Monthly Archives: September 2016

shruti ratios & Jati system

1 C(Sa), F(Ma), G(Pa), were called “Chatushshrutik”  meaning have 4 shruti distance before them.

2 D(Re), A(Dha), were called “Trishrutik” meaning they have 3 shruti  distance before them.

3 E(Ga) & B(Ni) were called “Dwishrutik” meaning they have 2 shruti distance before them.

4 It appears Dweepta type of shruti have position at centre of dividing chord into two parts            like  Sa (C tone ) , Ma (F tone ) , Ga 1st shruti (D# tone) , & Ni 1st shruti ( A# tone)

5 One shruti distance was understood as one shruti up called Mrudu or soft  by 80/81 ratio  One shruto down or ayata shruti or extended by (81/80) as seen in difference in positions of “Fifth tone of SaMa singing system which is A tone” on Mrudu being on 5/3 & Sharp being on 27/16  so 81/80 or 80/81 being one shruti called “Pramana shruti” or “ratio distance taken as unit for measurement”.

6 there were three scale described within an octave called three gram system 

   षड्जपंचमभावेन षड्जे ज्ञेयाः स्वराः बुधैः । ( C – G ratio was taken for knowing of tones in Shadja  gram by knwoledgable people )  

  गनिभावेन गांधारे मसभावेन मध्यमे ।। ( E – B ratio was for understanding Gandhara gram meaning E# & B#  in Gandhar gram & “F – C ratio” with corresponding “G – Octave C” ratio for knowing tones of Madhayam Gram )   

 यात रिषभ धैवत यांचा उल्लेख नाही कारण षड्जे, गांधारे, मध्यमे ’’ यांचा रोख ग्रामांकडे आहे.                       Meaning there is no mention about tone D & A  as these mentions C , E , F  tones as here this is description of gram system of Indian Music. 

मध्यम ग्रामे तु श्रुति अपकृष्टः पंचम कार्यः                                                                                         पंचम श्रुति उत्कर्षात अपकर्षात वा यद अंतरं                                                                               मार्दवात आयतत्वात वा तत् प्रमाण श्रुति  ( भरत ना.शा. अ.२८ पृ. ३१८ ) ( हिं.सं.प. अ.२ पृ. २२ )                                        This is usually mistaken as mention of pancham as fifth tone but here one has to understand that these descriptions are as par Sama gayan system where it is mentioned that “fifth tone is Dhaivat or A tone” and not fifth tone or G tone as interpreted by people !  

So as par C-G ratio system we get C on 1/1  then G tone comes on 3/2                   from G on 3/2 we get on 3/2 ratio (on 9/4 tone octave D#) so on 9/8 D#                 from D# on 9/8 so we get on 3/2 from there on 27/16 A# tone this is the fifth tone mentioned in Sama Gayan  Here we note that position of A is on 5/3 ratio as per shloka                                                                                                                                सपयोः  मध्यदेशे तु धैवतस्य श्रुतिः भवेत                                                                                                Meaning in the centre of C-G ratio which would be  on 5/3 as F – Octave C so F on 4/3 F & 6/3 octave C so 4/3  – 5/3  – 6/3  is the position of  A tone  & Ratio between A# on 27/16 and A tone on 5/3 is the “Pramana Shruti”  ratio of 81/80  so when you move Fifth tone A from its position 27/16 by one shruti distance  80/81 one gets Madhyam gram A on 5/3 by making it softer which is meaning of word मार्दवात आयतत्वात वा Mardavat is softer & Ayatatvat meaning extended by 81/80  on 27/16   Here we also understand meaning of terms described as types of shruti  ! 

षड्जः चतुःश्रुतिः ज्ञेय ऋषभः त्रिश्रुतिः स्मृतः । व्दिश्रुतिः  च अपि गांधारो  मध्यमः च चतुःश्रुतिः ।।           चतुःश्रुतिः पंचमस्यात त्रिश्रुतिः धैवतः तथा । व्दिश्रुतिः तु  निषादः स्यात षड्जग्रामे स्वरांतरे  ।।                                         

 

 

व सामगानात पाच सूरांचा वापर होत असे व रेध हे षड्जपंचम भावात ठेवले की परिणाम तसा होतो

य सामगायनाः प्रथम स वेण्णो मध्यम स्वर ।   ( In SaMa singing First was F tone (called Ma)     

