Derivation of the 22 Srutis


Transliteration scheme : -



a A i I u U e ai o au ( the anuswara and visarga do not figure in this  



k       kh      g       gh

ch      chh     j       jh

T       Th      D       Dh      N

t       th      d       dh      n (n gets modified as in tank, lung, lunch, enjoy )

p       ph      b       bh      m

y   r   l    v (w)  S   sh   s   h


The Tamizh words are transliterated as pronounced, with the use of E and O 

for the long vowels. The consonants denoted by zh, L and R are unique to 





Murali Sharma posted a primer on Hindustani music (written by Dinesh 

Prabhu) for inclusion in the FAQ some time ago.  The question of the 

number of SrutIs in an octave has arisen again.  As Dinesh says, the 

amount of confusion and controversy regarding the no. of SrutIs in an 

octave is huge.  However, I do not think that trying to make some sense 

out of all the conflicting claims, is a non-issue with respect to music as 

it is practised today.  The frequency ratio values that one derives may 

well be open to question, but the fact remains that some basis set is used 

in both Hindustani and Carnatic music as of today.  Out of  the various 

numbers 12, 16, 22, 24, 44, etc. to infinity that have been proposed, let 

us examine each number and see what can be acceptable.


If one accepts a working definition of Sruti as "the raise in pitch for 

the note to be identified as another one", the rigorous answer to the 

question is infinity.  On the other hand, there are some problems which 

this leaves unanswered. Say a musician slips out of pitch at the panchama. 

What is the means by which one identifies this as a 'slip from the 

panchama', rather than as a dhaivata or as a madhyama?  Such a problem 

forces one to try to identify musical intervals in a more precise way.


Both Hindustani and Carnatic music today, use the concept that shaDja and 

panchama are invariant notes, while the other five notes admit of 

variations.  It would therefore seem that Hindustani music uses 12 (two 

varieties each for r, g, m, d and n), while Carnatic music uses 16 (three 

varieties each of r, g, d and n, and two varieties of m).  The answer is 

not that simple however, because the various shades of the same note that 

are used in different ragas are not accounted for by these numbers. 

Furthermore, 16 arises only from a superposition of four notes with some 

from the set of 12, so that 12 is the number of swarasthanas that both 

systems use.  16 is pertinent only for the construction of the 72 

meLakarta system. 


The number 22 has been used historically by Bharata and in ancient Tamizh 

music as seen from the SilappadikAram references.  At least for the sake 

of historical evolution, 22 is of some interest.  24 is suggested from an 

argument that each of the 12 semitones should have a higher and a lower 

variety.  This does not make sense as far as sa and pa are concerned, so 

that if we reject two varieties for these two notes, we again end up with 

the number 22.  I am not conversant with the arguments in favour of or 

against the higher numbers like 44, 49 etc. which have been suggested, so 

I am not going to talk of them.


One possible significance for the number 22 has been suggested on the 

basis of pi, so that 22 SrutIs are distributed among 7 swaras.   

Personally, I do not think there is much to this theory except the 

remarkable coincidence.  I have yet to see a convincing argument for this, 

unless one accepts some sort of mystic significance, which cannot be 

scientifically validated nor falsified.


In the following posts, I shall attempt to rationalize the number 22 as 

used in ancient writings based on certain first principles.  I hope we can 

generate a discussion that will clarify matters enough so that we can have 

a comprehensive account in an FAQ. 


S. Vidyasankar


We all know that a vibration of a string or an air column can be studied 

in terms of the fundamental modes which give rise to the various 

harmonics.  The 2nd harmonic is the octave (called stAyi or iNai) while 

the third harmonic is the perfect fifth in the higher octave.  This 

directly gives us a value of 3/2 for the perfect fifth in the middle 

octave, with respect to the tonic as 1.  The octave (tAra stAyi shaDja) 

has a value 2.  Right at this stage, we have thus fixed three numbers (1, 

3/2 and 2) which are fundamental to our musical perception.  The fourth 

harmonic gives rise to the perfect fourth, which thus gets the value 4/3.  

The fifth harmonic is clearly important as it can be heard distinctly from 

a perfectly tuned tambUra.  This now gives the value 5/4 for the perfect 

third.  In all these cases, these numbers can also be interpreted as the 

reciprocals of the lengths of a vibrating string, as measured from the 

leftmost node. 


