भारतीय श्रुति विज्ञाना मागे असलेले मूलतत्त्व 

(कै.पं.भातखंडे हिं.सं.पद्धती भाग 2 पान 51

१) ध्वनिअविछिन्नविणायां  मध्ये  ताराकसः  स्थितः                                                              ( Centre of chord is the position of Upper Octave C meaning 1/2  )

२) उभायोर्षाद्जायोर्मध्ये मध्यमस्य  श्रुतीर्भवेत                                                                    ( Tone F is positioned at the centre between two C tone positions meaning 3/4 position on chord with frequency ratio 4/3 )

३) त्रिभागायात्माकः  वीनायां  पचंमः स्यातग्रीमे                                                                 ( G tone is positioned on 2/3 distance on the chord after making three parts of chord having frequency ratio 3/2 )

४) षड्जापन्चामायोर्मध्ये गांधारस्य श्रुतिर्भवेत                                                                   ( D# tone is situate in the centre between C tone & G Tone so on 5/6 ratio position with frequency ratio 6/5 )

५) सपयोहो पूर्वभागेच स्थापनीयो अथ रिस्वर                                                                    ( D tone is situated on proximal position after further divisions of       C – G 2/3 portion further so on 8/9 with frequency ratio of 9/8 )  

६) सपयोहो मध्यदेशेतु धैवतम स्वरं आचरेत। अथवा                                                               पंचमोत्तर्षडजाख्यमध्ये धैवतम स्वरं आचरेत ।                                                                ( A tone is situated in the centre of G tone on 6/8 & Octave C on 4/8 ..so on 5/8 is position of A Tone Here we get Also centre of  4/3 & 6/3 is 5/3 which is centre of C-G Ratio between F & Octave C which is other position of A indicating two positions of A Tone one on 8/5 other on 5/3 )

७) तत्रांशाद्वायसंत्यागात निषादस्य श्रुतिर्भवेत  ।। इति  शुद्धस्वराः ।।                                ( From same position leaving two positions fromG taking G on 6/9 or 12/18 on 10/18 or 5/9 is position of tone B with frequency ratio of 9/5 )  These are Shuddha or prime tones from Chord divisions  

८) भागत्रयान्विते मध्ये  मेरो ऋषभ संज्ञितात ।                                                                       भागद्वयोत्तरम मेरो कुर्यात कोमल रिस्वरम ।।                                                               From C position which is 8/8 and position of D which is 9/8 by dividing to further C from 8/8 to 16/16 on 15/16 is position of C# tone with frequency ratio of 16/15 )     

९) मेरुधैवतायोर्मध्ये तीव्रं गान्धारम आचरेत ।   Position of A tone being on 5/3 or 3/5 from C so centre of this being 4/5 being the position of E Tone with frequency ratio of 5/4 and 6/5 being ration position of D# tone    

१०) भागात्रायाविशिष्टेस्मीन तीव्रगांधार षड्जयोहो ।                                                                 पूर्वाभागोत्तरम मध्ये  मं तीव्रं आचरेत ।।                                                                                    The F Tone & G tone have the specific tri partitioning ratio of 9/8  with G on 3/2 & F on 4/3 So Here from E tone on the same tri partitioning ratio of 9/8 from 5/4  is the position of F# situated on 45/32 which is also 15/16 of G on 3/2 ! Here we get hint that from 16/15 from 4/3 on 64/45 is the 1st shruti of G ! 

११) भागत्रयान्विते मध्ये पंचमोत्तर षडजयो: ।                                                                           कोमलो धैवतः स्थाप्य पूर्वभागे मनिषीभी: ।।                                                                      As mentioned above the specific tri partitioning ratio of 9/8  starting with G on 3/2  is position of 27/16 A# & on 16/15 from 3/2 is position of 8/5 G# tone resembling D tone & C# tones Here we get ratio between 27/16 A# & and 5/3 A being on ratio 81/80 which was called Pramana Shruti or called as Coma of Pythagoras !   

१२) तथैव धसयोर्मध्ये भागात्रायसामान्विते ।                                                                           पूर्वभागद्वायात  उर्ध्वं निषादस्य श्रुतिर्भवेत  ।।  इति विकृत स्वराः  Similarly between A and Octave C on tri partitioning from 15/16 ratio from octave C on 2/1 we get 15/8 is the position of B which is on       9/8 ratio position (of tri partitioning) from 5/3 position of A is 15/8 is   B tone !  

Thus we get 81/80 as 1 shruti sistance , 25/24 as two shruti distance , 135/128 which is 81/80 of 25/24 as 4 shruti distance from any tone put on C or 1/1  !!!  

    So when any frequency is selected 1/1 automatic its 22 shruti take their places & swaras can be put on them as per requirement of the concerned Raga , its Vaadi (Main Tone) Samvadi the consonant perfect 5th , Varjya or omitted tones for that raga, Anuvadi the following tones which give or follow in consent with the require Raga also called chalan , Vivadi the on opposite to Samvadi as per direction wise if ascending (Arohi) Raga then Descending one becomes Vivadi as it changes the effect if used more frequently reversing the effect, & on the other hand in descending(Avrohi) Raga the opposite to samvadi on ascending side becomes Vivadi if used prominently changes the mood of Raga !     

 Before coming to Meaning of Shlokas                                                                            We must know Shruti was Defined as  श्रूयते इति श्रुति ।।  Meaning one which ears can differentiate is shruti …. So each swarachakra or Shruti Mandal or each cycle of scale will have 7 swaras called as Shuddha swaras or Basic defined swaras & Vikrit Swaras meaning swaras moved from its place in opposite direction to Shuddha or Basic swaras !  Vikrut is “Vi” meaning opposite “kruta” meaning done, They are Kruta but Viparit or Viruddha Kruta also moved in opposite direction of basic defined swaras Like F tone is called Shuddha Ma so its opposite Vikruti is Teevra Ma or Sharp F But, Shuddha Re or Dha both themselves are put on shuddha position & Vikruta position is called  Komal Re or Komal Dha which are C# or G # tones In western system also there is confusion about B & E tones with some calling A # others calling B flat also some calling D# others calling E flat these also have origin in worldwide Shruti system … One has to understand That As you make F sharper or move F towards sharper position result is G becomes starts sounding flat. In Indian classical system F is supposed to become sharper after 12 noon & after 12 midnight Sharper F starts becoming flat or shuddha & so it is indicator of day time raga where as F# is indicator of Next 12 hrs half of day starting from midnight 12 to 12 noon where F or Shuddha F (Ma) is played with Bhairavi with all komal ( sharp tones as per western label) with F (Shuddha Ma) is supposed to be at morning 6.00 AM &  Kalyan with all Shuddha or Teevra tones with F sharp or Ma Teevra is played at evening 6.0 PM 

Before coming to meanings of shlokas we must see how balanced is indian scale of 22 shruti

Formation of Shrutis is concept of frequcies of sound in a given scale ! This  originates from cyclical repetition of tones or swaras like if say a frequency of you put A tone or C tone ( Sa or Shadja of Indian music ) on fequency 1mhz then its next scale tone is in cycles of  1 – 2 – 4 – 8 – 16 – 32 – 64 – 128 – 256 – 512 – 1024 …. likewise…  Now if you see  E Tone of A or G tone of C has to be situated on ratio of 3/2 so frquency of tone E if calculated from A , or G calculated from C will be in cycles of 3 – 6 -…. – 96 – 192 – 384 – 768…likewise … So Shruti  of E or has to be on 3/2 ratio from shruti of A same in case of G has to be on ratio of 3/2 from tone C  This was concept of Shadja – Pancham Bhav of Indian music or Universal music called perfect 5th  Further one observes –  That to remove confusion   The Symetry of the positions of swaras is so perfect                                                                                                                                                                                       All the Twelve swaras are placed in perfect balance from C & Octave C  !            Rest 10 shrutis remaining are rest Aayata & Mrudu shrutis on 81/80 or 80/81  ratio of these !

