Hi there! And, a couple of questions...

[srikant1987]

Can you name some common ragam with this different Pa?

[twister]

Vijay, here is a rule that fits the CM idiom if we assume M1M2 is vivadhi'ish ( I realize dual ma ragas are common in HM )

There are 12 semi-tone intervals in an octave.
split that into two segments. SA-PA and PA-SA'

The similar aproach is described here (The RÄÂÂ

[Sathej]

I have seen several violinists adjusting exceedingly well to Shruthi Bedams during the Ragam or in instances where Krithis are rendered in the Madhyama Shruthi. And I have observed quite a few violinists playing with ease during informal sessions. Infact, for Krithis sung in Madhyama Shruthis - like those in Punnagavarali and even in Manji, I have seen violinists playing the entire Krithi without retuning. Have also heard MSG has played Varnams (like Saveri) in Madhyama Shruthi without retuning and so on..
Sathej

[twister]

Can anyone also tell me please, what kind of Ga and Ma are used in Thodi?

Rajan P. Parrikar declares G1 and M2, while there is a G2 and M1 in wiki-mela.

[arunk]

@ ArunK
Do you think that kanakAngi was the vEdas' scale?!

- Maybe you should read my post again. Since the entire post was about why i think i was not so.

But early mela authors did think that the mela with all suddha swaras as mukhAri, with "suddha swaras" implying the swaras of the grama system (doesnt also mean all 7 were in vedas). Their interpretation of suddha swaras matching to today's S R1 G1 M1 P D1 and N1 i.e. kanakAngi - which doesnt seem to gell for many reasons, like the ones I mention in my post. For some reason there seems this disconnect - although I still wonder how they could have been so off or disconnected with the grama system from which our mela system evolved.

Arun

[arunk]

twister -

* I think tODi in HM is not same as tODi in CM (carnatic music). tODi in HM (hindustani music), I believe is subhapantuvarali of CM. And tODi in CM is bhairavi in HM (?? not 100% sure)

* This nomenclature of G1, G2 etc. - you have to be very careful, as it is sort of confusing.

* First in CM, there are three ris, three gas, three dhas and three nis - hence R1,R2,R3; G1,G2,G3; D1,D2,D3; N1,N2,N3. All these do NOT occupy 12 different positions in the octave. There is some overlap (R2 and G1, R3 and G2, D2 and N1, D3 and N2). So the use of R3 G1 D3 N1 can be sort of confusing from layman standpoint as.
* In HM, there are only two of these and thus numbering is simply R1, R2; G1, G2; D1, D2 and N1, N2. *Even* some carnatic books, which ignore R3,G1,D3 and N1 (there is a stigma attached to these and some don't still like them), stick to this convention

Anyway,

G1 in HM <=> G2 in CM
G2 in HM <=> G3 in CM
N1 in HM <=> N2 in CM
N2 in HM <=> N3 in CM

R1, R2, D1, D2 are same for both.

There is no R3, G1, D3 and N1 in HM

Arun

[arunk]

Arun
Thanks for the lucid historic explanation.
I am willing to accept VK's postulate of M1M2 deserving vivaditavam. But then why was it rejected in CM while HM embraced it long ago? Any historical insight?

cmlover - M1M2 was probably at that point was considered much worse - as in disallowed in mela form.

One possible reason (just logical and guessing - not evidence based):
If M1 and M2 were allowed in mela form, if we follow what happens in the other vivadi case, we find that
either the M1 swarasthana (i.e. 4/3) has to give up its madhyama tag and assume the role gandhara
or
M2 must assume panchama role - which implies the regular panchama swarasthana (i.e. 3/2) is no longer the panchama (so either skipped or becomes dhaivata)

Perhaps they considered the swarasthana positions of suddha-madyama (4/3) and panchama (3/2) along with sadja (1/1) to be too important to function as anything other than ma, pa and sa respectively (i.e. 4/3 when used can only be the important ma, 3/2 when used can only be the important pa). Thus a M1 and M2 together maybe was not considered "healthy"

Arun

[vijay]

Wow this thread has really livened up - will need lots of time to digest this. Arun's depth of research is remarkable - would put most PhD theses in music to shame! Hats off boss...

