Pytgagoras...

[Yoshi.haruIto]

Hello,

 

I am interested in learning about the ratios and proportions used in musical instrument making. I believe that figures from ancient Greece, such as Pythagoras, Aristotle, and Aristoxenus, laid the foundational ideas for musical instruments.

 

When studying this field, are there other important historical figures I should know about? Even if they are not directly related to instrument-making, philosophers or scientists like Kepler or Leibniz, whose ideas are closely connected, would also be relevant.

 

If you happen to know any key references or books on this topic, I would greatly appreciate it if you could share them.

 

Thank you very much for your guidance.

 

 

[Rothwein]

I apologize that my memory is not clearer, but I recall at least one Renaissance sketchbook (da Vinci, even?) comparing the proportions of a lira da braccio to those of a horse's skull. 

You might do a Google search with [your search, maybe "geometry"] site:maestronet.com as it may have been discussed here in the past. I hope you find useful results!

(This site's own search function is not the favorite of its participants.)

[HoGo]

Yes, there are quite a few pages here about geometry and theories how the old guys created the shapes though no one really knows where is truth as the instruments are after 300 years worn and deformed and were not built to exact specs to start with. Basicly there are three types of theories.

1. the whole geometry was done using some predetermined ratios either whole numbers ore more exotic theories like golden section or such
2. the geometry was based upon basic measurements done with rulers of given unit (there were different length units in each town back then) and their divisions (some divided to 10 parts, some to 12...) which inevitably leads to whole number ratios between parts etc.
3. the geometry was done using some special types of curves like spirals or such that were applied thorough the whole geometry.
4. makers just copied older design and adjusted new forms by a tiny bit slowly evolving into shapes we see....

Oh, did I say three?

and then there is the other possibility that they used bananas as source of curves...

[Yoshi.haruIto]

Both of you, thank you so much!

 

It seems this “banana” thread will offer a lot of valuable insights.

 

Rather than focusing on drawing the design itself, I’d first like to understand the underlying philosophy behind the ratios.

[tartarine]

Geometry, Proportion And The Art Of Lutherie by Kevin Coates. Hardback published 1985. 

May be of interest to you ? I liked it

or the book form François Denis ? might be interessting too 

if your quest is about musical instruments

[David Beard]

17 hours ago, Yoshi.haruIto said:

Hello,

 

I am interested in learning about the ratios and proportions used in musical instrument making. I believe that figures from ancient Greece, such as Pythagoras, Aristotle, and Aristoxenus, laid the foundational ideas for musical instruments.

 

When studying this field, are there other important historical figures I should know about? Even if they are not directly related to instrument-making, philosophers or scientists like Kepler or Leibniz, whose ideas are closely connected, would also be relevant.

 

If you happen to know any key references or books on this topic, I would greatly appreciate it if you could share them.

 

Thank you very much for your guidance.

 

 

Hi Yoshi,

Violin making was a long evolved practice, protected and develop and developed within certain communities, guilds, and families.

You are not alone in desiring to find a philosophic or spiritual aspect behind their traditions of ratio use in making instruments.

However, the ratios observed in their surviving instruments, the ratios seen when we study their making traditions, these ratio methods only suggest pragmatism, non philosophy or idealism.

Related ratio methods can be observed in use across many generations of instrument making and makers.

The methods provided a way to repeat successful results.   This is first purpose of the ratios.  It is simply a way to work.

The use of ratios provided a structured way to explore variations in design.  This is the second big reason ratio methods were so successful.   If you normally made two parts in a 4 to 5, and you wanted to try making the smaller part slightly smaller this time, trying using a 3 to 4 ratio this time.

Using ratios provided a way to explore variations without trashing a traditional making rule, or just starting over.  You still made the same two parts related to each, just using a different ratio choice.

When we sign deeply into studying the ratio choices actually seen used in the old N Italian making, most of the design choices actually offer a small range of options in choosing the ratio for any particular design choices.

The ratios thus serve as a way of capturing an repeating their community learning or evolution of design choices, of their making traditions.

Learn more about their design ratio choices, and actual observing them in centuries of violin making examples:

 

[Marty Kasprzyk]

The violin has a length to width ratio of about two.  The attached pdf paper explains why this might have happened.

length:width ratio.pdf

[David Beard]

53 minutes ago, Marty Kasprzyk said:

The violin has a length to width ratio of about two.  The attached pdf paper explains why this might have happened.

length:width ratio.pdf 39.37 kB · 4 downloads

The observed working tradition's use of length to width ratios can be summed up as:

"A part stouter than 2 to 1"

So, if you take a 2 to 1 ratio, for example 5 to 10, and make it stouter by shorting the length by 'a part', you get 5 to 9.