The sixth harmonic gives again a note related to the perfect fifth, while 

the seventh harmonic is clearly unpleasant.  (This is something like "from 

this it follows that" in a math exam when you don't know how to complete 

the proof!)  Let us see how we can derive other frequency ratio values 

just based on these numbers i.e. 1, 5/4, 4/3, 3/2 and 2.


In the subsequent discussion, I shall use the following symbols for the 

twelve semitones


sa ri Ri ga Ga ma Ma pa dha Dha ni Ni


for the sake of convenience.  We have the following relationships between 

the various notes.


   Table I


 1.      sa : Sa         =       1 : 2,

 2.      sa : pa         =       1 : 3/2

 3.      sa : ma         =       1 : 4/3

 4.      sa : Ga         =       1 : 5/4


The other notes can be derived from a cycle of fifths (called iLikramam in 

Tamizh texts).


   Table II


 1.      sa's panchama   =       pa

 2.      pa's panchama   =       Ri

 3.      Ri's panchama   =       Dha

 4.      Dha's panchama  =       Ga

 5.      Ga's panchama   =       Ni

 6.      Ni's panchama   =       Ma


or from a cycle of fourths.


   Table III


 1.      sa's madhyama   =       ma

 2.      ma's madhyama   =       ni

 3.      ni's madhyama   =       ga

 4.      ga's madhyama   =       dha

 5.      dha's madhyama  =       ri


In each case, whenever the cycle takes you to the higher octave, i.e. 

gives you a number greater than 2, divide by 2 to get back to the middle 

octave.  This gives the following ratio values for the various notes.


       Table IV 


  sa      =       1

  ri      =       256/243

  Ri      =       9/8

  ga      =       32/27

  Ga      =       81/64

  ma      =       4/3

  Ma      =       729/512

  pa      =       3/2

  dha     =       128/81

  Dha     =       27/16

  ni      =       16/9

  Ni      =       243/128



If you notice the value calculated for Ga from the fifths cycle, it is 

higher than 5/4 by a factor of 81/80.  This is the value that Bharata 

calls pramANa Sruti.  The SilappadikAram characterizes this as 'pakai' 

meaning enmity.  This value 81/80 is the famous Pythagorean comma, that 

comes from the seven ancient Greek modes. This ratio of 81/80 has 

relevance if one has an instrument like the yaazh (like a harp), and is 

trying to tune the gandhara string.  The question that the musician then 

faces is whether to tune the gandhara string to be in tune with the fifth 

harmonic arising from the shaDja string (5/4), or to tune it as per the 

panchama cycle.  In addition to this, if one back calculates for Dha and 

Ri based on the value of 5/4 for Ga, one gets the values Dha = 5/3, 

instead of 27/16 and Ri = 10/9, instead of 9/8.  Similarly, the 

calculation for Ni gives Ni = 15/8, instead of 243/128.  In each case, 

this calculation is identical to applying the pramANa Sruti value of 81/80 

to the values already derived.  As an aside, it may be mentioned that the 

value 81/80 does not arise as a factor that relates the fifths cycle to 

the fourths cycle, as popularly thought.  It arises from the discrepancy 

introduced by carrying out the fifths cycle, as compared to the note 

arising from the fifth harmonic. 


This may be well and good as far as the notes related immediately to Ga = 

5/4 by the fifths cycle is concerned.  Is there any basis for applying the 

same ratio to the other notes also i.e. the ones obtained from the fourths 

cycle, and to the panchama itself?



We have calculated a set of 12 values for the 12 semitones, starting from 

basic principles of vibrating strings.  We have also seen the possibility 

of generating two different values for the same semitone (Ga or Ri or Dha 

or Ni) so that now the problem is one deciding between two different 

values for the same semitone.  If Indian music were to be based on 

straight notes, without any modification of the notes by means of 

oscillations and shakes (kampita gamaka), or by means of varying the 

stress on the note (spurita or pratyahata) etc. then the question of 

choosing one of the two values for a semitone is a tough problem.  Since 

we have the facility to accomodate a variety of frequency ratio values for 

the same semitone, let us go ahead with all the values which we have 

calculated now.


