Caleb Morgan

Mr. Morgan,

-- Your concepts are correct, the term "consonance" that I wrongly used for the relation 32805/32768 was inadvertently induced by the numerator 32805 with which I worked during the research. The notable Delezenne and Pythagoras were the fathers of that fundamental relation called schisma. In 1560, Zarlino used the chromatic semitone 135 /128 proposed by Delezenne and divided by the Pytagoras semitone to get a very small coma: (135 / 128) / (256 / 243) = (32805 / 32768). Some analysts accept to call it "schisma" and not "coma" or comma".

Conclusion:
The two numbers of the fraction 256 /243 don´t make consonance, however the fraction is the Pythagoras semitone. Here started the wrong custom of calling smallest consonance to ratio 32805 / 32768. In my case, it was a wrong typing.

-- I think that the correct terms for calling to 32805 / 32768 are two:

Your way : "the smallest interval that can be distinguished by the ear of man" and also:

"the smallest frequency ratio that can be distinguished by the ear of man". This second definition supposses that first we have to generate a frequency that is (135 / 128) = 1,0546875 times a reference frequency, then another (256 / 243) = 1,053497942 times the same reference, and compare the sounds.

I detected by ear that smallest comma by using the Piagui guitar,

Regards

MARIO PIZARRO

piagui@...