1)    C # & B are 16/15 from C & 15/16 from C (2/1)  respectively                                                                 C  ————↓———————————————————↓————   2/1C                                                   →→→→16/15 ( C#)                                                (B) 15/8 ←←←← (15/16)

2)     D & A # are 10/9from C &  9/10 from C(2/1)  respectively                                                                     C  ————————↓————————————↓———————   2/1C                                                     →→→→ →→→10/9                              (9/10)9/5 ←←←←←←←

3)     D# & A are- D# 6/5 from C & E 5/6 from C(2/1)   respectively                                                               C  ————————↓————————————↓———————   2/1C                                                    →→→→ →→→ 6/5 (D#)                          ( A ) 5/3 ←←←←←←←(5/6)

4)     E & G# are 5/4 from C & 4/5 from C(2/1)  respectively                                                                           C  ————————↓————————————↓———————   2/1C                                                     →→→→ →→→ 5/4 ( E )                         ( G# ) 8/5 ←←←←←←←(4/5)

5)     F & G are 4/3 from C & 3/4 from C(2/1)    respectively                                                                           C  ——————————↓————————↓—————————   2/1C                                                      →→→→→→→→→ 4/3                     3/4(3/2)←←←←←←←←←

6)     F# & G flat(1st shruti) are 45/32 from C & 32/35 from C(2/1)  respectively                                       C  —————————————↓—↓—————————————   2/1C                                                      →→→→→→→→→→    45/32  64/32(32/45)←←←←←←←←←

Here we must remember that G flat which is 1st shruti G called Pancham or fifth                             this concept is not understood while considering shruti system !                                                    Here one has to remember 81/80 of  F# (45/32)  comes on ratio 729/512                                          where as same way you see 80/81 of G 64/45  comes on 1024/729                                                    Here we realize that ratio of 81/80 of 16/15 which is 27/20 is tone re komal or D flat situated on 259.2 if C# is taken on 256 or D flat is situated on 281.6 if C# is taken on 278.1235 & it is Aayata shruti  !

Meaning of Shlokas in English

1) Undivided Chord of Veena ( Guitar one can say as it is also chord Instrument ) At the centre is the position of Octave C  or Upper scale C of the C of the wire or chord taken of whatever material or Length  This Defines for any 1st shruti & swara of Sa or C of 1/1 chord  On whole length there would be upper scale or octave Sa or C  on 1/2 chord length or 2/1 shruti ratio (Frequency ratio) This means Its upper scale would be on 1/4 chord position or 4/1 shruti ratio & this will be infitite 1/8 , 1/16 … etc

2) At the centre of two Shadja or Sa or C swaras is the shruti or swara position of Madhyam or Ma or F tone  so 1/1 & 1/2 (2/1) being the two positions of C or (for that mater even A tone if it is taken as base tone)  Then on 3/4 position on chrord at the centre between 1/1 , & 1/2  is  3/4      1/1 , 3/4(4/3) ,  2/4(1/2)  So Madhyama is Ma or F tone is on 4/3 Ratio & 3/4 position on chord

3) If you divide the chord into 3 parts then leaving proximal (1/3) on 2/3 chord length is Pancham or Pa or Fifth tone or G Tone on ratio of 3/2 so automatically 1/3 is its upper scale G or Pancham tone ! Here we can make out Pythagorian scale was based on perfect fifths & fourths was not different !                                                                                                                             Here we also note that Ratio between 3/2 Pa or G tone  & 4/3 Ma or F tone is 9/8 or 8/9 chord length !

4) At the centre of Sa C tone & Pa (G) tone is the swara or shruti positionof Gandhar or Ga              or E tone  centre of 1/1(6/6) , 5/6,   2/3(4/6) being 5/6 or ratio 6/5 is the central position of Shuddha Gandhar … Here we note because of Loss of knowledge due to war mongers & destructions of libraries Lower one was called Komal instead of Shuddha & upper one Teevra Gandhar or E sharp but if you watch according to ratio 4/4 (1/1) , 5/4 , 6/4 (3/2)  5/4 is the position again in the centre of Ratio of 3/2 of Pancham or Pa or G tone  & Sa or C tone on 1/1     so we get two shruti posiotions of Gandhar or E tone from this shloka ! This appears why Gandhar was called Dwishrutic or having two shruti ( distinct audible places ) on chord.

5)   This says on previous side of tri partitioned Sa Pa or C G distance is position of Rishabha or Re or D tone  Pa or G is situated on 2/3 of original tripartitioned whole length wire chord so when we further make three parts it becomes (2/3)6/9 , 7/9 , 8/9 , 9/9(1/1) so on previous part which is nearer to 1/1 is position 8/9 or ratio  9/8 this is the shruti swara position of Shuddha Rishabha or Re or D Sharp  Here Notable part is  Ma-Pa or F-G ratio is also 9/8 as mentioned in 3 rd shloka explaination ! This is the hint That  Poorvanga (Previous) & Uttaranga (Distal) is same as  C-G & F-C parts of two parts of what was described as Madhyama Gram related by centre positions  as opposed to Shadja gram which makes two parts as Sa -Ma & Pa -Sa or C-F & G-C which are related to each other by CG 3/2 ratio                                                                                        -Madhyama Gram being  Tones which maintain ratio of Ma & Sa or F & C which is 4/3 or 3/4       Sa(C) -Re(D) -Ga(E) – Ma(F) – Pa(G)  is same as Ma(F) – Pa(G) – Dha(A) – Ni(b) – Sa(Octave C)               -Shadja Gram Being  tones which maintain ratio of Pa & Sa or G & C which is 3/2 or 2/3                    Sa(C) -Re(D) -Ga(E) – Ma(F)  is same as Pa(G) – Dha(A) – Ni(b) – Sa(Octave C)                                         -Gandhar Gram being  tones whichmaintain ratio of Ga & Sa & Ni from Pa respectively                   Sa(C) – Re(D)  – Ga(E)  – Ma(F)  – Pa(G) – Dha(A)  is same as                                                                         Ga(E) – Ma(F) – Pa(G) – Dha(A) – Ni(b)  – Sa(Octave C)

6) In the same way “centre of Sa and Pa” is position of Dhaivat or G # Here we see that                 F on 4/3 & octave Sa on 2/1 is also Sa- Pa or C-G relation & so it would be on same ratio of 6/5 from Ma or F which is on 4/3 so 6/5 of 4/3 is 8/5 on Ratio proportions & from 3/4(6/8) chord length to 1/2( 4/8) center being 5/8  (4/8 , 5/8 , 6/8 ). so we get same Dha or A flat on 5/8 chord position & 8/5 ratio position this being 1st shruti of Dha or A flat or some calling it G sharp                                                                   Same if applied as per Shadja gram relation then G is on 3/2 so Dha (A) corresponds to Re(D) of rhe previous part of octave & D is on 9/8 so 9/8 of 3/2 which is 27/16 whould be position of A Shuddha or A #                                                                                                                                 Further same if applied to Ga or E  on 5/4 &  Ni or B on 15/8 which is also              Sa – Pa  or C- G Ratio of 3/2  so centre of this Sa – Pa or C -G ratio so center of                                     4/5 (8/10) 7/10, 6/10 , 5/10 &  leaving previous part  (poorva bhag ) next 6/10 ( 3/5 ) is the shruti position of A on 5/3 this is 2nd shruti of Dha or A  It is also place in the centre position or 4/3 F position from 5/4 Ga or E as 4/3 of 5/4 is 5/3 Dha or A tone It bears a Sa – Ma or C -F relation staring from Ga or E as it is Gandhar Gram !                                                                                   Here we got three shruti positions of Dha or A

7) Nishad is placed in the same way “leaving two degrees from Sa”  and in 12 th shloka it means between “Dha or A & Sa or octave C” then leaving 2 degrees from Octave C on 27/54 (1/2)               leaving previous two degrees is Shuddha Ni or B which is seen on 5/9 on chord or 9/5 ratio

So from A 16/27 (32/54)  -31/54 – (30/54) (5/9) – 29/54 – 28/54 – 27/54 (1/2) Octave C               Or if one takes A 3/5 (36/60)    then  20/15(2/3) –  36/60(3/5) – 34/60 – 32/60(8/15)  – 30/60                 Here we have seen from 36/60 is tripartitioned leaving 2 degrees from Octave C is 8/15 Ni(B)

Here we get two shruti swaras of Ni (B) tone on 9/5 & on 15/8 which are in ratio of                        C- G or Sa-Pa  or 3/2 from Ga (E) on 6/5 & 5/4  !                                                                                      B sharp or Ni Teevra is Sa-Ma or C-F ratio of 4/3  from 45/32 Ma or F#                                              B is on 9/5 which is Sa-Ga (C-E) ratio of 6/5 from  3/2 Pa or Pancham or G                                      Ni on 15/8 being  4/3 of Teevra Ma or F# on 45/32 &                                                                            Ni on 9/5 Being  4/3 of Ma 2nd shruti on 27/20 as per Indian Shruti system

Two shruti distance is 25/24 as defined by Ga(E) & Ni(B) which have two shrutis each                One shruti distance is defined as 81/80 by D on 10/9 & 9/8 also A on 5/3 & 27/16                      Four Shruti Sa or C on 1/1 gets defined by 16/15 ratio above being first shruti of Re or D &   bellow same on 15/16 ratio being 15/8  the last shruti of Ni !

