One of the greatest pleasures in my life has been to explore ancient Vedic knowledge and think about ways to apply this knowledge for betterment of our health. Because of my training as a physician and my keen interest in classical Indian music, I was particularly drawn towards the Vedic idea that music could play a great role in health maintenance. I have spent innumerable hours researching the Vedic insights about role of music in medicine and thinking about practical ways to apply these insights to improve our health.
I am creating this website to share my knowledge and thoughts with anyone who may be interested. Whether you are a fellow enthusiast interested in a stimulating discussion or someone who would like my advise to improve your health, this website is for you…..
I welcome you to read about my research and ideas. Please feel free to leave public comments or send me private messages if you prefer. All constructive feedback is highly appreciated.
If my work helps you, I would love to hear about your experience. If you know someone who could benefit from my work, please share this website with them. Here we remember Great Austrian American Scientist Nicola Tesla (1856-1943 ) who believed in improvement of humanity & not keeping knowledge secret !
I hope this website will be as enjoyable and helpful for you to use, as it has been for me to create…..
Dr. M. V. Gadrey
Basic argument in this site is “22 shruti of Indian Music” are balanced natural frequency positions for any octave with basic tone C called Shadja or Sa put on “any frequency” according to ratio mathamatics….
It is not surprising that In Ancient Indian Literature Musical scale or circle was described to have 22 shruti for 7 tones ( resembling value of Pie 22/7 !!! ) with C or the 1st tone of Indian music having 4 shrutis If you include four shrutis of the octave C then the cycle becomes of 26 shrutis where as English Language has 26 alphabets ! with ABCDEFG the first seven being musical tones of so called western music ! Further 22 shrutis & 4 shrutis of octave C making 26 alphabets of a musical language in this part of the world ! Further adding one space for exclamation marks, spaces, or full stops, commas, etc making 27 spaces representing 27 zodiac stars of Astrology ! These 27 zodiac stars were linked with 12 zodiac signs, 12 months of one year 12 hrs of day & night, each hour space divided into 5 minutes representing 5 senses related to 5 principles like Space (Akaash) , Earth (Solid Pruthvi) , Aap (Liquid or water) , Vayu (Gaseous state) , Agni (Fire or state of conversion or death & new birth as light ) ! These 60 minutes having 60 seconds making 360 degrees of a circle or time cycle ! 12 cycles of 360 yrs making 4320 yrs of a megacycle ! All this time , Astrology , Music , was related & this was understood by the 6th sense called mind ! 7th sense called Buddhi , & 8th called Ego or Will power to understand & do something good !
So as Sanskrit was language formed from All Prakrit languages or regional Languages , One of the language was English with its 26 Alphabets , with lullaby song telling Happy Happy we shall be when we will learn our ABC … A Being Dharana or base represented by Dhaivat tone , B being Nishad reaching stage where there are no Ishad or Ichhas wishes left reaching C the shadja representing the base of New cycle the Sa or C giving rise to further 6 tones & shrutis ! It was also Musical , astrological language indicating the world was in UNISON !
Here we say “so called western” because before approximately 2000 yrs there was No East & west division & even Pythagoras was supposed to have visited East & it was Universal music and being a mathematician he has described musical scale also ! Basic 7 tones , 7 colours, 7 seas , 7 heavens , leading to 12 tones , 12 hrs, 12 zodiac signs , 12 hrs day & nights, 12 months & may be 1200 cents representing 1200 years cycles !
What was the clue to solve this puzzle of Shruti positions ?
