Isaac Newton and 53-et

Check it out:

http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindly7.gif

--- genewardsmith <genewardsmith@juno.com> wrote:
> Check it out:
>
>
http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindly7.gif
>
>

Gene,

I like Newton's circular 53-et diagram. Would you
mind letting me (and any other interested parties)
know where you got it?

In her chapter of the book "Let Newton Be!", Dutch
musicologist Penelope Gouk mentions that Sir Issac's
notebooks show that in addition to 53=et, he also
looked at 12-et and 51-et and their product, 612-et!

According to Ms. Gouk, Newton did this in the late
1660's, decades before Werckmeister came up with
12-et, and he also, nearly two centuries before
Alexander Ellis, invented a logarithmic system for
comparing musical intervals that is virtually
identical to Ellis' cents system except for the
position of the decimal point. In Newton's system the
3/2 was 7.02, the 5/4 was 3.86, and the 6/5 was 3.16,
etc., but with the decimals carried out even further.
The 3/2 was actually the correct 7.0195 or whatever (I
don't have the exact figure at hand).

But I don't think Ms. Gouk mentioned the circular
53-et diagram. Thanks for posting it.

--Mark Rankin

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--- In tuning@y..., Mark Rankin <markrankin95511@y...> wrote:
> --- genewardsmith <genewardsmith@j...> wrote:

> I like Newton's circular 53-et diagram. Would you
> mind letting me (and any other interested parties)
> know where you got it?

I got it from the url I posted, and I got *that* by poking around on
http://mto.societymusictheory.org/

> In her chapter of the book "Let Newton Be!", Dutch
> musicologist Penelope Gouk mentions that Sir Issac's
> notebooks show that in addition to 53=et, he also
> looked at 12-et and 51-et and their product, 612-et!

Glad you said that, because I wanted another source than isacoff for the 612-et business.

Mark writes:
>According to Ms. Gouk, Newton did this in the late
> 1660's, decades before Werckmeister came up with
> 12-et,

Hm, Werckmeister "came up" with 12 ET? This is the first time I
have heard of this, could someone direct me to the source of this info? None
of the Werkmeister temperaments I have used are anywhere near ET.
Regards,
Ed Foote
Precision Piano Works
Nashville, Tn.
<A HREF="www.uk-piano.org/edfoote/well_tempered_piano.html">6 degrees</A>

Mark Rankin wrote:

>In her chapter of the book "Let Newton Be!", Dutch
>musicologist Penelope Gouk mentions ...

I'm not certain but it seems more that she's British.

>According to Ms. Gouk, Newton did this in the late
>1660's, decades before Werckmeister came up with
>12-et, and he also, nearly two centuries before
>Alexander Ellis, invented a logarithmic system for
>comparing musical intervals that is virtually
>identical to Ellis' cents system except for the
>position of the decimal point.

I've read this too in the book by Lindley and
Turner-Smith "Mathematical models of musical
scales".

Manuel

In a message dated 3/20/02 8:50:54 AM Eastern Standard Time, a440a@aol.com
writes:

> ,
>
> Hm, Werckmeister "came up" with 12 ET? This is the first time I
> have heard of this, could someone direct me to the source of this info?
> None
> of the Werkmeister temperaments I have used are anywhere near ET.
> Regards,
>

Ah, I was going to let this go. Mark, you slipped on this one banana peel.
Werckmeister never invented or ever endorsed 12-tET. Its a historical
misnomer that people pick up like ticks. But thanks for the interesting
Newtonian stuff...hmmn...off by a decimal point...wouldn't Ellis have read
Newton's stuff on pitch?

