Can guitar frets perform multiplication?

Posted by wibbily 4 days ago

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Comments

Comment by Syzygies 4 days ago

https://vimeo.com/194116649

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.

Comment by RickJWagner 3 days ago

Wow, that is cool.

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.

Comment by nipsnack 3 days ago

This is fantastic! What a find.

Comment by lioeters 4 days ago

This post is by the same author as the Lost Art of Logarithms. https://www.lostartoflogarithms.com/

Discussed about a year ago: https://news.ycombinator.com/item?id=43356314 (196 comments)

Comment by adrian_b 3 days ago

Also the author of the famous "Programming Windows" books.

Comment by devilbunny 3 days ago

And the marvelous book Code. He explains how a digital computer works. Not sophisticated ones, not how it works on silicon, but how you turn relays into computation.

Comment by lioeters 3 days ago

True, this book is a classic and worth mentioning.

Code: The Hidden Language of Computer Hardware and Software - Charles Petzold

Some reviews: https://www.goodreads.com/en/book/show/44882.Code

Comment by mdp2021 3 days ago

When I discovered it, "the Petzold" was called "the Windows bible".

Comment by JKCalhoun 3 days ago

I threw together a logarithmic slider for HTML (when I knew little about JavaScript and HTML). I hoped someone would take it and run with it and we would see more logarithmic slide rule calculators on the web.

(Top, yellow slider, cannot be interacted with):

https://www.engineersneedart.com/ohmslaw/index.html

Sources (such as they are):

https://github.com/EngineersNeedArt/SlideRule

Comment by Gravityloss 1 day ago

Oh my god, it's a beautiful way to explain how slide rules work. Without spending a single word. Thank you!

Comment by dofm 3 days ago

Regarding how people figured out the positions of the frets:

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.

Comment by coldtea 3 days ago

>Frets used to just be thick material (wire, strips of flexible wood or treated cord) tied around the neck of the instrument

Movable frets (they kind that you describe) used to be guts. Just like strings used to be.

Comment by brookst 3 days ago

And the “right” answer is exponential, so it seems like it must be possible to do geometrically. Though I admit my geometry is weak enough that I don’t see how.

Comment by analog31 3 days ago

You only have to get it right once, or copy another guitar. Today, people buy a pre-made gauge.

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.

Comment by bgrainger 3 days ago

Hard to believe that article doesn't contain the phrase "slide guitar".

Comment by forinti 3 days ago

This is not a case of maths giving you the Blues.

Comment by pazimzadeh 3 days ago

> How did people figure out the positions of the frets without calculators and precision measuring instruments?

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?

Comment by dvh 3 days ago

Take a guitar. Very gently put finger on string. Start sliding finger while continuously strumming with other hand. On some places (usually 3rd 5th 12th fret) the string will produce clean sounds, that's where the frets should be.

Comment by praash 3 days ago

This also results in a per-string just intonation ;)

Comment by pazimzadeh 3 days ago

right, isn't that kind of what i said? so isn't that how they did it back in ancient times?

Comment by Gravityloss 1 day ago

Those are so called flute sounds or harmonics, ie you don't press the string against the fretboard or fret normally at all. Instead you touch it very gently to force a vibration node there where your finger is. It doesn't work at all on most places along the string, you end up just damping the string. The easiest harmonic is halfway between bridge and nut, or at 12th fret, ie you force the string to vibrate with half the wavelength, or a node in the middle, or double frequency, or one octave higher, compared to free string. Then second easiest is 7th fret and then 5th (which is 2 octaves, ie quadruple frequency) and 9th. So you get less than pentatonic scale if you only use those, but they are useful pointers or anchors anyway.

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!

Comment by danbmil99 3 days ago

I have a friend who builds instruments. A bass player who worshiped Jaco, at first he made a couple fretless bass guitars.

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?

Comment by coverband 4 days ago

I'm blocked for some reason, probably too much HN referred requests...

Comment by altairprime 4 days ago

Enable JavaScript and let the site issue a “not an AI” cookie and it should then be usable. (I have a JS button for this on my toolbar and it’s come in handy a lot recently..)

Comment by karim79 3 days ago

Are you serious you have a "I am not an AI" widget?

Comment by scubbo 3 days ago

I read it as "a button for re-enabling JavaScript"

Comment by altairprime 3 days ago

This, with state default-off and remembered per-domain. Not my invention but glad for it!

Comment by montjoy 2 days ago

No mention of harmonics? Seems like a pretty big omission. I’ll admit I didn’t read the whole article but this seems like a classic, “I did the math but never actually touched the thing” type miss.

Comment by FpUser 4 days ago

The question is can those frets run Doom

Comment by karim79 3 days ago

Loved the article. Didn't love being blue-balled by the conclusion but still great stuff.

Comment by ddejohn 3 days ago

Absolute joy to read as a guitarist of 22 years, and having a degree in applied mathematics and a fondness for old calculators.

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.

Comment by HoldOnAMinute 4 days ago

Vibrating strings are Turing-complete

Comment by ycombiredd 3 days ago

That just reminded ne of something from here I had completely forgotten about. Someone had posted making sort of dubious claim of guitar power chords being Turing complete. I made some small improvements (as I saw it, chiefly around how they had implemented their clock) to the code they posted https://news.ycombinator.com/item?id=42294766 which lead me down a rabbit hole of guitar tab as opcodes, which eventually lead to something useful after throwing away the silly guitar virtual machine, since I had now done the work of implementing far more than the simple tablature parsing code I intended. That project that resulted from the silly toying around with tab notation as machine code lead to a midi-to-tab generator, which lead to audio to midi to tab, and a bunch more.

That project, for anyone interested in such things, is today https://github.com/scottvr/gtrsnipe There are useful demonstrations in the repo's wiki.

Comment by sph 3 days ago

My code editor is a 1979 Fender Stratocaster.

Comment by glouwbug 3 days ago

Now they need templates

Comment by cwmoore 3 days ago

citation please, sibling comment links are ~400

Comment by OntoSomething 3 days ago

[flagged]

Comment by scentoni 3 days ago

https://en.wikipedia.org/wiki/FRACTRAN

Comment by cwmoore 3 days ago

Betteridge’s Law confirmed (no):

“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.”

Comment by byako 3 days ago

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