Avery, You might want to mess with her a bit and tell her "A piano is tuned to the 12th root of 2" and see if she can figure it out. Mathematically, the octave ratio is 2:1. Assuming she's trying to tune an equal temperament, the octaves must be in tune. The thirds ratio is 5:4 (5/4 x 5/4 x 5/4 =125/64) whic is not equal to 2/1. (To be equal, it would have to 128/64 or 5.04/4 cubed.) To force the 3 contiguous 3rds to be equal, each third must be expanded by 14/100 of a semi-tone (14 cents). This action forces the reciprocal of the major 3rd (the minor 6th) to be contracted by an equal amount. Same is true of 4ths: Expand by 2 cents causes the reciprocal (the 5th) to contract by 2 cents. (For math students, 1 cent = 1/100 of a semi-tone) Solving mathematically, we are searching for the number that, multiplied by itself 12 times = 2 otherwise known as the 12th root of 2. That number is 1.059 No, I'm not a mathematician. Jim taught us this the first day of college, but Bartlett & I stayed anyway. Danny Avery Todd wrote: > List, > > A friend of mine forwarded this to me. Anyone want to answer this? :-) > In this context, I don't think I could even if I tried. > > Avery > > >Avery, if you have time would you answer this girls question! I don't > >think she would like my answer! :-) > > > >Thanks, > > >>Hi - I am a graduate student in Mathematics from the east coast. In one > >>of my mathematics classes there is a question which asks us how a piano > >>is tuned. So if you could please send me an email breifly describing > >>the process I would be grateful. Thank you very much in advance. > >> > >>Christine Palmer > >> > >>cpalmer@wpi.edu > > ___________________________ > Avery Todd, RPT > Moores School of Music > University of Houston > Houston, TX 77204-4893 > 713-743-3226 > atodd@uh.edu > http://www.uh.edu/music/
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