New Book: Pitch Analysis in South Indian Music

[Nick H]

Pitch Analysis in South Indian Music by Dr Madhu Mohan Komaragiri.

Web Page

I was at the launch of this book yesterday (ArKay Convention Centre).

The subject matter is waaay over my head (although Madhu spoke very accessibly) but I know that it is close to the hearts and minds of many fellow forumites, so better I post a brief announcement rather than it should get missed.

I understand there is a delay with the physical book production, but it should soon be available from Karnatic Book Centre and international sources soon.

[Rsachi]

He highlights the non-acoustical dynamic variability in intonation, influenced by perception. In line with this analysis, concepts such as the octave, intervals, scales, modal shift of tonic and consonance have been freshly re-examined.

With such a blurb, it seems to be too technical an offering, promising to confuse and confound in several ways the common rasika.

[harimau]

This book is based on the doctoral dissertation of Dr Madhu Mohan Komaragiri who is an engineer by vocation and also a musician.

I couldn't attend the book release because of a conflict with several other programs, in particular, Episode 9 of Myriad Forms of Siva by Gayathri Girish. I will have to get the book at a later date.

I had read a brief synopsis of the thesis a few months back in Pranavam, a magazine dedicated to music published out of Hyderabad. The thesis analyzed the music of N Ravikiran, T N Krishnan and one other musician (M Balamuralikrishna, IIRC) and concluded that 22 sruthis is bunk in the modern context. At least, that is what I got.

Take that with the findings of Dr Aravind who had analyzed N Ramani and a few others' music and also concluded that 22 sruthis is not to be found in the music performed by them and 12 tones are perfectly adequate to represent Indian music.

I guess someone will soon scientifically prove that even gamakas around these 12 tones are not needed.

In that case, NickH would be delighted to learn that the English Note would be the only acceptable Indian music.

He would be thrilled to learn that Harikesanallur Muthiah Bhagavathar has composed a few more along the lines of the English Note popularized by Madurai Mani Iyer.

Maybe, we will also retain Garudadhwani, Kathanakuthuhalam, Nalinakanthi and a few other ragas similar to them, throwing Thodi, Kalyani, Bhairavi, Kambhodi, etc., into the dust heap of history.

The current crop of youth, which is already swaying to the music of Agam, would create the "new sound" of Carnatic music.

Ravikiran could abandon the Gottuvadhyam and adopt the veena with its fixed frets and produce music with unornamented, plain notes.

Uday Shankar could abandon his chitravenu and switch to the didgeridoo.

At this point, I should confess to past error I have committed in considering the piano to be European in origin. South India does have a stringed instrument where music is created by striking the strings. Hence, the piano could be rightly considered the derivative of this Getthuvadhyam and rightly re-named the ati vichitra getthuvadhyam.

Ravikiran and Anil Srinivasan could create a band with the Gottuvadhyam and the ati vichitra getthuvadhyam. Since that is a mouthful, they could call themselves the Goat and the Geth.

When this future comes to pass, I shall be in need of liquid refreshment to drive myself into a stupor. Fortunately, there is a TASMAC store right around the corner, as there are in all neighborhoods of Chennai!

PS. The Goat and the Geth sounds like a nice name for a pub! :p

[Nick H]

Certainly it is technical, far too technical for me. This is a book for the specialists and the scientists among us. I can imagine Uday, VKV and a few others finding it most interesting. I doubt that I would be able to take it in, and, anyway, it would also not be meaningful to someone who is not well versed in raga.

However, from what I could understand...

22 sruthis is not to be found in the music performed by them and 12 tones are perfectly adequate to represent Indian music.

No. Quite the opposite. It is not there are no 22 tones because 12 (or five, or three, or one; Lou Reed says one chord is enough) is adequate, but because 22 is completely inadequate and one cannot ascribe a fixed pitch name to a moving-pitch note.

So no need to take to the TASMAC in fear of loosing gamakas or microtones. No need, either, to inflict that dreadfully tedious English Note on us!

[Rsachi]

[rshankar]

PS. The Goat and the Geth sounds like a nice name for a pub! :p

And here I was thinking that George Clooney was mad!