If we want to put Sa (C) on “Re (D) of 9/8” then we get on 15/16 ratio 135/128 the fourth shruti of Sa (C) which will become Ni (B Sharp) if we place Sa on Re (D) of 9/8 !                           So we get Fourth shruti of Sa on 135/128 with 2nd on 81/80                                                                As Pancham or Pa ( G ) is called four shruti situated on 3/2 will have on 15/16 which is 45/32 the last shruti of Ma or Ma Teevra & From Madhayam or Ma (F) which is also four shruti will give us on 16/15 of 4/3 F we get first shruti of Pancham or Pa or G on 64/45 !                                                      all 22 Shrutis of 7 swaras from these shlokas !  When You fix Shadja or Sa (C) tone on Frequency , any particular Frequency Automatically these 22 shrutis & swaras get fixed !

Of these 1/1 is called dweepta  , Next 81/80 becomes Ayata ,  16/15 is Karuna & 25/24 is Mrudu with 135/128 called Madhya !

In this way If we see on 16/15 we put Sa Shadja or C 3rd shruti above(13/125) would be 9/8 Re would be on 16/15 above 256/225 & Then Ni would be 1/1 and on 128/135 of 16/15  which would be 2048/2025 would be 1st shruti of Shadja bellow 16/15 as It will have Three shrutis above & three bellow & so called Shadja a producer of 6 shrutis !

Following shlokas mean some people who understand thinking behind shruti give 22 shruti example There are others who say 66 shrutis (this can mean three scales together 22 for each scale ) & there are others who include all scales ( Aasaama) say shruti are infinite !  Further next shloka adds 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 separation of this world from waves meaning shrutis !

  द्वाविंशतिं केचिद् उदाहरंति श्रुतीः श्रुतिज्ञानविचारदक्षाः ।                                                 षट्षष्टिभिन्नाः खलु केचिद्  आसाम अनंत्यम् प्रतिपादयंति ।।                                                                                                                                                                     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 )

म्हणजे ज्याप्रमाणे गगनात ध्वनि ची निर्मिती वा जलाशयात , समुद्रात लाटा वा तरंग , तसेच वीणेवर , यन्त्रवीणा असो वा गात्रवीणा असो श्रुती या अनंत असतात , जरी संगीतोपयोगी २२ श्रुति वर्णन केल्या असल्या तरीही !

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 ! 

From 5th shruti to 9 th shruti  are 5 shrutis of Re or D & Ga or E                                                     From 18th shruti to 22nd shruti  are 5 shrutis of Dha or A & Ni or B                                               Rest 12 shrutis are of Sa or C , Ma or F , & Pa or G , which are called 4 shruti swaras each making 22 shrutis.

Now comes question of frequecies & shrutis  Shruti system appears ratio proprtion when one put 1 st C tone called shadja at any Frequency  In western music Tone A is fixed at 440 htz frequency but in Indian system they have to tune up their tamborine or Tambora at own frequency by setting the wire cords tension by adjusting the keys given on the tambora to your own C tone or shadja (Sa) tone

How and when in the world this figuere 440 appeared ? so we get information on internet as follows

Prior to the standardization on 440 Hz, many countries and organizations followed the Austrian government’s 1885 recommendation of 435 Hz, which had also been the French standard since the 1860s.[1] The American music industry reached an informal standard of 440 Hz in 1926, and some began using it in instrument manufacturing. In 1936 the American Standards Association recommended that the A above middle C be tuned to 440 Hz.[2] This standard was taken up by the International Organization for Standardization in 1955 (reaffirmed by them in 1975) as ISO 16.[3] Although not universally accepted, since then it has served as the audio frequency reference for the calibration of acoustic equipment and the tuning of pianos, violins, and other musical instruments.

Until the 19th century there was no coordinated effort to standardize musical pitch, and the levels across Europe varied widely. Pitches did not just vary from place to place, or over time—pitch levels could vary even within the same city. The pitch used for an English cathedral organ in the 17th century, for example, could be as much as five semitones lower than that used for a domestic keyboard instrument in the same city.

Even within one church, the pitch used could vary over time because of the way organs were tuned. Generally, the end of an organ pipe would be hammered inwards to a cone, or flared outwards, to raise or lower the pitch. When the pipe ends became frayed by this constant process they were all trimmed down, thus raising the overall pitch of the organ.

From the early 18th century, pitch could be also controlled with the use of tuning forks (invented in 1711), although again there was variation. For example, a tuning fork associated with Handel, dating from 1740, is pitched at A = 422.5 Hz, while a later one from 1780 is pitched at A = 409 Hz, approximately a quarter-tone lower.[2]Overall, there was a tendency towards the end of the 18th century for the frequency of the A above middle C to be in the range of 400 to 450 Hz.

The frequencies quoted here are based on modern measurements and would not have been precisely known to musicians of the day. Although Mersenne had made a rough determination of sound frequencies as early as the 17th century, such measurements did not become scientifically accurate until the 19th century, beginning with the work of German physicist Johann Scheibler in the 1830s. The term formerly used for the unit of pitch, cycle per second (CPS) was replaced by hertz (Hz) in the 20th century in honor of Heinrich Rudolf Hertz. The two terms are equivalent: 1 CPS = 1 Hz.

During historical periods when instrumental music rose in prominence (relative to the voice), there was a continuous tendency for pitch levels to rise. This “pitch inflation” seemed largely a product of instrumentalists competing with each other, each attempting to produce a brighter, more “brilliant”, sound than that of their rivals. (In string instruments, this is not all acoustic illusion: when tuned up, they actually sound objectively brighter because the higher string tension results in larger amplitudes for the harmonics.) This tendency was also prevalent with wind instrument manufacturers, who crafted their instruments to play generally at a higher pitch than those made by the same craftsmen years earlier.[citation needed]

The diapason normal resulted in middle C being tuned at approximately 258.65 Hz . An alternative pitch standard known as philosophical or scientific pitch fixed middle C at 256 Hz (that is, 28 Hz), which resulted in the A above it being approximately 430.54 Hz . The appeal of this system was its mathematical idealism (the frequencies of all the Cs being powers of two).[4] This system never received the same official recognition as the French A = 435 Hz and was not widely used. This tuning has been promoted unsuccessfully by the Schiller Institute under the name Verdi tuning since Italian composer Giuseppe Verdi had proposed a slight lowering of the French tuning system. However, the Schiller Institute’s recommended tuning of A is 432 Hz rather than the mathematically derived 430.54 Hz.[5][6]

The Stuttgart Conference of 1834 recommended C264 (A440) as the standard pitch based on Scheibler’s studies with his Tonometer.[10] For this reason A440 has been referred to as Stuttgart pitch or Scheibler pitch.

It is designated A4 in scientific pitch notation because it occurs in the octave that starts with the fourth C key on a standard 88-key piano keyboard. On MIDI, it is note 69.

Piano Keyboard

An 88-key piano, with the octaves numbered and Middle C (cyan) and A440 (yellow) highlighted

Here one can seen in this 88 key piano , last key is of C is octave C of 7th scale & 1st key is A Tone key of scale 0 bellow 1st scale , two tones bellow C of 1st scale. Best part is F # tone of the fourth scale is at the centre of this Keyboard from A of 0 scale to C of the 8th scale In the central fourth scale also F # forms centre of C & Octave C  Here we can note that as per Indian Musical rules also Ma or F is situated in the centre between two Sa or C Tones When we speak of wire or chord instruments its Ratio is 4/3 or 3/4 distance on chord , When we speak of F# it is on 45/32 ratio & from this 45/32 ratio on 4/3 ratio is seen 2nd shruti of Ni or B on ration of 15/8 !            Also fourth shruti of Sa or C situated on 135/128 on ratio, on 4/3 is the position is F # on 45/32  Further from 45/32 position of F # , we can see in C – G ratio of 3/2 is the 135/64 which is the fourth shruti of octave C called Upper scale Sa !  This shows that So called Indian music was Universal Music !  But for the developement of equidistant harmoious harmonium scale TET scale of equitampered tones was developed using modern mathematics with logarithic scale instead of scale of Ratio proportions or Melodious Melody scale & adjustible on chord instruments !  Basic question being whether vocalist should adjust his tone as per instrument or Instrumentalist should adjust instruments os per change in the scale or shruti system of vocalist this was the fight ! This fight was who is main player Vocalist or fixed tone Instrumentalist !!

Here we can see that when A on 440 was accepted at that time C on 264 was take as base It is not surprizing that ration of this  A on 440 / C on 264   is 5/3  the ratio in Indian musical system of 2nd Shruti A or Dha on 5/3

Further mention that An alternative pitch standard known as philosophical or scientific pitch fixed middle C at 256 Hz    This give boost to Indian shruti system where Komal Re or tone C # which is on 16/15 with C or Sa Shadja fixed on 240 also comes on 256 which is C# or Komal Re  This this another proof that if original freqency of 1 is taken as 1st shruti then octave tone of that frequecis would be 1-2-4-8-16-32-64-128-256 with 256 frquency of  whatever original tone you label ABCDEFG  !!!  