Anyway, I guess we need to shift most of the posts above to the Vivadhi melas thread.

Twister, regd your query - Hindustani and Carnatic Thodis are different - HM Thodis uses M2 and N3 whereas CM Thodi uses M1 and N2. Let me also try and clear what at I suspect is an additional reason for your confusion:

In South Indian system, while the same 12 notes are employed the nomenclature is different from the North Indian system. This is because of the Vivadhi melas which have been heatedly discussed above. In the north Indian system the following 12 notes are used

S, R1, R2, G1, G2, M1, M2, P, D1, D2, N1 and N2

As I said, South Indian music uses the same 12 notes are used but there is the additional concept of Vivadhi Melas - in such melas, more than one variety of R, G, D, and N are used and respectively substitute G,R,N,D (i, e their immediately preceding or succeeding note). Thus, the first mela of the 72 mela scheme is: S R1 R2 M1 P D1 D2 S'. However (probably for better optical clarity), the vivadhi swaras, in this case, R2 and D2 (curious co-incidence there!) are assigned, shall we say, temporary tags of G and N which are otherwise absent from the scale. Thus the 12 note octave becomes:

S
R1
R2 = G1
G2 = R3 (G1 of HM octave)
G3 (G2 of HM octave)
M1
M2
P
D1
D2 = N1
D3 = N2 (N1 of HM octave)
N3 (N2 of HM octave)

Regd your query above, the confusion of G1/G2 can be seen from the list above. The Hindustani G1 is actually the carnatic G2 although the Gandhar is both Hindustani and Carnatic Thodis are the same.

Finally, to add to the confusion, some carnatic musicians/rasikas also occasionally refer to the Hindustani notations while describing non-vivadhi ragas. As a result we had decided to stick to the Carnatic system of notation (i. e 3 varieties for each of R, G, D and N) for avoiding confusion on this forum.

If this sounds confusing, just try and understand it from a friend/teacher who understands the melas better. It should take just 5 minutes to explain it in person...

[vijay]

Oho! Just noticed Arun has already explained...hah! thought I'd latch on to a relatively easy question but beaten to it!

[vijay]

Thodi in HM is Bhairavi, as in the Thaat...but the raag "Bhairavi" in HM is actually the CM Sindhu Bhairavi.

In HM, the scales (thaat) and raags are explicitly different unlike CM where in almost 99% of the cases (making a notable exception for Sankarabharanam), the raga and the scale have a 100% correspondence in terms of swaras.

Marwa is another example where the raag is actually the panchama varja version (equivalent to Hamsanandhi) of the Thaat (Gamanashrama)

[cmlover]

Arun
Thank you very much! That makes sense to me logically as it would have to our ancients. They as mathematicians would have considered 3/2 and 4/3 as desirable (even divine ?) as also musically pleasing and derived the rest including (22 shrutis) using the cycle of fourths and fifths. The M2 had to be accommdated musically (and also due to HM influence) which venkatamahi sanctified mathematically by the dichotomy as suddha/prati madhyama ragas.
Were our ancients aware of the 'equitempered' scale? Square roots (varga mUlam) were not mathematically strange to them.

[vasanthakokilam]

BTW, It is actually twelfth root of two. ( any way, not important for this)

By adopting M1M2P, they are not getting rid of any 'divine ratios', they will all be there. It is just that the cherished 4/3 would not be called Madhyamam, it would have been called Gandharam. Arun is speculating a name change of that cherished ratio may not have been kosher. That is a good speculation.

[arunk]

They as mathematicians would have considered 3/2 and 4/3 as desirable (even divine ?) as also musically pleasing and derived the rest including (22 shrutis) using the cycle of fourths and fifths.

While this is a popular sentiment the texts do not directly reveal that the ancients dealt with ratios as such. In fact I was wary of using ratios in the last post to refer to the respective sthanams - as I felt it will lead to too many tangents like this with cycle of fifths and fourths etc. etc.

