Frequency of notes
Nicky Sandhu
I had seen an article recently which compared the Western
musical notes to Indian shruti's. I am interested in knowing if there
was a mention of the frequency comparision as well. OR if anyone does
know of the exact frequencies of the notes (Sa at 240 Hz, I think)
could you post it?
Also, what is the smallest frequency difference that a normal
person (with a musical ear could detect)? i.e. without resorting to
comparision via beats or other techniques.(By listening to each
note seperately ).
Nicky Sandhu
KEDAR S NAPHADE
>Hi everyone,
> I had seen an article recently which compared the Western
>musical notes to Indian shruti's. I am interested in knowing if there
>was a mention of the frequency comparision as well. OR if anyone does
>know of the exact frequencies of the notes (Sa at 240 Hz, I think)
>could you post it?
One way to go about determining this is to use the fact that the frequencies of *consecutive* notes form a geometric progression, and the shadja in the higher octave has a frequence which is twice the frequency of the lower shadja. With twelve notes between the two octaves, the ratio of the geometric series is approximately 1.059. So if the Sa is at 240 Hz, then the following frequencies will hold for the other notes:
Shadja 240
Komal r.shabh 254.3
Shuddha r.shabh 269.4
Komal Gandhaar 285.4
Shuddha Gandhaar 302.4
Shuddha Madhyam 320.4
Teevra Madhyam 339.4
Pancham 359.6
Komal Dhaivat 380.9
Shuddha Dhaivat 403.6
Komal Nishaad 427.6
Shuddha Nishaad 453.1
Shadja 480
Now all this should be taken with a grain of salt. I believe that most likely this is the manner in which they tune all the electronic keyboards, especially the ones which have a frequency (pitch) adjustment feature. However, if one tunes one's harmonium or any other instrument in this fashion, it would perhaps be unsatisfactory to many veteran musicians. The reason is that the above geometric progression is not precisely valid in Hindustani music.
My harmonium teacher is also an experienced "tuner" of harmoniums. He tunes a harmonium for a solo in a differnt fashion and for accompaniement in a different fashion. A solo harmonium is usually tuned to "safed chaar" or F as the shadja. It will *not* sound well in other pitches, especially so in pitches other than the madhyam and pancham of safed chaar.
Another more obvious and extreme illustration is the different shades of the komal gandhaar in ragas like miya malhar and darbari kanada. These shades are at lower frequencies than the geometric ones. And that is something which is definitely detectable.
> Also, what is the smallest frequency difference that a normal
>person (with a musical ear could detect)? i.e. without resorting to
>comparision via beats or other techniques.(By listening to each
>note seperately ).
Because of the geometric natue of the notes, I somehow feel that the smallest detectable frequency difference may possibly depend on the frequencey too. for example if you can detect between two shades of gandhaar in a lower octave, then you can most probably do that in an upper octave also. However those two shades will be seperated by a larger frequency gap in the upper octave.
I am not sure about this, but if anyone knows about any research that has been done on this, please post or let me know.
Cheers !
Kedar
>Nicky Sandhu
Ajay P Nerurkar
: Hi everyone,
: I had seen an article recently which compared the Western
: musical notes to Indian shruti's. I am interested in knowing if there
: was a mention of the frequency comparision as well. OR if anyone does
: know of the exact frequencies of the notes (Sa at 240 Hz, I think)
: could you post it?
There is no such thing as an exact frequency for any notes in Indian music.
In Hindustani vocal performances., the tuning of the Tanpura defines what
the Sa is, and this depends on the singer. All other notes are
dependent on the Shadja. Again the vakra (komal,tivra) notes are not fixed
even relative to the Sa. Various ragas have various shades of these notes,
and for this purpose terms like 'Atikomal' are used.
: Also, what is the smallest frequency difference that a normal
: person (with a musical ear could detect)? i.e. without resorting to
: comparision via beats or other techniques.(By listening to each
: note seperately ).