It was the observation that Tones are placed overlapping each other from two poles One called “Meru which is 0 position on chord” and other is “full length of wire” which is 1/1 Further these can be from poles of tones C – F same as Sa – Ma or G – octave C same as Pa – Sa this is understanding of Sama Gana : 1. If you see G Tone is on 3/2 position from basic C on 1/1 where as F is on 2/3 position from octave C on 1/2 getting place 4/3 from C 1/1 2. If yous see E on 5/4 position which is on 15/16 from 4/3 F position where as C# is on 16/15 from C on 1/1 position 3. If you see D# placed on 6/5 position from C 1/1 where as D is placed on 10/9 position which is 5/6 of 4/3 F position ! 4. if you see F placed on 4/3 position is on 8/9 from G on 3/2 where as the so called 2nd shruti of D is on 9/8 position from C on 1/1 ! 5. if you see C# placed on 16/15 from C on 1/1 where as 4th shruti of C would come on 15/16 from 9/8 D which come to 135/128 the 4th shruti of C! 6. If you see E placed on 5/4 is on 25/24 position from D # on 6/5 where as you can see 25/24 is the 3rd shruti from C on 1/1 & from there on 81/80 is 135/128 the last 4th shruti of C …. this 81/80 ratio distance same between D on 10/9 & D on 9/8 ! 7. So you get automatic 1/1, 81/80, 25/24, 135/128 the 4 shruti of Sa or C with corresponding on 4/3 ratio we get 4 shruti of F & 4 shruti of G on reverse ratios from G or 4/3 ratio from C# ! 8. On C- G 3/2 ratio we get shruti of ABC Here you can seen C is called Shadja as it gets 6 shrutis 3 forward from 1/1 & 3 backward fro 1/1 It is supposed to give rise to 6 shruti & tones so called shadja one which is mother tone of six ( shruti as well as swaras ) !
This is an attempt to demystify the concepts behind 22 shrutis & the ratio mathematics !
- 2/1 ratio of frequency or 1/2 on wire chord is position of 23rd shruti or 1st shruti of next octave ! Because of this Frequency of C should be a multiple of 2 ( 128 – 256 – 512 – 1024.. ) but if you fix Frequency of A at 220 – 440 – 880 in that case C # would be at 260.740740
- 3/2 ratio of frequency or 2/3 on wire chord is position of 17th shruti or 1st shruti of Tone G called as Pancham in Indian Music in pythoagorian ratio called as Shadja Pancham bhav in the same octave !
- 4/3 ratio of frequecy or 3/4 on wire chord is position of 10th shruti or 1st shruti of Tone F called Madhyam in Indian music in a ration called as Shadja Madham Bhav in same next octave ! It is in pythagorian ratio of 3/2 in relation to C octave situated on 2/1 ! These two main tones Ma or F & Pa or G are situated on “4/3 from C” & “3/4 from Octave C” respectively & this continues ….! This appears the reseon why Madhyam or F is descibed as 1st tone in “Saam Gaan” of indian music !
- On 16/15 ratio from C & on 15/16 ratio from octave C(15/8) are C# or Komal Re & B# or Teevra Nishad…..!
- On 10/9 ratio from C & on 9/10 ratio from octave C (9/5) are D or Shuddha Re & B flat or Komal Nishad …..!
- On 6/5 ratio from C & on 5/6 ratio from octave C ( 5/3) are D# or Komal Gandhar & A # or Shuddha Dhaivat …..!
- On 5/4 ratio from C & on 4/5 ratio from octave C ( 8/5 ) are E or Teevra Gandhar & G # or Komal Dhaivat …..!
