Who Invented the First Guitar Strings and Amplifier? (Hint, you have to go waaaaaay back)

[redhouse_ca]

Nerd alert View attachment 1089320

Music scale math fun:
2^(1/12)=1.05946309435929...
This is an irrational number.
It's the ratio between note frequencies in an equal tempered 12 tone scale. (And also between string lengths of adjacent frets). Note that when you multiply this number by itself 12 times you get 2, which is the octave. Good for laying out a fretboard.

History of Irrational Numbers | Brilliant Math & Science Wiki

Irrational numbers are numbers that have a decimal expansion that neither shows periodicity (some sort of patterned recurrence) nor terminates. Let's look at their history. Hippassus of Metapontum, a Greek philosopher of the Pythagorean school of thought, is widely regarded as the first person...

brilliant.org

History of logarithms - Wikipedia

en.m.wikipedia.org

The interval of the perfect 5th is the closest we have to a rational number.
The ratio of the open string to the length at the 7th fret (to the bridge) is 1.49830707687668... which is really close to 3/2. I think that's the reason you find something like it in most music scale systems around the world. Other notes can be all over the map.

When the frequency ratio is a rational number, the waves line up and there are no beat notes, so it sounds "in tune".
In equal temperament, transposing to any key sounds equally out of tune because the ratios stay the same.

OK I'll stop now.

Hey man I suck at math and I had to read this a bunch of times to understand but still don't. I'm genuinely curious to understand how rational vs irrational effects character of sound in absolute terms (if that's what you mean). If you take instrument physical properties off the table, and take away any learned association between a note and it's frequency (ie., a conditioned sense of "in tune" for any given note), i don't get how all notes in the scale would sound out of tune? Not saying it won't, just jot getting why? Feel free to keep it overtly dumbed down, I won't be offended, I've been asking dumb questions my whole life, so all good). I can get the idea of relative base 12 dissonance of overtones , but not the absolute. Also, sorry but what's a neat note in the sense your use?

Thanks!

 

[redhouse_ca]

I thought that was down to Larry Lace.

You all friends? Secret handshake treehouse kinda thing?

 

[redhouse_ca]

Text-book history is tied to the development of known writing systems and covers the last 9,000 or 10,000 years. Everything else is prehistory meaning not much is known about it apart from what can be inferred from archeological remains. Since homo sapiens has been around for some 300,000 years and developed language around 150,000 years ago, text-book history doesn't cover much of that.

Someone could write a text book on that.

 

[Mjark]

Pictorial representations of musical instruments…and sporting events likewise testify to the importance of music in these ancient societies.

I bet they didn’t play the national anthem at the chariot races.

 

[trapdoor2]

Pictorial representations of musical instruments…and sporting events likewise testify to the importance of music in these ancient societies.

I bet they didn’t play the national anthem at the chariot races.

I bet they played an equivalent though. Humans like associative stuff. Music has almost always been associated with ritual...and racing is just another ritual (even today).

Nationalism may not have been a theme but it is conceivable there was something played, if only to please today's god or dignitary or simply to warn the race was about to start.

Strings...

Science is now thinking of adding string tech to the list of basic inventions like the inclined plane and the wheel.

We (banjo history geeks) have seen where the lack of availability of good strings has driven people to invent alternatives...and to re-invent them. Mimmo Peruffo (Aquilacorde) has really worked hard to re-invent gut and invent polyesters suitable for early banjos.

Back in the day (1840s) the only source was fiddle/violin strings but gauges were limited and quality was all over the map. As popularity rose, demand drove string makers to make better, more specific product...and designs changed to suit.

In the 1890s demand was so high for gut and availability so low that metal strings began to be used...though they had been in use since the 17thC on Citterns etc.

The same problems plagued guitars over their history...and they evolved to deal with it.

 

[guitar_paul1]

@redhouse_ca , this is all just my wacko theories. Don't take it as the authoritative last word.
Trying to explain how I think about it just made me question it again.

I'm grateful you made me look at this again, because I suspect my logic was not as clean as I hoped. I don't have a tight definition of what in tune means. I guess it means "lacking dissonance", but I don't have a great def of that either.