The values of the 22 srutis can be obtained by simply applying the ratio 

81/80 to all the notes obtained here.  In the case of the cycle of fifths, 

divide by this ratio, while in the case of the cycle of fourths, multiply 

by 81/80 i.e. augment the notes from the fourths cycle and flatten the 

notes from the fifths cycle.  Leave sa and Ma alone (yes Ma, not pa!).  If 

this is done, the set of numbers so obtained is the same as that described 

by Bharata.  The seemingly odd ratio 40/27 that is obtained for the 

flattened fifth was definitely described by Bharata in the madhyama grAma. 


What is the basis for doing this?  The answer lies in the fact that the 

various ragas in use in ancient times were derived by a technique of graha 

bheda (tamizh 'kural tiripu').  For example, Bharata's shaDja grAma was 

the same scale as that of kharaharapriya (kAfi thAT)


sa   Ri      ga      ma   pa  Dha   ni           =          shaDja grAma

1   10/9  32/27  4/3   3/2   5/3   16/9.


The other scales were obtained by graha bheda from shadja grAma.  

Similarly the basic scale of ancient tamizh music was pAlaiyAzh, the same 

scale as of harikambhoji (khamaj thAT), and the other pAlais (scales as 

opposed to paN = rAga) were obtained by kural tiripu from this scale.


sa   Ri   Ga   ma   pa   Dha   ni               =           pAlaiyAzh

1    9/8   5/4  4/3   3/2   5/3   16/9.


Seven scales can be obtained by shifting the reference to another note.  

The scales obtained are identical irrespective of whether we start from 

shaDja grAma or from pAlaiyAzh.  This is because these two scales 

themselves are derivable from each other by shifting the reference.  Thus 

pAlaiyAzh with pa as the tonic gives arumpAlai, which is the same as 

shaDja grAma.  Similarly the scale obtained from shaDja grAma, by shifting 

the tonic to ma is the same as pAlaiyAzh.  As one goes through the process 

of shifting the tonic, the only new ratios one generates are related to 

the values generated till now, by the ratio of 81/80.  This is because 

both scales contain two notes that deviate by this factor from the cycle 

of fifths value.  If we had used 9/8 and 27/16 instead of 10/9 and 5/3 

respectively in shaDja grAma, all ratios are related by the cycle of 

fifths and we would obtain no new ratio values by doing graha bheda. 


The ratios that are generated by this process are tabulated below.


      Table V


    sa = 1

    ri = 256/243, 16/15  = (81/80) x (256/243)

    Ri = 10/9,     9/8   = (81/80) x (10/9)

    ga = 32/27,    6/5   = (81/80) x (32/27)

    Ga = 5/4,     81/64  = (81/80) x (5/4)

    ma = 4/3,     20/27  = (81/80) x (4/3)

    Ma = 64/45 ,  45/32, 729/512 = (81/80) x (45/32)

    pa = 40/27,    3/2   = (81/80) x (40/27)

   dha = 128/81,   8/5   = (81/80) x (128/81)

   Dha = 5/3,     27/16  = (81/80) x (5/3)

    ni = 16/9,     9/5   = (81/80) x (16/9)

    Ni = 15/8,   243/128 = (81/80) x (15/8)


Note that we have a total of 24 values.  Surely all these values were 

calculated by ancient musicologists such as Bharata, because he clearly 

derives scales by graha bheda.  Still he talks of 22 SrutIs.  Similarly, 

the SilappadikAram talks only of 22 'mAttirais', though all the scales 

such as viLarippAlai, mErcempAlai etc. are derived by kural tiripu.  Did 

these people make a mistake when they counted 22 instead of 24?  I should 

think not.  Before we try to rationalize the 22 vs. 24 conflict let us 

have another look at the way these numbers are obtained.


The cycle of fourths and the cycle of fifths are based on two key 

consonances.  The fifth consonance (tamizh iLi) is based on the ratio 3/2 

and the fourth consonance (tamizh natpu) is based on the ratio 4/3.  Note 

that these consonances are reciprocal to each other. sa : pa = 3/2, but pa 

: sa (higher octave) = 4/3.  Bharata combines these in the phrase 

vadi-samvadi.  Thus the cycle of fourths is not independent of the cycle 

of fifths.  If we start from ni, and proceed by a cycle of fifths, we get


ni - ma - sa - pa - Ri - Dha - Ga, i.e. we have obtained all seven notes 

in an octave.  The other notes are obtained by carrying through this cycle 

once more to get


Ga - Ni - Ma - ri - dha - ga.


