Better late than never... had modem problems....... Paul Chick wrote.... +AHw-Being an aural tuner I can +AHw- relate to beat rates easier than cents deviations. Same here. The cents deal is an exercise in mathematics that is more of a hobby than a necessary chunk of knowledge needed to know how to tune by ear. Our musical scale has a mathematical basis because it obeys the simpler laws of physics relating to frequency. One of these laws is that two frequencies nearly the same will produce a phenomon known as a beat, or a beat frequency that is exactly the numerical diffrerence between the two frequencies. If you are setting A440 from the fork and you hear a beat of one beat per second (bps) you are either at 441 or 439.The arithmetic here is self evident. If you are setting the octave down from A440 or A4--A3, and you hear a beat of one cycle per second you are either at 220.5 or 219.5. Here it is not as simple until you realize the beat is caused by difference between the fundamental frequency of A4 and the frequency of the second partial of A3. Here the harmonic series of musical tones comes into play and how the partial series of a vibrating piano wire is close to that. So to hear a beat of one cycle per second between A4 and A3 you are hearing the 440 already tuned and the second partial (also called coincident partial) of the A3 you are tuning which would be either 441 or 439. Now it is easy to see where a beat of 1 per second comes from. Since this is the second partial, the fundamental freq would be half of that ie 220.5 or 219.5 This is just the beginning, there are books where everything is well explained. The classic is Wm Braid White, +AF8-Piano Tuning and Allied Arts+AF8-. A more modern book is Piano Servicing by Art Reblitz. A comprehensive explaination for the physics and math basis is +AF8-The Piano its Acoustics+AF8- by McFerrin. All three of these books can be gotten from the supply houses, and many municipal libraries. It is important to understand the harmonic series and how coincident partials occur in the various intervals as this is the source of beats used in tuning. For understanding cents there was an article in the Journal back in 2000 written by a piano tuner for piano tuners, +ADs- ) (I heard he was contemplating an article titled something like +ACI-Intrigue of the Intervals+ACI- but between the first note and the lost chord could easily go 10 chapters). But one only needs know how to use the cents formula rather than understanding that cents are actually logs of the base of two (multiplied by 1200) but have to be arrived at by converting logs of base 10. And you only need to know this formula if you working with spread sheets or want to figure out the cents value of various als. ---ric ----- Original Message ----- From: Paul Chick (EarthLink) +ADw-tune4+AEA-earthlink.net+AD4- To: +ADw-pianotech+AEA-ptg.org+AD4- Sent: Wednesday, June 05, 2002 8:10 AM Subject: Re: trichords unisons +AHw- Richard . Being an aural tuner I can +AHw- relate to beat rates easier than cents deviations. The math/science of +AHw- tuning is not my strong suit. Do you know of a book that would explain +AHw- this? My curiousity is getting to me. +AHw- +AHw- Paul Chick+AHw- ----- Original Message ----- +AHw- From: +ACI-Richard Moody+ACI- +ADw-remoody+AEA-midstatesd.net+AD4- +AHw- To: +ACI-Pianotech+ACI- +ADw-pianotech+AEA-ptg.org+AD4- +AHw- Sent: Tuesday, June 04, 2002 11:51 PM +AHw- Subject: Re: trichords unisons +AHw- +AHw- +AHw- +AD4- +AHw- +AD4- +AD4- The difference between 440 and 439 is almost 4 cents. +AHw- +AD4- From 880 to 879 nearly 2 cents. From 1760 to 1759 almost 1 +AHw- +AD4- cent.
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