new webpage: Ramos's division of the monochord

i've made a webpage with copious graphics illustrating
step-by-step exactly the procedure described by Ramos
for dividing the monochord into 5-limit ratios, from 1482:

http://sonic-arts.org/monzo/ramos/ramos.htm

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>>>> i've made a webpage with copious graphics illustrating
> step-by-step exactly the procedure described by Ramos
> for dividing the monochord into 5-limit ratios, from 1482:
>
> http://sonic-arts.org/monzo/ramos/ramos.htm

> -monz >>>>

Hello Monz, I wonder
(i) whether any work has been done on if and how far this can be compared with the four-fold string movement, demonstrated using two veenaa-s [sangitaratnakara 3.11-22];
(ii) whether any work has been done on if and how twenty-two shruti-s can be arrived at. Of course, shruti-s are not equidistant.

Regards,
Haresh.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> i've made a webpage with copious graphics illustrating
> step-by-step exactly the procedure described by Ramos
> for dividing the monochord into 5-limit ratios, from 1482:
>
> http://sonic-arts.org/monzo/ramos/ramos.htm
>
> -monz

there are a couple of odd claims on this page:

'Boethius discussed many of the subtle aspects of tuning that had be
written about in Greek books, and gave monochord measurements for all
three of the basic Greek genera: diatonic, chromatic, and enharmonic.
But due to the illiteracy of the ensuing centuries, his readers
failed to understand the less familiar chromatic and enharmonic, and
the diatonic, in Boethius's Pythagoran tuning, became firmly
established as "the" scale.'

is that really why the diatonic became established? or is it simply
that the diatonic was what everyone in europe was using to make
music, boethius or no boethius? i think you may be succumbing
to "theorism" here, like brian. music tends to follow its own path,
theory or no theory, literacy or illiteracy.

'Ramos's work of 1482 is the first mathematical description of 5-
limit tuning in Europe since the work of Ptolemy of c. 150 AD. After
a few decades of debate, it rapidly became the established tuning, at
least in theory.'

it sounds like you're saying ramos's tuning rapidly became the
established tuning. is that really true? btw, the evidence suggests
that in practice, some form of meantone tuning was already replacing
the older schismatic tuning by 1482.

--- In tuning@yahoogroups.com, "Haresh BAKSHI" <hareshbakshi@h...>
wrote:

> (ii) whether any work has been done on if and how twenty-two shruti-
>s can be arrived at. Of course, shruti-s are not equidistant.

plenty of such work has been done. what exactly did you have in mind?

hi paul,

thanks for the criticisms.

(... you're so *dependable* for that!)

i've made a few changes to the passages in question.
tell me what you think. i'll have to pursue it further
later when i have more time.

-monz

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: Friday, March 21, 2003 8:19 AM
Subject: [tuning] Re: new webpage: Ramos's division of the monochord

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > i've made a webpage with copious graphics illustrating
> > step-by-step exactly the procedure described by Ramos
> > for dividing the monochord into 5-limit ratios, from 1482:
> >
> > http://sonic-arts.org/monzo/ramos/ramos.htm
> >
> > -monz
>
> there are a couple of odd claims on this page:
>
> 'Boethius discussed many of the subtle aspects of tuning that had be
> written about in Greek books, and gave monochord measurements for all
> three of the basic Greek genera: diatonic, chromatic, and enharmonic.
> But due to the illiteracy of the ensuing centuries, his readers
> failed to understand the less familiar chromatic and enharmonic, and
> the diatonic, in Boethius's Pythagoran tuning, became firmly
> established as "the" scale.'
>
> is that really why the diatonic became established? or is it simply
> that the diatonic was what everyone in europe was using to make
> music, boethius or no boethius? i think you may be succumbing
> to "theorism" here, like brian. music tends to follow its own path,
> theory or no theory, literacy or illiteracy.
>
> 'Ramos's work of 1482 is the first mathematical description of 5-
> limit tuning in Europe since the work of Ptolemy of c. 150 AD. After
> a few decades of debate, it rapidly became the established tuning, at
> least in theory.'
>
> it sounds like you're saying ramos's tuning rapidly became the
> established tuning. is that really true? btw, the evidence suggests
> that in practice, some form of meantone tuning was already replacing
> the older schismatic tuning by 1482.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi paul,
>
>
> thanks for the criticisms.
>
> (... you're so *dependable* for that!)
>
>
> i've made a few changes to the passages in question.
> tell me what you think.

nice. you might mention that according to some authorities (schulter,
lindley, etc.) schismatic tuning was predominant in practice from c.
1420-1480, and meantone tuning immediately thereafter -- and *both*
of these are geared toward approximating 5-limit ratios.

