Origins of Preferred Numbers
Don Davis shows how to calculate the ISO fractional octave center frequencies.
Joseph Sauveur, 1653 – 1716, divided an octave, i.e., a 2/1 ratio, into 43 equal parts which he named “merides.” He then further divided merides into seven small equal intervals to obtain “eptamerides.” Again, subdividing eptamerides into ten equal parts resulted in “decamerides.”
Felex Savart, 1791 – 1841, having observed that 43 x 7 = 301, the first three figures of the mantissa of the common logarithm for two, divided the decade, i.e. = 10/1 ratio, into 1,000 parts which he called a “Savart.” A rounded version of the Savart 1/301 of an octave was the eptameride of Sauveur.
Can you find the base for the logarithm that would also equal Savarts?
Incidentally, Jean Baptiste Biot, 1774 – 1862, and Savart are known for their work on magnetic fields. The Biot-Savart Law, also sometimes termed LaPlace’s Law, is that the field intensity is by definition equal to the force per unit magnetic pole.
Col. Charles Renard, 1849 – 1905, in 1877 standardized the 425 different rope sizes for cables used to moor military observation balloons to 17. He had determined that the relevant parameters were mass per unit length. His use of the geometric series in which, by every fifth step, the mass per unit length of cable increased by a factor of ten.
These geometric series from 3-1/ 3 up to 80 became the basis in audio for the spacing of fractional decade filter frequencies that are the decade equivalent of 1/1 to 1/24 octaves. dbd