Clay, I know the algorithm. I thought that an enumeration (if superscript exponents were available, I would not have enumerated) would be more instructive to the OP. Euclid's Algorithm is one of the first that I coded on a micro (ASR33 console). It feared it would have been a distracting digression. Jerry
Re: trying to generate a wave file of 440 Hz...
Started by ●December 22, 2010
Reply by ●December 22, 20102010-12-22
On Dec 21, 11:59�pm, Jerry Avins <j...@ieee.org> wrote:> Clay, > > I know the algorithm. I thought that an enumeration (if superscript exponents were available, I would not have enumerated) would be more instructive to the OP. Euclid's Algorithm is one of the first that I coded on a micro (ASR33 console). It feared it would have been a distracting digression. > > JerryJerry, I'm not too suprised to learn that you already knew of (and implemented) the algo. But I don't think its mentioning is too much of a destraction. I'm sure some will find an occasional application. Sometimes just providing a name and an example of a process is enough to spur someone to go research something. Clay
Reply by ●December 22, 20102010-12-22
On Dec 22, 9:58�am, Clay <c...@claysturner.com> wrote:> On Dec 21, 11:59�pm, Jerry Avins <j...@ieee.org> wrote: > > > Clay, > > > I know the algorithm. I thought that an enumeration (if superscript exponents were available, I would not have enumerated) would be more instructive to the OP. Euclid's Algorithm is one of the first that I coded on a micro (ASR33 console). It feared it would have been a distracting digression. > > > Jerry > > Jerry, I'm not too suprised to learn that you already knew of (and > implemented) the algo. But I don't think its mentioning is too much of > a destraction. I'm sure some will find an occasional application. > Sometimes just providing a name and an example of a process is enough > to spur someone to go research something.Clay, mentioning it (and describing it) as you did is appropriate and useful. I thought that Interjecting it into an explanation of why a glitch-free loop would have a period that is a multiple of 0.2 seconds would not be. _Everyone_ should know Euclid's algorithm. It ranks with Euler's identity as a gem of mathematics. Jerry
Reply by ●December 22, 20102010-12-22
Wow thanks I was actually going through this very same thing in my head last night... only to wake up this morning and see it here! Many thanks to all. B.
Reply by ●December 22, 20102010-12-22
On this, um, remarkably musical note, I offer my best wishes to all for a Happy New Year (yes, the Solstice has come and gone), and a Happy Christmas if that is your thing; and I will offer a new note - 261.6255653 Hz (approx), a.k.a. Middle C. I look forward to seeing how that will be incorporated into this (to me) truly remarkable almost mystical thread which reveals the true genius of this list as never before! Richard Dobson
Reply by ●December 22, 20102010-12-22
On 12/22/2010 06:06 PM, Richard Dobson wrote:> On this, um, remarkably musical note, I offer my best wishes to all for > a Happy New Year (yes, the Solstice has come and gone), and a Happy > Christmas if that is your thing; and I will offer a new note - 261.6255653 Hz (approx), a.k.a. Middle C. I look forward to seeing > how that will be incorporated into this (to me) truly remarkable almost mystical thread which reveals the true genius of this list > as never before! > > Richard Dobson >Thank you Richard. BTW, why is middle C this frequency, i.e., why is A 440 (or thereabouts)? Why couldn't it be 273.1313... Hz (e.g.)? -- Randy Yates % "My Shangri-la has gone away, fading like Digital Signal Labs % the Beatles on 'Hey Jude'" yates@digitalsignallabs.com % http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO
Reply by ●December 23, 20102010-12-23
On Wed, 22 Dec 2010 20:32:38 -0500, Randy Yates <yates@ieee.org> wrote:>On 12/22/2010 06:06 PM, Richard Dobson wrote: >> On this, um, remarkably musical note, I offer my best wishes to all for >> a Happy New Year (yes, the Solstice has come and gone), and a Happy >> Christmas if that is your thing; and I will offer a new note - 261.6255653 Hz (approx), a.k.a. Middle C. I look forward to seeing >> how that will be incorporated into this (to me) truly remarkable almost mystical thread which reveals the true genius of this list >> as never before! >> >> Richard Dobson >> > >Thank you Richard. > >BTW, why is middle C this frequency, i.e., why is A 440 (or thereabouts)? >Why couldn't it be 273.1313... Hz (e.g.)? >-- >Randy Yates % "My Shangri-la has gone away, fading like >Digital Signal Labs % the Beatles on 'Hey Jude'" >yates@digitalsignallabs.com % >http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELOA can be 400, too. Actually, it can be anything, but 440 and 400 are aguably the most likely. ;) Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
Reply by ●December 23, 20102010-12-23
On 12/22/2010 05:32 PM, Randy Yates wrote:> On 12/22/2010 06:06 PM, Richard Dobson wrote: >> On this, um, remarkably musical note, I offer my best wishes to all for >> a Happy New Year (yes, the Solstice has come and gone), and a Happy >> Christmas if that is your thing; and I will offer a new note - >> 261.6255653 Hz (approx), a.k.a. Middle C. I look forward to seeing >> how that will be incorporated into this (to me) truly remarkable >> almost mystical thread which reveals the true genius of this list >> as never before! >> >> Richard Dobson >> > > Thank you Richard. > > BTW, why is middle C this frequency, i.e., why is A 440 (or thereabouts)? > Why couldn't it be 273.1313... Hz (e.g.)?I think the A440 scale is more or less arbitrary, starting from where music sounded pleasing and wandering around from there. There are other 'A' notes out there, most of them lower than A440. I think A438 is a popular one, and I think period-instrument baroque music is a bit lower yet. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" was written for you. See details at http://www.wescottdesign.com/actfes/actfes.html
Reply by ●December 23, 20102010-12-23
> > I think the A440 scale is more or less arbitrary, starting from where > music sounded pleasing and wandering around from there. �Kinda like the base 10 number system being built around our 10 or so fingers. ;) Seasons greetings!
Reply by ●December 23, 20102010-12-23
On Wed, 22 Dec 2010 20:48:08 -0800, SpreadTooThin wrote:>> I think the A440 scale is more or less arbitrary, starting from where >> music sounded pleasing and wandering around from there. > > Kinda like the base 10 number system being built around our 10 or so > fingers. ;) > > Seasons greetings!Yup. Base 12 is more versatile for factoring and such, base 16 or base 8 makes a lot more sense if you're in the early digital phase of your civilization. The Babylonians used base 60, I understand, but it was more of a base 6/10/6 system, which makes sense if your nominal year is 360 days + bonus days as assigned by the priesthood. -- http://www.wescottdesign.com
