Euler is the grandfather of us all

http://en.wikipedia.org/wiki/Leonhard_Euler

In 1739 he wrote the _Tentamen novae theoriae musicae_, hoping to
eventually integrate musical theory as part of mathematics. This
part of his work, however, did not receive wide attention and was
once described as too mathematical for musicians and too musical
for mathematicians.*

-Carl

* Calinger, Ronald (1996). "Leonhard Euler: The First St. Petersburg
Years (1727–1741)". Historia Mathematica 23 (2): 144–145.

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> http://en.wikipedia.org/wiki/Leonhard_Euler
>
> In 1739 he wrote the _Tentamen novae theoriae musicae_, hoping to
> eventually integrate musical theory as part of mathematics. This
> part of his work, however, did not receive wide attention and was
> once described as too mathematical for musicians and too musical
> for mathematicians.*
>
> -Carl
>
>
> * Calinger, Ronald (1996). "Leonhard Euler: The First St. Petersburg
> Years (1727–1741)". Historia Mathematica 23 (2): 144–145.

Hence, perfect for us! I have been trying to find this paper. If you
know where to find it, I would love to print it out and read it!

Paul Hj

At 09:59 AM 9/24/2007, you wrote:
>--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>> http://en.wikipedia.org/wiki/Leonhard_Euler
>>
>> In 1739 he wrote the _Tentamen novae theoriae musicae_, hoping to
>> eventually integrate musical theory as part of mathematics. This
>> part of his work, however, did not receive wide attention and was
>> once described as too mathematical for musicians and too musical
>> for mathematicians.*
>>
>> -Carl
>>
>> * Calinger, Ronald (1996). "Leonhard Euler: The First St. Petersburg
>> Years (1727­1741)". Historia Mathematica 23 (2): 144­145.
>
>Hence, perfect for us! I have been trying to find this paper. If you
>know where to find it, I would love to print it out and read it!
>
>Paul Hj

Sounds like one for monz (probably he has already got it translated
it out of Latin or whatever). I'd love to see it too!

By "grandfather of us all" I meant not only in the development
of pitch space, but also the grandfather of the math vs. music
"debate" (and I use that word generously).

-Carl

There is another interesting connection between Euler and musical
theory - this is via the Superticular Ratios, although he would not
himself have been aware of this.

The only known algorithm for finding all possible SR's for a given
prime is characterised by the solution of (many!) Pell equations,
x^2 - Dy^2 = 1.

Euler's first involvement is accidental - the term "Pell Equation" is
a misnomer attributed to him, a result of getting his wires crossed
in one his many letters. Pell had mentioned the equation in passing,
but was discussing other matters.

Western development of the solution to this equation was led by
Euler, Gauss, Lagrange, Legendre and Fermat, either directly or
indirectly.

Euler could not have known at the time that a century later, the Pell
equation would turn out to be instrumental (!) in solving the
Superparticular Ratio enumeration problem. This was discovered by
Carl Størmer in 1897.

I'm sure Euler would have been delighted, however, to know that the
Pell equation would later turn out to have a particular application
relating to music!

Cheers
Jim White
MSI, ANU

PS: I say "Western development" because the great European
mathematicians were unaware of significant knowledge that was already
available, and known to Indian mathematicians since the 7th century!

We now know (or should know) that Brahmagupta made significant
progress in India in the 7th century. Bhaskara II in the 12th century
then provided a crucial refinement. The remarkable fact is that these
two contributions alone provide a method for solving all of the key
forms, x^2 - Dy^2 = 1, 2, 4, -1, -2, -4

All of this was unknown to Fermat, Euler, Lagrange, etc. The Hindu
scholars' remarkable achievements (and their priceless clues to the
Pell equation) were virtually unknown at the time.

The first publication in Europe of any sort of treatment did not
appear until 1819, some decades after that peak period of the
European attack on the equation.

It also leaves questions that remain unanswered - the Hindu methods
are remarkably similar to those produced by the Europeans, but did
not involve the concept of a continued fraction. CF's on the other
hand are now regarded as necessary for solving the Pell equation.

The suggestion, as usual, is that there is still more to be learned
from the old players!