Best, Johnny Reinhard

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., Mark Rankin <markrankin95511@y...> wrote:
> > --- genewardsmith <genewardsmith@j...> wrote:
>
> > I like Newton's circular 53-et diagram. Would you
> > mind letting me (and any other interested parties)
> > know where you got it?
>
> I got it from the url I posted, and I got *that* by poking around on
> http://mto.societymusictheory.org/
>
> > In her chapter of the book "Let Newton Be!", Dutch
> > musicologist Penelope Gouk mentions that Sir Issac's
> > notebooks show that in addition to 53=et, he also
> > looked at 12-et and 51-et and their product, 612-et!
>
> Glad you said that, because I wanted another source than isacoff
for the 612-et business.

just to clarify, isacoff mentioned that newton derived 612-equal,
seemingly centuries before bosanquet and others mentioned 612-equal,
and gene was interested if this claim by isacoff could be verified.

--- In tuning@y..., a440a@a... wrote:
> Mark writes:
> >According to Ms. Gouk, Newton did this in the late
> > 1660's, decades before Werckmeister came up with
> > 12-et,
>
> Hm, Werckmeister "came up" with 12 ET? This is the first
time I
> have heard of this, could someone direct me to the source of this
info? None
> of the Werkmeister temperaments I have used are anywhere near ET.

it's a long-standing belief, promulgated especially in the german-
speaking world, that werckmeister advocated 12-equal (he certainly
didn't 'come up' with it -- that honor is usually given to Prince Chu
Tsai-yü (1584), Simon Stevin (1585), or even Marin Mersenne (1636)).
johnny reinhard has pretty convincingly debunked this belief, to the
best of my limited knowledge of this particular topic.

werckmeister was bach's 'tuning guru'. i hope mark rankin doesn't
believe the common myth that bach ever used or advocated anything
like 12-equal. mark?

--- In tuning@y..., Afmmjr@a... wrote:

> But thanks for the interesting
> Newtonian stuff...hmmn...off by a decimal point...wouldn't Ellis
have read
> Newton's stuff on pitch?

doubtful -- this stuff was only in newton's notebooks and not
published (as the sloppiness of the 53-equal diagram should suggest).

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> Check it out:
>
>
http://mto.societymusictheory.org/issues/mto.93.0.3/mto.93.0.3.lindly7
.gif

note that newton is using a 'major hexachord' here with steps

10:9, 9:8, 16:15, 9:8, 10:9

anyone know why newton would use the hexachord with these
specifications? was it a prominent ji-theoretical construct in his
day?

--- Afmmjr@aol.com wrote:
> In a message dated 3/20/02 8:50:54 AM Eastern
> Standard Time, a440a@aol.com
> writes:
>
>
> > ,
> >
> > Hm, Werckmeister "came up" with 12 ET?
> This is the first time I
> > have heard of this, could someone direct me to
> the source of this info?
> > None
> > of the Werkmeister temperaments I have used are
> anywhere near ET.
> > Regards,
> >
>
> Ah, I was going to let this go. Mark, you slipped
> on this one banana peel.
> Werckmeister never invented or ever endorsed 12-tET.
> Its a historical
> misnomer that people pick up like ticks. But thanks
> for the interesting
> Newtonian stuff...hmmn...off by a decimal
> point...wouldn't Ellis have read
> Newton's stuff on pitch?
>
> Best, Johnny Reinhard
>

Johnny,

I'll certainly take your word for it that Werckmeister
didn't invent 12-ET, but I'm equally certain that I
didn't make it up. I read it somewhere, somewhere
reputable, it seems to me. I'd like to know where so
I can lay this matter to rest. I don't like ticks!
(The ones here on the north coast of California are
much worse than those back east - apart from the Lyme
disease danger, they inject both a flesh-killing toxin
and a pain-killer. The pain can be exteme before the
nummness arrives, and the spot of dead flesh always
leaves a little scar.)

If you know where this particular banana peel came
from, please let me know!

The reason why Alexander Ellis would have missed
knowing about Newton's work was stated in Paul
Erlich's post: It was never published and appeared
only in Newton's notebooks.

Have it good,

--Mark Rankin

__________________________________________________
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In a message dated 3/28/02 8:10:32 PM Eastern Standard Time,
markrankin95511@yahoo.com writes:

> I'll certainly take your word for it that Werckmeister
> didn't invent 12-ET, but I'm equally certain that I
> didn't make it up.