The M2 had to be accommdated musically (and also due to HM influence) which venkatamahi sanctified mathematically by the dichotomy as suddha/prati madhyama ragas.

Like I mentioned earlier mention of M2 (or more precisely a sharper madyama) occurs. IMO it is not an "external entity" which somehow thrust into CM because of some external influence (or let us say that I am not sure evidence points this way). It is no more strange than say R1 as I will explain now.

One thing I thought of recently is this:

The sadja-grama i.e. kharaharapriyish scale is a set of tones. So imagine an old harp/vina i.e. 7 (or multiples of it) stringed instrument where the 7 strings are tuned to something close to s r2 g2 m1 p d2 n2. Note that in those days (grama system) there was no concept of sa being the only tonic. There are ragas mentioned that can omit sadja itself. Also consider that we know that in those days, the concept of different murchana/tonal-cycles starting at different swara (i.e. r g m p d n G R, g m p d n s R G etc.) existed - this concept of murchana is dealt with by Bharata and all subsequent authors.

Now we know today that kharaharapriya-todi-kalyani-harikambhoji-natabhairavi-????-Sankarabharanam form a cycle. So these 7 murchanas would be close to these

Note: ??? being a raga that interestingly has 2 mas but no pa - it is ri murchana of naTabhairavi and so it is s r1 g2 m1 m2 d1 n2 S - i.e. like toDi with m2 instead of pa. I vaguely remember a musician telling me about a rendu-madhyamam tODi that used to be popular in olden days .....)

Anyway, if we collect all the swarasthanas from all these 7 murchanes, even ignoring ?? - we get all the 12 non-vivadi swaras that we know today:
s (all)
r1 (from tODi)
g2 (from kharaharapriya, todi, natabhairavi)
g3 (sankarabharanam, kalyani, harikambhoji)
m1 (all except kalyani)
m2 (kalyani)
p (all except ???)
d1 (todi,natabhairavi)
n2 (kpriya, todi, hkambhoji, natabhairavi)
n3 (sankarabharanam, kalyani, hkambhoji)

Now without a fretted instrument (as then), with a 7-stringed based instrument, to play a song that was (roughly) tODi scale based, they probably do it based on the ri murchana of sadja grama. Now a "janya" of that which omitted the 7th degree of that scale (i.e. nishadam but only from the point of sa as tonic), would simply omit sa, it is "r g m d n r". Thus the concept of sa being omitted is no big deal as it is not the tonic (ri is) - and is not as crazy as it sounds.

Now also note that the concept of a flat-second degree (i.e. today's suddha rishabha) is played e.g by the gandhara when the rishaba murchana is taken of the kharaharapriya like sadja grama. In other words in the ri murchana of sadja-grama (i.e. ri is tonic), the ga is like suddha-rishaba for a tonic of sa. But it is not referred to as a rishab as it is today.

When the systems merged and perhaps with the emergence of fretted vina, they mapped all these to a single sa based octave - all murchanas above become sa based, and thus we have the intervals today. And now that gandhara of the ri murchana, really becomes the ri that is closest to sa, i.e. the R1 as we know today.

The reason I mention R1 this way is that in the old grama system with murchanas, there is no direct way to directly derive a mela like mayamalavagowla from either sadja or madyama grama. It requires a spacing between rishaba and gandhara to be 3 semitones - probably 6 sruthis in the grama system. No swara of that system can never be that wide. The same also applies to the D1 N3 (the nishada could never be wide as 6 sruthis either). As noted earlier, the very wide 6 sruthi swara makes its first documented appearance (as far as I know) at the ebb of the grama system in kallinAta's commentary (reference to nAttai ri). In grama system itself widest interval of a swara is 4 sruthis.

But the grama systems vanish, and the earliest texts (ramamatya etc.) that emerge a couple of centuries after that suddenly boast that the malavagowla mela (whose mapping maps to todays mapping) is "the best of all melas". That is sort of a mystery to me. I wonder if this mela came about AFTER the single tonic system was in place - which lead to 12 intervals sa-sa-sa, and thus gave way to the S R1 G3 M1 possibility (which did not exist in the 7 murchanas earlier).