This may have been the basis for reckoning an octave from ni rather than 

sa in olden times.  In fact the tamizh scales pAlaiyAzh, marutayAzh etc. 

were obtained by precisely this method.  However one must remember that 

these cycles can theoretically be carried on ad infinitum, because they 

will never give the correct value of 2 for the octave.  They are based on 

a geometric series with a ratio 3/2 (or 3/4 in order to keep each term 

between 1 and 2).  As such the number 2 is the limit of these cycles.  

Which is why the two cycles stop making practical sense beyond the first 

few terms.  How many is few?  The very fourth and fifth terms in the 

fifths cycle generate a dissonance with the notes obtained from the fifth 

harmonic, so that beyond the seventh or eighth term, we should probably 

not stick to this cycle.


In order to figure out the number of SrutIs in an octave, let us list the 

numbers we have obtained in two groups, in terms of the pUrvanga (sa to 

ma) and the uttarAnga (pa to Sa).  As of now, let us ignore the other 

values from the table.  Thus the two groups are



I.      sa        ri           Ri         ga        Ga       ma




II.     pa        dha       Dha           ni         Ni       Sa




Here the interval between two consecutive ratio values is marked by a  _ .  

>From this format, we see that


(1) the ma (4/3) is 9 intervals away from sa, in keeping with both 

traditions.  Other such 9 interval distances are -

ni (lower octave) to ga (32/27 : 8/9 = 4/3); Dha (lower octave) to Ri

(9/8 : 27/32 = 4/3) and pa to Sa (2 : 3/2 = 4/3), thus allowing us to say


  9 SrutIs        <=>  4/3.


(2) the intervals are not of equal distances.  In that sense one Sruti 

could mean different values in different contexts.  However between two 

values for the same note, the distance corresponds to 81/80 of the lower 

value.  This is what is called as 1 mAttirai or pramANa Sruti.


(3) the following 4 interval distances are equal.


  sa - Ri         =       9/8

  Ri - Ga         =       81/64 : 9/8          =  9/8

  pa - Dha        =       27/16 : 3/2          =  9/8

  Dha - Ni        =       243/128 : 27/16      =  9/8

  ni - Sa         =       2 : 16/9             =  9/8


Therefore,              4 SrutIs        <=>   9/8.


This is the reason for using the term ChatuSruti rishabha.  The Ri (9/8) 

is four SrutIs away from sa.  Similarly, the ChatuSruti Dhaivata (27/16) 

is four SrutIs away from pa. 


 The relationship between ni (of the lower octave) and ma is that 

of a fifth.  How many intervals are there between the two notes?  Since 

the number of intervals is simply additive, there are 4 (ni to sa) + 9 (sa 

to ma) = 13 intervals.   Similarly, the interval from pa to Ri (in the 

higher octave) is 9 (pa to Sa) + 4 (Sa to Ri) = 13 intervals.  The 

relationship is again that of the fifth.  Similarly, for Dha to Ga (higher 

octave) and for dha to ga (higher octave), the distance is again 13 

intervals and the relationship is that of the fifths.  Thus '13 intervals' 

is characterized by the consonance ratio 3/2. 


i.e.                  13 SrutIs         <=>    3/2


Therefore between sa and pa, there must be 13 intervals.  Since there are 

9 intervals between  sa and ma, there must be 13 - 9 = 4 intervals between 

ma and pa.  Is this valid?  The relationship between ma and pa is 3/2 : 

4/3 = 9/8.  In (4) above, we saw that 4 srutis = 9/8.  Thus the 

postulation of 13 srutis between sa and pa is consistent with the 

postulation of 9 srutis between sa and ma.  The number 22 for the number 

of srutis between sa and Sa can now be easily explained.  As there are 13 

srutis between sa and pa, and 9 srutis between pa and Sa, there are 13 + 9 

= 22 srutis between sa and Sa.  In the interval from sa to Ri, there are 

the following ratios - 1, 256/243, 16/15, 10/9 and 9/8.  Thus 9/8 is the 

fourth ratio from sa, which is why 9/8 represents a 4 sruti interval.  On 

the other hand, between ma = 4/3 and pa = 3/2, we have calculated the 

following ratio values in Table V.