[SrinathK]

But the equal temperament based system of tones is also not suitable for Indian music. IMHO, 22 tones is not entirely obsolete. It is needed where long kaarvais of sustained notes are needed and it resolves harmonic conundrums in western music that cannnot be adequately solved by 12 tone Et or Pythagorean apart from giving us a mathematical basis for graha bhedam. However it goes out when gamakas are brought in. Swaras with gamakas are no longer to be called tones or notes. Instead they are now labels for more fluid phrases characteristic of the raga.i think that the whole concept of analysing phrase based music in terms of note based theory is severely limited and there is always that unexplained "right brain" intuitive understanding in CM that doesn't get along well with left brain analysis of frequencies and intervals.

[girish_a]

I had mentioned this in a different thread, but since the topic of 22 tones has come up again, it is relevant to mention it here once again. There is an entire website dedicated to the subject: http://www.22shruti.com/

They are makers of musical instruments, but plenty of research material is also available on that site. Click on the "Research" tab at the top of the page.

[SrinathK]

Dear girish_a, one fundamental point to add there is that out of all the intervals in a 5 limit tuning system (refer Wikipedia for those who want to know what that means), these 22 are the only ones which satisfy all the harmonic criteria of Indian music. However to apply them to the modern phrase based carnatic system has severe limitations. There is definitely a very strong "right brain" intuitive basis of gamaka perception that makes it very difficult to analyze gamakas with the techniques more suitable to fixed pitch instruments in CM. Again the whole idea of seeing CM as just "tone based" music is itself erroneous. It should be seen as "phrase based" music in which plain tones do exist (and when they do they have to follow the right intervals), but for the overwhelming majority of the time notes are just labels for unique raga phrases and so the ancient system does not apply to our music today.

However the 22 tones do have uses outside the CM system as well, as they can resolve several harmonic difficulties unattainable by ET. All technical jargon and academic verbiage aside, this is really the gist of the whole topic that needs to be explained to the average rasika.

[vasanthakokilam]

Srinath, what you say make a lot of sense. There are certainly major disconnects between theory and practice. Theoreticians may blame the practitioners as diluting the music and practitioners snicker at theoreticians as being out of touch.

People who are not in either camp ( which includes a lot of us here, including me, and including a lot of self-professed serious and knowledgeable rasikas ) believe that the current practice and old theory are consistent. We hold such beliefs at a vague and 10000 foot level. When some one points out the reality that today's practice is not consistent with old theory, that does not quite jibe well. Sometimes this even results in a lot of mud-slinging ( there is a long history of threads in various forums that deal with this topic )!

Having said all this, Srinath, outside of the tuning differences between ET and JI, what ragas employ a long kArvai flat notes that is outside of the accepted CM tuning of the base 12 notes. At least this way, we can document those things ( notes are sharper or flatters than the accepted swarasthan values ) without really getting into 22 sruthis etc.

[Nick H]

There are certainly major disconnects between theory and practice.

Paraphrasing what I heard (or thought I heard) at the launch: theory is important, all performing artists should know some theory, at least, but what they actually do on stage is art, not science.

[vasanthakokilam]

Nick. Thanks. That makes sense. This led me another point I was thinking about.

Scientific basis for Aesthetics: That is what we are talking about here. Here the moral authority is with the practicing artist. A pure theoretician/scientist can only go so far.

Aesthetic basis for science: As the scientists among us know fully well, there is indeed such a thing, though not well known outside of the community. Truth and beauty often walk hand in hand. Simple is considered beautiful, complex and unwieldy things even with sufficient explanatory power are looked upon suspiciously ( "there has got to be a better explanation than this mess!" )

'Aesthetically pleasing scientific basis for aesthetics - combination of these two.

That is a mouthful, but it just points to our natural inclination to look upon simple ratios like 3/2, 4/3, 5/4 etc. as contributing to pleasing consonance and look upon suspiciously at monster ratios like 256/243 . No wonder an even bigger monstrosity, the twelfth root of 2, does not sit well with us as a naturally beautiful thing I It can not even be represented as a ratio, that is how monstrous it is. "How can THAT silly thing be the truth when it is obviously a made up thing". A lot of us, though not all, have a preference for that kind of scientific aesthetics ( and also based on how those intervals sounds to us). That includes myself even though my swara gyana and aesthetic sense is not fine enough to distinguish between such small variations. ( may be G3 is an exception of late )

[Nick H]

NB, again, paraphrased by the ignorant, but I'll do my best...

Dr Mohan, in his all-too-brief presentation, pointed to graphical analysis of given srutis in given ragas as sung by authoritative artists. He pointed out that they differed, not only from each other, but from any theoretically laid-down frequency for that sruti, but commented that we cannot possibly say that those notes, sung by those artists were wrong, or that that their performance of the raga was wrong.

