, and this is particularly so in pentatonic scales, because there are only 5 notes, so the intervals between two consecutive notes can be of many kinds. The intervals are based on the number of semi-tones (each of 100 cents) between two consecutive notes, and are named as follows: 1 (semi-tone), 2 (tone), 3 (minor third), 4 (major third), 5 (fourth), 6 (augmented fourth), 7 (fifth), 8 (minor sixth), 9 (major sixth), 1000 (minor seventh), 1100 (major seventh), and 1200 (octave).]
 


THĀṬ
NOTES
INTERVALS
NOTES
1. Bilāval
SRGM   PDNŚ
221   2221 
All Śuddha
2. Khamāj
SRGM   PDnŚ
221   2212  
n
3. Kāfī
SRgM   PDnŚ
212   2212  
gn
4. Āsāvarī
SRgM   PdnŚ
212   2122  
gdn
5. Bhairavī
SrgM   PdnŚ
122   2122  
rgdn
6. Kalyāṇ
SRGm   PDNŚ
222   1221 
m
7. Mārvā
SrGm   PDNŚ
132   1221 
rm
8. Pūrvī
SrGm   PdNŚ
132   1131 
rmd
9. Toḍī
Srgm   PdNŚ
123   1131 
rgmd
10. Bhairav
SrGM   PdNŚ
131   2131 
rd
11. ĀnandBhairav    
SrGM   PDNŚ
131   2221 
r
12. Paṭdīp                  
SRgM   PDNŚ
212   2221 
g
13. NaṭaBhairav       
SRGM   PdNŚ
221   2131 
d
14. AhīrBhairav       
SrGM   PDnŚ
131   2212  
rn
15. Kiravāṇī               
SRgM   PdNŚ
212   2131 
gd *
16. Cārukeśi               
SRGM   PdnŚ
221   2122 
dn *
17. Basantamukhārī   
SrGM   PdnŚ
131   2122  
rdn
18. Madhuvantī          
SRgm   PDNŚ
213   1221 
gm
19. Vācaspati              
SRGm   PDnŚ
222   1212 
mn *
20. SarasvatīRanjanī 
SRgm   PDnŚ
213   1212  
gmn
21. Lalat
SrGM   mdNŚ
131   1231 
rmd -P+M
22. AhirLalat            
SrGM   mDnŚ
131   1312 
rmn -P+M
23. Pañcam                
SrGM   mDNŚ
131   1321 
rm -P+M
24. Meladalan             
SrgM   mdnŚ
122   1222  
rgmdn -P+M


As we saw, V. N. Bhatkhande in 1909 analyzed and classified the scales of Hindustani into 10 thāṭs. However, long before him, Venkaṭamakhin, a minister in the court of Thanjavur had analyzed and classified the scales in Carnatic music in his treatise "Caturdaṇḍi-Prakāśikā", written somewhere around 1650.

His classification included not only all the 32 natural heptatonic scales, but 40 more scales based on a novel classification of the notes: a total of 72 meḷas.
He classified the eight notes r, R, g, G, d, D, n, N in such a way that four of them (R, g, D, n) had two different names each, and could, in separate rāgas and meḷas, be treated as two different notes in forming scales:
r = śuddha ṛṣabha -    R1
R = catuśruti ṛṣabha or śuddha gandhāra -    R2 or G1
g = ṣaṭśruti ṛṣabha or sādhāraṇa gandhāra -    R3 or G2
G = antara gandhāra -    G3
d = śuddha dhaivata -    D1
D = catuśruti dhaivata or śuddha niṣāda -    D2 or N1
n = ṣaṭśruti dhaivata or kaiśikī niṣāda -    D3 or N2
N = kākalī niṣāda -    N3

Thus, in a Hindustani heptatonic scale, we can get the combinations rg, rG, Rg, RG, dn, dN, Dn, DN. In the Carnatic scales, Venkatamakhin's classification also brought in four more combinations: rR, gG, dD, nN (treated as R1G1, R3G3, D1N1, D3N3 respectively because of the dual nomenclature).