यो द्वितीय स गांधार तृतीय ऋषभ स्मृत ।।  ( The second one was E tone & third was D tone )

चतुर्थः षड्ज इति आहुः पंचमो धैवतो भवेत्  । ( fourth tone was called C  with fifth being A tone)

षड्जे निषाद विज्ञेय सफ्तम पंचम स्मृत ।।  ( Sixed was known to be B tone and seventh was G tone)

 म्हणजे म रे सा नि – प   या क्रमाने सात सूर लावले जात हे स्पष्ट आहे. ( This means tones were expressed in order  F – E – D – C – A – B – G  )   

साम  गायनात स्वर अवरोही क्रमात होते हे स्पष्ट वर्णन केले होते  अवरोहणात प्रतिषड्ज म्हटलेला पंचम सां-नि-ध-प चतुर्थ येतोच 

पुढे

दीफ्तायता तु करुणानाम्  मृदुमध्यमयोस्तथा ।  

 श्रुतीनाम् यो अविशेषज्ञो न स आचार्य उच्यते ।।

 दीफ्ता मंद्रे द्वितीये च प्रचतुर्थे तथैव तु ।

 अतिस्वारे तृतीयेच कृष्टे तु करुणाश्रुति ।। ( ना.शि.कं. 7, 9-10 पृ.40-41)

                                                       (हिं.सं..भा.2 पृ.14)

  “Dweepta” obtained by “dividing into two” Also Karuna (situated on 16/15 resembling smallest moon after No moons day ! after full moon day of dweepta the brightest tone !) In between being Madhyama or centre position ratio 15/16  from  9/8 which is 135/128 the position & before it mrudu position 80/81 of 135/128 being 24/25 or 25/24 ratio which is ration distance between two shruti positions of E tone or Gandhar of the two E being situated on 15/16 from 4/3 F tone which is dweepta so E is Madhyma shruti where as D# tone which is 1st shruti of Gandhar is Dweepta as it is centre of C & G so on 5/6 ratio !

   तर करुणा ही अतिस्वारे वा ध व तृतिय म्हणजे रे आणि पंचमात (कृष्टे) यातच असतात  This means Karuna type is seen in Atisware rone which is fifth tone comming after Shadja or C tone in SaMa singing , also in third tone which is C# tone or 1st shruti of Re or D tone called as C# & also in G tone called Krushte meaning one which is in attraction or consonant with C tone with though 1st shruti of this G tone. Its Karuna as it is on 16/15 ratio from Dweepta shruti of tone F !  

This indicates that This Jaati or type lable of shruti positions is linked with positions of tones as well as planets & Pythagorus had knowledge of this  as this knowledge was universal ! 

यातूनच वादी संवादी साकारतात असे जाणवते रे, रे , सा , नि इत्यादि.

हे श्रुति जातीचे ज्ञान असले तरच तो आचार्य संबोधला जातो. If Teacher has knowledge of these positions of shruti system then only he was called Acharya meaning worth following him ! 

याप्रकारे हे श्रुतिंचे ज्ञान असले की मगच त्यास आचार्य संबोधता येते.

 

याप्रमाणे ग्रामांप्रमाणे श्रुति स्थानांचा तक्ता सध्याच्या 1/1 सा 1 श्रुति करून असा होतो

                                    षड्ज  ग्राम  ( सारेगम पधनिसां ) षड्ज पंचम भाव

5 A(Dha) is the 5 th tone described in Sama Gayan or Sa-Ma or C – F system of Samaveda singing    as per shloka at 405

 

 

1. C (Sa) = 240 x 3/2 = 360 (17shruti) 360G or Pa G ( C X 3/2 )                 (Pa)
2. G (Pa) = 360 x ¾ = 270         (7th shruti) 270 D# or  Re D  ( C X 9/8 )                (Re)
3. D (Re) = 270 x 3/2 = 405         20th shruti 400 A or Dha(19shruti)  A = 19 shruti C X 5/3 = Dha          A = 20 shruti (C X 27/16= Dha)
4. A (Dha) = 405 x 3/4 = 303.75303 300 E or       Ga (9th shruti) E = (CX 5/4 (Ga)  of A 19th shruti E = (CX 81/64)(Ga) of A 20 shruti Fixed at 300 ( C X 5/4) as shloka
5. E (Ga) = 303.5 x 3/2 =455.625