- In case of Shadja Gram to Madhyam we have “One shruti reduction of Dhaivat which is called Pancham as par Saam Gaan system” ( “Panchamo Dhaivato Bhavet” )
यः सामगानाम प्रथमः स वेन्णो मध्यमः स्वरः । यो द्वितीय स गान्धारः तृतीयः रिषभः स्मृतः ।। चतुर्थः षडज इति आहुः पंचमो धैवतो भवेत । षष्ठः निषाद विज्ञेय सप्तमो पंचमो स्मृतः ।।
द्वे वीणे तुल्यप्रमाणतन्त्र्यौपवादनदंडमूर्छने षड्जग्रामाश्रिते कार्ये । तयोरेकतरस्याम मध्यम ग्रामिकी कृत्वा । पंचमस्य अपकर्षे श्रुतिं तामेव पंचमवशात षड्ज ग्रामिकी कुर्यात इति ।। (ना. शा. अ. २८ पृ. ३१८) (हिं. सं. प. भाग. २ पृ. २२ )
Here it clearly mentions that fifth tone or Pancham tone by reduction of one shruti becomes madhyama gram but this reference is from pancham of saamgaan as mentioned if upper shloka which clearly states pancham swar in saam gaan is Dhaivat & it gives clear sequce.! or This reduced by one shruti to 27/16 to 5/3 with parallel Rishab put on 9/8 to 10/9 Giving us Third shruti of Rishabh & Dhaivat …..! This also gives us Praman Shruti ratio of 81/80 ….! Further It is specifically mentioned about gram system that
षडज पंचमभावेन षडजे ज्ञेया स्वराः बुधैहि। गनि भावेन गांधारे मस भावेन मध्यमे ।। meaning in shadja gram it is C-G ratio or Shadja Pancham bhav or 3/2 ratio is important & in Gandhar gram it is Gandhar Nishad ratios of 25/24 between komal & teevra swaras are improtant where as in madhyam gram ma sa bhav meaning centering of swars to madhyam shadja positions is imortant !
- Further from 9/8 Rishabh on 15/16 position is 135/128 which whould be last shruti of the C tone or Shadja with 16/15 from 1/1 being the 1st shruti of Rishabh swara….!
- Shruti Jaati are labelled as Dveepta Ayata tu Karunanam Mridu Madhyamyoho tatha shrutinam Yo avisheshdnyah Na sa Acharya Ucchyate …. ! Making it clear that on any shruti system 1/1 is Dveepta , 81/80 is Ayata ,25/24 is mridu , & 135/128 is Madhyam Jaati ending in 16/15 which will be karuna which is 1st shruti of Komal Rishabh ….!
- Madhayam on 4/3 will also have its 4 shruti 4/3 , 27/20 , 25/18 & 45/32 last on ratio of 135/128 from 4/3 & on 16/15 from 4/3 would be 64/45 which will be karuna shruti of Pancham which will match Karuna Shruti of Komal Rishabh … ! Further from 3/2 Pnacham situated on 16/15 is 8/5 the karuna shruti of Dhaivat which will match karuna shruti of Komal rishabh ….!
- Further where to put which shruti to create desired effects depends on Acharyas who understand Shruti Principle ….. !
द्वाविंशतिं केचिद् उदाहरंति श्रुतीः श्रुतिज्ञानविचारदक्षाः । षट्षष्टिभिन्नाः खलु केचिद् आसाम अनंत्यम् प्रतिपादयंति ।। Now why here it is said that some people say there are 22 shrutis who have knowledge about shrutis & they are allert about the concept & thoughts behind & about shruti system some others say say 66 & some really say there are no end to shrutis they are infinite ! This was written as the value of a circles perimeter is expressed by C =2πR or vale of π = C/D this applies to music & C is shrutis & 2r are two parts of octave Sa to Ma or C to F & Pa to Sa or G to C with C being common point diameter is of 7 swaras & shruti are there circle of vibrations or C value of π was fixed as 22/7 where C is shruti circle & 7 is the D or diameter so what is called swara mandal or cycle of octave has 22 shruti for 7 tones ! So some can say (44 shruti when they count 14 tones or two octaves ) 66 shruti if they count 21 tones or three octave cycles ! others admit that there is no end to these shruti cycles !