So the 72 meḷas of Carnatic music are as follows:

               THĀṬ / MEḶA
NOTES
INTERVALS
HINDUSTANI
1. Kanakāṅgī                        
SrRM   PdDŚ
113   2113

2. Ratnāṅgī                           
SrRM   PdnŚ
113   2122

3. Gaṇamūrti                        
SrRM   PdNŚ
113   2131

4. Vanaspati                         
SrRM   PDnŚ
113   2212

5. Mānāvatī                          
SrRM   PDNŚ
113   2221

6. Tānarūpī                          
SrRM   PnNŚ
113   2311

7. Senāvatī                            
SrgM   PdDŚ
122   2113

8. Hanumaṭṭoḍi                     
SrgM   PdnŚ
122   2122 
Bhairavī
9. Dhenukā                           
SrgM   PdNŚ
122   2131

10. Nāṭakapriyā                    
SrgM   PDnŚ
122   2212

11. Kokilapriyā                     
SrgM   PDNŚ
122   2221

12. Rūpāvatī                         
SrgM   PnNŚ
122   2311

13. Gāyakapriyā                   
SrGM   PdDŚ
131   2113

14. Vakulābharaṇam            
SrGM   PdnŚ
131   2122 
Basantamukhārī
15. Māyāmālavagauḷa           
SrGM   PdNŚ
131   2131 
Bhairav
16. Cakravākam                   
SrGM   PDnŚ
131   2212 
AhīrBhairav
17. Sūryakāntam                  
SrGM   PDNŚ
131   2221 
ĀnandBhairav
18. Hāṭakāmbarī                  
SrGM   PnNŚ
131   2311 

19. Jhanakāradhvani            
SRgM   PdDŚ
212   2113

20. Nāṭabhairavī                   
SRgM   PdnŚ
212   2122 
Āsāvarī
21. Kiravāṇī                          
SRgM   PdNŚ
212   2131 
Kiravāṇī
22. Kharaharapriyā              
SRgM   PDnŚ
212   2212 
Kāfī
23. Gaurīmanoharī               
SRgM   PDNŚ
212   2221 
Paṭdīp
24. Varuṇapriyā                   
SRgM   PnNŚ
212   2311

25. Mārurañjanī                     
SRGM   PdDŚ
221   2113

26. Cārukeśī                            
SRGM   PdnŚ
221   2122 
Cārukeśi   
27. Sarasāṅgī                           
SRGM   PdNŚ
221   2131 
NaṭaBhairav
28. Harikāmbhojī                    
SRGM   PDnŚ
221   2212 
Khamāj
29. Dhīraśaṅkarābharaṇam     
SRGM   PDNŚ
221   2221 
Bilāval
30. Nāganandinī                       
SRGM   PnNŚ
221   2311

31. Yāgapriyā                          
SgGM   PdDŚ
311   2113

32. Rāgavardhanī
SgGM   PdnŚ
311   2122

33. Gāṅgeyabhūṣaṇī                    
SgGM   PdNŚ
311   2131

34. Vāgadhīśvarī                
SgGM   PDnŚ
311   2212

35. Śūlinī                                 
SgGM   PDNŚ
311   2221

36. Calanāṭa                            
SgGM   PnNŚ
311   2311

37. Sālagam                             
SrRm   PdDŚ
114   1113

38. Jalārṇavam                        
SrRm   PdnŚ
114   1122

39. Jhālāvarālī                         
SrRm   PdNŚ
114   1131

40. Navanītam                         
SrRm   PDnŚ
114   1212

41. Pāvanī                                
SrRm   PDNŚ
114   1221

42. Raghupriyā                        
SrRm   PnNŚ
114   1311

43. Gavāmbodhi                       
Srgm   PdDŚ
123   1113

44. Bhāvapriyā                         
Srgm   PdnŚ
123   1122

45. Śubhapantuvarāli               
Srgm   PdNŚ
123   1131 
Toḍī
46. Ṣaḍvidhamārgiṇī                
Srgm   PDnŚ
123   1212

47. Suvarṇāṅgī                         
Srgm   PDNŚ
123   1221

48. Divyamaṇi                          
Srgm   PnNŚ
123   1311

49. Dhavalāmbarī                    
SrGm   PdDŚ
132   1113

50. Nāmanārāyaṇī                   
SrGm   PdnŚ
132   1122

51. Kāmavardhanī                   
SrGm   PdNŚ
132   1131 
Pūrvī
52. Rāmapriyā                         
SrGm   PDnŚ
132   1212

53. Gamanaśrama                    
SrGm   PDNŚ
132   1221 
Mārvā
54. Viśvambarī                         
SrGm   PnNŚ
132   1311