455 Ni

450 à B ( C X 15/8) (CX243/128) (Ni)
6. B (Ni) = 455.625 x ¾ = 341.72

= 341 ma

337.5 à F# sharp or          (Ma sharp)

(C X 45/32 )( C X 729/512)

7. F # (Ma)

 (sharp)

= 341.72X3/4 = 256.29

   256 re

 256 à C#    Fixed               (Re. Soft)

 ( C X 16/15)(C X2187/2048)

8. C #

Re (soft)

=  256,29 X3/2

 

= 384.43

384 dha

384à G#(sharp)                  Dha(soft)

( C X 8/5 )(C X 6561/4096)

9. G# sharp Dha(soft) =  384.43 X ¾ = 288.325

288 ga

288 à D# sharp or               (Ga soft)

( C X 6/5 )(CX19683/16384)

10. D# sharp Ga(soft) = 288.33X 3/2

 

= 432.488

432 ni

432 à A# sharp or                (Ni soft)

( C X 9/5 )(C X 59049/32768)

11. A# sharp Ni (soft) = 432.49  x ¾

 

= 324.366

324  Ma

320 à F                                (Ma soft)

( C X 4/3) (CX177147/131072)

12. F ( Ma )

 

= 324.37 x 3/2

 

= 486.549

   486 Sa

480 à C(Upper)    (CX2)   (Sa upper)

 (CX 531441 / 262144 )

Here C or Sa Tone starts

 

One can see after every third tone calculation calculation a correction of 81/80 becomes applicable to correct the tone to positions comming as per sanskrit shlokas giving ratio proportions  these are  C – G – D – A – E – B – F# – C#G# – D# – A# – D#  – B –  F – C

Why C was kept on 240 in Indian music  ?  Answer is Circle is 360 degree & from 360 on 2/3 ratio is the frequency of 240 & 360 degree if divided 1/3 then it is 120….                                                   So 120 degree three parts form three parts of day from morning 8 to 12 am then afternoon being from 12 to 4 pm & then from 4 to 8 pm being evening  This was concept of trikal or threee parts of day & further 3 parts of night from 8 to 12 mid-night then 12 mid night to to 4 am midnight time & from 4 am to 8 am early morning  like wise musical Classical Raag system was divided to suit the times  & was played all over world on the gates of villages & Temples This classical music was called “Marg Sangit” or Music indicating the direction in which you are travelling !  Apart from this their was “Desi Sangit” or locally popular music !  Over a period of time people forgot rules of Classical music & local music became popular dividing world by music in addition to local languages !  As people stopped understanding sanskrit nobody could answer questions about shruti -swara- Raga system !  This is attempt to demystify the same !                                                                                                                                                                                   C – G – D – A – E – B – F# – C#G# – D# – A# – D#  – B –  F – C                                                                      when we start 1 st tone on C on 1/1 then G tone comes on 3/2 on 17th shruti !                                Then rom G tone on 3/2  from this G on 3/4  is 9/8 which is ratio of D tone on 7th shruti !              from this D tone on 9/8 , on ratio distance of 3/2 is 27/16 which is A tone on 20th shruti !              After this rom A tone on 27/16 if you see on ratio 3/4 we get 81/64 which is E tone 303.75 but      4 th A tone or Shuddha Dhaivat which comes on 405 is correctd by 80/81 so on 400 then this A on 400 is the 19th shruti of A tone !  This A tone or Dhaivat is 19th shruti of A tone or Dhaivat !     After this 5 th E tone or Teevra Gandhar gets automatically correctd by 80/81 so from 303.75 to 300 then                                                                                                                                                        then from this E tone on 300 we get on 3/2 ratio B tone on frequecy 450 which is 22nd shruti !  we start from reverse end                                                                                                                           23 rd shruti Octave C on 480 so on 2/3 is F tone or Shuddha Madhyam on 320 is 10th shruti  !    then from this F tone on 320 on ratio of 4/3 is                       10 th

