TtR -

One of the most thorough analyses of most of what has been discussed can be found in the Dover paperback On the Sensations of Tone, by Hermann Helmholtz. The original "2d edition" that Dover copied dates to 1885, but one advantage of its age is that it discusses measurement of sounds in terms of apparatus and techniques that are a little more accessible to the amateur than some of the more modern stuff. The Dover edition is still in book stores in my area, and you should be able to pick it up for $15 - $18 (US) or so.

It should be noted that Helmholtz made some minor errors, that later research has found, but they shouldn't detract from usefulness of the book. It should also be noted that it's nearly 600 pages of analysis, experiment, and discussion of fairly technical stuff - so you need a serious interest to get through it all. All the ratios and deviations between just and tempered note frequencies are there.

More recent, Fundamentals of Musical Acoustics by Arthur H. Benade, originally published 1976, is also available as a $18 US or so Dover reprint.

As to measuring notes that you've tuned by ear, most electronic "tuners" will give you some indication at least whether the note is sharp or flat relative to "standard" for the nearest note. Somewhat better ones allow you to change the "A" frequency so that you can shift all of the notes. You do need to get into a true "metering" tuner in order to be able to read how far you are away from the "standard" note, and unless you shop around you can easily pay $100 (US) or more for a good one.

As mentioned previously, most simple tuners have a "sample and hold" mode built in, so that they hold the reading for the first few cycles that they "hear." This makes it impossible to measure the difference between the initial pitch when you pluck a string and the pitch it settles to as the sound decays. You'll have to look pretty hard to find a cheap tuner with a "rapid mode" if you're interested in this phenomenon.

If you're mechanically inclined, you can do it like Pythagorus did and make yourself a one string dulcimer with a movable "fret." Tune the open string to a known value, and move the "fret" until it sounds a match to your chosen note. Calculate the frequency from the active string length. (He really did do it that way, I'm told.)

John