Traditionally, a shruti is defined as the smallest sub-division of a note
that is noticeable to a trained humar ear. But there is no universal
agreement on the number of shrutis in the scale, figures ranging from 22 to
infinity are bandied about.
--
Ajay
A N Sreeram
In a recent posting there were a few questions and comments regarding the
division of the octave in Indian classical music (shrutis). I've to disagree
with reply/comments made as they are incomplete and antifactual.
It is true that the shadaja (Sa) in Indian classical music is amorphous, but
once Sa is fixed, as correctly surmised, by the tuning of the tanpura, all other
tones are automatically fixed relative to Sa. The earliest available literature
on our musicological theory is the natyashastra written by Bharat muni. This
text is dated variously between 1500 b.c. all the way upto the first century b.c
.;
by the westerners. The ancient Hindu musical theory beleives it to be an
extension of the Gandharvaveda, most of which got lost in the puranic age.
Neverhteless, no one can deny it to be very very old. Such confusion is apparent
as there have been at least ten different Bhatta, six Someshwara, four Damodara
etc. who have authoured various musical texts, and there have been at least
two sangita-ratnakara, three sangita-narayana, four bharata-shastra and so
on......but enough of that digression.
The natyashastra gives some detail regarding shrutis. However, comments on
the text by Dattila and Kohala in the early part of the previous millinium leaves
no doubt. The octave is divided into a total of 66 shrutis, 22 of which are
`resting positions' (sthanas) and the rest 44 are undulating (andolit). It also
mentions that the octave CAN be divided into an infinite number of
acoustically (harmonically) correct shrutis, however, the number 66 is arrived
at by assuming that the human ear (a very well trained musical ear that is) can
clearly distinguish between the 81st harmonic from the 80th, that brings us
to the second part of the earlier posted question-the smallest frequency
differnce; its actually, the smallest frequency ratio difference. Let me comment
that the divison of the octave presented in the ancient texts (which is still
followed in Hindustaani classical is acoustically correct, where as the
Western scale (equal temperament) is not. When you play (or sing) more than one
the note of the western scale together you hear noise (beats-in acoustic
treminology) and all cords are acoustically discordant; but you do the same
with any of the shrutis, they are always, in priciple acoustically harmonic.
You can easily prove it for yourself with a little help from any standard book
on sound waves. Let, me get back to shrutis later and first address the question
of smallest interval.
According to Natyashastra and also Birhadesi (written by Matanga muni
written a few centuries after the comments by Kohala and Dattila, the smallest
interval (shruti) is defined as the difference between Dha , considered as
upper fourth from Ga, and Pa as the lower fourth from Ri (Re), which is
nothing but 81/80, as mentioned before. Proof:-
Ri = 9/8xSa; Tar Ri = 9/4 (Sa); Sa->Madhya saptak
Ga = 5/4xSa
Ma = 4/3xSa and Dha = 5/3xSa
therefore, Ga raised to Ma is 5/4x4/3 = 5/3 which is Dha-----I
Re (tar) reduced by fourth (Ma) is 9/4x3/4 = 27/16-----------II
difference between II and I is 27/16x3/5 = 81/80 Q.E.D.
which is called (and termed both in Natyashastra and Brihadesi) to be `pramana shruti'.
The Greeks later called it as comma diesis.
But, remember, Sa is `floating'; but once fixed by tuning, say tanpura, that being the most
common practice, all else is fixed and very clearly defined.
Now, lets get back to the problem of the shruti division. As mentioned before, there are
sthanas and andolans in the shrutis. Only the 22 sthanas can be used to make ragas (using the
principal of `murchanas'; which is another topic) and the other 44 andolans can never be
sthanas, but the 22 shatnas (shrutis) can be used both as sthanas (sustained note/tone) and
as andolit (undulating). And not all of the 22 shatans can be used in a single raga.
The andolan (the rest 44 of the 66) are called kan; n pronounced as n in Ganesh.
