Old masters views on 22shruti

 

Old masters have tried to solve the question of 22 shruti giving different positions on cords for different shruti positions which are available on internet as follows                                                     Basically a frequency is fixed for a tone say A then 2A is the shruti of A in upper scale completeting the circle of shruti called Shrutimandal , this is the concept

Frequency of C at 256 hz. was not new & it was called Alternative pitch standard known as philosophical view or scientific pitch fixed middle C at 256 Hz with A placed on 432 by Schiller Institute                                                                                                                                                       Best part being Ratio mathematics puts ratio of 432/256 as  27/16  !!! Which is Indian Shadja gram ratio of  A/C when C is put on 256 or Black 1 st key !!!

19th- and 20th-century standards[edit]

The strongest opponents of the upward tendency in pitch were singers, who complained that it was putting a strain on their voices. Largely due to their protests, the French government passed a law on February 16, 1859, which set the A above middle C at 435 Hz.[2] This was the first attempt to standardize pitch on such a scale, and was known as the diapason normal. It became quite a popular pitch standard outside France as well, and has also been known at various times as French pitch, continental pitch or international pitch (the last of these not to be confused with the 1939 “international standard pitch” described below).

The diapason normal resulted in middle C being tuned at about 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]

 

This shows shruti number ratio proportion calculated bellow (followed by percentile calculations)

shruti Achrekar mulay Clement Omkarnath Brihaspati Bharat Ranade Gadrey
1 0/1 (1/1) 0 (1/1) 0 (1/1) 0 (1/1)
2 2048/2025 1024/1003 64/63 81/80 658/625 531441/524288 256/243 81/80
3 256/243 3200/3009 200/189 135/128 16/15 256/243 2187/2048 25/24
4 16/15 819200/731187 15/14 2259/2048 4096/3645 2187/2048 65536/59049 135/128
5 4096/3645 10240/9027 640/567 9/8 256/225 9/8 9/8 16/15
6 256/225 1152/1003 8/7 729/640 144/125 4782969/4194304 32/27 10/9
7 32/27 1200/1003 25/21 1215/1024 6/5 32/27 6/5 9/8
8 65536/54675 102400/81243 135/112 5/4 512/405 19683/16384 8192/6561 6/5
9 512/405 1280/1003 80/63 81/64 32/25 81/64 81/64 5/4
10 4/3 1296/1003 9/7 6561/5120 162/125 4/3 4/3 4/3
11 8192/6075 1250/1003 225/168 10935/8192 27/20 177147/131072 1024/729 27/20
12 45/32 12800/9027 256/189 45/32 64/45 1024/729 729/512 25/18
13 64/45 1440/1003 10/7 729/512 36/25 729/512 262144/177147 45/32
14 3/2 1500/1003 3/2 753/512 3/2 3/2 3/2 64/45
15 1024/675 1536/1003 32/21 243/160 79/50 1594323/1048576 128/81 36/25
16 405/256 1600/1003 100/63 405/256 8/5 128/81 6561/4096 40/27
17 8/5 409600/243729 45/28 5/3 2048/1215 6561/4096 32768/19683 3/2
18 2048/1215 5120/3009 320/189 27/16 128/75 27/16 27/16 8/5
19 128/75 1728/1003 12/7 2187/1280 216/125 14348907/8388608 16/9 5/3
20 16/9 1800/1003 25/14 3645/2048 9/5 16/9 9/5 27/16
21 32768/18225 51200/27081 405/224 15/8 237/125 59049/327768 4096/2187 9/5
22 256/135 1920/1003 40/21 243/128 48/25 243/128 243/128 15/8
shruti Achrekar mulay Clement Omkarnath Brihaspati Bharat Ranade Gadrey
0 (1/1) 0 (1/1) 0 (1/1) 0 (1/1)
2 1.011358 1.0209371 1.5873 1.25 5.28 1.3641 5.349 1.25
3 5.34716 6.34759 5.820007 5.46872 6.664 5.34708 6.786 4.16666
4 6.66 11.98404 7.14285 10.62282 12.336 6.787732 10.98 5.46875
5 12.37135 13.43744 12.87476 12.49998 13.77776 12.5 12.5 6.6666
6 13.7777 14.85543 14.28571 13.90663 15.312 14.03304 18.51 11.1111
7 18.51851 19.64107 19.04761 18.65234 20 18.522 20 12.5
8 19.86 26.04162 20.53571 25 26.408 20.13573 24.85 20
9 26.41975 27.61714 26.98412 26.5625 28 26.5625 26.56 25
10 33.33 29.21236 28.57142 28.14453 29.6 33.33 33.33 33.33
11 34.8477 34.59621 33.92857 33.48388 35 35.1524 40.46 35
12 40.46637 41.7968 35.44972 40.62498 42.2222 40.46132 42.38 38.8888
13 42.2222 43.56929 42.85714 42.38281 44 42.38309 47.97 40.625
14 50 49.55134 50 47.07031 50 50 50 42.2222
15 51.7037 53.14057 52.38095 51.875 58 52.05723 58.02 44
16 58.02469 59.52143 58.73015 58.20312 60 58.02 60.19 48.1481
17 60 68.05547 60.71428 66.66 68.512 60.18098 66.47 50
18 68.55964 70.15617 69.04761 68.74997 70.66664 68.7477 68.75 60
19 70.6666 72.28315 71.42886 70.85937 72.8 71.05035 77.77 66.6666
20 77.77 79.46161 70.57142 77.97851 80 77.77 80.2 68.75
21 79.79697 89.06244 80.80357 87.5 89.6 80.2036 87.2875 80
22 89.62962 91.42572 90.47719 89.84375 92 89.84413 89.84 87.5
shruti   Achrekar     mulay       Clement   Omkarnath      Brihaspati    Bharat     Ranade     Oke