55. Śyāmalāṅgī                         
SRgm   PdDŚ
213   1113

56. Ṣaṇmukhapriyā                  
SRgm   PdnŚ
213   1122

57. Siṁhendramadhyamam      
SRgm   PdNŚ
213   1131

58. Hemavatī                            
SRgm   PDnŚ
213   1212 
SarasvatīRanjanī
59. Dharmavatī                         
SRgm   PDNŚ
213   1221 
Madhuvantī
60. Nītimatī                               
SRgm   PnNŚ
213   1311

61. Kāntāmaṇi                          
SRGm   PdDŚ
222   1113

62. Ṛṣabhapriyā                        
SRGm   PdnŚ
222   1122

63. Latāṅgī                                
SRGm   PdNŚ
222   1131

64. Vācaspati                             
SRGm   PDnŚ
222   1212 
Vācaspati   
65. Mecakalyāṇī                        
SRGm   PDNŚ
222   1221 
Kalyāṇ
66. Citrāmbarī                          
SRGm   PnNŚ
222   1311

67. Sucaritrā                             
SgGm   PdDŚ
312   1113

68. Jyotisvarūpiṇī                     
SgGm   PdnŚ
312   1122

69. DhātuvarDhāni                      
SgGm   PdNŚ
312   1131

70. Nāsikabhūṣaṇī                     
SgGm   PDnŚ
312   1212

71. Kosalam                              
SgGm   PDNŚ
312   1221

72. Rasikapriyā                         
SgGm   PnNŚ
312   1311



 
These meḷas, like the thāṭs of Hindustani music, are usually parent-scales (or janaka rāgas) as well as rāgas to be sung and played.

Now let us see the same above 76 heptatonic thāṭs/meḷas (including the 4 Mm scales) as per intervals (numbered as per the meḷa list above):

1. Intervals: 11 22222 (3 Interval Patterns, 13 scales):
THĀṬ / MEḶA
NOTES
INTERVALS
2222211
11. Kokilapriyā                      
SrgM   PDNŚ
122   2221
62. Ṛṣabhapriyā                     
SRGm   PdnŚ
222   1122
2222121
10. Nāṭakapriyā                     
SrgM   PDnŚ
122   2212
23. Gaurīmanoharī   (Paṭdīp)               
SRgM   PDNŚ
212   2221
26. Cārukeśī                          
SRGM   PdnŚ
221   2122
64. Vācaspati                         
SRGm   PDnŚ
222   1212
2221221
8. Hanumaṭṭoḍi  (Bhairavī)                        
SrgM   PdnŚ
122   2122
20. Nāṭabhairavī  (Āsāvarī )                    
SRgM   PdnŚ
212   2122
22. Kharaharapriyā  (Kāfī )               
SRgM   PDnŚ
212   2212
28. Harikāmbhojī  (Khamāj)                  
SRGM   PDnŚ
221   2212
29. Dhīraśaṅkarābharaṇam  (Bilāval) 
SRGM   PDNŚ
221   2221
65. Mecakalyāṇī  (Kalyāṇ)                     
SRGm   PDNŚ
222   1221
Mm. Meladalan                      
SrgM   mdnŚ
122   1222