Shruti Positions table

                                        SHRUTI POSITIONS & SHRUTI TABLE

There were also names given to shrutis & they corresponded with consonance dissonance of these shrutis of C -G or Shadja Pancham Bhav or 2:3 ratio proportion with corressponding rat io position as per frequency ratio with position on cord being inverse Last F – Octave C ratio crrespond with upper scale making it 26 shruti Cycle like 26 Alphabets of English language  !   That is the reson we sing Happy Happy we shall be when we will learn our A-B-C  !!!                            There is 27 the position which completes the 27 stars in 12 zodiac signs !                                           This 27th is gap of unknown or silence as we do not know value of π pi  ! So the Astrology & Music & Alphabets were connected with unknown position whether Singer or programme will be successful or not ……

Follwing table shows how  C-D-E-F  tones parallel positions & Names of shruti also parallel to play between concept of “Purush” & “Prakruti”

  1.  C Tone  (Shadja )  1  Teevra ( तीव्रा )  – 1/1  —          14  G Tone  Kshiti  (क्षिती )  –  64/45                                                 2 Kumudvati (कुमुद्वती ) – 81/80 — 15         Rakta ( रक्ता )   – 243/160                                          3  Manda  ( मंदा )  – 25/24                  — 16     Sandeepani (संदीपनी) – 75/48                                4  Chhandovati (छंदोवती )-135/128           –17       Alapinee ( आलापिनी ) – 3/2
  2. D Tone ( Rishabh)  5 Dayavati  ( दयावती ) – 16/15  –18  A Tone  Madanti ( मदन्ति ) – 8/5                                            6 Ranjani   ( रंजनी ) – 10/9              — 19                   Rohini  ( रोहिणी ) – 5/3                                     7 Raktika   ( रक्तिका ) – 9/8                 — 20                  Ramya  ( रम्या ) – 27/16
  3. E Tone ( Gandhar) 8 Raudri   ( रौद्री ) – 6/5       — 21 B Tone   Oogra ( ऊग्रा ) –  9/5                                                         9 Krodhi   ( क्रोधी ) – 5/4         — 22   Kshobhinee ( क्षोभिणी ) – 15/8
  4. F Tone ( Madhyam) 10 Vajrika ( वज्रिका ) – 4/3             — 01  Octave C   Teevra ( तीव्रा ) – 2/1                                         11 Prasararini (प्रसारिणी)-27/20  — 02        Kumudvati (कुमुद्वती ) – 81/40                                     12 Priti ( प्रीति ) – 25/18                 — 03             Manda  ( मंदा ) – 25/12                                             13 Marjinee ( मार्जिनी ) – 45/32  — 04 Chhandovati (छंदोवती)-135/64

Bellow  Chart shows                                                                                                                                     *9)* shruti is the E tone of Gandhar Gram  & corresponding *22)* shruti of B tone

No.  & Tone & Shruti No. & Type       Ratio             Modern freq. scale     Old Indian freq. scale                                                                                                   with A# at 440                with C at 240

20)  ध (A3)  रे  4 श्रुति            मध्या     प्रमाण   27/16                   220                           202.5

21)  नि (A#)   1 श्रुति            द्वीप्ता   प्रमाण     9/5                   234.6666                     216

22) नि (B)    2 श्रुति            मध्या         प्रमाण    15/8                     244.444444                   225

*22) *नि (B)    2 श्रुति      आयता   प्रमाण    243/128                247.5                      227.8125

1)   सा (C1) 1 श्रुति          द्वीप्ता     प्रमाण        1/1                   260.74074                      240                                                                                                                                                                                                       2)   सा (C2)  2 श्रुति         आयता   प्रमाण        81/80                 264                                  243                                                                                                                                                                                                       3)   सा (C3) 3 श्रुति         मृदु        प्रमाण       25/24                   271.6049382                 250

4)   सा (C4) 4 श्रुति         मध्या     प्रमाण      135/128                275                                 253.125

5)    रे  (C#) 1 श्रुति         करुणा  प्रमाण        16/15                     278.1234567                 256

6)    रे  (D1) 2 श्रुति          आयता   प्रमाण       27/25                    281.6                              259.2

7)    रे  (D2) 3 श्रुति          मृदु       प्रमाण     10/9                          289.7119341                 266.6666

7)    रे  (D3)4 श्रुति          मध्या     प्रमाण        9/8                         293.3333325                 270

8)   (D#) 1 श्रुति          द्वीप्ता   प्रमाण            6/5                       312.888888                   288