The previous reply was therefore incorrect and incomplete in terms of shruti frequencies;
one talks about frequency ratios and not absolute frequencies in Indian classical music. That
is essentially how sound waves behave, by frequency ratios. You can always, back-calculate
the absolute frquencies once Sa has been fixed; but Indian classical musicians and musicologists
do not talk in terms of absolute frequencies, but always in frequency ratios, i.e. things that
emanate once Sa has been tuned.
Regarding the same e-mail posted, the author had expressed
confusion regarding atikomal and komal swaras; there is no confusion, these are totally
different swaras. I guess, the reason behind the confusion is perhaps when the ragas are
classified as sampurna, shadava, odava etc. All it means is that if any kind of all swaras
are present then its a sampurana raga. Let me give you an example; let's consider a very
popular (and difficult to perform) raga, raga Darbaari Kanada; it has atikomal andolit
komal gandhar (kk-Ga) and also atikomal dhaivat (kk-Dha). But its still called a sampurna raga
(it has in addition, Sa, Ri (Re) Ma Pa and Ni). Do not confuse between komal and atikomal
swaras; they ARE different swaras. Lets take another e.g. say Ramdasi malhaar or Miyan ki malhaar,
both have all kinds of Ni [atikomal Ni (16/9xSa), komal Ni (9/5xSa), shuddha Ni (15/8xSa)
and tivra Ni (243/128xSa)], yet it is notated (by westerners) as having only komal and shuddha Ni,
and that other `shades' are shown, in effect, you now know what these `shades' mean, just
various nuances of Ni shrutis.
It is important not to look at ragas from the western musical approach, i.e., containing these
swaras and not containing those swaras etc.. This does give you a rough idea as to what the
contents of the raga are, but it is incomplete. The swaras are like the skeleton, it is the
meends (glides between notes/tones) that give the shape of the body of the raga. The continuity
of tonal space is not there in the western musical theory, so they look at ragas just by what
notes they have and often wrongly term shrutis as quatertones, etc. They are not `quarter-tone'
intervals, they are strict microtonal harmonic subdivisions of the tonal space. I always
quote a very common example (raga Bhupaali and Shuddha Kalyan) whenever people ask me
regarding this.
Both, raga Bhupali and Shuddha Kalyan have the notes Sa, shuddha Re, shuddha Ga, Pa & shuddha
Dha, both in accent and descent. So in the simplistic approach, both ragas are identical,
(both are performed in the evenings and have the same notes/tones); certainly not. The
mood of raga bhupali is that of bhakti (devotion) and that of shuddha kalyaan is that of
gambhir (seriousness). It is the way the meends are given that makes these two ragas
sound exceedingly different. Shuddha kalyaan also uses a more vakra (zigzag) pattern of
notes/tones than bhupali, but it is the way to connect Ga to Pa and Dha to Sa (both in
ascent and descent) that brings out the difference; and the shuddha kalyan
thus becomes extermely difficult to perform. Please do not, therefore, restrict yourself as to
what notes/tones are present in the ragas, look (listen very very carefully, again and agian) at
how the continuity in tonal space is acheived.
A good example is to look at raga shuddha kalyan performances by Pt. Bhimsen Joshi, 1922-
(I know of three recordings; 1991/92 Moment records (CD), Maestro's Choice (both tape and CD)
and in a four cassette complilation by HMV, 1992, titled `The Multifaceted Pt. Bhimsen Joshi',
there is a CD of the same title which essentially is a selection from those 4 tapes, but I
am not sure if it has shuddha kalyan). Then compare it to
another great performance, raga bhupaali by Ustd. Bade Ghulaam Ali Khan, 1901-69, which is
an All India Radio release of the performance through HMV. I cited these two, because
they are two of the greatest vocalists of the century, and why not listen to the subtle
differences between the two ragas performed by the very best. There is, of course, a multitude
of recordings of these two ragas, both in vocal and instrumental available; but be cautioned,
there are two kinds of shuddha kalyaan, the one cited here is called the bhup-ang, the other
being the yaman-ang, in which, the ascent is the same, but in the descent Ni and Ma (both
shuddha) are used in addtion as `resting' positions (sthanas and not andolanas).
