Musical Notes: Is
Madhyam “Śuddha and Tīvra” or “Komal and Śuddha”?
Shrikant G. Talageri
In every field of study, there are certain conventional ways of representing the data. When presumptuous scholars decide they know better, and “correct” the data by processes of renaming the categories or the identifying marks of the data, they only end up muddying the waters to a great extent.
In studying the Rigveda, one irritant for me was the tendency of some western scholars to use their own discretion in the numbering of the hymns in Book 8:
Book 8 has 103 hymns. Of these 103 hymns, it is a well known fact that hymns 49-59, collectively called the Vālakhilya hymns, are later than the rest of Book 8, and were inserted into the middle of the book after hymn 48 before the book was given its final form.
Now, that these hymns were inserted later is certainly an important point to keep in mind when analyzing the Rigveda. But certain Indologists went a few steps further in presumptuousness, and decided to change the numbering of the hymns in Book 8 to incorporate the fact the hymns 49-59 are inserted hymns. So, in their translations of the Rigveda, and citations from the text, they removed the 11 Vālakhilya hymns (numbered 49-59) from the middle of Book 8 and placed them separately as an appendix after Book 8, numbering them as Vālakhilya 1-11, and changed the numbers of hymns VIII.60-103 to VIII.49-92.
The amount of problem that this created for people quoting or citing references from the Rigveda from these hymns (VIII.49-103), when the Indologists being cited were these presumptuous ones, can only be imagined. Whenever I cited Griffith for example, one of these presumptuous Indologists, in respect of any of these hymns, I ended up giving wrong hymn numbers. I tried to be very careful and meticulous, but, when citing hundreds of verses, I ended up inadvertently giving many wrong hymn numbers, for example, VIII.64.5 (as per Griffith) instead of VIII.75.5 (as per the actual Rigveda), and so on, without noticing the mistakes until much later if at all.
Likewise, when citing E.W.Hopkins, similar mistakes took place. If I cited Hopkins to the effect that the word vasavāna occurs in VIII.88.8 − without noticing that it was a post-49 hymn from Book 8 and that I should therefore cross-check – it became a wrong citation because the actual reference is VIII.99.8!
Hopkins later realized the confusion that his “corrected” numbering was causing, and restored the original numbering as per the actual Rigveda in his subsequent articles/papers: so that his earlier papers and later papers give different hymn numbers for the same reference. Naturally, this dual numbering only compounded the confusion since the same reference was given different numbers in different articles/papers.
I cannot explain the amount of inconvenience I encountered while doing my analysis of the Rigveda because of top-grade and responsible, and otherwise extremely great, scholars making presumptuous and unwarranted changes in established conventions of identifying data. The problem is firstly that the “corrected” numbering causes confusion between the citations of these presumptuous scholars and the original verses they are citing; and this problem is compounded by the fact that when studying the writings of different scholars who have analyzed the Rigveda, some using the correct original numbering and some using this presumptuously “corrected” numbering, there is even more confusion.
Now I am studying musical scales in order to identify Hindi and Marathi songs in different rāgas. And, again, I find myself up against presumptuous scholars making presumptuous and unwarranted changes in established conventions of identifying data: in this case, the data concerned is musical notes.
I have already written a very detailed article on the subject (which had to be uploaded in two parts):
https://talageri.blogspot.com/2020/02/musical-scales-that-and-raga-i_48.html
https://talageri.blogspot.com/2020/02/musical-scales-that-and-raga-ii_88.html
There are conventionally seven tones and twelve semitones.
In Indian convention, the seven tones are as follows:
Seven Tones: Ṣaḍja, Ṛṣabh, Gandhār, Madhyam, Pañcam, Dhaivat, Niṣād.
In short, they are known as Sa, Re, Ga, Ma, Pa, Dha, Ni. or S R G M P D N.
Of these Sa and Pa are known as achal swaras since they are accepted as having only one form each.
The other five tones have two forms each.
In the case of Re, Ga, Dha and Ni, the upper semitone is considered pure or Śuddha, and the lower semitone is considered flat or Komal.
Thus, we get r and R, g and G, d and D, n and N.
In the case of ma, however, the lower tone is considered pure or śuddha, and the upper semitone is considered sharp or tīvra.
So we get the full set of twelve semitones (capitals representing śuddha notes):
S, r, R, g, G, M, m, P, d, D, n, N.
Many people do not seem to understand the logic by which the upper note is always considered to be the pure note in the case of R, G, D, N, but in the case of M alone, it is the lower note which is considered to be the pure note. And therefore, they choose to correct what they think is an illogical convention by interchanging the symbols for M and m so that now M also has a pure upper note!
So the twelve semitones are represented by these scholars as follows:
S, r, R, g, G, m, M, P, d, D, n, N.