Indian Music  gives all 22 shrutis their own names & type called Jaati system  described in shlokas as follows … ( These are the original indian literature on which musical shruti system & swaras & Grama system are based so it is important to understand the meanings of these ) 

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. १४ )

Here specifically Dveepta shruti is mentioned on  Mandre meaning        F Tone or Ma Dvitiye meaning E Tone or Ga , Prachaturthe tathaiva  Tu meaning simmilarly on C Tone or Sa , & , B Tone or Ni tone as in SaaMa Gaan we have understand that Ma or F & Ga or E is comparable to Sa or C & Ni or B which tones are plaved on exact divisions into two parts so called Dveepta !                                                      Where as Atisware meaning Dhaivat or A tone & Trutiya meaning third which is after F & E third is D or Re Tone , & krushte meaning Pa or Pancham or G tone these 3 tones have karuna shruti !                                              This completes distribution of 1 st shruti of seven tone !                          Further Aayata is extended from Dveepta , Mrudu is one before Madhya shruti completing sequence of Dveepta , Aayata , Mrudu , Madhya & Karuna shrutis of any tone used as 1st tone of an octave ! 

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  ।।                          

 षडज पंचमभावेन षडजे ज्ञेया स्वराः बुधैहि  ।                                                                      गनि भावेन गांधारे मस भावेन मध्यमे  ।।

मध्यमग्रामे तु श्रुति अपकृष्टः पंचमः कार्यः                                                                   श्रुति उत्कर्षात अपकार्षात वा यदन्तरम                                                                   मार्दवात आयतत्वात वा तत्प्रमाणश्रुतिः ।।                                                                                   (ना. शा.  अ. २८ पृ. ३१८) (हिं. सं. प. भाग. २ पृ. २२ )

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

Here it mentions in madhyam graam of Indian music moving fifth tone above one can achieve formation of madhyam graam or or moving bellow one can achieve position back to shadja graam and this one shruti distance is same as seen in making tone mrudu or soft or making tone aayata shruti or sharp or extended ! In the next one it clearly states this & this fifth is as par ssam gaan system where it mentions that in saam gaan fifth tone is the Dhaivat or A tone ! Here every one gets confused thinking fifth mentioned is Pancham or tone G !

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 )


आनंत्यं हि श्रुतीनां च सूचयन्ति विपश्चितः  ।                                                                     यथा ध्वनिविषेशाणां अमानं  गगनोदरे  ।।                                                                         उत्तालापावनो द्वेज्जलराशि समुद्भवाः ।                                                                           इयत्यः प्रतिपद्यन्ते न तरंगपरम्पराः  ।।

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


ऋषभो त्त्थाः षड्जहतो धैवत सहितः च पंचमो यत्र  ।                                                     निपतति मध्यमरागे तं निषादं षाडवं विद्यात ।।                                                           यदि पांचमो विरमते गाण्धारः च आंतरः स्वरो भवति ।                                                 ऋषभो निषाद सहितस्तं पंचममीदृशं विद्यात ।।                                                     गान्धारस्याधिपत्येन निषादस्य गतागतैः ।                                                                       धैवतस्य च दौर्बल्यात मध्यमग्रामं उच्यते ।।

ईषत्स्पॄष्टो  निषादस्तु गान्धारःच अधिको भवेत ।                                                           धैवतः कम्पितो यत्र षडजग्रामं विनिर्दिशेत ।।

षडज मध्यम गान्धाराः त्रयो ग्रामाः प्रकीर्तीताः ।                                                                 भूलोकात जायते षड्जो भूवःलोकात च मध्यमः ।।                                                         स्वर्गात्नान्यत्रो गान्धारो नारदस्य मतं यथा ।                                                             स्वरारागाविशेषेण ग्रामारागा इति स्मृताः ।।                                                                            (ना. शि. कं. २, १-८, पृ. १५-१६) (हिं. सं. प. भाग. २ पृ. १२-१३ )

रिमयोः एकैकं गान्धारस्चेत समाश्रितः ।                                                                    पश्रुति धो निषादस्तु ध श्रुतिं सश्रुतिं स्थितः ।। १. ४. ४. पं. शारंगदेव                                      धत्ते रिमायोः अन्यादिमे श्रुति निराप्युमू धसयोः ।                                                               धः पान्त्यां चेद्गान्धारग्राम स्वर्गलोकेन्यः ।। रागविबोध १. ४ पं. सोमनाथ

विवादिनस्तु ते येषां स्याद्विंशतिं स्वरामन्तरं ।                                                                   तद्यथा ऋषभ – गान्धारौ , धैवत -निषादौ ।।

Basically question remains why A Tone was adjusted on 440 from where this figure has come ??

Answer is very Simple Indian Music which was actually universal music from most ancient literature Vedas in which Sama Veda was for music itself its name itself originating from “Sa” which is Shortform for Shadja or C Tone & “Ma” which is shortform for Madhyam or F Tone , making it Sama Veda which indicates how important was use of tones in singing hymns of Vedas. There originates the concept of musical tones & 22 shruti were part of ratio proportions when any tone or frequency is taken as Sa or C !                                    Here Original Indian literature describes C on 240 & Octave C on 480 a ratio of 2/1 !  Now In preparation of “Equitemparament tones yet maintaining 22 shruti … One can easily seen that if C is put on 220 then we get 440 octave C & in between 22 equidistant tones starting from 220 to 430 with rise of 10 , we get…….                           220,230,240,250 …..at 430 we get 22nd shruti with 440 being Octave C Further at 240 is Indian C So 220 becomes A , 230 becomes B , & 240 C So 220 & 440 get labelled as A which is Dhaivat or Dha tone of Indian Music ! It was simple 110 to 220 numbers give 11 tones  !

So A Tone which is Dhaivat or Dha was fixed at 440 & Even Modern 88 key piano starts from A Tone or Dha third shruti & ends on C of 8th scale as seen in picture given above !  from this 440 on a ratio propoertion of 16/27 is 260.740740 frquency of C tone or Sa or Shadja 1st shruti  of Indian music which matches with charts given bellow of modern table of shrutis its corrected table is given next to it bellow !

There is lot of  confusion about use of terms like Vaadi , Anu-Vaadi , Sam-Vaadi ,and  Vivaadi as these apply to swara positions situated on shruti positions.  It appears that Ragas were classified as Arohi & avrohi Ragas Labelling them as Purush & Stree Ragas would produce different effects Arohi Ragas being stimulants & avarohi being pacifiers ! But that depends on singers !                                                             As far as correct positions would be as follows 

 1)  Teevra                Dveepta           1/1                      240            260.74074                                                                                                                                          2)  Kumudvati        Aayata             81/80                  243            264                                                                                                                                                         3)  Manda                Mrudu              25/25                  250            271.6049                                                                                                                                               4)  Chhandovati     Madhya         135/128               253.125      275                                                                                                                                                       5)  Dayaavati           Karuna            16/15                 256              278.1235                                                                                                                                             6)  Raanjani              Aayata             27/25                259.2            281.6                                                                                                                                                   7)  Raktika                Madhya           9/8                     270               293.3333                                                                                                                                           8)  Raudri                  Dveepta          6/5                      288               312.8888                                                                                                                                           9)  Krodha                 Madhya           5/4                      300              325.9259                                                                                                                                           10)  Vajrika                Dveepta          4/3                      320              347.6543                                                                                                                                           11)  Prasarini             Aayata           27/20                   324               352

  12)  Priti                      Mrudu             25/18                 333.3333    362.134                                                                                                                                             13)  Marjani                Madhya         45/32                   337.5         366.6666                                                                                                                                           14)  Kshiti                    Karuna           64/45                  341.3333   370.8313                                                                                                                                           15)  Rakta                    Aayata           36/25                   345.6         375.4666                                                                                                                                           16)  Sandipani            Mrudu           40/27                    355.5555   386.2826                                                                                                                                           17)  Aalapini                Madhya        3/2                         360           391.1111                                                                                                                                           18)   Madanti               Karuna         8/5                          384         417.1853                                                                                                                                             19)   Rohini                   Mrudu          5/3                          400          434.5679                                                                                                                                           20)  Ramya                   Madhya       27/16                       405            440                                                                                                                                                   21)  Oogra                     Dveepta      9/5                           432         469.3333                                                                                                                                             22)  Kshobhini             Madhya       15/8                          450        488.8888

 Following is the table showing present thoughts about shruti positions but they do not explain C – G Ratio or shadja Pancham Bhav or relations to all shrutis as lack of understanding  of the shlokas which actually give ratio proportions of shrutis & swaras or tones Corrected cents values and ratio proportions are given in next chart In the next chart C is taken on 261.6256 from this C on ratio of 16/15 we get 279.0673 which is C # , further on ratio 27/16 we get A # tone on 441.4932 !