Hi Carl and everyone else,

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> At 09:59 AM 9/24/2007, you wrote:
> >--- In tuning-math@yahoogroups.com, Carl Lumma <carl@> wrote:
> >> http://en.wikipedia.org/wiki/Leonhard_Euler
> >>
> >> In 1739 he wrote the _Tentamen novae theoriae musicae_,
> >> hoping to eventually integrate musical theory as part
> >> of mathematics. This part of his work, however, did not
> >> receive wide attention and was once described as too
> >> mathematical for musicians and too musical for
> >> mathematicians.*
> >>
> >> -Carl
> >>
> >> * Calinger, Ronald (1996). "Leonhard Euler: The First
> >> St. Petersburg Years (1727­1741)". Historia Mathematica
> >> 23 (2): 144­145.
> >
> > Hence, perfect for us! I have been trying to find this
> > paper. If you know where to find it, I would love to print
> > it out and read it!
> >
> >Paul Hj
>
> Sounds like one for monz (probably he has already got it
> translated it out of Latin or whatever). I'd love to see
> it too!

(Wow, a whole week passed before i saw this! Obviously
i haven't been reading this list very much lately ...)

I have never seen the _Tentamen_ itself, but i made this
webpage years ago, translating Patrice Bailhache's paper
about it from French into English:

http://tonalsoft.com/monzo/euler/euler-en.aspx

Here's where to find the _Tentamen_ itself:

Euler, Leonhard. 1739.
Tentamen novae theoriae musicae. Sint Petersburg.
In Opera Omnia series III volumen I,
Teubner, Leipzig, 1926.

English translation by Charles Samuel Smith,
PhD diss., Indiana University,
Bloomington, June 1960.

-monz
http://tonalsoft.com
Tonescape microtonal music software

At 10:30 PM 10/1/2007, you wrote:
>Hi Carl and everyone else,
>
>
>--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>>
>> At 09:59 AM 9/24/2007, you wrote:
>> >--- In tuning-math@yahoogroups.com, Carl Lumma <carl@> wrote:
>> >> http://en.wikipedia.org/wiki/Leonhard_Euler
>> >>
>> >> In 1739 he wrote the _Tentamen novae theoriae musicae_,
>> >> hoping to eventually integrate musical theory as part
>> >> of mathematics. This part of his work, however, did not
>> >> receive wide attention and was once described as too
>> >> mathematical for musicians and too musical for
>> >> mathematicians.*
>> >>
>> >> -Carl
>> >>
>> >> * Calinger, Ronald (1996). "Leonhard Euler: The First
>> >> St. Petersburg Years (1727­1741)". Historia Mathematica
>> >> 23 (2): 144­145.
>> >
>> > Hence, perfect for us! I have been trying to find this
>> > paper. If you know where to find it, I would love to print
>> > it out and read it!
>> >
>> >Paul Hj
>>
>> Sounds like one for monz (probably he has already got it
>> translated it out of Latin or whatever). I'd love to see
>> it too!
>
>
>(Wow, a whole week passed before i saw this! Obviously
>i haven't been reading this list very much lately ...)
>
>
>I have never seen the _Tentamen_ itself, but i made this
>webpage years ago, translating Patrice Bailhache's paper
>about it from French into English:
>
>http://tonalsoft.com/monzo/euler/euler-en.aspx

Thanks. What's OO, 3a, I, 515?

And, does that 1764 paper have any 3-D lattice diagrams or
matrices?

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:

> > I have never seen the _Tentamen_ itself, but i made this
> > webpage years ago, translating Patrice Bailhache's paper
> > about it from French into English:
> >
> > http://tonalsoft.com/monzo/euler/euler-en.aspx
>
> Thanks. What's OO, 3a, I, 515?

"OO" = "Opera Omnia" = "Complete Works"

That's a page citation. You trimmed my bibliographic
reference from your quote of my post, so here it is
again:

Euler, Leonhard. 1739.
Tentamen novae theoriae musicae. Sint Petersburg.
In Opera Omnia series III volumen I,
Teubner, Leipzig, 1926.

More info is here:
http://math.dartmouth.edu/~euler/operaomnia.html

You can buy it for 165.00 euros:
http://www.springer.com/dal/home/birkhauser/historyofscience?SGWID=1-40295-22-34452439-0&teaserId=56218&CENTER_ID=122072

So that citation translates to:

page 515
of volume I
of series 3a
of the edition of Euler's complete works

> And, does that 1764 paper have any 3-D lattice
> diagrams or matrices?

I have never read any of the source material
from Euler, other than what Bailhache quoted,
so i can't say.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Thanks!