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: Friday, March 21, 2003 10:29 AM
Subject: [tuning] Re: new webpage: Ramos's division of the monochord

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > hi paul,
> >
> >
> > thanks for the criticisms.
> >
> > (... you're so *dependable* for that!)
> >
> >
> > i've made a few changes to the passages in question.
> > tell me what you think.
>
> nice. you might mention that according to some authorities (schulter,
> lindley, etc.) schismatic tuning was predominant in practice from c.
> 1420-1480, and meantone tuning immediately thereafter -- and *both*
> of these are geared toward approximating 5-limit ratios.

OK. the reason i didn't add that yet is because i want
to be really clear on what you mean by "schismatic tuning".

that's not a temperament in the usual sense of a slight
mistuning on some or all notes, right? it's the case
where 3^-8 is used to represent 5^1 (e.g., if the 1/1 is C,
then the Pythagorean Fb is used to represent the JI 5/4),
yes?

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> that's not a temperament in the usual sense of a slight
> mistuning on some or all notes, right? it's the case
> where 3^-8 is used to represent 5^1 (e.g., if the 1/1 is C,
> then the Pythagorean Fb is used to represent the JI 5/4),
> yes?

This gives you a slightly mistuned 5/4; you need to clarify what
you are trying to say.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> To: <tuning@yahoogroups.com>
> Sent: Friday, March 21, 2003 10:29 AM
> Subject: [tuning] Re: new webpage: Ramos's division of the
monochord
>
>
> > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > > hi paul,
> > >
> > >
> > > thanks for the criticisms.
> > >
> > > (... you're so *dependable* for that!)
> > >
> > >
> > > i've made a few changes to the passages in question.
> > > tell me what you think.
> >
> > nice. you might mention that according to some authorities
(schulter,
> > lindley, etc.) schismatic tuning was predominant in practice from
c.
> > 1420-1480, and meantone tuning immediately thereafter -- and
*both*
> > of these are geared toward approximating 5-limit ratios.
>
>
>
> OK. the reason i didn't add that yet is because i want
> to be really clear on what you mean by "schismatic tuning".
>
> that's not a temperament in the usual sense of a slight
> mistuning on some or all notes, right? it's the case
> where 3^-8 is used to represent 5^1 (e.g., if the 1/1 is C,
> then the Pythagorean Fb is used to represent the JI 5/4),
> yes?
>
>
>
> -monz

right. but we have no way of knowing whether in practice, the tuning
was more like this or more like the schismic temperaments of
helmholtz, groven, and sabat-garibaldi. given that the fifths differ
by only 1/4 of a cent between the two systems, it's likely that any
meaningful distinction between the two would be swamped by the
standard deviations of the tunings implemented at the time (15th
century). the point is that the 5-limit seems to have already been in
use in keyboard temperaments quite some time before ramos published
his monochord.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> >
> > ----- Original Message -----
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > To: <tuning@yahoogroups.com>
> > Sent: Friday, March 21, 2003 10:29 AM
> > Subject: [tuning] Re: new webpage: Ramos's division of the
> monochord
> >
> >
> > > --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> > > > hi paul,
> > > >
> > > >
> > > > thanks for the criticisms.
> > > >
> > > > (... you're so *dependable* for that!)
> > > >
> > > >
> > > > i've made a few changes to the passages in question.
> > > > tell me what you think.
> > >
> > > nice. you might mention that according to some authorities
> (schulter,
> > > lindley, etc.) schismatic tuning was predominant in practice
from
> c.
> > > 1420-1480, and meantone tuning immediately thereafter -- and
> *both*
> > > of these are geared toward approximating 5-limit ratios.
> >
> >
> >
> > OK. the reason i didn't add that yet is because i want
> > to be really clear on what you mean by "schismatic tuning".
> >
> > that's not a temperament in the usual sense of a slight
> > mistuning on some or all notes, right? it's the case
> > where 3^-8 is used to represent 5^1 (e.g., if the 1/1 is C,
> > then the Pythagorean Fb is used to represent the JI 5/4),
> > yes?
> >
> >
> >
> > -monz
>
> right. but we have no way of knowing whether in practice, the
tuning
> was more like this or more like the schismic temperaments of
> helmholtz, groven, and sabat-garibaldi. given that the fifths
differ
> by only 1/4 of a cent between the two systems, it's likely that any
> meaningful distinction between the two would be swamped by the
> standard deviations of the tunings implemented at the time (15th
> century). the point is that the 5-limit seems to have already been
in
> use in keyboard temperaments quite some time before ramos published
> his monochord.