So the concept of a flat-2nd, flat-6th and raised-4th existed if we take the murchanas as scales with different swaras as tonic (and this is a popular interpretation). But they could have emerged as shades of ri (i.e. R1), da (D1) and ma (M2) respectively perhaps later in the post-grama world.

Again just a theory (and I wont be surprised if musicologists have already explored this angle).

Were our ancients aware of the 'equitempered' scale? Square roots (varga mUlam) were not mathematically strange to them.

Like vk mentioned it is 12th root and I am fairly certain no. Equitempered sort of ruins all the samvAdi stuff i.e. nice harmonic ratios. So I am not sure they would have bought into it.


Arun

[arunk]

the condundrum posed there is that if there was a murchana that can be interpreted as scale with two madhyamas (i.e. the ??? above - rendumadhyama tODi), then did it simply disappear such that it wasn't considered a valid possibility for a mela structure by venkatamakhin? Of course, tODi itself (along with kalyani) were not considered very highly from him. In general, from what I can gather, the mela authors were not exactly sure how the music got to how it was then from the grama music. There were 100% sure it came from grama music but couldn't trace their music to that music from a technical standpoint. That also is a mystery to me.

I also have intermittent doubts about the logic for interpreting each of those murchanas as scales i.e. graha-bedham because of annoyances, and open questions like this . But in general, it does make sense.

Arun

[uday_shankar]

It is impossible to completely reconcile "ancient" sruti values for the notes (whichever particular values we choose based on our "best" judgment) with mUrchana based evolution of melakarta ragas. The latter is a relatively "modern" activity, perhaps post 16th century.

The speculations about mUrchanas of the ancient shadja grama and it's minute srutis should not be confused with the (relatively) modern effort to show that say, KHPriya-Kalyani-SBharanam-etc.., are all related through mUrchanas.

The key missing element in the "modern" speculations is the evolution of the 12-frets-per-octave fretted Saraswati vina. I think all modern thinkers, Venkata makhi etc, must have been influenced by it.

The tuning of the veena frets is an entirely heuristic and non-standard thing determined completely by craftsmen who had no connection to the theories and the music of the users. Their mandate was probably a simple one - divide the octave into 12 somewhat equal parts. Hence the vina fret tuning is neither "just" nor equally tempered but approximates equal temperament quite well. With these 12 approximately equal intervals, all manner of mUrchanas can be derived.

So there are three separates irreconcilable streams of thought:

1. Ancient sruti values, gramas, dhruva vina, chala vina, etc... This is ancient history and has only a vestigial connection to anything modern (i.e., 16th century onwards)

2. The actual evolution ragas themselves, based completely on traditions and without much thought about intervals, etc... Thus evolved the wonderful Panns, for example, which were later retrofitted into musically crude formalisms like the Melakarta system. Takkesi and Kausikam were wonderful melodic prototypes sung for centuries before they were accorded the artificially created adoptive parents of Harikamboji and Natabhairavi (really, what a travesty) respectively. The Hindustani thaat system is much better.

3. Modern raga classification (including mElakarta) and mUrchanas based on 12 approximately equal intervals in an octave.

[vasanthakokilam]

The sadja-grama i.e. kharaharapriyish scale is a set of tones. So imagine an old harp/vina i.e. 7 (or multiples of it) stringed instrument where the 7 strings are tuned to something close to s r2 g2 m1 p d2 n2. Note that in those days (grama system) there was no concept of sa being the only tonic. There are ragas mentioned that can omit sadja itself. Also consider that we know that in those days, the concept of different murchana/tonal-cycles starting at different swara (i.e. r g m p d n G R, g m p d n s R G etc.) existed - this concept of murchana is dealt with by Bharata and all subsequent authors.

Arun, just so I understand the subtleity involved, let us use your imagery of a harp type instrument where each string represented a swara. ( they probably needed more than 7 so they have strings to pluck when they move the tonic, say, to the second string. ). I assume in this imagery, the strings are fixed to a specific tuning and not changed when the shift of tonic happens. Please check if this assumption is correct.