1            0  (1/1)        0  (1/1)        0 (1/1)      0  (1/1)           0 (1/1)        0 (1/1)          0 (1/1)      0 (1/1)       2        1.011358    1.0209371   1.5873         1.25          5.28           1.3641                 5.349    5.3497       2       2048/2025   1024/1003     64/63        81/80        658/625   531441/524288  256/243 256/243   3       5.34716      6.34759        5.820007    5.46872      6.664       5.34708              6.786     6.6666       3         256/243       3200/3009   200/189     135/128      16/15      256/243          2187/2048   16/15   4        6.66             11.98404     7.14285      10.62282        12.336    6.787732         10.98    11.1111      4          16/15    819200/731187   15/14   2259/2048  4096/3645  2187/2048   65536/59049  10/9

5    12.37135    13.43744     12.87476    12.49998        13.77776        12.5               12.5          12.5      5      4096/3645   10240/9027   640/567    9/8               256/225        9/8                   9/8           9/8       6     13.7777       14.85543    14.28571     13.906625     15.312           14.03304      18.51     18.5185    6     256/225     1152/1003      8/7            729/640        144/125  4782969/4194304  32/27  32/27     7     18.51851     19.64107    19.04761    18.65234         20.0               18.5220         20.0        20.0       7       32/27       1200/1003    25/21       1215/1024       6/5                32/27                6/5             6/5

8    19.86     26.04162    20.53571             25.0               26.408           20.13573             24.85       25.0 8   65536/54675 102400/81243 135/112   5/4       512/405       19683/16384    8192/6561    5/4       9    26.41975     27.61714    26.98412      26.5625         28.0              26.5625         26.56         26.5625 9   512/405        1280/1003    80/63           81/64            32/25            81/64              81/64         81/64

10     33.33            29.21236    28.57142      28.14453       29.6                 33.33      33.33      33.33         10     4/3             1296/1003   9/7              6561/5120    162/125         4/3               4/3               4/3       11    34.8477        34.59621    33.92857       33.48388      35.0                  35.1524  40.46     35.0           11  8192/6075    1250/1003   225/168      10935/8192     27/20  177147/131072   1024/729  27/20 12     40.46637    41.7968       35.44972       40.62498      42.2222          40.46132  42.38    40.625       12   45/32        12800/9027    256/189       45/32            64/45          1024/729      729/512   45/32     13     42.2222      43.56929     42.85714       42.38281      44.0        42.38309       47.97         42.3828 13    64/45       1440/1003      10/7            729/512        36/25      729/512   262144/177147  729/512

14     50.0            49.55134      50.0                47.07031     50.0                 50.0            50.0         50.0       14     3/2          1500/1003       3/2                753/512           3/2               3/2               3/2              3/2     15    51.7037       53.14057     52.38095       51.875          58.0                  52.05723      58.02    60.0     15   1024/675     1536/1003    32/21        243/160         79/50  1594323/1048576    128/81   128/81 16   58.02469     59.52143    58.73015        58.20312      60.0                  58.02          60.19         60.0   16    405/256      1600/1003    100/63        405/256         8/5                 128/81         6561/4096   8/5   17    60.0             68.05547     60.71428         66.66           68.512          60.18098      66.47    66.6666   17     8/5        409600/243729   45/28          5/3            2048/1215    6561/4096  32768/19683  5/3

18    68.55964    70.15617     69.04761         68.74997     70.66664        68.7477    68.75    68.75         18  2048/1215   5120/3009     320/189        27/16          128/75        27/16             27/16        27/16     19   70.6666       72.28315     71.428857      70.85937      72.8                 71.05035     77.77    77.77     19   128/75       1728/1003     12/7          2187/1280    216/125  14348907/8388608    16/9   16/9     20    77.77            79.46161      70.57142        77.97851      80.0                 77.77        80.20     80.0       20     16/9          1800/1003      25/14           3645/2048    9/5              16/9                 9/5           9/5