      ma                      Ma                        pa

 4/3  x  27/20  x  45/32  x  64/45  x  729/512  x 47/20  x  3/2


Clearly we have calculated more ratios in this interval than in the sa to 

Ri interval.  Yet the sa to Ri and the ma to pa intervals are both 

characterized by the ratio 9/8.   This means that some of the values 

obtained for Ma need to be discarded.  Which were the values that Bharata 

discarded?  It is clear that Bharata retained 40/27 as a valid ratio, 

because it appears in his madhyama grAma.  Hence he must have discarded 

some of the values calculated for Ma.   Is there a basis for selectively 

discarding some values of Ma?   To clarify these issues, let us look at 

other relationships between the various ratios.  Since we have now 

satisfactorily shown that an octave does indeed contain 22 srutis, in the 

sense that 4 srutis = 9/8 and 9 srutis = 4/3, we can easily see the 

following relationships.  In these, addition of sruti intervals 

corresponds to multiplication of ratio values.


sa - Sa = sa - ma + ma - pa + pa - sa

       <=>  9     +   4     +     9

 = 4/3 x 9/8 x 4/3

 = 2.


sa - Sa = sa - pa + pa - sa

       <=>  13    +     9

 = 3/2 x 4/3

 = 2.


In the tamizh pAlaiyaazh,


sa-Sa = sa-Ri + Ri-Ga + Ga-ma + ma-pa + pa-Dha + Dha-ni + ni-Sa

     <=>   4  +   3   +   2   +   4   +   3    +    2   +   4

      = 9/8 x 10/9 x 16/15 x 9/8 x 10/9 x 16/15 x 9/8 = 4/3 x 4/3 x 9/8

      = 2.



In shaDja grAma


sa-Sa = sa-Ri + Ri-ga + ga-ma + ma-pa + pa-Dha + Dha-ni + ni-Sa

     <=>  3   +   2   +   4   +   4   +   3    +   2    +    4

      = 10/9 x 16/15 x 9/8 x 9/8 x 10/9 x 16/15 x 9/8 = 4/3 x 9/8 x 4/3

      = 2.


Since the other major scales were all obtained by shifting the 

tonic from shadja grAma or from pAlaiyaazh, they all preserve this 

division of the octave into three 4 Sruti intervals, two 3 Sruti intervals 

and two 2 Sruti intervals.  When we talk of a 4 Sruti interval, we mean a 

ratio of 9/8.  Similarly a 3 Sruti interval refers to 10/9 and a 2 Sruti 

interval refers to 16/15.  In all cases, the distance is with respect to 

sa.  This is because 9/8 is the 4th Sruti from sa, 10/9 is the 3rd Sruti 

from sa and 16/15 is the 2nd Sruti from sa.  When we talk of a certain 

number of SrutIs, we always mean that ratio whose position is that many 

intervals away from sa.  Thus 1 sruti is 256/243.  Can the value of 1 

sruti also be 81/80?  This is context specific, because the number 81/80 

refers to the relative distance not from sa, but between two values of the 

same note.  It is to distinguish this fact that Bharata has used the word 

pramANa Sruti for the value 81/80.  Thus the number 22 for the number of 

srutis in an octave arises not from some mysterious association with a 

circle's circumference and its diameter, or from a mindless repetition of 

the cycles of fourths and fifths, but from criteria based on valid musical 

principles of consonance  and dissonance, coupled with the technique of 

shifting the tonic to obtain different melodic scales.  The use of Sruti 

intervals gives numbers that can be added instead of using ratios that 

needed to be multiplied, without resorting to logarithms.  For example, if 

the number 22 is broken up as a sum of two numbers, in all possible 

combinations, we have


22 =     1 + 21 (<=> 256/243 x 243/128 = 2)

 =       2 + 20 (<=> 16/15 x 15/8 = 2)

 =       3 + 19 (<=> 10/9 x 9/5 = 2)

 =       4 + 18 (<=> 9/8 x 16/9 = 2)

 =       5 + 17 (<=> 32/27 x 27/16 = 2)

 =       6 + 16 (<=> 6/5 x 5/3 = 2)

 =       7 + 15 (<=> 5/4 x 8/5 = 2)

 =       8 + 14 (<=> 81/64 x 128/81 = 2)

 =       9 + 13 (<=> 4/3 x 3/2 = 2).


