Determining the golden section?

[Johnmasters]

quote:

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Originally posted by:

David Burgess

"Bacon", one could legitimately claim that music

is

math. My proposition would merely be that Mozart wasn't thinking in this context when scribbling notes on paper.

Was music originally created by math or analysis, or were these things imposed upon it at some point?

People love to figure things out and come up with systematic explanations for things, myself included. Has it ever been otherwise?

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David,

Back to Eigenmodes.... There are only special cases where the set of normal modes of a vibrating body are a set harmonic overtones. A thin string approximates this, a violin body does not. That is one reason people model the system as a string driving another body. All of the horns and woodwinds we see were laboriously worked out to "sound" right, with recognizable pitches. Nobody did any math, but the description can now be worked out mathematically with a good deal of difficulty. The shape of a bore, the placement of holes etc were all determined empirically.

It is no coincidence that the harp and flute are two of the oldest instruments. (Lyre and bone flute for example) The harp is obvious, the flute was easy to make and experiment with. Perhaps somebody noticed that changing the length of a pipe made the pitch change. Then somebody drilled a hole. They were off to the races, and it happened at the dawn of recorded history or before. People in Africa learned to tune drums to a degree. Walt Disney once made a film regarding the origins of music, and I think he was spot on.

The point is that the ability to describe mathematically is there, it just was not used. I will agree that numerology may have been a hot topic with Andrea Amati and Bach for example. Pythagorus felt (Falsly) that everything in nature had to do with numerologies of various sorts. He was right about strings, however, and perhaps that is where part of his notions came from. For centuries, people spoke of the "Music of the Spheres."

I feel that the violin evolved and if there were any numerological inputs, it was coincidental to the final outcome of the sound. This thread was not a waste of time, it was in fact interesting. But people looking for tone in these things ARE wasting their time. Visual aesthetics are another thing.

The math that CAN describe a musical instrument was invented much later by people who have mostly not been interested in applying it to instruments. They are more likely to regard it as a very messy engineering problem. One problem with this thread is that many people have laymen's definitions of "math" and "design." As a parting shot, I am going to suggest that Darnton left the forum because it has become rather a desert of decent ideas. Perhaps he still lurks.......

[Michael_Molnar]

Polkat,

You had a splendid question. Don't fret. It was some of the misleading notions of others that I have issue with and so should you.

Reread the thread in its entirety and you should see what I mean. Notice how the focus changes.

[David Burgess]

quote:

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Originally posted by:

Johnmasters

I feel that the violin evolved and if there were any numerological inputs, it was coincidental to the final outcome of the sound. This thread was not a waste of time, it was in fact interesting. But people looking for tone in these things ARE wasting their time. Visual aesthetics are another thing.

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That's pretty much what I think too. I've experimented enough myself, and seen enough good sounding instruments with odd dimensions to believe that whatever systems were applied weren't sacred to sound.

Not to take anything away from Tom King. His presentation was one of the best "system" approaches I've seen, particularly in that it didn't rely on superimposing so many lines on a violin that something almost has to line up. I've spent enough time around him to want to pay attention when he has something to say.

[Bacon]

It was either King or Andrew Dipper who suggested that Capra was a family relitive and had an influence on Stradivarius arching. However seeing that Capra died in 1626 , I'm not sure how he could have had an influence , perhaps his family carried his knowledge. I f you are not aware Capra is most famous for his piracy of Galileo's ideas. Speaking of Galileo his father Vincenzo , a musician, composer, and theorist, could perhaps be one of the great ties of math and musical instruments. He is credited with teaching his son the importance of testing theories. Applying science in a practical manner rather than from an arm chair. In this way he disproved the Pythagorean Boethius theory that if you double the tension on a monochord you get the octave, you don't you get the the tritone, half an octave. Mr Burgess , I as well doubt Mozart was concerned with math when he composed. In Instrument design I am inclined to think harmonic proportions rather than numbers. Relationships rather than integers.

Stephen Bacon

[Bacon]

Just an addenda in response to John-masters , If we are attempting to understand how the violin evolved to the golden period then I disagree with you that these paths of simple mathematical relationships had no relationship to tone. Perhaps it makes little sense with or current understanding of acoustics. And it is easy to find a rational for things just evolving thru trial and error. I read thru a great many of the modern design theories and feel most folks are just over thinking it and looking for clues to such an extent that they end up creating them. I admit I am not beyond this either. However as I spend a good deal of my time studying musical instrument evolution , I find that the ancient laws of harmonics play a very important role in the evolution of tone of musical instruments. stephen

[Torbjörn Zethelius]

quote:

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Originally posted by:

BACON

It was either King or Andrew Dipper who suggested that Capra was a family relitive and had an influence on Stradivarius arching. However seeing that Capra died in 1626 , I'm not sure how he could have had an influence , perhaps his family carried his knowledge. I f you are not aware Capra is most famous for his piracy of Galileo's ideas.

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It's a different Capra we're talking about. It was Andrew Dipper who got it from Elia Santoro, I think. If I remember the story correct Stradivari rented his first house from the architect Allessandro Capra when he first married Francesca Ferraboschi who was the widow of Giovanni Giacomo Capra who committed suicide in April 1664. Giovanni was son of Allessandro Capra. Dipper speculates that Antonio may have studied geometry with Allessandro.

It's very late and I'm going to bed now. Hope someone checks the facts. Or I'll do it in the morning. Goodnight.

[Bacon]

That sounds right to me , as he told it Allessandro was a specialist at bridge arch construction. I wonder if Allessandro was the son of Baldessar.

http://www.ursusbooks.com/item88462.html

stephen

[Ken Pollard]

Well this is fascinating (it's new to me, at least). Has anyone seen inside Alessandro Capra's book to know how his bridge design was done? What type of math did he use? $4750 is a bit steep.

To help keep things a bit off-topic, I did find this popular press item

http://findarticles.com/p/arti...20060520/ai_n16415931

as well as the VSA article on housing in Cremona

http://www.vsa.to/amati.htm

[polkat]

Thanks Michael. Believe me, I have been fasinated by many of the responses to this thread. I have now tried King's idea for setting F holes, and it seems to work nicely (although since I don't use pins in my making, so I use the full length of the plate). I also set my arches and graduate my plates mostly by feel (though I do measure thickness while graduating). The other info provided here is great, although I'm not certain if I could apply any of it to those fiddles I make out in my shed. But I do agree that even the stupid questions can often generate volumes of info.

[Bacon]

Ken , Thank you for the links , great evening read. Alesandro wrote "La Nuova Architettura Familigiarel" the copy I linked to for sale is just the fifth text of a set , it is on machines not on bridge archings. I have been trying to find access to other editions, no luck yet. There are some rather nice plates and and explanations on applied geometry in Diderot which is later but much more accessible. I am relatively new to this sight and am trying to catch up with the archives but I believe I have seen the math for arching presented here. For those of you upset about the drifting of the topic I apologize for my part. I admit I was being rather reactionary to statements being made. As for the comment on Darnton , I am sure he is busy at present in LA teaching the lucky few here who are in attendance at his workshop . I'm not sure he would have much use for the golden ratio in F hole setting as there are simpler ways with historic merit to achieve placement of the ff holes. But to state that he would see the forum as a desert of decent ideas, especially in this discussion seems contrary to his style of openness and informative teaching. I read him as being cynical of armchair theory not the possible application of historic data. Hasn't he been trying to get us to see this process not thru our over amped minds but thru the eyes of the old masters.

stephen

[Tets Kimura]

This radio programme is quite interesting. They talk a little about the golden section in music towards the end.