why 7, not 12

[cacm]

"shankar vaidyanathan"
Dr.VKV,
I have seen a painting similar to what you describe. Kindly post a photo at your convenience

Dear S.V.,
DO YOU HAVE THE BOOK "MUSINGS ON MUSIC" BY S.RAJAM? In that book he has Sapthaswaras painrtings based on details available from Sri. Harikesanallur Muthiah Bhagavathar's "Sangeetha Kapla Drumam". The paintings he specially painted for my wife & me are QUITE DIFFERENT & uses availabe datafrom many other sources.
It will take quite a bit of time to photograph them & mail them. Where do you live? Pl write your email. I live in Los Alamos, N.M. Regs, VKV

[sung]

The simplest explanation is that you have 7 solfa syllables, 5 of which have two swarasthanas a H(igher) one and a L(ower) one. A scale should only have either the H or the L variety. That is it. If you had 12 solfa syllabes or ( 16 ) the equivalent rule will be quite complicated to state.

I must first apologize that I have not been able to follow the thread as closely as I would like to since I happen to be professionally very busy after I asked the question. As is almost always the case in forums, it appears that there are so many digressions from the main question by some contributors, which has made it difficult for me to follow the discussions while being so busy.

However, this forum is indeed very fortunate to have a person like VK (namely Vasanthakokilam) who has, in my opinion, always paid very close attention to the question itself before attempting the answer. I know very well that this is a rare talent. (In fact, after I ask a question on this forum, I have come to look for VK's post. No offense meant to others.)

I want to thank VK and Ranganayaki for rephrasing my original question. I am sorry about the way I phrased it originally.

Now, VK, can you please explain why a scale should only have either the H or the L variety? This appears to be a fundamental idea that will help answer my question. So, I want to understand it further.

I noticed this morning that there are 50 or so posts, but I have read only up to VK's above post. Don't know how soon I would be able to at least skim through the others.

I am very eager to see the answer to the above question from VK and an ensuing discussion by others as well. Thanks a lot in advance.

[arunk]

sung - In VK's post, he said "let us ignore vivadi swaras". If you include then then the explanation "A scale should only have either the H or the L variety" would not be true (as VK himself would know). Including them does complicate things - you have 16 swarasthana labels (R1, R2 etc.) super-imposed on 12 positions, but you still have 7 swara labels (S, R, G).

However, scale(s) using vivadi swaras has been around for quite some time - even before they were officially included into mela system, at least nattai was mentioned and to use a ri. Not every vivadi swara and every scale, but the concept did exist early on (see below).

In any case, the answer to why only "7" is IMO just a product of how our music system evolved. Long ago (time of Bharata and Dattila - say 1st-5th century AD), there was only 7 official swara positions and they were called sa, ri, ga, ma, pa, da, ni. There is some text that mention that the swara after sa is ri, and thus the swara after ri is ga etc. This is probably why that even though even at that early period, ga and ni had alternate positions (they were termed antara and kakili although never elevated to official position) they were still called as ga and ni. In other words, any position that comes after ri and before ma was deemed "ga territory" and thus termed ga, and similarly anything after da and before sa is ni. What is also notable is at this time, there is no evidence from text to suggest that "sa" was ALWAYS the tonic position. It was the first swara, but besides that it may have been at the same status as others.

The mention of nattai ri comes in a text around 13th-14th century (there is also explicit mention of a raised-madhyama i.e. m2 in the same text for a raga called ramakriya).

Fast forward to say 14th-16th century AD is when "sa" becomes tonic, and all 12 positions are noted on a fretted veena (and also all 16 labels). Here also the convention was any swara after sa and before ga is a ri. Thus the nattai ri (which has same position as sadharana-ga) is still called ri, because you do have antara ga.

So I say it is more of convention which itself was due to adherence to tradition/wordings of old texts.

My 2 cents.


Arun

[shankar vaidyanathan]

Dr. VKV,

I have sent you an email through this forum. I have seen images of various paintings by Late S. Rajam on internet. I have not come across the book that you quoted. Thank you for the referral.

Best,
Shankar Vaidyanathan
Houston.

[vasanthakokilam]

If you include Vivadhi then then the explanation "A scale should only have either the H or the L variety" would not be true (as VK himself would know)

Very true Arun but a small tweak will fix that. "A scale should have only one variety of a solfa syllable'.

Inventing the aliases R3, G1, D3 and N1 is a great theoretical device to accommodate ragas like Nattai while still preserving the spirit of the above rule.

While we still use the diatonic concept of 'pick 7 from 12' but with vavadhi intervals we expand it quite widely with the use of more semi tone intervals but in a well bounded fashion. Quite a brilliant theoretical device indeed and I am always appreciative of a nice hack like that ('hack' used in the highest possible positive connotation).

Btw, Sung's question is 'why 7 and not 12' and not 'why 7' or 'why 12'. 'We are attempting to answer all three questions here and in addition a fourth question about the origin and meaning of the solfa syllable names themselves. Those are all great but for the sake of maximum clarity it is good to keep in mind that is what we are doing.

