It can be measured by the 'Musical Quotient' (Swaranka) as per the research work of Dr.Govind Ketkar of Dombivli (Dist. Thane, Maharashtra, India). He has found that if a Swara changes by 2.5 %, a normal person can perceive the difference. And, a musician can find the difference even if the Swara changes by only 1.5 %. He has also shown that by practicing certain Yoga-like techniques, this ability can be improved. This ability is not measured in Hz because, at the lower end of a keyboard, 1 % of 'A' (110 Hz) is 1.1 Hz; whereas in the higher Saptak (Octave) of a keyboard, 1 % of the same note 'A' (880 Hz) is 8.8 Hz ! Therefore, the unit of this measurement is not 'Hz', but '% change from Hz of Shadja'. Further, my own observation is that, if the 2 notes are played 'together' (at the same time), an average trained ear of a performing musician (like myself) can measure as minute a difference as 0.0594631 % ! This difference is nothing but '1 Cent' between any 2 consecutive keys on a keyboard or = 1 % of the difference in Hz between the two consecutive keys on a keyboard. (For eg., if we start from key A (220 Hz) of the keyboard, the next key B flat will be at 220 x 1.0594631 = 233.081882. The difference between these 2 keys is 233.081882 minus 220 = 13.081882 (or 100 cents). Therefore, 1 cent will be = 0.13081882. This is 0.0594631 % of 220.)
Such an extreme ability of a trained listener allows us to tune a Tanpura or any other instrument perfectly well with any Shadja on Harmonium, as we normally do before a concert. Remember however, that '1 Cent' varies in 'Hz' from lower to higher Saptak on a keyboard.
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