That recipe can give you a wide range of possible body ratios.  The tradition Cremona/Brescia/Venice violin family ratios all come from this pool of candidates.

5 to 9 is one of the most common traditional ratios for violins and violas.

 

 

 

[Nick Allen]

Has anyone ever considered Occam's Razor in these kind of musings?

[Yoshi.haruIto]

Thanks for the amazing video—it was really helpful!

 

I'm curious to learn more about ancient Greece.

I read that Pythagoras saw simple ratios of string lengths—like 1:1, 2:1, 3:2, 4:3—as the root of harmony.

 

I tend to think of this not just in terms of musical intervals, but also as reflecting the relationship between the wood and strings, and the underlying order and resonance of the whole instrument.

For example, 1:1 seems to represent completeness, 2:1 represents generation or doubling, 3:2 stable harmony, and 4:3 balance and tension.

 

What I really want to understand, though, is why Pythagoras himself saw these ratios this way—the story behind it.

Do you happen to know anything about that?

 

[David Beard]

That stuff is rather standard history, especially for music theory.  The basic idea is that some early Greek observed that things that make a musical sound tend to make a musically related sound if you change the proportions of the thing in simple ratios.

Generally if you make two sound making things identical in all other respects, but you change on measurement by simple ratio, you tend to get a musical interval between the two.  Things in a 1 to 2 ratios make octaves.  Things in a 1 to 3 ratio make perfect fifths.  Things in a 1 to 5 ratio make major thirds.

So, strings that are twice as long do make octaves (if all else is equal).  Air tubes twice as long do this.  

Also, strings tensioned by hanging weights pretty much do this is you double the weight.  Etc.

No one truly knows who discovered these things.  But, Pythagoras and his followers are historical given credit.

The details get complicated, to put it mildly.  But, the basics of harmonics are very interesting and simple in a way.

[Yoshi.haruIto]

.

[David Beard]

Sorry. I don't seem to be able to translate this.

[Yoshi.haruIto]

4 hours ago, David Beard said:

Sorry. I don't seem to be able to translate this.

I’m sorry . I accidentally posted something that had already been translated into Japanese by Google Chrome.

 

Thank you very much.

This theory is based on a kind of intuitive understanding, and I find it fascinating at this stage.

 

When Renaissance thinkers adopted the proportions of ancient Greece, it may have been as a nostalgic means of recreating the cosmic beauty those ratios embodied. Perhaps they gave the proportions narrative or symbolic meaning, effectively reinterpreting them in accordance with their own era?

 

For example, I can understand the harmony inherent in the perfect fifth, but I’m curious whether, at the dawn of the Renaissance, these ratios were used purely as formal structural elements without symbolic meaning, or whether from the outset they were intentionally imbued with philosophical and symbolic significance

[David Beard]

37 minutes ago, Yoshi.haruIto said:

I’m sorry . I accidentally posted something that had already been translated into Japanese by Google Chrome.

 

Thank you very much.

This theory is based on a kind of intuitive understanding, and I find it fascinating at this stage.

 

When Renaissance thinkers adopted the proportions of ancient Greece, it may have been as a nostalgic means of recreating the cosmic beauty those ratios embodied. Perhaps they gave the proportions narrative or symbolic meaning, effectively reinterpreting them in accordance with their own era?

 

For example, I can understand the harmony inherent in the perfect fifth, but I’m curious whether, at the dawn of the Renaissance, these ratios were used purely as formal structural elements without symbolic meaning, or whether from the outset they were intentionally imbued with philosophical and symbolic significance

Just as a matter of opinion, I believe people have wanted to attach symbolic meanings to ratios and numerology.  It seems the original Pythagoreans attached a great deal of philosophy and meaning to numbers.

However, your questions are also connecting to music.   In both instruments making, and in music making, there is a practical reality to the use of numbers and ratios.  And, that practical side tends to override any philosophically motivated concerns.

The use of ratios in music theory is very different than in instrument making.

Music theory uses numbers for both rhythmic theory, and for intervals and harmony.  If you want to understand Renaissance and early baroque use of numbers in harmony, you could try reading Zarlino.  If you want to better understand the old rhythmic theory, you could ready Morley.

There is very little philosophy in such music theory uses of numbers.  The only thing that comes about is that the old theory called rhythmic division into 3 parts 'perfect', and division into 2 parts 'imperfect'.  This was explained as honoring the Holy Trinity of Christianity.

Likewise, for instrument making, the use of ratios is driven by practicalities, not by any conceptual idealism.