In order to account for the sums 10 + 12 and 11 + 11, we first need to 

decide what the 10th, 11th and 12th srutis are.  In Bharata's system, we 

are certain that the 12th sruti is 40/27, because that is the value of the 

panchama in his madhyama grAma, and it is deficient with respect to the 

perfect panchama (3/2) by one pramANa Sruti.  If that were the case, in 

order to satisfy 10 + 12 = 22, the 10th sruti has to be 27/20 i.e. the 

value obtained by augmenting the ma by one pramANa Sruti.  The 11th Sruti 

can rigorously satisfy the relationship 11 + 11 = 22, only if the 11th 

sruti is given a value 2^(1/2).  Thus


22      = 10 + 12 (<=> 27/20 x 40/27 = 2)

        = 11 + 11 (<=> 2^(1/2) x 2^(1/2) = 2).


If we now go back to the ratio values obtained between 4/3 and 3/2 

in the table, we find the numbers 27/20 and 40/27.  However, 2^(1/2) is 

impossible to find there, simply because 2^(1/2) is not a ratio.  It is an 

irrational number.  2^(1/2) is the value for Ma in the tempered scale of 

Western classical music.  We however have three different values 45/32, 

64/45 and 729/512 for Ma in our table.  45/32 and 64/45 are actually very 

close approximations to 2^(1/2).  Are there any musical guidelines by 

which we can choose one of these to be the Ma?  Is this supported by 

actual musical practice?  The answer is yes, because we do not see many 

shades of Ma in either Hindustani or Carnatic music.  Is there a 

sufficiently strong argument to discard some values of Ma and retain only 

one?  It would seem so, because although the sa-Ri interval and the ma-pa 

interval are mathematically equivalent, there are some crucial differences 

between them.  The human ear can distinguish at least two distinct shades 

of ri (as in sAveri and Ahir Bhairav) and Ri (as in KharaharapriyA and 

SankarAbharaNam) in the sa-Ri interval, whereas  between the ma and pa, 

one is not able to distinguish that many shades of prati (tIvra) madhyama.  

This is because the melodic experience is conditioned by the pitch of the 

tonic.  The ability or inability to distinguish various values of a note, 

is a direct consequence of relating that note to the shadja.  In 

Hindustani music, and in panchama-varja Carnatic ragas like Ranjani, where 

the prati madhyama is a plain note, the vadi-samvadi relationship 

projected is that between Ni and Ma.  In most Carnatic ragas, the prati 

madhyama is handled in conjunction with the panchama.  In no raga is the 

fourths relationship between ri and Ma prominent.  In either case, the 

prati madhyama is a very weak note, that uses some other note as a crux, 

in order to define itself.  All the more reason why it does not make much 

sense in practical terms to count all the calculated ratio values for Ma 

as defining valid Sruti intervals.  This uneasy position of the prati 

madhyama in the octave, may be one reason why there are so few ragas using 

this note that are in current practice, as compared to the profusion of 

rAgAs using the suddha madhyama.  However, it is not possible to 

confidently assert that Bharata used this or that value and rejected the 

others.  What we are certain about is that he did retain only one value 

out of the three calculated.  As for the ancient Tamil music, the ratios 

40/27, 27/20, 729/512, 45/32 and 64/45 all figure in the scales derived by 

kural tiripu.  Still as only 22 mAttirais are talked of in one octave, two 

of these ratios were definitely discarded for practical purposes.  It is 

possible that  the 10th and 12th srutis in the Tamil system were also 

27/20 and 40/27, in order to be consistent with the sum 10 + 12 = 22.  

This is not so sacrosanct however.  The description of 22 srutis or 

maattirais was based on contemporary practice and not just on dry 

arithmetic.  Consequently, it is difficult to say with any degree of 

certainty, which ratios were actually used. The other definition of the 

word Sruti is helpful in understanding this. A Sruti has been described as 

the raise in pitch necessary before the note can be distinguished as 

another note.  Consequently, even if two different values are used for a 

prati madhyama, the higher value is still not identifiable as the 

panchama.  Thus it does not make much sense to talk of a musical interval 

between two values of the prati madhyama.  On the other other hand, 

because of the perception of the fifth harmonic, it does make sense to 

distinguish between two values for the Ga (5/4 and 81/64), because that is 

definitely perceived as a dissonant interval.  Therefore, the grouping of 

all possible Ma values under one musical interval is still consistent with 

actual practice.


It is pertinent to close this discussion with a note of how these 

22 SrutIs affect our musical perception.  As an individual's sensitivity 

grows, the ability to detect minute variations in pitch becomes better.  

Consequently, even a small change in pitch sounds dissonant and 

unpleasant.  In that context, the number of Sruti intervals is infinite.  

