Measuring time in inches with a pendulum for a metronome
May 18, 2016 4:16 PM   Subscribe

I have several music books published during the mid to late 1800s. It seems to have been a period before metronomes, however there are things like “quarter note=pend. 10 inches,” which I take to be a metronome marking of sorts using pendulum. How does this work?

I hung a weight from my music stand and swung it (apparently you’re supposed to count when it’s at the bottom of the stroke) and determined that 10 inches was about mm 112 and 22 inches was about mm 80. My question is: is this even the right methodology? I could find nothing about it on the web. And if it is right, is there a table that would show me the corresponding metronome marking for a lot of measurements? One example of a volume that has this type of notation is "Ancient Irish Music" by P.W. Joyce, published in 1873 and digitized on the web.
posted by jackmcc to Media & Arts (4 answers total) 6 users marked this as a favorite
the period of a pendulum (an ideal one) depends only on the length (ie not the mass), so yes, it works. the period is 2 pi sqrt(L/g) where L is the length and g is the acceleration due to gravity.

in your case you seem to be counting twice per complete swing, so the frequency would be double what that implies.

10 inches is about 0.254m, g is 9.8 kgm/s2 so twice the frequency would be 2/(2*3.1*sqrt(0.254/9.8)) which is 2.0

so a 10 inch pendulum should pass through the bottom of the swing about twice per second. that's equivalent to 120 beats per minute (mm 120). so it's pretty close to what you got.
posted by andrewcooke at 4:25 PM on May 18, 2016 [4 favorites]

sorry, wrong units for g. it's 9.8 m/s2. doesn't change the answer above.
posted by andrewcooke at 4:44 PM on May 18, 2016

In Fig. 2 of the article "New Light on Late Eighteenth-Century Tempo: William Crotch's Pendulum Markings" by Emmanuel Rubin, there's a table that converts pendulum lengths, BPM, and MM. They list 10 inches as MM 119 and 22 inches as MM 80.
posted by mhum at 4:53 PM on May 18, 2016 [2 favorites]

Argh. We actually translated a looong series of scholarly articles about metronome use in the 19th century.
One of the things I recall, just and especially in Irish sources, was that there was some mixed usage in counting the backs and forths of the pendulum, so in some cases, a modern "tic" was equivalent to one sway of the pendulum from, say, right to left, but in some cases, it was supposed to be right, left and right again, thus halving the tempo. I also remember that in some of the music from those sources, this was indicated by some "x2" kind of indication (don't remember precisely), and in some other music it was not (but evident because of the sheer unplayability in the indicated tempo).

(This goes too far here, but there are some people who seriously claim that all metronome markings up to some point in the late 19th century should be taken at half tempo. That's most certainly nonsense)
posted by Namlit at 1:33 AM on May 19, 2016 [4 favorites]

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