 

Of course, people are never content with this.   In a physics department, quantum mechanics is expressed in equations.  There's lots of chalk and no mystic philosophy.   

But on social media, quantum mechanics is high jacked by mystical fantasy.

Similarly, music theory and the harmonic ratios behind that are practical rather than conceptual.  But again, on social media 'harmony' becomes a jumping off point for fantasies of 'harmonies of the spheres'.   And this is not a new phenomena.  Even in past eras, even in Greek times, people prefer to take these practical things and fantasize about them.  Perhaps it's the combination of recognizing that something structured and meaningful is definitely going on in these fields, together with them being a bit too arcane for the casual student to understand clearly without great effort, that combination is readily met by fantasizing grand untethered meaning.

[Yoshi.haruIto]

1 hour ago, David Beard said:

Just as a matter of opinion, I believe people have wanted to attach symbolic meanings to ratios and numerology.  It seems the original Pythagoreans attached a great deal of philosophy and meaning to numbers.

However, your questions are also connecting to music.   In both instruments making, and in music making, there is a practical reality to the use of numbers and ratios.  And, that practical side tends to override any philosophically motivated concerns.

The use of ratios in music theory is very different than in instrument making.

Music theory uses numbers for both rhythmic theory, and for intervals and harmony.  If you want to understand Renaissance and early baroque use of numbers in harmony, you could try reading Zarlino.  If you want to better understand the old rhythmic theory, you could ready Morley.

There is very little philosophy in such music theory uses of numbers.  The only thing that comes about is that the old theory called rhythmic division into 3 parts 'perfect', and division into 2 parts 'imperfect'.  This was explained as honoring the Holy Trinity of Christianity.

Likewise, for instrument making, the use of ratios is driven by practicalities, not by any conceptual idealism.

 

Of course, people are never content with this.   In a physics department, quantum mechanics is expressed in equations.  There's lots of chalk and no mystic philosophy.   

But on social media, quantum mechanics is high jacked by mystical fantasy.

Similarly, music theory and the harmonic ratios behind that are practical rather than conceptual.  But again, on social media 'harmony' becomes a jumping off point for fantasies of 'harmonies of the spheres'.   And this is not a new phenomena.  Even in past eras, even in Greek times, people prefer to take these practical things and fantasize about them.  Perhaps it's the combination of recognizing that something structured and meaningful is definitely going on in these fields, together with them being a bit too arcane for the casual student to understand clearly without great effort, that combination is readily met by fantasizing grand untethered meaning.

 

I agree that both music theory and instrument making must be grounded in practicality.

 

Yet I feel there is a clear philosophical lineage in music from Pythagoras to Desprez, Bach, Beethoven, Rachmaninoff, Mahler, and Arvo Pärt.

 

Between theory, numbers, and the act of listening or performing, there seems to exist another layer: a dimension of truth and philosophy.

 

Without that layer, people might not feel resonance or emotion, and music itself could lose its very necessity.

 

In instrument making, practicality is indeed essential.

However, if an instrument carries no sense of truth or philosophy and exists merely as a tool, then the performer cannot be enlightened through it.

 

In Japan, we have the culture of the tea bowl.

In the tea ceremony, the vessel is a practical object for drinking tea, yet its form and presence embody a profound philosophy.

A tea bowl holds a silent, Zen-like depth, inviting the drinker into contemplation.

 

I feel that the violin is very close to this cultural spirit.

 

However, no literature I have found discusses instruments in such a philosophical dimension.

And yet, when I encounter the works of Amati or Stradivari, I can unmistakably sense that presence the philosophy within their instruments.

 

[Rothwein]

The field in which you are searching as related to Instruments and their design is called Organology. You might find a lot more in Government/public or College/research libraries using that as a search rerm.

It might be easier to find actual Literature if you begin with a College freshman level textbook (in the US, "Music 101")  and check online for the works cited in footnotes and bibliography. Those are often available in PDF format from online libraries (academia.com is a good tool for access. Just be aware that there is a subscription tier.)

[Yoshi.haruIto]

31 minutes ago, Rothwein said:

 

 

 

31 minutes ago, Rothwein said:

The field in which you are searching as related to Instruments and their design is called Organology. You might find a lot more in Government/public or College/research libraries using that as a search rerm.

It might be easier to find actual Literature if you begin with a College freshman level textbook (in the US, "Music 101")  and check online for the works cited in footnotes and bibliography. Those are often available in PDF format from online libraries (academia.com is a good tool for access. Just be aware that there is a subscription tier.)

 

Thanks!! I'll see it.