And this is done by many scholars who have done really incredibly great work on the subject of Indian musical scales, and a search on the internet will demonstrate the chaos this creates wherever the madhyam swaras are concerned. For example, George Howlett, who has this really great and detailed site on rāgas:
https://ragajunglism.org/ragas/
Two of the most basic scales or thāṭ-rāgas in Indian music are Bilawal and Kalyan/Yaman, which should be represented as follows:
BILAWAL: S R G M P D N S.
YAMAN: S R G m P D N S.
Howlett however represents them as follows:
BILAWAL: S R G m P D N S.
YAMAN: S R G M P D N S
https://ragajunglism.org/ragas/bilawal/
https://ragajunglism.org/ragas/yaman/
In Indian tradition, a particularly “cute” child (and every child is particularly “cute” for its parents) is protected from the evil eyes of others by applying a spot or two of black kajal on his cheeks. Are the great works of these scholars being sought to be protected from evil eyes by making these presumptuous distortions in presentation and causing distortions in otherwise splendid scholarly works?
The senselessness of this kind of presumptuous “correction” can be understood if we speculate as to what would have been the result of Griffith and others applying to the whole of the Rigveda the same principle that they applied to the hymns of Book 8:
All scholars are agreed that of the ten books in the Rigveda, six, Books 2-7 are older than the other four, Books, 1,8,9,10 [That the actual chronological order within the older books is 6,3,7,4,2, is another matter. Here we will only take the conventionally and universally accepted fact that Books 2-7 are older than the other four, Books, 1,8,9,10]. What if these scholars had decided to rename (i.e re-number) the books of the Rigveda to reflect this, so that the Rigveda started with Books 2-7 followed by Books 1,8,9,10, with Books 2-7 renumbered as Books 1-6, and Books 1,8,9,10 renumbered as Books 7,8,9,10 (or whatever other order they thought correct)? One cannot even imagine the chaos that would have resulted in the field of Rigvedic studies.
The same goes for the renaming of the musical notes M and m as m and M respectively. It makes the study of Indian musical scales with its thousands of rāgas (most of them containing one or both forms of the madhyam swara) a chaotic affair (especially when studying different scholars, many using the conventional names and symbols and many others using the “corrected” or “revised” ones).
But, apart from the confusion resulting from renaming M and m as m and M, is it even musically correct from a strictly academic point of view?
The scholars using the “corrected” names or symbols m and M seem to think that they are correcting an anomaly in the traditional understanding of these notes. That, just as the second of each other pair (ṛṣabh, gandhār, dhaivat, niṣād) is considered the śuddha form, the second of the madhyam pair should also logically be considered the śuddha form.
However, this is musically wrong: madhyam is not in the same musical category as ṛṣabh, gandhār, dhaivat, niṣād. It is in fact in the same musical category as Pa:
1. In my earlier article on Musical Scales, I pointed out how the octave (of twelve notes or semitones totaling 1200 cents) was derived from a basic “tonic” note (ṣaḍja) by a recurring cycle of “fifths” (i.e. two notes at a distance of 700/702 cents from each other):
“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.
[…]
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.”
Clearly, the main (or śuddha) madhyam swara note is the lower of the two madhyam swaras and not the upper one.
2. In fact, the upper of the two madhyam swaras is only a madhyama swara by convention (since the octave is derived by an upward movement of the cycle of fifths). It could also be classified as komal pa or p, since it occupies exactly the middle position between the two śuddha swaras Ma and Pa, both of which are at a distance of a fifth from a ṣaḍja.
Which is why, while the different pure seven note thāṭs in North India Classical Music have M-P (and no m) or m-P (and no M), but there also at least two pure seven note thāṭs which have M-m (and no P):
Lalat: S r G M m d N S
Ahir Lalat: S r G M m D n S.
In both these (and the other theoretically possible 14 thāṭs with M-m and no P) the m is actually a komal pa.
Again, it is clear that this upper madhyam swara, which can also be interpreted as a komal pañcam cannot be the śuddha form of madhyam.
To sum up, my only objective in writing this article was to alert readers (especially people who may be looking up the notes of rāgas on the internet or in the works of musicologists) to the fact that it must be checked whether the particular person giving the notes in any rāga is using the correct original sequence of M-m or the incorrect “corrected” sequence of m-M.
In the case of the otherwise very useful site of George Howlett referred to above, it is at least possible to understand that he is taking the upper madhyam as śuddha, since each page of his site contains the following chakra of twelve semitones:
[The following chakra is from his page on the rāga Bilawal]
It must be noted that while distorting the traditional Indian names of the madhyam notes (by symbolizing śuddha madhyam and tīvra madhyam as komal madhyam and śuddha madhyam respectively, i.e. as m and M respectively), he is himself clear that this is wrong: see the fourth row of his table below, where he classifies the two notes as 4 and #4 respectively instead of as b4 and 4 as he should have done to make his symbolization consistent with the first row: i.e. in the fourth row, he accepts that the second form is the sharp version of the first form, rather than that the first form is the flat version of the second form)
But in the case of many of most others giving the notes of rāgas on the internet, it is not easy for a layman reader to understand whether the sequence given is M-m or m-M.