At 08:08 AM 10/2/2007, you wrote:
>--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
>> > I have never seen the _Tentamen_ itself, but i made this
>> > webpage years ago, translating Patrice Bailhache's paper
>> > about it from French into English:
>> >
>> > http://tonalsoft.com/monzo/euler/euler-en.aspx
>>
>> Thanks. What's OO, 3a, I, 515?
>
>
>"OO" = "Opera Omnia" = "Complete Works"
>
>That's a page citation. You trimmed my bibliographic
>reference from your quote of my post, so here it is
>again:
>
>Euler, Leonhard. 1739.
>Tentamen novae theoriae musicae. Sint Petersburg.
>In Opera Omnia series III volumen I,
>Teubner, Leipzig, 1926.
>
>
>More info is here:
>http://math.dartmouth.edu/~euler/operaomnia.html
>
>You can buy it for 165.00 euros:
>http://www.springer.com/dal/home/birkhauser/historyofscience?SGWID=1-4
>0295-22-34452439-0&teaserId=56218&CENTER_ID=122072
>
>
>So that citation translates to:
>
>page 515
>of volume I
>of series 3a
>of the edition of Euler's complete works
>
>
>> And, does that 1764 paper have any 3-D lattice
>> diagrams or matrices?
>
>I have never read any of the source material
>from Euler, other than what Bailhache quoted,
>so i can't say.
>
>
>-monz
>http://tonalsoft.com
>Tonescape microtonal music software

--- In tuning-math@yahoogroups.com, "monz" <monz@...> wrote:
>
> --- In tuning-math@yahoogroups.com, Carl Lumma <carl@> wrote:
>
> > > I have never seen the _Tentamen_ itself, but i made this
> > > webpage years ago, translating Patrice Bailhache's paper
> > > about it from French into English:
> > >
> > > http://tonalsoft.com/monzo/euler/euler-en.aspx
> >
> > Thanks. What's OO, 3a, I, 515?
>
>
> "OO" = "Opera Omnia" = "Complete Works"
>
> That's a page citation. You trimmed my bibliographic
> reference from your quote of my post, so here it is
> again:
>
> Euler, Leonhard. 1739.
> Tentamen novae theoriae musicae. Sint Petersburg.
> In Opera Omnia series III volumen I,
> Teubner, Leipzig, 1926.
>
>
> More info is here:
> http://math.dartmouth.edu/~euler/operaomnia.html
>
> You can buy it for 165.00 euros:
> http://www.springer.com/dal/home/birkhauser/historyofscience?
SGWID=1-40295-22-34452439-0&teaserId=56218&CENTER_ID=122072
>
>
> So that citation translates to:
>
> page 515
> of volume I
> of series 3a
> of the edition of Euler's complete works
>
>
> > And, does that 1764 paper have any 3-D lattice
> > diagrams or matrices?
>
> I have never read any of the source material
> from Euler, other than what Bailhache quoted,
> so i can't say.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software

Thanks, monz, for all the info. I have wanted to read this paper for
years. But $240.00 is a little steep. I wonder if there is a way to
read it online, say for $10 (I doubt it)

- paulhj

Hi Paul and Carl,

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<phjelmstad@...> wrote:

> Thanks, monz, for all the info. I have wanted to read
> this paper for years. But $240.00 is a little steep.

Yeah, well, now you know why after all these years
*i* still haven't read Euler! And this, despite the
fact that i'm the one who acknowledged that his work
led the way to my own (lattice diagrams).

> I wonder if there is a way to read it online, say for
> $10 (I doubt it)

The way to do it is to search worldcat.org and try to
find it in the closest library to you. Unfortunately,
the closest one to me (i'm in San Diego) is at the
University of Regina, in Saskatchewan -- 1300 miles away!
But i could always try interlibrary loan.

-monz
http://tonalsoft.com
Tonescape microtonal music software

monz wrote:

> The way to do it is to search worldcat.org and try to
> find it in the closest library to you. Unfortunately,
> the closest one to me (i'm in San Diego) is at the
> University of Regina, in Saskatchewan -- 1300 miles away!
> But i could always try interlibrary loan.

That's strange, one of the closest to me (I'm in China, and it won't even recognize the province) is in the University of Califorina, San Diego. "Leonhard Euler's Tentamen novae theoriae musicae a translation and commentary" by C S Smith on microform.

For the original Latin, I can see you'll have trouble.

Graham

Hi Monz,

I can get the papers about Euler through the University if you
provide me bibliographic details.

I was trying to get in touch with you off line many times and
and also in the past but I get the messages returned by the way!

Tony Salinas

Hi Graham,

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> monz wrote:
>
> > The way to do it is to search worldcat.org and try to
> > find it in the closest library to you. Unfortunately,
> > the closest one to me (i'm in San Diego) is at the
> > University of Regina, in Saskatchewan -- 1300 miles away!
> > But i could always try interlibrary loan.
>
> That's strange, one of the closest to me (I'm in China, and
> it won't even recognize the province) is in the University
> of Califorina, San Diego. "Leonhard Euler's Tentamen novae
> theoriae musicae a translation and commentary" by C S Smith
> on microform.