2. Intervals: 111 222 3 (15 Interval Patterns, 33 scales):
THĀṬ / MEḶA
NOTES
INTERVALS
3111222:
12. Rūpāvatī                          
SrgM   PnNŚ
122   2311
3112122
24. Varuṇapriyā                    
SRgM   PnNŚ
212   2311
32. Rāgavardhanī
SgGM   PdnŚ
311   2122
3112212
30. Nāganandinī                    
SRGM   PnNŚ
221   2311
34. Vāgadhīśvarī                   
SgGM   PDnŚ
311   2212
44. Bhāvapriyā                       
Srgm   PdnŚ
123   1122
3112221
9. Dhenukā                             
SrgM   PdNŚ
122   2131
35. Śūlinī                                
SgGM   PDNŚ
311   2221
56. Ṣaṇmukhapriyā                 
SRgm   PdnŚ
213   1122
66. Citrāmbarī                       
SRGm   PnNŚ
222   1311
3121122                    
68. Jyotisvarūpiṇī
SgGm   PdnŚ
312   1122
3121212
46. Ṣaḍvidhamārgiṇī                
Srgm   PDnŚ
123   1212
70. Nāsikabhūṣaṇī                   
SgGm   PDnŚ
312   1212
3121221
14. Vakulābharaṇam  (Basantamukhārī )               
SrGM   PdnŚ
131   2122
21. Kiravāṇī                             
SRgM   PdNŚ
212   2131
58. Hemavatī  (SarasvatīRañjanī)                            
SRgm   PDnŚ
213   1212
71. Kosalam                             
SgGm   PDNŚ
312   1221
3211221
50. Nāmanārāyaṇī                    
SrGm   PdnŚ
132   1122
3122112
47. Suvarṇāṅgī                         
Srgm   PDNŚ
123   1221
3122121
16. Cakravākam  (AhīrBhairav)                       
SrGM   PDnŚ
131   2212
27. Sarasāṅgī  (NaṭaBhairav)                            
SRGM   PdNŚ
221   2131
59. Dharmavatī  (Madhuvantī)                         
SRgm   PDNŚ
213   1221
3122211
7. Senāvatī                      
SrgM   PdDŚ
122   2113
17. Sūryakāntam  (ĀnandBhairav)                                  
SrGM   PDNŚ
131   2221
63. Latāṅgī                               
SRGm   PdNŚ
222   1131
3212121
52. Rāmapriyā                          
SrGm   PDnŚ
132   1212
3212211
2. Ratnāṅgī                               
SrRM   PdnŚ
113   2122
19. Jhanakāradhvani                
SRgM   PdDŚ
212   2113
53. Gamanaśrama  (Mārvā)                    
SrGm   PDNŚ
132   1221
3221211
4. Vanaspati                             
SrRM   PDnŚ
113   2212
25. Mārurañjanī                      
SRGM   PdDŚ
221   2113
3222111
5. Mānāvatī                              
SrRM   PDNŚ
113   2221
61. Kāntāmaṇi                          
SRGm   PdDŚ
222   1113


3. Intervals: 1111 2 33 (12 Interval Patterns, 24 scales):
THĀṬ / MEḶA
NOTES
INTERVALS
2111313
49. Dhavalāmbarī                       
SrGm   PdDŚ
132   1113
2111331
67. Sucaritrā                               
SgGm   PdDŚ
312   1113
2113113
1. Kanakāṅgī                               
SrRM   PdDŚ
113   2113
51. Kāmavardhanī  (Pūrvī)                       
SrGm   PdNŚ
132   1131
Mm. Pañcam                               
SrGM   mDNŚ
131   1321
2113131
13. Gāyakapriyā                           
SrGM   PdDŚ
131   2113
69. Dhātuvardhanī                        
SgGm   PdNŚ
312   1131
2113311
31. Yāgapriyā                               
SgGM   PdDŚ
311   2113
2131113
3. Gaṇamūrti                                
SrRM   PdNŚ
113   2131
54. Viśvambarī                       
SrGm   PnNŚ
132   1311
55. Śyāmalāṅgī                              
SRgm   PdDŚ
213   1113
2131131
15. Māyāmālavagauḷa  (Bhairav)                    
SrGM   PdNŚ
131   2131
57. Siṁhendramadhyamam           
SRgm   PdNŚ
213   1131
72. Rasikapriyā                             
SgGm   PnNŚ
312   1311
Mm. AhirLalat                            
SrGM   mDnŚ
131   1312
2131311
33. Gāṅgeyabhūṣaṇī                      
SgGM   PdNŚ
311   2131
60. Nītimatī                                    
SRgm   PnNŚ
213   1311
2311113
6. Tānarūpī                                    
SrRM   PnNŚ
113   2311
2311131
18. Hāṭakāmbarī                            
SrGM   PnNŚ
131   2311
43. Gavāmbodhi                              
Srgm   PdDŚ
123   1113
2311311
36. Calanāṭa                                   
SgGM   PnNŚ
311   2311
45. Śubhapantuvarāli  (Toḍī)                      
Srgm   PdNŚ
123   1131
Mm. Lalat
SrGM   mdNŚ
131   1231
2313111
48. Divyamaṇi                                 
Srgm   PnNŚ
123   1311


 
4. Intervals: 1111 22 4 (3 Interval Patterns, 3 scales):
            THĀṬ / MEḶA
NOTES
INTERVALS
4112211
38. Jalārṇavam                              
SrRm   PdnŚ
114   1122
4121211
40. Navanītam                               
SrRm   PDnŚ
114   1212
4122111
41. Pāvanī                                     
SrRm   PDNŚ
114   1221


5. Intervals: 11111 3 4 (3 Interval Patterns, 3 scales):
            THĀṬ / MEḶA
NOTES
INTERVALS
4111311
37. Sālagam                                    
SrRm   PdDŚ
114   1113
4113111
39. Jhālāvarālī                                
SrRm   PdNŚ
114   1131
4131111
42. Raghupriyā                               
SrRm   PnNŚ
114   1311