9)   (E) 1 श्रुति            मध्या    प्रमाण     5/4                                 325.925925                  300

*9) *  (E) 1 श्रुति          आयता    प्रमाण     81/64                               330                          303.75

10)  म (F1)  1 श्रुति         द्वीप्ता  प्रमाण      4/3                              347.65432                     320

11)  म (F2) 2 श्रुति          आयता  प्रमाण     27/20                            352                                 324

12)  म (F3)  3 श्रुति          मृदु    प्रमाण     25/18                               362.1399166                333.3333

13)   (F4) 4 श्रुति          मध्या  प्रमाण     45/32                              366.666666                  337.5

 14) प  (F#)  1 श्रुति          आयता प्रमाण     64/45                             370.8312746                341.3333

15) प ( G1) 2 श्रुति            द्वीप्ता  प्रमाण     36/25                             375.466666                 345.6

16) प (G2) 3 श्रुति           मृदु    प्रमाण     40/27                                   386.2825788               355.55555 

17) प (G3)  4 श्रुति          करुणा  प्रमाण     3/2                                      391.111111                 360

18)  ध (G#) 1 श्रुति           करुणा    प्रमाण     8/5                                    417.1851851               384

18)  ध(A1)  रे   2 श्रुति         आयता    प्रमाण   81/50                              422.4                             388.8 

19)  ध(A2)  रे   3 श्रुति           मृदु         प्रमाण    5/3                                434.5679                      400

20)  ध (A3)  रे  4 श्रुति            मध्या     प्रमाण   27/16                            440                                405

21)  नि (A#)   1 श्रुति            द्वीप्ता   प्रमाण     9/5                               469.333333                   432

22) नि (B)     2 श्रुति           मध्या        प्रमाण    15/8                                 488.888888                  450

*22)* नि (B)     2 श्रुति        आयता   प्रमाण    243/128                          495                                455.625

(23)(1)  सा (C1)1 श्रुति        द्वीप्ता     प्रमाण      2/1                               521.481481                    480                           

दीफ्तायता तु करुणानाम्  मृदुमध्यमयोस्तथा ।  

 श्रुतीनाम् यो अविशेषज्ञो न स आचार्य उच्यते ।।

 दीफ्ता मंद्रे द्वितीये च प्रचतुर्थे तथैव तु ।

 अतिस्वारे तृतीयेच कृष्टे तु करुणाश्रुति ।। ( ना.शि.कं. 7, 9-10 पृ.40-41)

                                                       (हिं.सं..भा.2 पृ.14)

आयतत्वम् तु नीचे स्यात्  मृदुत्वम् तु विपर्यये  । स्वे स्वे स्वरे तु मध्यत्वम् तत् समीक्ष प्रयोजयेत्                                

1.     Here  द्वीप्ता means shruti or position of tone , or one obtained by dividing into two.       2.     Here  आयता means shruti or position of tone obtained by or extendng by 81/80 or one shruti distance which is equivalent to Praman Shruti  Syn-tonic or Ptolemaic comma.       3.     Here  करुणा means shruti or position of tone obrtained by or is situated on 16/15 which is first shruti of immidiate next four shruti swar as seen in tones Ma & Pa or F tone & G tone & Sa & Re or C tone & D tones which depict diffwrence in female & male octaves with these two both on situated on ratio proportions 9/8 C to D sharp or F to G sharp tones  in case of both Re or C sharp & Pa first shruti or G flat labelled करुणा  shruti situated or positioned on one shruti distance  which is equivalent to 80/81 ratio of Praman Shruti or Syn-tonic or Ptolemaic comma distance from Ayata shruti or extended shruti of the same  tone ,  Here it becomes  मृदु  or softened by 80/81 or one shruti distance which is equivalent to Praman Shruti  Syn-tonic or Ptolemaic comma.                     4.    Here मृदु  or Mrudu meaning softened by 80/81 or one shruti distance which is equivalent to Praman Shruti  Syn-tonic or Ptolemaic comma                                                        5.    Here we see the meaning of स्वे स्वे स्वरे तु मध्यत्वम् ,                                                                   This means fourth shruti or position of  that tone as we know Pa or G tone is positioned on 3/2 ratio Sa or C tone is positioned on 1/1 ratio with करुणा shruti placed on 16/15 so Madhya shruti is placed on ratio 15/16 from the prime tones Sa or C & Pa or G  from 3/2 on 15/16 bellow we get 45/32 which woild be position of Madhya shruti of Ma ,                     6. Further from 4/3 Ma or F tone on 15/16 bellow we get 5/4 madhya shruti of Ga or E tone, Next from 1/1 C tone or Sa on 15/16 on lower scale on 15/8 is the मध्या or Madhya shruti of tone B sharp or Ni tone are seen.                                                                                           7.   Now as Re or D tone is placed on 9/8 which is Mahya shruti  (as  F & G parallel to C & D with ratio of 9/8) so from 9/8 shruti position on 15/16 ratio is 135/128 ratio position of fourth shruti of C or Sa tone                                                                                                                        Here we see the sequence 