During those times, different ragas are played using a new tonic. So the concept of a tonic existed, it is just that for one raga, the tonic is the first string, for another raga, tonic is the second string etc. Check me on this as well.

Assuming so, I understand what you are saying about the birth/invention/discovery of the 12 swarasthanas when you overlay all these different scales on a fixed Sa based system. In other words, I can imagine, one fine day, an upstart smartalec questioning a musical scholar about if there is a way to play Kalyani from the first string. Being scolded and sent away to stand in the corner for disobeying divine laws, our revolutionary figured it out that night...ah, I need a few more strings in between those 7 strings.

With the new touch based products from Apple, I sort of resort to this 2000+ year old practise. The piano keyboard is shiftable and so if I want to play thodi, I play the same white keys but I move the keyboard to the left

[twister]

If this sounds confusing, just try and understand it from a friend/teacher who understands the melas better. It should take just 5 minutes to explain it in person...

Great explanation! Thank you - I've caught it up - it's now absolutely clear for me! Actually, this is the reason why I turned my head to the CM
- Less dogma, more esthetics. Now, I'll try to adopt the naming you've described

[twister]

This nomenclature of G1, G2 etc. - you have to be very careful, as it is sort of confusing.

Arun,

Thank you! The question is now clear to me Now, ask me, to explain the same to the newbies

[twister]

Were our ancients aware of the 'equitempered' scale? Square roots (varga mUlam) were not mathematically strange to them.

There was a precedent in Ancient Greece, but there was not an octave tempered using equal ratios, but it was suggested to invent an equally tempered sruti (I guess this sounds most likely as what I am really trying to say)..

[arunk]

Uday,

I agree that it is pretty much impossible to completely reconcile those ancient sruthi value notes.

I also agree that going correlation between ragas we know today (or venkatamakhin and later) to earlier one is a very foggy road that can quickly lead one astray, or "fantasy land" - and i have been there too

But...

There is *direct* evidence in the texts that the grama system practioneers considered murchanas in terms of tonal shift or atleast in terms of using to arrive one "scale"/"tone system" from other. The best example is sArngadEva's explanation of how the madyama grama can be arrived from sadja grama by (paraphrasing) "treating sa of the sadja grama as ma, and raising ga by two sruthis". Also explanations for many jatis, and ragas (found in even earlier texts) refer to the murchana as the basis (i.e. this raga uses the rishabha murchana - there is a name for it too).

the (relatively) modern effort to show that say, KHPriya-Kalyani-SBharanam-etc.., are all related through mUrchanas.

This particular set isn't really a modern evolution. Human race as a whole has known this for a long time. For example, this cycle of diatonic scales is the same as those of the ancient greek modes (i.e lydian, ionian,phrygian). Even in the Indian music world, in all probability, it is not a recent "discovery" that the base tone-sets of these ragas can be derived from each other (the ragas themselves (i.e. kpriya, hkambhiji) came later - but I am talking about just the tone-set or the "mela"). Let me explain.

The grama proponents had two 7 tone systems. Just take the one - sadja grama. Let us assume it is one of these 7 scales/modes (we think it is close to kpriya). We also know they knew about different murchanas and that they had some concept of deriving atleast one other (madyagrama - which is close to harikambhoji if ma is tonic). Now when they knew this from the pre-Bharata to Sarngadeva, I dont know (i think this sadja-grama madyama-grama equivalence appears earlier to sArngadEva also but not sure now).


Even if the original set is NOT one of these 7 (i.e. our speculation that it is close to kpriya is not true), the fact is they did seem to aware with what we know term as grahabedham. But there is good logic to believe it is kpriya. And if that is true, it is highly probable that they experimented enough to know all the 7 scales/modes in that cycle. This in turn implies, that they knew and used all 12 intervals. Thus the 12 intervals were well known and practiced in the grama system itself.

What the mela system (or say singe tonic, and a fretted instrument) brought is new combinations of the 12 - not just vivadi ones, but also non-vivadi ones. I wondered if mayamalavagowla came at the end of the grama era or post-grama.