Method of calculating Cent value is                                                                     Cent value = 3866.4460836 X Log of (f2/f1)                                                       where f2/f1 is frequecy ratio of given shruti ratio position !

 ¢ or c = 1200 × log2 (f2 / f1)
log 2 = 0.301029995

This formula can also be
written using a log 10 function, available on most scientific calculators via the log button:                           C = 1200 X 3.222038403 log10 (f2/f1) or                                                                                                   C = 3866.4460836 X log10 (f2/f1)

c = 1200 × 3.322038403 log10 (f2 / f1)
1/log 2 = 1/0.301029995 = 3.322038403
The formula expressed using log10 rather than log 2.

                                                                                                                                                                                                                                        So In following table C at 261.6256 is fixed & NOT A # at 440


Shrutis 12-TET Notes 53-TET Notes Perfect FIFTHs
Name Indian Shruti Ratio Cents Frequency
Name Frequency
Tīvrā 1 0 261.6256 C 261.6256 0 261.6256 0 261.6256
Kumudvatī 81/80 21.51 264.8959 C♯ 277.1826 4 275.6763 -5 275.622
Mandā 25/24 70.67 272.5267 5 279.3053 7 279.3824
Chandovatī 135/128 92.18 275.9333 D 293.6648 8 290.4816 -10 290.3672
Dayāvatī 16/15 111.74 279.0673 9 294.3056 2 294.3288
Ranjanī 10/9 186.10 290.6951 D♯ 311.1270 13 310.1114 -3 310.0747
Raktikā 9/8 203.91 294.3288 14 314.1937 9 314.3052
Raudrī 6/5 315.65 315.64 E 329.6275 17 326.7661 -8 326.6631
Krodhā 5/4 386.31 327.032 18 331.0677 4 331.1199
Vajrikā 4/3 498.04 348.8341 F 349.2282 22 348.8478 -1 348.8341
Prasāriṇī 27/20 519.57 353.1946 23 353.4401 11 353.5933
Prīti 25/18 568.74 363.3689 F♯ 369.9944 26 367.5829 -6 367.496
Mārjanī 45/32 590.24 367.911 27 372.4218 6 372.5098
Kṣiti 64/45 609.81 372.0897 G 391.9954 31 392.4229 1 392.4384
Raktā 36/25 631.30 376.7409 G♯ 415.3047 35 413.4982 -4 413.433
Sandīpanī 40/27 680.47 387.5935 36 418.9415 8 419.0736
Ālāpinī 3/2 701.98 392.4384 A 440.0000 39 435.7053 -9 435.5508
Madantī 8/5 813.71 418.6011 40 441.441 3 441.4932
Rohiṇī 5/3 884.39 436.0427 A♯ 466.1638 44 465.1488 -2 465.1121
Ramyā 27/16 905.89 441.4932 45 471.2721 10 471.4578
Ugrā 9/5 1017.63 470.9261 B 493.8833 48 490.1298 -7 489.9947
Kṣobhinī 15/8 1088.30 490.548 49 496.582 5 496.6798
Tīvrā 2 1200 523.2512 C 523.2511 53 523.2512 0 523.2511


Notes nine and 13 shrutis from each other are mutually samvādi (consonant). The notes that are at the distance of two and 20 shrutis are mutually vivādi (dissonant). The remaining ones, at the distance between 2 and 20 shrutis, are called anuvādi (assonant).

This is over simplification of Indian system Indian Ragas have first one Vadi swar which is the one which is used more often & also Raga is started with achieving stability at that swara then anuvaadi other swaras follow leaving the varjya swaras & you go to Samvadi which is 13 shruti above or 9 shruti bellow in uttarng vaadi swaras as 9 shruti bellow & 13 shruti above is same completeing 22 shruti circle or mandal  !  Vivadi is dissonant  tone or swar which fails to reach this distance and falls short by 2 shruti or 20 shruti in opposite directions  !                                                            In case of Aarohi ragas or poorvang vaadi ragas the Vaadi – Samvaadi are 13 shruti above like   C – G , D – A , E – B , F – C (octave)  In case of Avarohi Ragas also distance remains same if Vaadi is in the uttarang of next half of octave like G – C , A – D , B – E , Octave C – F  !  But for Aarohi Ragas with Vaadi G – C# , A – D# , B – F# , C# – G#  these become the consonant partners ! Varjya swaras are as a rule not to be used in a given Raga it has nothing to do with Vivadi swar !


The shruti table below shows the mathematical ratios considered to correspond to the system described by Bharata and Dattila, along with the comparable notes in common Western 12-TET tuning and comparable notes in 53-TET tuning. The names of the 22 shrutis were provided by Śārñgadeva.                                                                                                                                                                                                                                                                                                                                      Corrcted chart is given with its cents values   & corrcts ratio proportions is given above

This is the data which is shared internationally but  Sa or Shadja swar or tone is  four shruti further Re or Rishabh tone or D is supposed to be of three shrutis with 9/8 shruti ratio D should be on 7 th shruti , 8th & 9th being Ga or E tone  with F situated on 10th is seen. They appear more adjusted as per as per modern concepts than anything to do with Sharangdev …                                                                                                                                                                                  


Shrutis 12-TET Notes 53-TET Notes Perfect FIFTHs
Name Ratio Cents Frequency
Name Frequency
Kṣobhinī 1 0 261.6256 C 261.6256 0 261.6256 0 261.6256
Tīvrā 256/243 90 275.6220 C 277.1826 4 275.6763 -5 275.622
Kumudvatī 16/15 112 279.0673 5 279.3053 7 279.3824
Mandā 10/9 182 290.6951 D 293.6648 8 290.4816 -10 290.3672
Chandovatī 9/8 203 294.3288 9 294.3056 2 294.3288
Dayāvatī 32/27 294 310.0747 D 311.1270 13 310.1114 -3 310.0747
Ranjanī 6/5 316 313.9507 14 314.1937 9 314.3052
Raktikā 5/4 386 327.0319 E 329.6275 17 326.7661 -8 326.6631
Raudrī 81/64 407 331.1198 18 331.0677 4 331.1199
Krodhā 4/3 498 348.8341 F 349.2282 22 348.8478 -1 348.8341
Vajrikā 27/20 519 353.1945 23 353.4401 11 353.5933
Prasāriṇī 45/32 590 367.9109 F 369.9944 26 367.5829 -6 367.496
Prīti 729/512 612 372.5098 27 372.4218 6 372.5098
Mārjanī 3/2 702 392.4383 G 391.9954 31 392.4229 1 392.4384
Kṣiti 128/81 792 413.4330 G 415.3047 35 413.4982 -4 413.433
Raktā 8/5 814 418.6009 36 418.9415 8 419.0736
Sandīpanī 5/3 884 436.0426 A 440.0000 39 435.7053 -9 435.5508
Ālāpinī 27/16 906 441.4931 40 441.441 3 441.4932
Madantī 16/9 996 465.1121 A 466.1638 44 465.1488 -2 465.1121
Rohiṇī 9/5 1017 470.9260 45 471.2721 10 471.4578
Ramyā 15/8 1088 490.5479 B 493.8833 48 490.1298 -7 489.9947
Ugrā 243/128 1110 496.6798 49 496.582 5 496.6798
Kṣobhinī 2 1200 523.2511 C 523.2511 53 523.2512 0 523.2511

The 53-TET approximation has a maximum error of 1.5%, while the perfect fifths approximation has a maximum error of 2%.


Corrected positions are as follows


सामवेदाच्या सुरावटीत हे खालील सूर सांगितले जातात                                                                                           नि – सा – को.रे , – सा – को. रे – ग, ग – को.रे – सा,  नि – सा – को.रे                                                                              यात नि – सा – को.रे या सुरांना जे महत्त्व आहे त्याला कारण त्यांच्यात असलेले                                                     समान श्रुत्यंतर प्रमाण  नि – सा – को.रे  हे ( 225 – 240 – 256 ) 16/15 या सम अंतरावर आहेत तेच अंतर ती.म – प – को.ध या सुरांत ( 337.5 – 360 – 384) 16/15 या सम अंतरावर आहेत. याप्रकारे कोठेही सा लावला तरी या सम अंतरावरील सूरगायनास साम गायन म्हटले होते व या सम अंतरावर सूर ठेवण्याने विशिष्ट समयी उत्तेजित मन शांत करण्यास हे उपयुक्त असते.