Wow, thanks! I've been looking for that but never did
a worldcat search for it, and it's been sitting in the
UCSD library (definitely a place i visit a lot!) all
this time!

> For the original Latin, I can see you'll have trouble.

Yeah, i want that one too. So interlibrary loan it is.

-monz
http://tonalsoft.com
Tonescape microtonal music software

Hi Tony,

--- In tuning-math@yahoogroups.com, "J.A.Martin Salinas" <tony@...>
wrote:
>
> Hi Monz,
>
> I can get the papers about Euler through the University if you
> provide me bibliographic details.

Wow, thanks! I would appreciate that very much.
If you can get me the English translation by Smith,
i'll take it ... but that one is relatively easy for
me to get myself. Anyway, here's the info:

Leonhard Euler's Tentamen novae theoriae musicae
a translation and commentary
by C S Smith; Leonhard Euler
Language: English
Publisher: 1960.
Dissertation: Thesis--Indiana University.
OCLC: 5733293

I'm guessing you'll only find that on microform,
but there's always the possibility that the University
bought a paper copy.

The Latin original is the one i'd really like you
to help me get:

Euler, Leonahard. 1739.
Tentamen novae theoriae musicae. Sint Petersburg.
In Opera Omnia series III volumen I,
Teubner, Leipzig, 1926.

> I was trying to get in touch with you off line many
> times and and also in the past but I get the messages
> returned by the way!

Sorry about that. I never mentioned this here, but
i guess it's time to make it known: we were getting
so much spam at our tonalsoft.com email addresses
that it started causing problems with our server,
so we had to kill all of those addresses.

That really sucks because i had made the tonalsoft
address my main one for anyone who wanted to contact
me regarding music or tuning.

You can write to me at any of the following:

joemonz(AT)yahoo.com
monz(AT)juno.com
monz(AT)cox.net

The yahoo address is the one i check most.

-monz
http://tonalsoft.com
Tonescape microtonal music software

monz wrote:

> The Latin original is the one i'd really like you
> to help me get:
> > Euler, Leonahard. 1739.
> Tentamen novae theoriae musicae. Sint Petersburg.
> In Opera Omnia series III volumen I,
> Teubner, Leipzig, 1926.

They have this one in Kyoto:

Tentamen novae theoriae musicae
by Leonhard Euler
Type: Book
Language: Latin
Publisher: New York : Broude Brothers, 1968.
OCLC: 1692129

Graham

Thanks Graham!

Kyoto might be easier for me if we are talking about microtechnology!

Do you know which library is that and the format?

Tony

On 2007/10/04, at 13:42, Graham Breed wrote:

> monz wrote:
>
> > The Latin original is the one i'd really like you
> > to help me get:
> >
> > Euler, Leonahard. 1739.
> > Tentamen novae theoriae musicae. Sint Petersburg.
> > In Opera Omnia series III volumen I,
> > Teubner, Leipzig, 1926.
>
> They have this one in Kyoto:
>
> Tentamen novae theoriae musicae
> by Leonhard Euler
> Type: Book
> Language: Latin
> Publisher: New York : Broude Brothers, 1968.
> OCLC: 1692129
>
> Graham
>
>

J.A.Martin Salinas wrote:
> Thanks Graham!
> > Kyoto might be easier for me if we are talking about microtechnology!
> > Do you know which library is that and the format?

Doshisha Women's College, Liberal Arts Library. Book.

I suggest waiting for Monz to read the translation in San Diego so that he knows what parts he's interested in getting copies of.

Graham

Hi Graham and Tony,

--- In tuning-math@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> They have this one in Kyoto:
>
> Tentamen novae theoriae musicae
> by Leonhard Euler
> Type: Book
> Language: Latin
> Publisher: New York : Broude Brothers, 1968.
> OCLC: 1692129

and in another post:

> I suggest waiting for Monz to read the translation
> in San Diego so that he knows what parts he's
> interested in getting copies of.

Well, thanks for that bibliographic citation!

I searched WorldCat for that one and found a copy
at San Diego State University.

So between UCSD and State i can get both the
English and the original Latin.

Now the question is ... when the heck will i find
time to read them? ;-)

-monz
http://tonalsoft.com
Tonescape microtonal music software

I'm sure this has already been mentioned, but just in case:
http://www.math.dartmouth.edu/~euler/pages/E033.html

Keenan