21  79.79697       89.06244      80.80357       87.5               89.6               80.2036    87.2875    87.5       21  32768/18225   51200/27081  405/224    15/8       237/125      59049/327768   4096/2187  15/8 22  89.62962      91.42572      90.47719       89.84375      92.0           89.84413         89.84    89.84375 22   256/135       1920/1003    40/21           243/128          48/25        243/128        243/128   243/128

shruti   Achrekar     mulay            Clement   Omkarnath      Brihaspati    Bharat          Ranade         Oke

1            0  (1/1)        0  (1/1)        0 (1/1)      0  (1/1)           0 (1/1)        0 (1/1)          0 (1/1)      0 (1/1)       2       2048/2025   1024/1003     64/63        81/80        658/625   531441/524288  256/243 256/243   2        1.011358    1.0209371   1.5873         1.25          5.28           1.3641                 5.349    5.3497       3         256/243       3200/3009   200/189     135/128      16/15      256/243          2187/2048   16/15    3       5.34716      6.34759        5.820007    5.46872      6.664       5.34708              6.786     6.6666        4          16/15    819200/731187   15/14   2259/2048  4096/3645  2187/2048   65536/59049  10/9    4        6.66             11.98404     7.14285      10.62282        12.336    6.787732         10.98    11.1111      5      4096/3645   10240/9027   640/567    9/8               256/225        9/8                   9/8           9/8        5    12.37135    13.43744     12.87476    12.49998        13.77776        12.5               12.5          12.5      6     256/225     1152/1003      8/7            729/640        144/125  4782969/4194304  32/27  32/27     6     13.7777       14.85543    14.28571     13.906625     15.312           14.03304      18.51     18.5185   7       32/27       1200/1003    25/21       1215/1024       6/5                32/27                6/5             6/5       7     18.51851     19.64107    19.04761    18.65234         20.0               18.5220         20.0        20.0       8   65536/54675 102400/81243 135/112   5/4       512/405       19683/16384    8192/6561    5/4       8    19.86     26.04162    20.53571             25.0               26.408           20.13573             24.85       25.0 9   512/405        1280/1003    80/63           81/64            32/25            81/64              81/64         81/64 9    26.41975     27.61714    26.98412      26.5625         28.0              26.5625         26.56         26.5625 10     4/3             1296/1003   9/7              6561/5120    162/125         4/3               4/3               4/3       10     33.33            29.21236    28.57142      28.14453       29.6                 33.33      33.33      33.33         11  8192/6075    1250/1003   225/168      10935/8192     27/20  177147/131072   1024/729  27/20 11    34.8477        34.59621    33.92857       33.48388      35.0                  35.1524  40.46     35.0           12   45/32        12800/9027    256/189       45/32            64/45          1024/729      729/512   45/32     12     40.46637    41.7968       35.44972       40.62498      42.2222          40.46132  42.38    40.625       13    64/45       1440/1003      10/7            729/512        36/25      729/512   262144/177147  729/512 13     42.2222      43.56929     42.85714       42.38281      44.0        42.38309       47.97         42.3828 14     3/2          1500/1003       3/2                753/512           3/2               3/2               3/2              3/2     14     50.0            49.55134      50.0                47.07031     50.0                 50.0            50.0         50.0       15   1024/675     1536/1003    32/21        243/160         79/50  1594323/1048576    128/81   128/81 15    51.7037       53.14057     52.38095       51.875          58.0                  52.05723      58.02    60.0     16    405/256      1600/1003    100/63        405/256         8/5                 128/81         6561/4096   8/5   16   58.02469     59.52143    58.73015        58.20312      60.0                  58.02          60.19         60.0   17     8/5        409600/243729   45/28          5/3            2048/1215    6561/4096  32768/19683  5/3 17    60.0             68.05547     60.71428         66.66           68.512          60.18098      66.47    66.6666   18  2048/1215   5120/3009     320/189        27/16          128/75        27/16             27/16        27/16     18    68.55964    70.15617     69.04761         68.74997     70.66664        68.7477    68.75    68.75         19   128/75       1728/1003     12/7          2187/1280    216/125  14348907/8388608    16/9   16/9     19   70.6666       72.28315     71.428857      70.85937      72.8                 71.05035     77.77    77.77     20     16/9          1800/1003      25/14           3645/2048    9/5              16/9                 9/5           9/5       20    77.77            79.46161      70.57142        77.97851      80.0                 77.77        80.20     80.0       21  32768/18225   51200/27081  405/224    15/8       237/125      59049/327768   4096/2187  15/8 21  79.79697       89.06244      80.80357       87.5               89.6               80.2036    87.2875    87.5       22   256/135       1920/1003    40/21           243/128          48/25        243/128        243/128   243/128 22  89.62962      91.42572      90.47719       89.84375      92.0           89.84413         89.84    89.84375

Here we can examin what is the way they have thought & what is the proper way