Can guitar frets perform multiplication?
charlespetzold.com
charlespetzold.com
Steve Martin in conversation, 2002. 34:20 to 36:00 is this exact question.
Later, Robin Williams joins him on stage. My cameo starts at 1:01:40, inaudible and off-camera, because I'd traded a seat up close for two in the balcony so my future wife could join me.
I’m curious about Steve’s banjo. He usually ( but not always ) plays in Scruggs style, which should result in wear on the head down by where the pinky is anchored. But this banjo shows wear up above the strings, where a clawhammer player usually shows wear.
Either this is one of Steve’s clawhammer practice banjos or the wear is from a previous owner, I’d guess.
(Top, yellow slider, cannot be interacted with):
https://www.engineersneedart.com/ohmslaw/index.html
Sources (such as they are):
Discussed about a year ago: https://news.ycombinator.com/item?id=43356314 (196 comments)
Code: The Hidden Language of Computer Hardware and Software - Charles Petzold
Some reviews: https://www.goodreads.com/en/book/show/44882.Code
Frets used to just be thick material (wire, strips of flexible wood or treated cord) tied around the neck of the instrument. They were added, moved and removed for different scales, and "tuning" might have involved choosing fret positions that sat well with other instruments that could not be tuned, etc.
They were inherently movable. Sitar frets still are tied to the neck this way.
You can do this yourself with cable ties which make tolerable frets for experimental purposes.
So this would have allowed the knowledge of precise tuning to evolve over time.
A viola da gamba still has tied frets, made from the same material as the strings -- cattle or sheep intestines. Among other things, movable frets mean you can tweak things for intonation and temperament. I've seen instruments that had double frets, so you could play in more than one temperament.
Movable frets (they kind that you describe) used to be guts. Just like strings used to be.
If you had perfect pitch (maybe relative pitch is enough) then couldn't you just make marks in each position on the fretboard where it sounds like a new full note, and then go back and listen for the half-notes and do the same thing?
But this is not exact!
Music harmonics are just about multiples. Ie one note rings at some frequency and another note that sounds nice with it rings at some multiple of it. Or they have some common factor. The twelve note system and the twelvth roots are just approximations for some of these harmonies. There's even very recent innovation like true temperament frets. But I don't think that works with all the different song keys and tunings... Maybe it's another reason why I should buy a guitar for every song key we have!
One day he called me with a fascinating question. He was making his first guitar, and he wanted to know: Where do I put the frets?
As an aside, I love the simplicity of the interactive elements in TFA. Something I desperately wish I could have done with the side-by-side Galilean and modern guitars was instead of strumming at the actual fret on a given string to get the note to which that fret corresponded, be able to place "fret holders" by clicking at the intersection of the string and the fret that held the string down at that fret for you and then simply strumming the open strings so that you could compare how chords sound between the two guitars.
That project, for anyone interested in such things, is today https://github.com/scottvr/gtrsnipe There are useful demonstrations in the repo's wiki.
“One of the themes of The Lost Art of Logarithms is that many phenomena in our natural and human-made world can be interpreted logarithmically. That includes music but it does not include guitar frets.”