हेच सूर जगातील विविध पंथीय वापरताना दिसतील कारण स्वार्थासाठी पंथांच्या वेगळ्या चुली वेगळी कर्मकांडे सांगत मांडलेल्या असल्या तरी मूळ एकच आहे ज्यास सनातन सत्यधर्म म्हटले जाते व ज्यास दुसरा पर्याय नसतो. सामांन्याना पंथ व धर्म यातील भेद कळत नाही व असामान्य, हा भेद कळणारे काय फरक पडतो स्वार्थ साधणे पसंत करतात त्यावेळी सत्ययुग संपते. ज्यावेळी काळाच्या महिम्याने हे आवरणदूर केले जाते

त्यावेळेपासून सत्ययुगाकडे वाटचाल सुरू होते.  कोणी म्हणेल की त्या काळात कंपनसंख्या माहीत नसताना हे जाणणे हे अशक्य आहे. पण 400 – 500 वर्षात एवढी प्रचंड प्रगति करणारा मानव त्या आधी लाखो वर्षे सतत अश्मयुगात राहिला व तरी भाषा, संगीत, कला या तेवढय़ा प्रगत होत्या व संस्कृत भाषा, वेद, गीता हे त्या अप्रगत लोकांनी रचले होते हे  म्हणणेच अशक्य कोटीतले व आधीच्यांना अप्रगत ठरविण्यासाठी रचलेले कुभांड आहे हेच खरे आहे हे लक्षात यावयास हवे. स्वतच्यापंथाला वा पेशाला सोयीस्कर संशोधन करणे ही स्वार्थी संशोधकांची फार जुनीच पद्धत आहे.

यामुळेच सामवेदात कमीतकमी तीन पेक्षा जास्त सूर आवश्यक म्हटले गेले होते.

सारेग या तीन सुरांच्या सुरावटीत सारे हा पूर्वार्ध व रेग हा उत्तरार्ध धरला तरी सा चा वादी रे व रे चा वादी ग होतो. याप्रकारे सारे रेग गम मप पध असे वादी संवादी होतात व परिणाम उलट होण्यासाठी आरोह वादी धरला तर अवरोह संवादी करावा लागतो नाहीतर विरुद्ध परिणाम साधणे शक्य होत नाही.  मात्र सारे हा पूर्वार्ध व गम हा उत्तरार्ध होतो व   सा चा संवादी ग व रे चा म होतो व साग व रेम अशी व पुढे पनि व धसा अशा जोडय़ा जमल्यातरी आरोह-अवरोह हेच परिणामांसाठी महत्वाचे ठरतात.  पुढे सारेग व मपध याप्रकारे पूर्वार्ध व उत्तरार्ध होतात व सा-म, रे-प, ग-ध हे वादी संवादी ठरतात. त्यापुढे सारेगम व पधनिसां याप्रकारे पूर्वार्ध व उत्तरार्ध होतात व सा-प, रे-ध, ग-नि, म-सां                                  हे वादी संवादी ठरतात.                                                                                                                                             याचाच उपयोग वेगवेगळ्या प्रकारे विविध रसोत्पादनासाठी केला जाऊन                                                               मूळ उत्तेजित करणारे, शांत करणारे , व मध्यम (स्थिती कायम) ठेवणारे याप्रकारे करता येतो.

याप्रकारचे हे गणित हिंदुस्थानी संगीतात आहे.                                                                                                      पुढे थाटांचे वर्गीकरण कै.पं.वि.ना.भातखंडे यांनी फार सुंदरपणे 10 थाटात दाखविले आहे.

1) संधिप्रकाशानंतरचे थाट – बिलावल, कल्याण, खमाज                                                                                          2) संधिप्रकाशाआधीचे धाट – काफी, आसावरी,तोडी,भैरवी                                                                                         3) संधिप्रकाशकालीन थाट – मारवा, पूर्वी, भैरव

संक्रांत हा संध्यासमय व मकर संक्रांतीनंतर उष्णतावृद्धी व कर्क संक्रांतीनंतरशीततावृद्धी होते.                                     ज्याप्रकारे वर्षामधे उन्हाळा(उत्तरायण) व हिवाळा(दक्षिणायन)  हे ऋतू                                                                     तसेच महिन्यात शुक्लपक्ष(ऊष्ण) व कृष्ण पक्ष (थंड),                                                                                       दिवसांत उत्तरांग ऊष्ण (रा.12 ते दु. 12) व पूर्वांग थंड (दु.12 ते रा. 12).                                                              त्यापुढे जाऊन आपल्या प्रकृति स्थितीनुसार ( ऊष्ण वा थंड )                                                                            अनुरूप अन्न, औषध, रंग, सुरांचा वपर हे लक्षात ठेऊनच त्यानुसार                                                                         थंड व ऊष्ण सुरांचा रागांचा प्रयोग करावा हा मूळ संगीतोपचाराचा नियम.

आरोह हा ऊष्ण व अवरोह हा थंड कारक असल्यानेच सामवेदांचे गायन, जे यज्ञप्रसंगी करत असत ते अवरोहात्मक असे.

संगीतात सूरांमध्ये पूर्वांग (सा रे ग म प) व उत्तरांग ( म प ध नि सां ) असे विभाग केलेले आहेत तसेच रागांमधेही पूर्वराग ( दु. 12 ते रा. 12 पर्यंतचे) व उत्तरराग ( रा. 12 ते दु. 12 पर्यंतचे )असे  विभाग केलेले आहेत.

रा. 12 पासून ऊष्णतावृद्धी होते तेंव्हा गायचे ते उत्तरराग. तर दु. 12 पासून शीततावृद्धी होते तेंव्हा गायचे ते पूर्वराग.

इथे हे लक्षात घ्यावयास हवे की ही मूळ शास्त्रशुद्ध संकल्पना आहे.

पूर्व व दक्षिण या ऊष्ण दिशा व खंड तर पश्चिम व उत्तर या थंड दिशा व खंड

कारण पूर्व दिशेला सूर्याची म्हणून ऊष्ण व उत्तरेला जास्त भूखंड म्हणून ती थंड दिशा

व या विरुद्ध त्या अनुक्रमे (पश्चिम) थंड व (दक्षिण) ऊष्ण दिशा हे स्पष्ट होते. त्यामुळे दिवसातील स.6 (सूर्योदय) ते सं.6(सूर्यास्त) हा पूर्वखंड(ऊष्ण) व सं.6(सूर्यास्त) ते स.6(सूर्योदय) हा उत्तरखंड(थंड)  जरी असला तरी पूर्व-उत्तर            हे द्वैत जसे जगात तसेच शरीरात अखंड सुरूच असते ज्यामुळे तपमान सामान्य मध्यम राखले जाते.

त्यामुळे दु. 12 ते रा. 12 हा थंड म्हणून उत्तर खंड व रा. 12 ते दु. 12 हा ऊष्ण म्हणजे पूर्वखंड होतो तरी या काळात राग हे विरुद्ध आधी पूर्वराग (ऊष्ण) व नंतर उत्तरराग (थंड) त्याही पुढे या दोनही भागात मिळून आठ प्रहर( दीड-दीड तासांचे दोन एकत्र करून) तीन-तीन तासांचे चार प्रहर बनवले गेले.

थंड-ऊष्ण वा आरोही-अवरोही मग ऊष्ण-थंड वा अवरोही-आरोही  हे पूर्वोत्तर चक्र न बदलता केले गेले.

पण रा. 12 ते दु. 12 हा उष्णता वृद्धीचा खंड व दु. 12 ते रा 12 हा  शीतलता वृद्धीचा खंड आधी उत्तरराग ( थंड राग ) व नंतर पूर्वराग ( ऊष्ण राग ) असे जाणवले तरी अनुभव येतो तो या कल्पनेशी पूर्णपणे जुळणारा नसतो.

त्यामुळे अनुभवसिद्ध वेळांप्रमाणे संध्याकाळी 4 ते 7 ही वेळ व पहाटे 4 ते 7 ही वेळ हे अनुक्रमे संध्याकाळचे व सकाळचे संधिसमय आहेत. हे सूर्योदय(दिवसाचे) व सूर्यास्ताचे(रात्रीचे)s वेळ म्हणूनच प्रधम प्रहर धरून त्याप्रमाणे शरीराचे घडय़ाळ लावून घेण्यास  (सेट करण्यास) उपयुक्त ठरले व या सेट करण्यास “ संध्या ’’ हे नामकरणकेले गेले.               त्यानंतर स. 7 ते 10 व रात्री 7 ते 10 हे अनुक्रमे सकाळचे व रात्रीचे द्वितीय प्रहर होतात.  त्यानंतर स. 10 ते 1 व रात्री 10 ते 1 हे अनुक्रमे सकाळचे व  रात्रीचे तृतिय प्रहर होतात.  त्यानंतर दु. 1 ते 4 व रात्री 1 ते 4 हे अनुक्रमे सकाळचे व रात्रीचे चतुर्थ प्रहर होतात.