I starting thinking along these lines to see if "R1" appeared AFTER grama system (which possible, seemed a bit too surprising and improbable as it is very late in the game as in after 13th centiry), or was it there before. Again, R1 got labelled "suddha-rishaba" (along with D1), and these are all some of cause of later day confusion.

The key missing element in the "modern" speculations is the evolution of the 12-frets-per-octave fretted Saraswati vina. I think all modern thinkers, Venkata makhi etc, must have been influenced by it.

Most certainly. Both rAmamaTya and vEnkaTamakhin pay *huge* importance to vIna and devote chapters to construction, placement of frets (such as to yield swaras) etc.

Arun

[arunk]

I assume in this imagery, the strings are fixed to a specific tuning and not changed when the shift of tonic happens. Please check if this assumption is correct.

Yes. That is the assumption of the theory (it is still just that - but this is not new, i.e. i think all musicological books talk about it.

During those times, different ragas are played using a new tonic. So the concept of a tonic existed, it is just that for one raga, the tonic is the first string, for another raga, tonic is the second string etc. Check me on this as well.

Yes.

Assuming so, I understand what you are saying about the birth/invention/discovery of the 12 swarasthanas when you overlay all these different scales on a fixed Sa based system.

No - that is not what I mean. I am not saying that the intervals came AFTER they went to a fixed sa. I am saying, they were always there and I think the practioneers knew that - they just did not treat it like we do in the "sa is the only tonic system".

When they went to "sa is the only tonic" system, they NOW treated ALL "second degrees" of a scale as rishaba, all third degrees as gandhara, all fourth degrees as madhyama, all sixth as dhaivata and all seventh as nishada.

If true, how does this help? At the sake of repeating myself, it explains why the mela authors may have mistakenly considered R1 as "the rishaba of the grama system, assigned it not only suddha-rishaba, and thus were compelled to assign it the 3 sruthis that the grama texts prescribed. The "flat second" degree was never the rishaba in the grama system.

If you read early mela texts, their swarasthanams match what we have today. However, their attempts at sruthi assignments AND still maintain "vadi" relationships etc. as mentioned in earlier texts start to breakdown. The explanation that musicologists arrive at is that it all started to go down, when they assigned the 3-sruthi to the wrong rishaba (and 3-sruthis to the wrong dhaivata), and not realizing that, still were trying to reconcile with the information in the old texts and tradition (which of course they wanted to adhere to).

If I am not mistaken, there is only one post-grama but medieval text which says "komal rishaba" is the old rishaba reduced by one sruthi i.e. flattened form of the old rishaba. I forget the title - but it is a book after the north and south systems diverged, and this book was more about the northern tradition. This is the only one that may have got it right.

Arun

[uday_shankar]

Arun,

You and I have discusssed the notion of "raising a note by one or two shrutis" and have come to the conclusion that such an exercise is practically impossible and the very notion is ridiculous. Hence your excellent online thesis (couldn't find the link readily) on trying to get to various shrutis indirectly, by comparing consonances and beats, as I too have experimented haphazardly.

So there's still the great question mark...what were Bharata and subsequent authors thinking (or more likely smoking) when they think they can stipulate that a certain string should be "raised or lowered by a shruti" ? Even the error in the tension between various strings on the same instrument can cause the raising or lowering by a "shruti" and nobody will be any the wiser. We often raise or lower a string by "a shruti" (which itself can be 81/80 or 256/243 or anything in between!!) to achieve unison. Several notes in the equally tempered scale are off by several shrutis permanently and nobody is any the wiser.

The sheer unscientificality and meaninglessness of Bharata (if he is to be interpreted as we now do) is mind boggling. In control theory terms, this would be a completely feed-forward mechanism and hence all bets are off.

The challenge to savants like you is to keep away from the "raising by a shruti" verbiage when quoting ancient texts !

