Re: [tuning] Re: Cents/Sense (NON-Cents?)

Gene>"So where's the problem? The average string player doesn't play a 400 cent major third, and you experience no difficulty getting them to play what you'd like them to play, and yet you are upset over what they
"know", which is apparently merely definitional. "

   I think that argument is rather straw-man-like as compared to what Steve appears to be saying.  Of course a good string player can FIND the major third by ear.  That is not a show/proof of strength of the Cent measurement...it's a show/proof that string instrument players have good tuning ears. :-D

  However, the question is can a musician, after being told what a cent is, quickly figure out the major third JUST by looking at the cent value IE without hearing it?

  The most natural thing to do first is try simple multiples of cents IE 400 cents and then subtract a bit from it...since they know a Just major third is flat of a 12TET major third.  But how much to subtract?  There is virtually no numerical pattern that says 386 cents is more likely to be selected in such a process than, say, 395 cents or 370 cents.

  Now let's say that same person guessed using 31TET value and found 1000 31TET "cents" (the 10th step of 31TET) as the answer.  That's within about a 12TET
cent of the perfect answer...and finding it takes about as long as it takes to count to 10 (100,200,300,400,500....1000).
  Not to mention 1000 for a major third and 800 for a minor third...is much easier to memorize than 386 for a major third and 315 for a minor third (where's the easily memorizable numeric pattern there...it seems obvious to me there IS none!)

   Of course, you could do the same with 72TET, but then you get something like 2300 72TET "cents" (counting to 23) before you hit the major third.  And, to note, 2300 can not be divided by 6 to get the 12EDO equivalent...only 2400 can...and with 2400 you get, guess what...the same problem of the 14 cent off just error you get with 12TET.

   But you know what?  Cents are so highly used within instruments and software...there are sadly probably very few people willing to make the jump to get a system that's easier to see patterns in and to
memorize steps with minimal errors to Just intervals (again...how many people who know cents can correctly guess/figure-out how many cents flat of a 400 12TET cent major third and Just major third is given only the information that 100 cents = 1 semitone?...I dare anyone to try that question on a non-microtonal musician off-list).