So far, we have seen scales with 7 notes (i.e. heptatonic scales). It must be noted that the above are thāṭs (parent-scales) as distinct from rāgas (melodies or melodic-scales): there can be many rāgas within each thāṭ (all using basically the same notes, but completely different from each other in the various different characteristics that make up a rāga, which we will see later in more detail). A rāga is the actual melody, a thāṭ is the full set of all the notes used in the rāga. Usually, a thāṭ has the same name as a prominent rāga from within that thāṭ.
A rāga may have the full set of the 7 notes of a thāṭ in the āroh (ascending form) and have a note or two missing in the avaroh (descending form), or vice versa. Or there may be certain different notes missing in the āroh or avaroh, while having, both (āroh and avaroh) put together, all the 7 notes of the thāṭ. In all these cases, the rāga is still clearly identifiable with that thāṭ.

The complication in classification arises when we examine rāgas with 6 notes (hexatonic scales) and rāgas with 5 notes (pentatonic scales). This leads to confusion if one wants to classify them within heptatonic thāṭs: for example both the pentatonic rāgas Deskār and Bhūp have the same 5 notes SRGPDŚ (with M and N missing).
If we compulsorily classify these rāgas into the 10-heptonic-thāṭ paradigm, do we classify them as belonging to the Bilāval thāṭ (assuming that the missing M and N are shuddh notes), to the Kalyāṇ thāṭ (assuming that the missing M and N are tīvra and shuddh notes respectively), to the Khamāj thāṭ (assuming that the missing M and N are shuddh and komal notes respectively), or to the Vācaspati thāṭ (assuming that the missing M and N are tīvra and komal notes respectively)?
In common practice, due to the modern convention of force-fitting all rāgas into the artificial 10-heptatonic-thāṭs paradigm, Deskār  is classified as belonging to the Bilāval thāṭ (assuming that the missing M and N are shuddh notes), and Bhūp as belonging to the Kalyāṇ thāṭ (assuming that the missing M and N are tīvra and shuddh notes respectively)!
Generally, in such cases, the thāṭ is arbitrarily decided, not on the basis of the set of notes in it, but on the basis of other characteristics: as already pointed out, each thāṭ is named after a certain typical rāga as well: thus Bilāval, Kalyāṇ, etc. are thāṭs as well as rāgas with special characteristics. So the rāga under consideration, e.g. Deskār , is classified on the assumption that its aṅga (characteristic features) more resembles the aṅga of rāga Bilāval, and that of Bhūp, which has the exactly same notes, more resembles the aṅga of rāga Kalyāṇ. Clearly, all this has nothing really to do with the classification of the set of notes in the rāga.
This force-fitting is therefore not correct, and so here we are classifying it as an independent pentatonic thāṭ Bhūp, containing already two different rāgas with the same five notes.

Here, therefore, we will note the nature of hexatonic and pentatonic melodies or melodic structures (rāgas), as independent scales (thāṭs). Usually, these scales represent both the thāṭ and rāga. Here, on the basis of the notes in both the āroh and avaroh combined, we are taking into count as thāṭs only rāgas which do not ordinarily have both the forms of any note (i.e. both r and R, or both g and G, etc), except three hexatonic scales (there may be more not counted by us) belonging to the rR-gG-dD-nN meḷa variety of southern scales.




II.B. HEXATONIC Scales of Indian Classical Music:

1. Intervals: 222222 (1 Interval Pattern, 1 scale):
SCALE
NOTES
INTERVALS
222222
Sehrā                              
SRGm   dnŚ
222   222


2. Intervals: 2222 1 3 (3 Interval Patterns, 14 scales):
                  SCALE
NOTES
INTERVALS
322122
GopikāBasant               
SgMP   dnŚ
322   122
GorakhKalyāṇ             
SRMP   DnŚ
232   212
Śaṅkarā                         
SRGP   DNŚ
223   221
RṣabhīMālkauns           
SrgM   dnŚ
122   322
NāyakīKānaḍā              
SRgM   PnŚ
212   232
Naṭanārāyāṇī                
SRGM   PDŚ
221   223
322212
Manoharī
SgMP   DnŚ
322   212
Nāgagāndhārī
SRMP   DNŚ
232   221
Bhavānī
Srgm   dnŚ
123   222
SampūrṇaMālkauns     
SRgM   dnŚ
212   322
Śivakāmbhojī 
SRGM   PnŚ 
221   232
YamunāKalyāṇī           
SRGm   PDŚ
222   123
321222
Navamanoharī 
SRMP   dnŚ
232   122
Mṛganandana
SRGm   DNŚ
222   321