Anyways, here's a frequency ratio table of the shrutis (I am giving the 22 sthanas only):-
# name of the shruti frequency ratio (from Sa)
0(22) Shadaja Sa 1/1
1 Atikomal Ri 256/243
2 Komal Ri 16/15
3 Madhya Ri 10/9
4 Shuddha Ri 9/8
5 Atikomal Ga 64/54
6 Komal Ga 6/5
7 Shuddha Ga 5/4
8 Tivra Ga 81/64
9 Shuddha Ma 4/3
10 Ekasrhuti Ma 27/20
11 Tivra Ma 45/32
12 Tivratara Ma 729/512 (64/45)
13 Panchama Pa 3/2
14 Atikomal Dha 128/81
15 Komal Dha 8/5
16 Tishruti Dha 5/3
17 Shuddha Dha 27/16
18 Atikoma Ni 16/9
19 Komal Ni 9/5
20 Shuddha Ni 15/8
21 Tivra Ni 243/128
22 Shadaja (tar) Sa 2/1
Note:-
1. The intervl between atikomal ri and komal ri is (16/15)/(256/243) = 81/80, other
intervals being 256/243 and 25/24 ( for these 22, more for the total of 66).
2. The Carnatic shruti is sligthly different for only a few, but Hindustaani shrutis are
just as above (given in natyashastra, though only the Ri-garama part of that text is available,
the above is for Sa-grama, i.e. frequency ratio from Sa, all of the S- Ri- Ga- and Ma-gramas
were already calculated by the ancient munis and rishis).
3. The western musicians use only 12 in all, viz., #s 0, 2, 4, 6, 7, 9, 11, 13, 15, 17, 19,
20 and 22; this used to be their earlier scale (the do re mi fa so la........). Ironically,
thier earlier scale is harmonically truer than thier modern scale, which is called equal
temperament, where all of these 12 are spaced 2 to the power of 1/12 each, which leads to
`noise'.
One interesting thing, if you missed it, is that all of the shrutis, the above 22,
can be experessed as products (and dvisors) powers of 2, 3 and 5, which are in acoustically
correct ratios, once the assumption of pramana shruti is made. If you feel like it, you can
derive all of these shrutis and rest of the 44 to prove it to yourself. If you are very much
more enthusiastic, find even a smaller pramana srhuti and make their # larger or even infinite,
but it will collapse in tonal space so close that, for human ears, most of them will be
indistinguishable.
Quote for Brihadeshi:-
``Aanantyam tu shrutinaam cha darshayanti vipashchitaha, yatha dhvani visheshanaamaananyam
gaganodare''
Translation:-
the adept ones show the infinity of shrutis, thus there is the infinity of
particular dhvanis in the `belly' of the space (tonal).
``idaaneem shashtashista bhedabhinnah shrutayah kathayante''
Translatio:n-
Now shrutis are being shown as being differentiated into sixty-six kinds...............
.
.
then Matanga muni, proceeds its derivation and shows how a vina can be tuned to 22 shrutis
and also how all of 66 can be `generated' from the instrument..............
Boy, that was a huge e-mail, and I thought I could have addressed the question briefly!
Navid Badie
: Also, what is the smallest frequency difference that a normal
: person (with a musical ear could detect)? i.e. without resorting to
: comparision via beats or other techniques.(By listening to each
: note seperately ).
: Nicky Sandhu
Apparently, sensitive ears can detect a frequency change of 1 Hz at
500 Hz. This translates to an interval of about 3.5 cents, or 1/30th
of a tempered semitone. That is pretty amazing to me, but it is reported
in many references. In french texts, they have a unit called
a "savart" which represents 4 cents, which must be related to this
maximum sensitivity.
Cheers,
--Navid Badie