[Dr. Mark]

7 hours ago, David Beard said:

  There's lots of chalk and no mystic philosophy

Not to sidetrack the discussion, but this is an interesting assertion for some other time and place.

20 hours ago, Nick Allen said:

Has anyone ever considered Occam's Razor in these kind of musings?

I believe so because I remember it being mentioned in a post, but I couldn't point to where off the top of my head.   But now, to once again pull out the big guns for philosophical musings:

3200-2800 BC figurine (Smithsonian Institution) - one of many such, some as bar back as ca 10,000 BC.  I speculate that male attraction to the female figure is a contributor, perhaps a critical factor, in the visual development of the violin family of instruments.  I think I can argue for other instruments as well.  The weight of these various factors (rather than their presence) will likely vary among various instruments:

[Marty Kasprzyk]

4 hours ago, Dr. Mark said:

Not to sidetrack the discussion, but this is an interesting assertion for some other time and place.

I believe so because I remember it being mentioned in a post, but I couldn't point to where off the top of my head.   But now, to once again pull out the big guns for philosophical musings:

3200-2800 BC figurine (Smithsonian Institution) - one of many such, some as bar back as ca 10,000 BC.  I speculate that male attraction to the female figure is a contributor, perhaps a critical factor, in the visual development of the violin family of instruments.  I think I can argue for other instruments as well.  The weight of these various factors (rather than their presence) will likely vary among various instruments:

Notice the upper and lower bouts are the same width.  Thousands of years later thing was seen in the violin's ancestors.  But fingering in the upper positions was difficult with a wide upper bout so eventually the upper bout was made narrower but the lower bout was kept wide to maintain a large cavity volume.  This shape evolution was seen with Lyra de braccios.

[Yoshi.haruIto]

2 hours ago, Marty Kasprzyk said:

Notice the upper and lower bouts are the same width.  Thousands of years later thing was seen in the violin's ancestors.  But fingering in the upper positions was difficult with a wide upper bout so eventually the upper bout was made narrower but the lower bout was kept wide to maintain a large cavity volume.  This shape evolution was seen with Lyra de braccios.

Thank you for the wonderful information.

I was wondering, is there any tradition suggesting that Christian religious questions influenced the shape of instruments like the lyre or lute..?

 

[Dr. Mark]

10 hours ago, Yoshi.haruIto said:

I was wondering, is there any tradition suggesting that Christian religious questions influenced the shape of instruments like the lyre or lute..?

I don't claim any expertise, but in my lifetime I have never heard or read of any influence of religion - Christian or otherwise - (unless Greek numerological cults and myths are considered 'religions') on instrument shape.  You may want to be more specific - according to Britannica, "lute, in music, any plucked or bowed chordophone whose strings are parallel to its belly, or soundboard, and run along a distinct neck or pole."  Internet scholarship aside, perhaps you can find somewhere that the three strings of the rebec are symbolic of the trinity; or the single string of the nun's fiddle of poverty, sacrifice, and/or single-minded devotion to Christ.  I don't know of any supportive evidence, but that doesn't mean much.

[Yoshi.haruIto]

54 minutes ago, Dr. Mark said:

I don't claim any expertise, but in my lifetime I have never heard or read of any influence of religion - Christian or otherwise - (unless Greek numerological cults and myths are considered 'religions') on instrument shape.  You may want to be more specific - according to Britannica, "lute, in music, any plucked or bowed chordophone whose strings are parallel to its belly, or soundboard, and run along a distinct neck or pole."  Internet scholarship aside, perhaps you can find somewhere that the three strings of the rebec are symbolic of the trinity; or the single string of the nun's fiddle of poverty, sacrifice, and/or single-minded devotion to Christ.  I don't know of any supportive evidence, but that doesn't mean much.

Thank you for your thoughtful reply to my rather spontaneous question.

It has always felt a bit strange to me that, even though musical instruments emerged during the 1500s and 1600s 'a time of religious music' their design doesn’t seem to reflect much Christian philosophy.

Now that I think about it, Christianity avoids idolatry, doesn’t it?

I wonder if that might have had an influence as well.

 

 

 

[Marty Kasprzyk]

11 hours ago, Yoshi.haruIto said:

Thank you for the wonderful information.

I was wondering, is there any tradition suggesting that Christian religious questions influenced the shape of instruments like the lyre or lute..?

 

Lots of angels played stringed instruments but I'm guessing they were human inventions.

[Dr. Mark]

3 hours ago, Yoshi.haruIto said:

Now that I think about it, Christianity avoids idolatry, doesn’t it?

In principle I suppose - the golden calf and all that - but that can be problematic.  What are you looking for?