आयतत्वम् तु नीचे स्यात्  मृदुत्वम् तु विपर्यये  । स्वे स्वे स्वरे तु मध्यत्वम् तत् समीक्ष प्रयोजयेत्                                

   Dweepta – Ayata – Mrudu – Madhya – Karuna – Ayata – mrudu – Madhya -Dweepta – Madhya 

 मृदु  or Mrudu meaning softened by 80/81 or one shruti distance which is equivalent to Praman Shruti  Syn-tonic or Ptolemaic comma is seen on 80/81 of 135/128 which is  25/24 ratio position is the position of third shruti of Sa or C tone                                                  Here we see Mrudu shruti is one Praman shruti  are  one obtained by dividing into three & four  each F tone on  3/4 and G tone on 2/3 respectively  getting 15/16 & 8/9 So Karuna करुणा is situated on ratio proportion of 16/15 & Madhya मध्या situated on 135/128 ratio from either Dweepta द्वीप्ता or Karuna करुणा  !  So the sequence is Dweepta , Ayata , Mrudu , Madhya to Karuna and from Karuna again Karuna , Ayata , Mrudu , Madhya to Dweepta ! 

 

द्वाविंशतिं केचिद् उदाहरंति श्रुतीः श्रुतिज्ञानविचारदक्षाः ।                                                 षट्षष्टिभिन्नाः खलु केचिद्  आसाम अनंत्यम् प्रतिपादयंति ।।                                                                         (बृहद्देशी पान ४-५) (हिं.सं. प. पृ. ४५ )

Above shlokas mean “some people who have knowledge about thinking behind shruti system say there are 22 shruti positions useful.                                                                                                     There are others who say 66 shrutis (this can mean three scales together 22 for each scale ) or if we put shadja C tone on any tone we find six tones of each then there can be infinite shrutis with calculations of ratio proportions fro each tone !  These are those who include all scales meaning continuous ( Aasaama meaning all SaMa or C- F ratio being same as G – Octave C ratio this way they point out shruti are infinite !

आनंत्यं हि श्रुतीनां च सूचयन्ति विपश्चितः  ।                                                                 यथा ध्वनिविशेषाणां अमानं गगनोदरे ।।                                                                       उत्ताल पवनोद्वेल्लज जलराशि समुद्भवाः ।                                                                   इयत्य प्रतिपद्यन्ते न तारंगपराम्परा ।।                                                                               (बृहद्देशी पृ. २९-३०) (हिं.सं. प. पृ. ४५ )

Further This next shloka further explains that those who understand infinity of shrutis describe there resemblance to infinity of sounds in the sky or Infinity of no. of waves in the oceans produced by wind force ! That is why they state that there is no limmit to cycles of different waves separating this world full of different cycles of waves  ( like shrutis) !

आता किती श्रुति होतात ते पाहिल्यास 22 , 66, वा  अनंत का म्हटले आहे ते कळते.  या सुराचा 81/80 वर वा खाली सूर ठेवला की 66 श्रुति मिळतात. सध्या ध 440 वर असतो तर भारतीय शास्त्रा प्रमाणे  सा  240 वर ठेवतात , पण गंधर्व ग्राम जे सध्या लुप्त झाले आहे म्हणतात त्याचे वर्णन करताना म्हटले गेले होते की स्वरांची श्रुत्यंतरे अगदी समान होऊन जातात आणि सा हा नि वर ठेवला जातो त्यामुळे सामानांतर श्रुति ध  

 

Bharat Muni in his thesis on Music called “Natya Shastra” has described