आता काळानुक्रमे सकाळ ही कफप्रकृतिची (रात्रीच्या थंडीमुळे), दुपार ही पित्तप्रकृतिची (सकाळच्या उष्णतेमुळे),           व संध्याकाळ वातप्रकृतीची वेळ ( दिवसभराच्या कुपथ्यामुळे) ठरविली गेली आहे.                                                तसेच उन्हाळा हा पित्तप्रकृतीचा, पावसाळा हा कफप्रकृतीचा(उन्हाळ्यातील थंड खाण्यामुळे)  तर हिंवाळा हा वातप्रकृतीचा ( उन्हाळा-पावसाळ्यातील कुपथ्यामुळे) ठरविले गेले आहेत.

तरी शास्त्रीय दृष्टया विचार केला तर सकाळचा प्रथम प्रहर कफ प्रकृतिचा तर द्वितिय प्रहर कफजन्य – वाताचा                  दुपारचा प्रथम प्रहर पित्त प्रकृतिचा तर द्वितिय प्रहर पित्तजन्य – वाताचा याप्रकारेच                                                        हिवाळ्याचा प्रथम भाग कफ प्रकृतिचा तर द्वितिय भाग कफजन्य – वाताचा                                                                उन्हाळ्याचा प्रथम प्रहर पित्त प्रकृतिचा तर द्वितिय भाग पित्तजन्य – वाताचा  असे वर्गीकरण दिसते.

पुढे कफ प्रकृतिला पथ्यकर ऊष्ण तर कफजन्य वाताला आधी थंड मग ऊष्ण उपचारांची गरज असते.                          तर पित्त प्रकृतिला पथ्यकर थंड तर पित्तजन्य वाताला आधी थंड मग पण थंडच उपचारांची गरज असते.

हे आगांतूक होणाऱया कफ-पित्त-वात यांना जसे लागू आहे तसेच सार्वकालीक पथ्याला पण लागू असते.

सकाळचा प्रथम प्रहर कफ प्रकृतिचा म्हणून ऊष्ण तर द्वितिय प्रहर कफजन्य – वाताचा म्हणून थंड,

दुपारचा प्रथम प्रहर पित्त प्रकृतिचा म्हणून थंड  तर द्वितिय प्रहर पित्तजन्य – वाताचा म्हणून थंडच

तसेच याप्रकारेच  हिवाळ्याचा प्रथम भाग कफ प्रकृतिचा  म्हणून ऊष्ण                                                                    तर द्वितिय भाग कफजन्य – वाताचा म्हणून थंड

उन्हाळ्याचा प्रथम प्रहर पित्त प्रकृतिचा  म्हणून थंड                                                                                              तर द्वितिय भाग पित्तजन्य – वाताचा म्हणून थंडच  याप्रकारे उपचारांची गरज असते

आता खालील तक्त्या प्रमाणे मांडणी करता चित्र असे दिसते.

कफ-कफवात                                                                                          पित्त-पित्तवात

State of Sympathetic inadequacy                                  State of parasympathetic inadequacy

What is seen is breathlessness                                        What is seen is acidity

Sympathetic stimulation tratment                             Parasympathetic stimulation treatment             as internal sympathetic goes into fatigue                as internal parasympathetic goes into fatigue

(patient in fight or flight for breath)                            (patient wants Sleep healing repair)

Treatment causes acidity.                                                Treatment causes breathlessness.

औदासिन्य/ कफ-कफवात यासाठी                                               उत्तेजितावस्था/ पित्त-पित्तवात यासाठी

आधी 1 मग 2 गति 1 कडून 2                                                     आधी 2 मग 1 गति 2 कडून 1

 1 कफ काल                                                                                     2 पित्तकाल

कर्क ते मकर संक्रांत – जुलै ते जानेवारी                                      मकर ते कर्क संक्रांत – जानेवारी ते जुलै  आधी उत्तरराग (उत्तरांगवादी राग)रा.12तेदु.12                               आधी पूर्वराग(पूर्वांगवादी राग)दु.12ते रा.12

उत्तर काळ उष्णतावृद्धीचा                                                            पूर्व काळ शीतलता वृद्धीचा

(पथ्यकर आधी ऊष्ण मग थंड)                                                           (आधी पथ्यकर थंड मग ऊष्ण)

(काळाशेवटी उष्ण कमी करून शीतची गरज)                        (कालाशेवटी शीत कमी करून ऊष्णतेची  गरज)

रा. 12 ते दु.12 (24 ता. चक्राप्रमाणे)                                               दु. 12 ते रा. 12 (24 ता. चक्राप्रमाणे)

स.6 ते दु. 12 उष्णतावृद्धी                                                               दु.12 ते सं 6 शीतलता वृद्धी (शारिरीक)                  कारक रवि रा.12 ते स. 6 शीतलता वृद्धी                                 सं 6 ते रा 12 उष्णतावृद्धी (मानसिक) कारक चंद्र

आरोह हा ऊष्ण व अवरोह हा शीतल सर्गमीचे पूर्वांग हे ऊष्ण व उत्तरांग हे शीतल.

सारेगमपधनिसां या सप्तसर्गम मध्ये सारेगम पूर्वांग व पधनिसां उत्तरांग

प – ध – नि – सां (उत्तरांग)                                                               सा – रे – ग – म (पूर्वांग)

सां – नि – ध – प                                                                              म  – ग – रे – सा

पण सारेगम व पधनिसां या मूळ दोन सरगम मध्ये  सारे व पध ही पूर्वांग आणि गम व निसां ही उत्तरांग या दृष्टीने

ग  – म (उत्तरांगवादी)                                                                     सा – रे (पूर्वांगवादी)

नि – सा (उत्तरांगवादी)                                                                     प – ध (पूर्वांगवादी)

( 12 ता. चक्राप्रमाणे 6 तासाचे विभाग)                                            ( 12 ता. चक्राप्रमाणे 6 तासाचे विभाग)

तापमान सुरवातीस थंड                                                                        तापमान सुरवातीस ऊष्ण

सुरवातीस आकाश काळे लाल                                                               सुरवातीस आकाश शुभ्र निळे

शेवटी आकाश निळे शुभ्र                                                                         शेवटी आकाश लाल काळे

आसन उभे वा पाश्चिमात्य                                                                     आसन बैठक वा भारतीय

उजवी कुशी                                                                                             डावी कुशी

शब्द आवाहनात्मक शांत गंभीर                                                              शब्द आव्हानात्मक उत्तेजक

लय मंद                                                                                                      लय द्रुत

ताल शांत                                                                                                  ताल उत्तेजक

गति विस्तार सफ्तक तार कडून मंद्र कडे                                      गति विस्तार सफ्तक मंद्र कडून तार कडे

उत्तरांगवादी                                                                                               पूर्वांगवादी

स्वर अवरोही (अवरोह स्वरूपदर्शी)                                                       स्वर आरोही  (आरोह स्वरूपदर्शी)

आधी कोमल ध/ को.रे मग शुद्ध ध शु.रे                                           आधी स्वर कोमल नि/ को.ग  मग शुद्ध नि शु ग

आधी ती. म मग शु. म                                                                            आधी  शु. म, मग शु.ती. म

कल्याण / सिंधुभैरवी                                                                                     भैरवी / बिलावल

आसावरी                                                                                                             तोडी

खमाज                                                                                                                 मारवा

काफी                                                                                                                     पूर्वी

भुपाळी(देसकार)                                                                                                   मालकंस

हिंडोल (कल्याण थाट)                                                                                               तोडी

औदासिन्य/ कफ-कफवात यासाठी                                           उत्तेजितावस्था/ पित्त-पित्तवात यासाठी

तोडी व हिंडोल हे पूर्वापार पासून उपचारांसाठी उल्लेखित आहेत त्यातही

कोमल सुरांचा तोडी व उत्तेजक लहर सोडणारा हिंडोल हे पण यात शास्त्रशुद्ध

पद्धतीने विरुद्ध परिणाम का करतात ते येथे दिसून येते.

मूळ सकाळी कोमल सुरांच्या भैरवीने सुरवात करून दुपारी आसावरी आळवत संध्याकाळी कल्याणनी शेवट तसेच, संध्याकाळी शुद्ध सुरांच्या पण कालदर्शी ती.म असलेलेया कल्याणनी सुरवात करून मध्यरात्री खमाज आळवत शेवट सकाळच्या भैरवीने करावा. मधल्या काळात सकाळी तोडी, बिलावल व संध्याकाळी पूर्वी,मारवा यांचा वापर करत व को.रेध असलेल्या काफी चा विश्रांतीसाठी सावली सारखा वा संध्याकाळी पावसाच्या सरी(मल्हार) सारखा                       वापर करावा.

