The best lesson I can suggest is by taking Tunelab 97 and do the following simple exercise. Tune A4 (1) to 440. Then set the tuning partial to read the 3rd partial, and while playing the A4 adjust the offset on Tunelab so that the phase display stops. Note the frequency in Hz on a piece of paper. Then tune A3 so that it stops the dial. This gives you a perfect 6:3 octave type. Now set Tunelab to read the 3rd partial of A3 and adjust the offset while playing A3 til the display stops again, and note this frequency down as well. It will be approximately half of the first frequency you noted. Now divide the frequency for A4(3) by that of A3(3). This will yeild a number just a tad over 2... somthing like 2.00582... or whatever... just barely over 2. This represents the inharmonicity spread for the 3rd partials of these two notes with same tuned as a perfect 6:3 octave type. Take the 12th root of this number. Then starting with A3 (3) mulitiply the frequency times this 12th root of just over 2 to find the frequency for the next note up. Continue such until you reach A4 again. The resulting curve is a linear perfectly spaced division of the 3rd partials of all the notes from A3 to A4. And as a temperament octave it actually works quite well most often. Ok... this is the basic curve... and things get a bit more complicated after that as we actually have several things to take regard to... several partials each with there own theoretical curves that dont match up neccessarilly so well when we tune to just one... and well a whole bunch of other things we try to compromise together to come up with a "best" solution. But this is as good a place as any to start learning about how RCT, SAT, and to some degree Tunelab work. I would suggest you do this a few times...and use Tunelabs numerical editor to accompish the same thing as manually finding the 12th root of 2(+ the spread) to get all the frequencies for the temperament octave. When you have a good feel this much start asking more questions. We have several enthusiasts here and I am sure between us you will find some good answers to most of your questions as you find out more. Cheers RicB Charles Neuman wrote: >Richard, or anyone, > >I'm curious what algorithms are used to calculate a tuning curve based on >harmonic measurements of 1 or more notes. Is that information available? > >I'd like to try to do this manually sometime: I'd measure the offsets of >each harmonic of the test note(s) (using an ETD) and then use that info to >calculate the tuning curve. I'd like to try different methods. > >I suppose I could come up with a way to do this, but I'm sure people have >spent a good deal of time thinking this through thoroughly. Anyone know if >these algorithms are published anywhere? > >Charles Neuman Richard Brekne RPT NPTF Griegakadamiet UiB
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