3. Intervals: 222 11 4 (9 Interval Patterns, 19 scales):
                  SCALE
NOTES
INTERVALS
412221
HariNaṭa
SGMP   DNŚ
412   221
Trimūrti
SRgP   dnŚ
214   122
Ravicandrikā               
SRGM   DnŚ
221   412
Ratnakāntī
SRGm   PNŚ   
222   141
ŚuddhaSimantinī 
SrgM   PdŚ 
122   214
412212
Jujahuli                       
SGMP   DnŚ
412   212
Niṣādī
SRmP   DNŚ
241   221
Kaśyapī
SrgP   dnŚ
124   122
Śrīrañjanī                    
SRgM   DnŚ
212   412
Vilāsinī
SRGM   PNŚ
221   241
412122
Sarasvatī
SRmP   DnŚ 
241   212 
411222
Jaganmohan 
SRmP   dnŚ  
241   122 
421221
Pheṇādyutī 
SrMP   dnŚ 
142  122 
Mānavī 
SRgP   DnŚ 
214   212 
Hamsavādinī 
SRGM   DNŚ 
221   421  
421212
Salagavarāli
SrgP   DnŚ
124   212
421122
Jyoti 
SGmP   dnŚ 
421   122
422121
Rasāvalī 
SrMP   DnŚ 
142   212 
422211
Jīvantikā 
SrMP   DNŚ 
142   221 




4. Intervals: 22 11 33 (10 Interval Patterns, 16 scales):
SCALE
NOTES
INTERVALS
112323
GujarīToḍī
Srgm   dNŚ
123   231
Vasantavarālī              
SRMP   nNŚ
232   311   
113232
Pūriyā                         
SrGm   DNŚ
132   321
Nīleśvarī 
SgMm   PnŚ  
321   132  
113322
Rasachandra              
SRGM   mDŚ
221   133   
121233
KaiśikiRañjanī            
SRgM   dNŚ
212   331 
121332
Malayamārutam              
SrGP   DnŚ
133   212
Rañjanī
SRgm   DNŚ  
213   321 
122133
Sarasānana 
SRGM   dNŚ 
221   331
131223
Latikā                              
SRGP   dNŚ
223   131
Rāgamālinī 
SrGM   PDŚ  
131   223 
131232
Vijayanāgarī                     
SRgm   PDŚ
213   123
131322
Gopikātilakam 
SRgm   PnŚ
213   132
132132
Jaikauns                           
SgMm   DNŚ
321   321   
Indupriyā  
SrGm   PnŚ 
132   132 
Nīlāṅgī 
SRgm   dDŚ 
213   213 


5. Intervals: 2 111 3 4 (9 Interval Patterns, 14 scales):
SCALE
NOTES
INTERVALS
211314
Indumatī                          
SGmP   dNŚ
421   131
ŚuddhaSohanī                 
SrGM   DNŚ
131   421
211413
Dhavalāṅgam 
SrGm   PdŚ  
132   114
213114
Jogia                                 
SrMP   dNŚ
142   131
Vijayavasanta   
SGmP   nNŚ 
421   311
Śyāmalam 
SRgm   PdŚ 
213   114
213141
Cakravāka
SrGM   DnŚ
131   412
Amarasenapriyā                             
SRgm   PNŚ
213   141
214113
Mandhārī                          
SrGm   PNŚ
132   141
214131
BaṅgālBhairav              
SrGM   PdŚ
131   214
231141
Candrajyoti                       
SrRm   PDŚ
114   123
231411
Śrīvantī
Srgm   PNŚ
123   141
241131
CandraKalyāṇ                  
SRmP   dNŚ
241   131
Gauḷa                          
SrGM   PNŚ
131   241



6. Intervals: 111 333 (3 Interval Pattern, 4 scales):
SCALE
NOTES
INTERVALS
331131
Kalagaḍa   
SrGP   dDŚ
133   113
331311
Triveṇī   
SrGP   dNŚ
133   131
Gaurīkriyā   
SgmP   nNŚ
331   311
313131
Devamuni  
SgGP   dNŚ
313   131


[The rest of the article is continued in part II]

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