if you say 1st shruti is any 1/2 then its upper C becomes 2/1 & automaticaly 1/1, 2/1, followed by 3/2 , 4/3 , 5/4 , 6/5 these shrutis of Pa or G on 3/2 , shruti Ma or F on 4/3 , then 5/4 shruti of Ga or E , further shruti of Komal Ga or D# on 6/5 follow but … these further give rise to 4/3 of 5/4 which is 5/3 the shruti of Dha or tone A , further 2/3 of 5/3 is 10/9 shruti of Re or D , 9/8 as 3/4 of 3/2 which is Re or D, 4/5 of 4/3 which is 16/15 which is C# , Further 5/6 of 5/4 gives 25/24 which would be another shruti of Sa or C on ration of two Ga shrutis or distance between E /D# 15/16 of 9/8 gives us 135/128 which would be another shruti of Sa or C tone , & by Now it depends on Those who understand principle of shruti given by shloka descibing shruti jaati
द्वीप्ता आयता तु करूणानाम मृदु मध्यमयोह स्तथा । श्रुतीनाम यो अविशेषज्ञः न स आचार्य उच्चते ।। द्वीप्ता मंद्रे द्वितीयेच प्रचतुर्थे तथैव तु । अतिस्वारे तृतीयेच कृष्टे तु करुणा श्रुतिः ।। (ना. शि. कं. ७, ९-१०, पृ. ४०-४१) (हिं. सं. प. भाग. २ पृ. ४०-४१ )
This means from 1st dweepta meaning one obtained by dividing into two parts Here we see in case of Sa or C Tone , Ma or F Tone Ga or E tone and Ni or B tones first shruti of these four are obtained after dividing distances into two It appears as meant by term Dweepta further Aayata meaning extended one from Dweepta this is second shruti cmming after Dweepta one. Further tu Karunaanaam mrudu madhyamayoh meaning, also upto Karuna the last with in between Mrudu & Madhyam t his is reverse order Dweepta Aayata .. to Karuna with mrudu which is previous to madhyam which forms the center of these five making sequence as Dweepta , Aayata ,Mrudu ,Madhya , & 5 the “Karuna” which is descibed as 1st shruti of Re or D tone , Pa or G Tone & Dha or A tone only ! as they are situated on ratio of 16/15 of their respective previous 4 shruti swaras or tone they being Sa or C tone , Ma or F tone & Pa or G tone situated on 1/1, 4/3 & 3/2 ratios respectively ! & in Madhyam gram swaras or tones are kept on Madhyama shruti position as mentioned in shlola
आयतत्वम् तु नीचे स्यात् मृदुत्वम् तु विपर्यये । स्वे स्वे स्वरे तु मध्यत्वम् तत् समीक्ष प्रयोजयेत् ॥
Here it says Aaayata shruti is next bellow & Mrudu is opposite one above or opposite direction one bellow is Ayata & one above is mrudu but this can be from any swara which will be in the centre of it then further it says position of the tone should be given medium position considering these positions so third shruti jaati is Mrudu & fourth Madhya as it says “swe swe swareshu madhyatvam madhyatvam Tatsameeksha prayojayet” meaning this is with reference from the position of that swara ! one above is mrudu one bellow is ayata with reference to that swara defined by shlokas ! Once you understand this then you can put Sa or Shadja on any tone & further the shruti positions get automatically fixed for that octave but if you call it octave then total comes to 22 shruti plus 4 shruti of octave C making it 26 shruti … It is not surprising that English alphabets are 26 & tones are labelled A,B,C,D,E,F,G & A which is called Dha of indian tones is placed first as it is also based on Yoga Dha stands for Dharana which is first step towards samadhi in sequence of
Dharana , Dhyana & Samadhi these are A, B, C, or Dha , Ni , Sa of Music & so the first rhyme teaches us ABCDEFG ….. HIJKLMN .. OPQRSTU… VWXYZ Further saying Happy Happy we shall be if we have learnt our …….. A…B… C tones or Dha, Ni, & Sa indian tones !
It Was Universal System Now seen as divided system… Dha, Ni, Sa being A, B, C , or Dharana , Dhyana , & Samadhi ! This is the secret behind Indian Shruti System …. ! Hope Masters will appreciate …. the efforts & Realization behind ! Dr.Mukund V. Gadrey. M.D.