I run out of steam and metal capacity very soon after numbers are mentioned. I'm sure this book would provide the basis of good conversation among you guys who are able in those departments.

By the way, IIRC, Mohan is a student of BMK. If I remember right, he has a concert on 24th November, at Arkay. People might be interested to see how science may have affected the art --- although he must be very, very far from the first performing musician to be also a musicologist and scientist.

[SrinathK]

The monster ratios simply arise from harmonic relationships between the major third, fourth and fifth. By a process of graha bhedam from these ratios all 24 ratios in a scale are derived out of which 2 wolf tones are removed at sa and pa (for tanpura alignment) to give the 22 srutis.

I have made a huge excel of graha bhedha positions from each of these 22 positions. I'm just giving it the finishing touches and will upload it here soon enough.

While 22 srutis may have no relevance now to gamakas, those positions are the ideal ones for carrying out graha bhedam as they can fully express the 12 tone scale from any of these position maintaining the relative intervals within those positions. To explain I have to show the excel sheet.

By contrast sruthi bhedam on the positions of just 12 of the 22 tones has severe limitations and this was the reason why Equal temperament gained popularity on fixed pitch instruments.

The thing is that the relevance of 22 srutis w.r.t. graha bhedam is not appreciated much because unlike Western music, CM and HM tend to stay in the same sruthi for the whole concert and it is practically much more difficult to change the position of the shadja in our gamaka and raga based music as compared to plain note western music where they simply transpose fingerings. Not to mention the practical difficulties for instruments that would need retuning for key changes and the resultant negative fallout on manodharma. Therefore this is more of an academic topic at the moment.

[vasanthakokilam]

While 22 srutis may have no relevance now to gamakas, those positions are the ideal ones for carrying out graha bhedam as they can
fully express the 12 tone scale from any of these position maintaining the relative intervals within those positions. To explain I have to
show the excel sheet.

Good point. Please share the spreadsheet along with some explanations. I am intrigued.

[uday_shankar]

I do have some thoughts (again, with a hefty bias toward the "practical" ) on this. Will post when I get time.

[cmlover]

SrinathK
I too am eagerly waiting for your spreadsheet and the related discussions.
Your query of swarabhedam based on 12 tones vs 22 shrutis is on the spot!

VK
The just scale based on rational numbers (ratios) is not justifiable on physiological grounds
As per Fechner's law (psycho physics) human sensations are based on a logarithmic scale.
Hence the exponential scale of the WM should be the natural choice.
Having said that, CM because of the inherent gamakams cannot be bounded by the 12 or 22 or any number of digital number of shrutis.
shruti anantam is the logical choice, which leads us to the analog aspects of chitra vina/chitra venu...

[SrinathK]

I'll put up the sheet today by evening. However Fechner's law applies better to the relative perception of weight or relative loudness or light intensity but not to musical pitches. For starters just play a major third on a harmonium and see the dissonance then do the same on a violin and it will be easy to get much better alignment. The 22 sruti system includes JI and PT but also goes much further.

Technically speaking, trying to correlate or assign sruthis to gamakas and moving phrases is not only confusing but well...for want of a more polite word -- meaningless. Sruthi as used in this context refers to fixed relative intervals in an octave bound by specific harmonic relationships derived using a specific algorithm from shadja and it is for this reason that there are so many sruthis in an octave and not just any arbitrary interval in 5 limit tuning. If sruthi is used in the context of various swaras in different ragas throwing in phrases and gamakas then by that understanding there are as many of them as there are raga phrases and therefore, srutiranantam!!

[SrinathK]

Finally! Here's the big excel I was talking about. It has several sheets analyzing the 24 tones before moving on to the 22 sruthis. I've included only a few short notes owing to lack of time so we can always discuss the rest. You can also refer to the 22shrutis.com website, but this excel contains additional information that is not found there.

https://db.tt/qECizUPf

In the graha bhedam sheets, each column takes the relative shadja at 100% or 1/1 to a different position and the positions of the other 23 tones in the octave (without changing their absolute positions) are analyzed therefore those sheets are to be read column wise. Here I've also included variations in fractions, decimals and the values of the intervals in cents, as well as the percentage lengths on a string.

There are also other sheets where I have included what would happen if the tanpura sruthi were to be changed entirely to a different key altogether and in those sheets the frequencies for a particular position are located along a single row and they are meant to be read row wise.