'Why 12' is a question that can be answered quite scientifically with a good measure of consonance based aesthetic theory thrown in. Srinath has answered this question quite completely in this thread and elsewhere as have Arun and Uday over the years. It is derived out of consonance principles mixed with some fairly simple ratio based mathematics. Beginners can stay at this level. Knowing 'why 12' itself is a broad topic which brings in the different tuning systems like Just Intonation. Equal temperament etc. 'Why only 12 and why not 22 or 24' is a corollary to this subject and is good for advanced study.

'Why 7' is a different question which leads us to a lot of fascinating and speculative discussions. A restatement of the question is 'In a scale why do we use a maximum of 7 out of the 12 possible swarasthanas'. My own take is that it is fundamentally due to a natural and fairly universal principle to have a combination of semi tones and whole tones intervals in a scale and keep those semi tone intervals apart by inserting some whole tone intervals for maximum aesthetic effect. Given 12 semitone intervals (swarasthanas), 7 sounds like a good optimal number to achieve that.

(as stated above, and just to be sure, the question is not about the actual name of the seven solfa syllable, it can be Sa ri ga ma or do re mi or C D E etc. 'Why those names' is a different question and we have tried to answer that in this thread as well )

Given the above two 'Why 7 and not 12' needs to be rephrased as 'why only 7 solfa syllables and why not 12 solfa syllables' It is actually a simpler question to deal with if we keep the focus quite narrow as stated. If one buys into any of the answers for 'why 7' and 'why 12' and convinces oneself 7 is a good number, then 'why not 12 solfa syllables' question can be answered with a simple 'why 12 sofla syllables?'. That is, when 7 will do, why complicate matters with 12 distinct sofla syllables? . The rules are tougher to state. So there is no real need to have 12 solfa syllables and if you invent 12 you are only buying trouble for your self. ( though that narrow focus may not satisfactorily capture the intent of the question and the real question may be 'why 7'. If so, go to the previous paragraph )

[Ranganayaki]

Given 12, why no more than 7?

[sung]

If you include Vivadhi then then the explanation "A scale should only have either the H or the L variety" would not be true (as VK himself would know)

Very true Arun but a small tweak will fix that. "A scale should have only one variety of a solfa syllable'.

When I read Arun's, that is exactly what I was thinking also.

Sung's question is 'why 7 and not 12' and not 'why 7' or 'why 12'. 'We are attempting to answer all three questions here and in addition a fourth question about the origin and meaning of the solfa syllable names themselves. Those are all great but for the sake of maximum clarity it is good to keep in mind that is what we are doing.

That is a wonderful way of describing the nature of the digressions in this thread. I assume this helps many of those who always try to digress in forums. One thing that might help is to always check whether we are answering the question asked or just want to expose to others our own deep knowledge level for our own pleasure. But, this might not always be the reason. A common reason is a complete lack of what logical connections are all about, thus not realizing that there is no connection between the answer given and the question asked. (Sorry. I say all this only because it is important to realize how frustrating it can be to novices when they ask questions on forums.)

My own take is that it is fundamentally due to a natural and fairly universal principle to have a combination of semi tones and whole tones intervals in a scale and keep those semi tone intervals apart by inserting some whole tone intervals for maximum aesthetic effect. Given 12 semitone intervals (swarasthanas), 7 sounds like a good optimal number to achieve that.

That appears to be the final answer. Wow! The idea of mixing semi-tone intervals with whole-tone intervals (and one-and-a-half-tone intervals, if I understand it right, as in the case of mayamalavagoula) in order to get a maximum aesthetic effect indeed appears to be a fundamental idea. I didn't think of that. I am very happy I asked the question.

I am going to try to play on my gaayaka the collection of all 12 swarasthanas in the correct order and see how it does not sound aesthetic. I think I can do that with the help of asterisks for the foreign swaras after choosing any one particular melakarta. I am very eager to try it later this morning.

Thank you so much VK!

In the absence of such a lack of aesthetic effect, no matter what the prior evolutionary history might be, a change would have occurred at some point of time when people would have introduced 12 swarasthana scales. This might be the answer to Arun's prior post.

While we still use the diatonic concept of 'pick 7 from 12' but with vavadhi intervals we expand it quite widely with the use of more semi tone intervals but in a well bounded fashion. Quite a brilliant theoretical device indeed and I am always appreciative of a nice hack like that ('hack' used in the highest possible positive connotation).

In light of the answer to my question, this statement appears to be quite profound. I like 'but in a well bounded fashion'. Great! Thanks again VK!

[Nick H]

The idea of mixing semi-tone intervals with whole-tone intervals (and one-and-a-half-tone intervals, if I understand it right, as in the case of mayamalavagoula) in order to get a maximum aesthetic effect indeed appears to be a fundamental idea.

It is the fundamental idea, and I suppose it could just be said, "because it sounds good." Then, the question in my mind is, "Is that because it is good, or simply because we are used to hearing it?" The numbers baffle me on sight, but it seems, if I understand what the numbers people are getting at, that they do offer an objective verification.

