IF by "it" is meant a major third instead of the devil's interval, then: Yes, it is 1/3 of an octave since it is 4 half-tones. (If "it" means the devil's interval, then it's 1/2.) —Dan -----Original Message-----
From: Mike Stay <metaweta@gmail.com> Sent: Jan 17, 2018 5:50 PM To: Dan Asimov <dasimov@earthlink.net>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Touch Tone frequencies
It's not 1/3 of an octave, it's the third note up (using 1-indexing).
On Wed, Jan 17, 2018 at 6:11 PM, Dan Asimov <dasimov@earthlink.net> wrote:
In what sense is it 1/3 of an octave???
—Dan
-----Original Message-----
From: Cris Moore <moore@santafe.edu> Sent: Jan 17, 2018 2:56 PM To: Dan Asimov <dasimov@earthlink.net>, math-fun <math-fun@mailman.xmission.com> Subject: Re: [math-fun] Touch Tone frequencies
Right, but it’s 1/3 of an octave, so in the equal-tempered scaled it would be 2^(1/3).
- Cris
On Jan 17, 2018, at 12:23 PM, Dan Asimov <dasimov@earthlink.net> wrote:
The "devil's interval" of sqrt(2) was certainly considered dissonant.
But I never heard that about the major third, whose ratio is 1.25, which is more like 10% off sqrt(2) than 1%.
—Dan
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