I took care for it to be as accurate as possible but if there are any errors please do bring it to my notice. I would very greatly appreciate the help.

[uday_shankar]

Thanks for the painstaking effort SrinathK. I will go through it when I find enough time to focus on it both from a theoretical and practical standpoint and offer my comments.

[cmlover]

Yes! Need time to digest your magnum opus

[vasanthakokilam]

I think it will help if we catch up on this 5-limit tuning to digest Srinath's spreadsheet. I am going to do that in the next day or so.
http://en.wikipedia.org/wiki/Five-limit_tuning

[SrinathK]

In retrospect, the tables I made in that excel are rather clumsy to understand. For one although they tell you how many of the 22 shrutis are available when a graha bhedam is carried out, unless you have all the values of those intervals in memory you would not know which of the 22 are available and which are not -- for example when shruti bhedam is done at the position of prati madhyamam (m2), the following intervals -- r2, g2, M2, d2 and n2 do not exist but I don't see realize that immediately by looking at that table. I'll work on that over the weekend.

The goal of that sheet was to show if at least 12 tones are available from any position in graha bhedam -- which would then allow a single instrument to play in multiple keys while mathematically establishing graha bhedam as a musically valid technique. The answer to that is a resounding yes.

Ultimately the result of all this work shows a few interesting things :

1) The goal of 22 micro tones was not to have 22 tone scales but 12 tone scales under graha bhedam. Having 22 intervals in the first place was only to ensure that 12 tone music would be possible with both melodic and harmonic applications. 12 tone ET was "Made in China" to be able to play 12 tone music from any key, but the Indian solution was more elegant harmonically speaking. Ancient Indian musicians realized that 12 tone music alone could not handle graha bhedam / key changes and were the first to go further.

2) The harmonic implications of the 22 shruti system and it's parent 24 tone system are massive. Like the "Pythagoras theorem", the Indians had discovered the tuning system first.

3) The original 24 tone scale was reduced to 22 tones because S' and P' were dissonant and they created asymmetry between ascending and descending scales. But they can be used in music that does not need the tanpura in the background. This is because in the 24 tone scale each note has it's own perfect 5th and 4th within the scale itself.

4) In graha bhedam, shifting the sa causes some relative intervals from the new position to go out by a small interval of 1.9537 cents (schisma). For example if I shift Sa to the position of R2, then the intervals N1 and N2 will correspondingly shift to the upper r1 and r2. But if the upper r1 and r2 are kept aligned to the tanpura, the RELATIVE interval develops a small inaccuracy of 1 schisma. This is also true vice versa. The only problem is when chords are played -- should the notes be individually true to the tanpura, or should the chord notes be in tune with each other? Indian music rarely, if ever uses chords.

A similar problem actually exists in Western classical music (Bach's music for example) and it is much worse at their end because of the relative dissonance of 12 tone Equal temperament. It has been discussed how different players have used different approaches based on their personal aesthetic considerations.

That is due to the dilemma as to whether the 22 tones must be aligned to the tanpura shadja or aligned to each other instead and absolute alignment is favoured over the relative. The schisma however is far too small for a normal ear to even detect and it is virtually impossible achieve by humans -- on a violin string it is less than 0.03 mm at it's widest.. The average vibrato on the other hand can be as wide as 50 cents!

It is possible with computer algorithms to extend the 22 shrutis to a system of 42 micro tones that introduce 20 "corrective tones" to take care of these schismas and create perfectly consonant chords from any of the 22 positions -- something that is more important in WM or Classical music that doesn't require a tanpura. For practical purposes 22 tones are enough and ancient Indian music allows chords that are far more in tune than Equal temperament and go far beyond both JI and Pythogorean scales.

5) Pretty much the only place where Indian music is not applicable is where the music requires dissonance or where intervals such as 7/4 that use the dissonant 7th harmonic (7-limit tuning) are used.

Though the 22 sruti system has been shown the door because of the evolution of the gamaka in CM, it is surprisingly more relevant to all other systems of music. In fact it's potential is so great both melodically and harmonically that we can say that what we call "world music" is actually "Indian music" all along! No doubt this is probably mathematical proof for @harimau's statement that the piano's ancestor was also from India. Getthu indeed! QED.

In the mean time, I've uploaded another sheet on the harmonic potential of ancient Indian music here : https://db.tt/6ZvK95VB

I'll open another thread for further points as this thread is about Pitch analysis in today's gamaka oriented CM where pretty much none of the above apply except for the sruti bhedam and plain note parts.