In all the vikrti swaras, the usage of kampita and other gamakas gives us 

the flexibility to actually produce all possible ratios that we derived, 

and possibly other intermediate values as well.  However in the case of 

the prakrti swara pa, what role does a number such as 40/27 play?  The 

answer lies in the fact that the concept that pa is a prakrti swara with 

no variations is a later evolution in the history of Indian classical 

music.  Similarly, the ratio 81/64 is used in ragas like kalyANi, where 

the Ga is higher than in say SankarAbharaNam, but then the dissonance is 

masked by the use of a large shake given to the Ga.  In general, we tend 

to use 5/4 for the Ga, in ragas which have Ri, Ga and ma, while we use 

81/64 also in ragas with ri, Ga and ma or Ri, Ga and Ma.  Similarly 5/3 is 

used for the Dha in ragas in which the immediately following note is ni, 

whereas if it is Ni, the higher value of Dha (27/16) is prominent.  The ma 

in a rAga like bEgaDa in Carnatic music is definitely higher in pitch than 

the perfect fourth, and it corresponds to a value of 27/20.  Thus which 

specific srutis are used in a given raga, is a matter of tradition and 



On the other hand, the ratio 81/80 is a dissonant interval arising 

naturally out of the laws which govern the very production of musical 

sound.  It is the recognition of this natural phenomenon which led our 

ancient musicologists to derive the concept of 22 SrutIs.  The 22 Sruti 

concept represents a non-logarithmic approach to deal with simple numbers 

which can be added instead of ratios which need to be factored or 

multiplied.  It was by means of this concept that the "just" intonation in 

Indian music was represented in terms of simple numbers without recourse 

to logarithmic values or equally tempered scales.  Furthermore, it is the 

Sruti concept which takes into account the fact that our perception of any 

note is always with respect to the reference sa.  This is a basic 

prerequisite in a musical system that is based on melody rather than 

harmony.  22 SrutIs arise naturally out of the application of the concepts 

of 1) consonance and dissonance to the swaras in a scale, and 2) 

derivation of new scales by shifting the tonic.  The shifting of the tonic 

is a powerful method to obtain new scales from existing ones, and has been 

used later in the history of Carnatic music, in the formulation of the 

meLakarta scheme.  The rationalization of the 22 sruti concept, as shown 

here, shows us how the successive application of the fourth or fifth 

relationship can be carried only upto a point.  Thus the fifths cycle is 

used only upto the prati madhyama (sa-pa-Ri-Dha-Ga-Ni-Ma) and the fourths 

cycle upto the suddha rishabha (sa-ma-ni-ga-dha-ri).  Even upto this 

point, the two cycles generate dissonance because of the closeness of the 

notes thus obtained, to those arising out of the 5th, 6th, 8th and 9th 

harmonics.  This is a consequence of our constant perception of the 

reference sa, which has components of all these harmonics, as seen from 

the physical laws of vibrations, which hold for vibrating strings and for 

air columns e.g. the human voice or the flute.  The concept of 22 srutis 

is thus an extremely neat technique of systematizing these consonance and 

dissonance relationships.  This is very important both for Hindustani and 

for Carnatic music, and represents an important, early development in the 

history of a melody based musical system. 


As for contemporary practice, since we have essentially discarded 

the possibility of another value for pa, we need to discard the ratio 

40/27.  That would bring the number of SrutIs to 21.  If we however take 

into account that we actually use two Ma's in practice, a plain Ma as in 

ranjani or hamsAnandi and a higher pitched Ma as in varALi, the number 

goes up to 22 again.  We will thus still have 13 SrutIs from sa to pa and 

9 SrutIs from sa to ma.  In contemporary Hindustani music, ratio values 

like 81/64 and 243/128 are coonspicuous by their absence.  5/4 and 15/8 

are the only values used for Ga and Ni in Hindustani music today.  Which 

is why some people feel that the nishAda in Hamsadhwani as rendered by a 

Hindustani musician is much more prominent than in Carnatic music. 


The alternative derivation of 22 SrutIs as explained by taking 

twelve terms from each of the fifths and the fourths cycles and discarding 

the value of the panchama obtained from the cycle of fourths does not make 

much sense for reasons stated before.  Clearly the origin of the concept 

is related to the accounting for the 5th harmonic also, which these cycles 

do not take into consideration at all.


S. Vidyasankar