भैरवी, तोडी , काफी,देसकार, आसावरी ,(रात्री खमाज),/बिलावल,काफी,(रात्री मालकंस), पूर्वी,(सकाळीभैरव),मारवा,कल्याण

या प्रकारे नवरसात्मक सकाळ ते संध्याकाळ बारा तासांचे वर्गीकरण केले होते

सा,रे,ग,म,प हे पूर्वांगाचे वादी व आरोहात म तीव्र सुद्धा घेणे हे दु. 12 ते रा 12 या पूर्वांगवेळेची खूण.

म,प,ध,नि,सां हे उत्तरांगाचे वादी व आरोहात म तीव्र वर्ज्य करणे हे रा. 12 ते दु. 12 या उत्तरांगवेळेची खूण.

1) म तीव्र का शुद्ध  2) वादी स्वर 3) वर्ज्य स्वर 4) चलन आरोहात्मक का अवरोहात्मक

5) सर्व कोमल सूर थंड म्हणून सकाळी (सृष्टि थंड झालेली वेळ) व सर्व शुद्ध सूर संध्याकाळी (सृष्टि ऊष्ण झालेली)

यावर रागांची वेळ ठरते. अयोग्य राग रोगकारक ठरतात.

सकाळी 7 चा सूर्योदय धरला तर सकाळी 7 ते 10 हा सकाळचा प्रथम प्रहर होतो.

पण काही स.4 ते 7 हा प्रथम प्रहर तर काहीनी पूर्वांगात व उत्तरांगात प्रथम द्वितीय केल्याने व देशादेशातील

उदयास्त वेळा भिन्न असल्याने गोंधळ होणे साहजीक असते पण सूरांवरून वेळा कळतात.

राजद्वारी, संगीतसभेत, व उपचारात यात जरुरीप्रमाणे / परिस्थितीप्रमाणे बदल करावा लागतो.

Before coming to application of music for therapy it is important to understand Mind & Sensory system 

                   इंद्रिय ज्ञान गम्य जगाचे स्वरूप                                                                ( understanding sensory systems & Universe)  

        जगाचे रूप हा जो भास आपण इंद्रिय जन्य ज्ञानाने अनुभवतो त्याचे थोडे विश्लेषण  यापुढे केले आहे. इथे हे लक्षात घ्यावयास हवे की जेवढी उष्णता वाढत जाते तेवढे स्थूल चे सूक्ष्म मध्ये रुपान्तर  होते. तसेच जेवढी उष्णता तापमान कमी होत जाते किंवा शीतलता वाढत जाते तेवढे  सूक्ष्म चे स्थूल मध्ये  रुपान्तर होते. हाच अपरा वा कनिष्ठ वा निर्जीव प्रकृतीचा नियम परा वा श्रेष्ठ वा सजीव प्रकृतीत ( सृष्टीत ) उलट असतो म्हणजे जेवढी उष्णता तापमान कमी होत जाते वा ऊर्जा कमी होत जाते किंवा शीतलता वाढत जाते तेवढे सूक्ष्म रूप वाढते पण याला मर्यादा असतात या ओलान्डल्या की परा वा सजीव सृष्टीचे अपरा वा निर्जीव प्रकृतीत रूपान्तर होते तसेच याउलट उष्णता तापमान वाढ होत जाते वा ऊर्जा वाढत जाते तशी सजीव सृष्टी अवतरते ! सामान्यतः स्थूल सृष्टी स्थूल बदल सूक्ष्म गोष्टी सूक्ष्म बदल घडवितात.  औषधे या स्थूल तर योग हा सूक्ष्म ट्रीटमेन्ट म्हणतात  दोन्हीचे योग्य प्रयोजन करणे गरजेचे असते  !                                                                                                                          स्थूल ज्योति भेद जाणून , ज्योतिचे इच्छित (ज्योत इष इति ) या ज्योतीभेदाच्या परिवर्तनाचा कालनिर्णय म्हणजेच ज्योतिष शास्त्र  !

We Humans are gifted with sensory system with 5 main sensory organs ,Eyes , Ears, Nose , Toungue & Rest of skin in addition there is one more sensory organs called Mind ! There are certain things which evolved minds only will understand ! Basically Heat & Cold these are the reasons for changes in evolution !  As the heat goes on increasing it increases unrest and movement away from each other clashes & violence ! On the other hand as heat reduces cold season comes all systems start reducing the speed increased co-operations diminished fights & peaceful spells ! This alternates in the universe ! Those who keep themselves fit & maintain reserves they survive !  This is true at indivisual level also & at level of sensory organs also… lastly it applies to MIND !  More peaceful it understands better as the fights between thoughts reduce & clarity improves !  

Bellow it is describe how increased heat ( Loss of peace) to decreased heat ( Increased peace affects different sensory system   

 1) Mater (Touch sensation) spectrum  or स्पर्शज्ञान गम्य वा स्पर्शाने जाणता येणाऱ्या जगाचे तीन भाग

स्थूल दृष्य अदृष्य                        स्पर्शगम्य दृष्य अदृष्य                  सूक्ष्म दृष्य अदृष्य                                              Macro structures                   touchable structures             Micro structures

2)  Light or viscible spectrum or   दृष्टि ज्ञान गम्य   जगाचे तीन भाग

स्थूल दृष्य अदृष्य                        स्पर्शगम्य दृष्य अदृष्य                  सूक्ष्म दृष्य अदृष्य                                              Macro structures                Viscible  structures             Micro structures

Low Fr. Increased wavelength increased external distance covered but decreased internal penetration

High Fr. Decreased wavelength  increased internal distance penetration but decreased external penetration 

Power  –Radio  —-Micro–I.Red–  Viscible spectrum   — U.V. —-  X rays —–Gamma

 Macro Waves                              Normal Human Range      One which end with steady mind

3) Audio spectrum For Human Ears

 श्राव्य  अश्राव्य                        स्पर्शगम्य श्राव्य  अश्राव्य                सूक्ष्म श्राव्य  अश्राव्य                                   Macro frequencies                Audible frequencies             Micro frequencies

आहत स्वर वा नाद  कानाने ऐकू येतात अनाहत नाद मनाला ऐकू येतात

4) Movement or Motion Spectrum ( गति ज्ञान गम्य जग )

There is nothing in the universe without motion ….. this motion is seen at times in form of inspiration & expiration or Day and Night or No Moon day to full moon day or summer and winter cycles or actual hormonic motions  seen आत macro as  well as micro levels ! In Living Kingdom it is seen as Birth and death !  End of one direction to other is death of old and birth of new direction ! The people who understand this they can try their best to maintain status called स्थिरत्व  ! that is the meaning of  ” स्थिरत्त्वम योगं उच्यते ” 

         Inviscible spectrum            Viscible spectrum               Inviscible spectrum  ( In Nature )

            Deep Inspiration               Inspiration – Expiration            Deep Expiration

                 Birth                                       Life                                              Death           (Direcion )

              No Moon                              first to 29 days moon           Back to No Moon                        

Deep summer /winter   Monsoon summer/winter crops     progression to winter/summer

 Past History/mythology     Present history/mythology         Future predictions/projections 

        Tolerrent laws                               Balanced laws                        Intolerrent laws

 Mixed music use of music & Noice                  Music                                           Noice

5)  Karma or behavioural tendencies  ( कर्म गति ज्ञान गम्य जग  )

 Understanding of good /Bad deeds         Behaviour         forgetfullness of good /Bad deeds  

         स्मृति जागृति                                                     कर्म                                  स्मृति विस्मरण   

 Here is what is meant by the shloka in Geeta –  

अहं च सर्वस्य ह्रिदि संन्निविष्टो । मत्तैव स्मृतिः ज्ञानं अपोहनम च ।।                                                                          वेदैहि च सर्वैहि अहं एव वेद्यो । वेदान्तकृत वेदविद एव च अहं  ।।

Meaning I am situated in everything’s heart  !                                                                                     I am the reminder , the knowledge ,& forgetfullness producer !                                                     All Vedas are to know me and yet I am the one who knows vedas !                                                as well as bring one to End of Vedas knowledge” (as time comes ) !  

Vedant ( वेदान्त ) being another name for “Geeta”

Beauty of Sanskrit language is by itself the word means it is a product of sanskars also called as samskaras ! Which means it is prepared from various “Prakrit Languages” or “Regional languages” for some purpose that some is “Sam” to equalize the phonetic patterns & pattern of meanings !               As it gets transformed in english to “San” confusions are created ! Words & Letters have meanings !  S is the Visarga pronunciation ! So When you say Yes it also is called Yeh ! as S is pronounces as H  Same is Sindhu & Hindu So it was labelled as Indus Civilization ! It is Sindhu River called Indus River meeting Hindu Ocean or Indian Ocean !