keyboard *tunings*, sorry.

wallyesterpaulrus wrote:

>the point is that the 5-limit seems to have already been in
>use in keyboard temperaments quite some time before ramos published
>his monochord.

I was just searching for that today. Would you please supply any reference?
Thank you

Leonardo

--- In tuning@yahoogroups.com, Leonardo Perretti <dombedos@t...>
wrote:
> wallyesterpaulrus wrote:
>
> >the point is that the 5-limit seems to have already been in
> >use in keyboard temperaments quite some time before ramos
published
> >his monochord.
>
> I was just searching for that today. Would you please supply any
reference?
> Thank you
>
> Leonardo

searching for a reference to schismatic tuning in the 15th century?
here's one:

/tuning/topicId_28704.html#28704

re:
http://sonic-arts.org/monzo/ramos/ramos.htm

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, March 22, 2003 2:31 PM
> Subject: [tuning] Re: new webpage: Ramos's division of the monochord
>
>
> > OK. the reason i didn't add that yet is because i want
> > to be really clear on what you mean by "schismatic tuning".
> >
> > that's not a temperament in the usual sense of a slight
> > mistuning on some or all notes, right? it's the case
> > where 3^-8 is used to represent 5^1 (e.g., if the 1/1 is C,
> > then the Pythagorean Fb is used to represent the JI 5/4),
> > yes?
> >
> >
> >
> > -monz
>
> right. but we have no way of knowing whether in practice, the tuning
> was more like this or more like the schismic temperaments of
> helmholtz, groven, and sabat-garibaldi. given that the fifths differ
> by only 1/4 of a cent between the two systems, it's likely that any
> meaningful distinction between the two would be swamped by the
> standard deviations of the tunings implemented at the time (15th
> century). the point is that the 5-limit seems to have already been in
> use in keyboard temperaments quite some time before ramos published
> his monochord.

OK, of course you're right about that.
i'll put something in about schismatic tuning.
in fact, i should have a page about that in
the Dictionary.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> re:
> http://sonic-arts.org/monzo/ramos/ramos.htm
>
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > To: <tuning@yahoogroups.com>
> > Sent: Saturday, March 22, 2003 2:31 PM
> > Subject: [tuning] Re: new webpage: Ramos's division of the
monochord
> >
> >
> > > OK. the reason i didn't add that yet is because i want
> > > to be really clear on what you mean by "schismatic tuning".
> > >
> > > that's not a temperament in the usual sense of a slight
> > > mistuning on some or all notes, right? it's the case
> > > where 3^-8 is used to represent 5^1 (e.g., if the 1/1 is C,
> > > then the Pythagorean Fb is used to represent the JI 5/4),
> > > yes?
> > >
> > >
> > >
> > > -monz
> >
> > right. but we have no way of knowing whether in practice, the
tuning
> > was more like this or more like the schismic temperaments of
> > helmholtz, groven, and sabat-garibaldi. given that the fifths
differ
> > by only 1/4 of a cent between the two systems, it's likely that
any
> > meaningful distinction between the two would be swamped by the
> > standard deviations of the tunings implemented at the time (15th
> > century). the point is that the 5-limit seems to have already
been in
> > use in keyboard temperaments quite some time before ramos
published
> > his monochord.
>
>
>
> OK, of course you're right about that.
> i'll put something in about schismatic tuning.
> in fact, i should have a page about that in
> the Dictionary.
>
>
>
> -monz

hmm. i didn't mean to suggest a different term, schismatic, as
distinguished from schismic:

http://sonic-arts.org/dict/schismic.htm

the idea is the same, and pythagorean tuning can be used schismically
(or schismatically, if that's the term you prefer). i don't know if
we really need two terms. but i could see "schismatic" as a shorthand
for "schisma thirds - ic", and i think "schisma thirds" was lindley's
term in the context of the 15th century tuning.