As to digression... it happens in any conversation, and a forum thread is only a conversation. At least it has all been close to topic. But... I digress

[sung]

I am going to try to play on my gaayaka the collection of all 12 swarasthanas in the correct order and see how it does not sound aesthetic. I think I can do that with the help of asterisks for the foreign swaras after choosing any one particular melakarta. I am very eager to try it later this morning.

I just repeatedly played and heard all 12 swarasthanas in the increasing order (of frequency). It doesn't seem to sound good (to quote Nick H). I think I realize the limitations associated with having all 12 together.

Now, let us say that we assign 12 distinct solfa syllables to the 12 swarasthanas (along the lines of my original question) and attempt to construct scales. There should be only one melakarta, right? (There is only one way of selecting 12 out of 12.) All the other scales formed by omitting this or that swarasthana from this melakarta would simply be janya ragas. Hmm, that would make it plain boring and the so-called melakarta "system" would simply be meaningless! (Thank God, they didn't assign 12 distinct solfa syllables to the 12 swarasthanas!)

Recently I decided to go back to square one and have been practicing sarali varisais in the following 4 melakartas: 8 (thodi), 15 (mayamalavagoulai), 22 (karaharapriya) and 29 (shankarabharanam) with a view to attempting to master the different swarasthanas (of course, ma2 excluded for now). (I was originally exposed to only 15 with respect to sarali varisais, as is generally the case, and then we moved on to higher levels such as varnams and kritis.) It is during this recent practice that the original question that started this thread arose in me.

Well, from what I just did on gaayaka, it appears that I can now practice all 12 swarasthanas together (ma2 included), feel how they compare in their frequencies and try to master their 'sthanams'. Is there any potential pitfall in attempting this?

[SrinathK]

Just to add, the number 7 has many important spiritual connections to us Indians -- 7 lokas, 7 spiritual centres in yoga, 7 visible grahas (including the sun and moon, but not including the moon nodes) -- it is considered to be a highly spiritual number and this might have been the original reason for the use of seven notes even in music. As to why there are 12 variations of these 7 notes, one answer comes from harmonic theory. Another might have to do with the 12 constellations of the zodiac as well. There is a connection to the human body and yoga here as well.

The idea of having different variations for a single note keeping 7 main note labels has been around right from the beginning of Indian music. The old system from the Natyashastra assigned various sruthis to each of these notes (sruthis, not swarasthanas mind you). At that time there was no tonic note. Therefore this might have been an attempt at absolute pitch by the ancient Indians. It did not survive over time, but it evolved into a system of 12 relative pitch positions that exists today. This is why you still see labels like "chatushruti rishabham" -- a remnant of the old system.

Now to your last post. Practicing chromatic scales is very essential in fact to gain command over the semitones -- to make it easier I would specifically recommend practicing vivadi ragas. It is rather strange to me that there is no exercise for chromatic scales even after the point where you have realized that there are 12 distinct notes in an octave. As of today, it still remains an unexplored area in Carnatic Music.

[SrinathK]

Yet another answer seems to come from yoga. Here I must digress away as I have been flooded with some ideas not unlike a Semmangudi's imagination that went into overdrive and would not settle down even after the concert. Owing to the sheer length of it, I've removed from here. Instead, here's the link. You can read it there :

https://www.dropbox.com/s/k94htc3jvwa3c ... a.txt?dl=0

[vgovindan]

Srinath,
Thanks.

[Nick H]

Just to add, the number 7 has many important spiritual connections to us Indians ...

The whole world has seven days in a week! (as far as I know: I bet someone now tells me some obscure culture with a radically different calendar!) And seven is regarded as having importance in other spiritual/esoteric traditions too. Seems to be a number that we just can't get away from. Especially music lovers.

[vasanthakokilam]

Speaking of Gayaka software, you can do one interesting experiment. Let me call it Chroma Extreme. There is a facility to do fine adjustments on each swarasthana at the granularity of 1 cent. Increase it by 1 cent. When I did that, I could not tell a difference. I then kept increasing it in 1 cent increment and there is no perceptible change.

This link https://en.wikipedia.org/wiki/Cent_(music) says that it is hard to tell the difference of even 5 cents for most people. So someone who is sufficiently skilled can try a trick. Turn the tambura off. Hold a note, increase the pitch by, say, 5 cents at a time, hold it for a bit at each level and take it to a 100 cents difference which is a semitone. May be most people will think you are still playing the same note Then in one shot go back to where you started from. That difference will be heard by most people and it will be interesting to find out how people perceived that. Say, if you started at S and took it to R1 slowly and then come back to S, will they say you are now back to S or you went to N3?

I tried this with Gayaka on myself. It is lot of fun and strange at the same time.

[ganesh_mourthy]

Also that I noticed that when you ask a beginner to tune an instrument to align with a pitch slowly , they easily get confused. It has to be done quick.