[arunk]

Uday,

Let us stick to the point at hand and not rehash all that. The import of that statement is that they thought one tone-set was derivable from the other albeit with an extra adjustment. This indicates they knew about concepts like tonal shifts. I thought you were skeptical they knew about this. So I quoted it.

Also, this "raising sruthi" or "lowering sruthi" - it is just their terminology for adjusting string pitch . Not exactly a modern day, cutting edge technique is it? Yes there are some tough steps in that experiment like the 22-cent drop in first step albeit a drop that takes a pitch of a string from sa-pa consonance with one string to sa-ma type of consonance with another string. I mean this doesnt require computers/machines to pull off. But solidly constructed instruments -- yes. Still error prone depending on various factors - yes. And yes, it is certainly ok to be skeptical that this was done reliably with the required precision in the first half of first millenium. But because of that, let us not dismiss the simple concept of raising/dropping pitch of a string. I mean humans have been doing that for millenia.

Oh btw, in this particular case, the string is raised by one semitone (assuming our reconstructed ratios are close to what they had), not the minute one

Arun

[uday_shankar]

Arun's right. I'll take my irrelevant rants offline.

BTW, Arun, how can you be sure of bringing a string down by a semitone, or even a fifth, without a reference? Try this experiment with musicians as well rasikas...measure the pitch of a single string (record it and run the FFT), say your guitar E without any other reference. Then ask your subject to tune it down by a fourth (i..e, bring it down to the Pa below). Measure again and see how many cents they are off from a true Pa. Conclusion: Without consonance reference nothing is guaranteed.

Anyways, hope nobody's offended by my cavalier remarks about ancient sages of Indian music . No offence meant. I am just unable to fathom what they might have said. Sorry for the rants.

[arunk]

BTW, Arun, how can you be sure of bringing a string down by a semitone, or even a fifth, without a reference? Try this experiment with musicians as well rasikas...measure the pitch of a single string (record it and run the FFT), say your guitar E without any other reference. Then ask your subject to tune it down by a fourth (i..e, bring it down to the Pa below). Measure again and see how many cents they are off from a true Pa. Conclusion: Without consonance reference nothing is guaranteed.

I agree without a consonent reference nothing is guaranteed. Guitarists can bring their guitar into tune without using beats and consonance (i have seen this done), just by adjusting the open sound of the strings (i.e. they check by how the arpeggio of the open strings sound). Now does this bring it into tune within the required precision at question here? I cant vouch for it, but I cannot dismiss it either. But it is very easy to do additional checks in guitar - so I would guess most guys do perform it to make sure it is in perfect tune. So some reference I think is mandatory to remove human error/imprecision.

In that very first step of the experiment. The "pa" is supposedly dropped down "1 sruthi", which is 22 cents if we are right about the ratios. Prior to the step sa-pa has fifth reference. The step is to bring pa down so that it has ri-pa as a fourth reference. Once you do that, my proposal was you bring other strings down "accordingly" to maintain the sadja grama tuning. Again the theory was they knew how to tune to the grama, and were very familiar with the "sound" of the open strings (say arpeggio).

But the the bigger question is how do they bring the vina initially into sadja grama (and thus here "tune accordingly"), when "ri" and "da" has no direct fifth or fourth relationship with any other swaras? That is still a very valid question.

You can get sa (of course), pa, ma, ni, ga just based on fifth or fourth. But ri and da - they are on their own albeit derivable from 5/4 as in 5/4*4/3 = 5/3 the da (but 5/4 which is most probably also their ntara gandhara as today was explicitly delegated an unimportant status).

I thought you were of the feeling that it is possible to arrive at 5/3 (the da) just from sa if one has a keen sense of all this (?).

Arun

[arunk]

uday,

dont the chitraveena practioneers sometimes tune sympathetic strings to different melas/ragas right (same for some HM instruments)? What references (i.e. fourth/fifth consonance reference points) are used in those cases?

Arun

[uday_shankar]

Arun

Suffice it to say that there are different leagues of hearing and tuning and the guitar stuff is of a much coarser variety. I too can twist the key in a single motion and bring it down "precisely" at the required place and the harmonics can be cross-verified adequately. This misses the more subtle heirarchies of listening and tuning required to grapple with 22 cent differences and smaller intervals.