Mark, it's been a misreading of Werckmeister for whatever purposes for a long
time. Essentially, equal use of all keys became all keys are identical.
Werckmeister promoted his irregular temperament throughout his career. Even
his last published book (1707 published posthumously) indicates he still
supported his earlier views.

Sorry you were taken in. It's like a left-handed wrench.

best, Johnny

--- paulerlich <paul@stretch-music.com> wrote:
> --- In tuning@y..., a440a@a... wrote:
> > Mark writes:
> > >According to Ms. Gouk, Newton did this in the
> late
> > > 1660's, decades before Werckmeister came up with
> > > 12-et,
> >
> > Hm, Werckmeister "came up" with 12 ET?
> This is the first
> time I
> > have heard of this, could someone direct me to
> the source of this
> info? None
> > of the Werkmeister temperaments I have used are
> anywhere near ET.
>
> it's a long-standing belief, promulgated especially
> in the german-
> speaking world, that werckmeister advocated 12-equal
> (he certainly
> didn't 'come up' with it -- that honor is usually
> given to Prince Chu
> Tsai-y� (1584), Simon Stevin (1585), or even Marin
> Mersenne (1636)).
> johnny reinhard has pretty convincingly debunked
> this belief, to the
> best of my limited knowledge of this particular
> topic.
>
> werckmeister was bach's 'tuning guru'. i hope mark
> rankin doesn't
> believe the common myth that bach ever used or
> advocated anything
> like 12-equal. mark?
>
>

Paul,

Thanks for the mention of pre-Newtonians Prince Chu
Tsai-yu (1584), Simon Stevin (1585), and Marin
Mersenne (1636).

I have never heard or read that Werckmeister advocated
12-ET. As I have replied to Johnny in a separate
post, I'll take his (and your) word for it that
Werckmeister didn't invent 12-ET, but I didn't make it
up, I read it somewhere.

I would certainly hope that paul erlich doesn't
believe that I believe the common myth that Bach used
or advocated anything like 12-ET. paul?

Have it good,

--Mark Rankin

P.S. I've known Johnny R. far too long to believe
anything of the like!

__________________________________________________
Do You Yahoo!?
Yahoo! Movies - coverage of the 74th Academy Awards�
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Paul,

In case the northeast blackout ate my reply to your
last e-mail, I'm writing to say that I did reply to
your last message two weeks ago. I had forgotten that
I had already sent you the introductory literature
about my interchangeable fretboard kits.

Now the viruses are keeping the computers at our
Community Center off the internet, so I'm 22 miles
from home at the nearest library. Another reason why
snail mail may be a better means of communicating!
Anyway, I'll leave it up to you as to which medium to
use.
BTW, I'll be on vacation from Sept. 16th until Oct.
2nd.
--Mark Rankin

--- paulerlich <paul@stretch-music.com> wrote:
> --- In tuning@y..., a440a@a... wrote:
> > Mark writes:
> > >According to Ms. Gouk, Newton did this in the
> late
> > > 1660's, decades before Werckmeister came up with
> > > 12-et,
> >
> > Hm, Werckmeister "came up" with 12 ET?
> This is the first
> time I
> > have heard of this, could someone direct me to
> the source of this
> info? None
> > of the Werkmeister temperaments I have used are
> anywhere near ET.
>
> it's a long-standing belief, promulgated especially
> in the german-
> speaking world, that werckmeister advocated 12-equal
> (he certainly
> didn't 'come up' with it -- that honor is usually
> given to Prince Chu
> Tsai-y� (1584), Simon Stevin (1585), or even Marin
> Mersenne (1636)).
> johnny reinhard has pretty convincingly debunked
> this belief, to the
> best of my limited knowledge of this particular
> topic.
>
> werckmeister was bach's 'tuning guru'. i hope mark
> rankin doesn't
> believe the common myth that bach ever used or
> advocated anything
> like 12-equal. mark?
>
>

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