What is the exact reason that a perfect fifth interval is so close to a frequency ratio of 3:2? And why does it sound so harmonious and not dissonant?

I need to get two sin generators and plug them in together.

 

[guitar_paul1]

I found this site

Addition of sine waves

Addition of sine waves

www.geogebra.org

and it just about makes a liar out of me. My thinking was way oversimplified. I still think it might be true about the waves lining up, but it's waaay more complicated than I imagined. Like Rosanna Danna said " neeeeeever mind"

 

[guitar_paul1]

I probably should start a new thread on this.
Sorry about drifting.

Pythagorean tuning - Wikipedia

en.m.wikipedia.org

Cool stuff -- the "Pythagorean comma" I would bet (but can't prove) comes about because of rational vs irrational numbers.

String harmonics:
Vibration modes are a rational number sequence
Mid point 2x frequency
Third of the way up 3/2 the frequency
Quarter of the way 4x frequency
Etc but it damps out pretty quick



String harmonics occur at fractional divisions of string lengths. So they're all rational numbers.
OK.
They're pretty far apart. Maybe we just arbitrarily chop up the octave into a bunch of notes to get notes that are closer together because that's easier to make melodies. And maybe making melodies is related to how we talk, since we're wired for that.

When I make progress I'll check back in.

 

[ficelles]

String harmonics occur at fractional divisions of string lengths. So they're all rational numbers.

It's simple mathematics - harmonics are always a multiple of the fundamental frequency and, as you say, a corresponding division of the string length:

1st harmonic = fundamental x 1 = fundamental
2nd harmonic = fundamental x 2 = octave
3rd harmonic = fundamental x 3 = octave + fifth
4th harmonic = fundamental x 4 = octave x 2
5th harmonic = fundamental x 5 = octave x 2 + major third
6th harmonic = fundamental x 5 = octave x 2 + fifth

etc.

 

[redhouse_ca]

I found this site

Addition of sine waves

Addition of sine waves

www.geogebra.org

and it just about makes a liar out of me. My thinking was way oversimplified. I still think it might be true about the waves lining up, but it's waaay more complicated than I imagined. Like Rosanna Danna said " neeeeeever mind"

I don't think liar is the right word, and I don't mean to challenge what you posted, it may be right. I think dissonance between overtones is about as good a absolute definition for out or tune as any (with the exception of "closeness with a defined standard of 'in tune'", like A=440, which is arbitrary but realizable. I enjoyed reading this stuff.

 

[redhouse_ca]

I found this site

Addition of sine waves

Addition of sine waves

www.geogebra.org

and it just about makes a liar out of me. My thinking was way oversimplified. I still think it might be true about the waves lining up, but it's waaay more complicated than I imagined. Like Rosanna Danna said " neeeeeever mind"

I bookmarked that url. It's pretty cool.

 

[guitar_paul1]

Harmonic series (music) - Wikipedia

en.m.wikipedia.org

I really will start a new thread. I'm in the middle of a bunch of stuff right now, but I've been mentally composing some thoughts.

In the meantime, this wiki link is relevant. I send Wikipedia the meager profit from the few t shirts I sell on tee public.

 

[redhouse_ca]

I

Hmm... basic google search:

"Pentatonic scales are one of the oldest known scales in the world. Archaeologists have dug up ancient flutes carved out of bird bones, with many of them tuned to the pentatonic scale. Some are thought to be as old as 40,000 – 60,000 years old!"


I only know our 7 Degrees Harmony Law
Perhaps as old as the Universe and mathematics.

I came across this podcast with a guy who gets deep into the math of music. I figured you or others may find it interesting,

 

[Oxidao]

Aw Man… I’m not so smart on Maths.

I’ll give a try anyway, thanks

 

[redhouse_ca]

There's a Hittite wall carving that shows a little guy playing a roundback lute (neck, angled headstock, etc.)...and he looks like he's duck walking a la Chuck Berry!

I wish I could find the pic of it...

fyi, i was just in turkey and visited a ton of hittite sites, including Hattusha. all were amazing. thought you might get a kick out of the fact that everywhere i went i was looking for this wall carving. not in any sort of obsessive way, just thought about your comment while i was there and thought it would be cool if i could come back with a pic. didn’t see it, but i may just photo shop one for kicks.