I thought you were of the feeling that it is possible to arrive at 5/3 (the da) just from sa if one has a keen sense of all this

Might you be missing the distinction here ? There are two types of experiments here:

1) Bring up or down a single string by a certain interval WITHOUT any other string for interval reference. Get it ? Now don't try to tell me that the Dhruva vina is there for "reference". It is not...Bharata seems to ask you to somehow do a naked tune down on a string by 1 shruti !

2) The second experiment is highly practicable. In this case, one string is permanently tuned to a reference say Sa or 1. Now tune a second string at a fixed interval from the first string. Here, I can guarantee a high degree of accuracy for many ratios with respect to it... 9/8, 5/4, 4/3,3/2,15/8, 5/3, etc... This is what I meant by 5/3 being possible. When the Sa reference is always on, all things are possible.

[arunk]

1) Bring up or down a single string by a certain interval WITHOUT any other string for interval reference. Get it ? Now don't try to tell me that the Dhruva vina is there for "reference". It is not...Bharata seems to ask you to somehow do a naked tune down on a string by 1 shruti !

I am not sure I understand. The seven strings at the start are

s r g m p d n

Here sa-pa have fifth consonance.

He asks to bring the pa down "so that it becomes the madyama grama pa". Now he certainly does not spell out how to do this etc. But the madyama grama pa has the fourth consonance relationship with ri i.e. the ri string above. So there is a reference for the "target pitch" one needs to achieve for the pa (post lowering) - it is the ri string.

Maybe I am still not following why this isnt a reference.

Arun

[uday_shankar]

He asks to bring the pa down "so that it becomes the madyama grama pa". Now he certainly does not spell out how to do this etc. But the madyama grama pa has the fourth consonance relationship with ri i.e. the ri string above. So there is a reference for the "target pitch" one needs to achieve for the pa - it is the ri string

Then I stand corrected. Bharata makes sense . Of course, he doesn't spell out how the two "vinas" got magically tuned to the two gramas initially. But still, isn't there somewhere an instance where Bharata asks for a naked reduction by 1 shruti without any consonance reference ? Wasn't the inclusion of consonance at every step your unique contribution in that online essay ?

As regards chitravina, there are standard practices based on consonances to tune the sympathetic strings. There are basically 12 sympathetic strings tuned to mpdnsrgmpdns, typically "shankarabharanam" (typically 1 9/8 5/4 4/3 3/2 5/3 15/8) but changed sometimes to any major raga's melakarta parent.

[arunk]

Dont get me wrong. I do share your some of your skepticism. I have always had this about this 22 cent ifferential particularly when you compare the sa murchana of sadja-grama and sa mucharana of madyama-grama, and similar (if you had the murchanas of both gramsas, you have 14 of them. And there are 7 pairs, which are identical (if you treat them as a scale/model), except for a 22 cent differential. What possible pratical use could that minute difference have served?

Btw, just for kicks. We also dont know whether what "base frequency" sa is typically there in those days. Suppose it is 5 kattai or say 180Hz. 22 cents higher is 182.305Hz i.e. 2.305Hz difference (and for pa of that i.e. 180*3/2 = 270, it would be higher > 3Hz, 266.6 or so). This should be detectable this difference with beats - right? You may not precisely get to 22 cents. But tell the difference between a string at 266.6 vs 270 (against a known reference point of course)

Arun

[arunk]

Wasn't the inclusion of consonance at every step your unique contribution in that online essay ?.

No - certainly not mine. I saw it mentioned in Mukund Lath's book on Dattilam (one of the references quoted in my essay). As soon as I first read it, I must say it was "aaaaahh!!!! So that was how they could have done this seemingly crazy stuff !!!"


Arun

[arunk]

I dont think Bharata (nor others) talks about consonance in relation to this step - so a literal reading and interpretation would lead us to take it as a naked reduction only. But consonance (samvadi) was a huge concept for them - so it is a reasonably good guess that they would have used it in tuning. But still a guess.

Arun