Dodekaphony

I notice that Dodekaphony insists on the 81/64 Major third.

Though incidental I cannot help but quote our man Partch:

"As the first revelation of the nature of tone among a restless and curious people, Pythagoras' 3/2 was a brilliant omen. However, the advocate of this ratio seemed to reason that if one 3/2 were good, twelve were twelve times good, and after 2500 years we a re still trying to correct the excesses of his judgement" Genesis of A Music... p363 (2nd Ed Da Capo)

I still don't accept that the 'natural' basis of music should limit its gamut to 12 pitch-classes.

M

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
> I notice that Dodekaphony insists on the 81/64 Major third.
>
> Though incidental I cannot help but quote our man Partch:
>
> "As the first revelation of the nature of tone among a restless and
> curious people, Pythagoras' 3/2 was a brilliant omen. However, the
> advocate of this ratio seemed to reason that if one 3/2 were good,
> twelve were twelve times good, and after 2500 years we a re still
> trying to correct the excesses of his judgement" Genesis of A
Music...
> p363 (2nd Ed Da Capo)
>
> I still don't accept that the 'natural' basis of music should
limit
> its gamut to 12 pitch-classes.
>
> M

Hi Mark

That's what 'natural' is all about. Dodekaphony emerges naturally
from the series of natural numbers. Anything else is 'contrived',
which doesn't necessarily diminish its value, but which means it just
ain't natural. Either you grok the node of the powers of 2 and 3 or
you don't. No one is forcing you.

Peter

>That's what 'natural' is all about. Dodekaphony emerges naturally
>from the series of natural numbers. Anything else is 'contrived',
>which doesn't necessarily diminish its value, but which means it just
>ain't natural. Either you grok the node of the powers of 2 and 3 or
>you don't. No one is forcing you.

There are other nodes of the powers of 2 and 3, such as 17, 19, 29,
31, 41, 53. . . But there are also other measures of goodness which
may be more appropriate, especially beyond the 3-limit, and if you
pay very close attention around here you might learn about some of
them.

-Carl

on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
>> I notice that Dodekaphony insists on the 81/64 Major third.
>>
>> Though incidental I cannot help but quote our man Partch:
>>
>> "As the first revelation of the nature of tone among a restless and
>> curious people, Pythagoras' 3/2 was a brilliant omen. However, the
>> advocate of this ratio seemed to reason that if one 3/2 were good,
>> twelve were twelve times good, and after 2500 years we a re still
>> trying to correct the excesses of his judgement" Genesis of A
> Music...
>> p363 (2nd Ed Da Capo)
>>
>> I still don't accept that the 'natural' basis of music should
> limit
>> its gamut to 12 pitch-classes.
>>
>> M
>
> Hi Mark
>
> That's what 'natural' is all about. Dodekaphony emerges naturally
> from the series of natural numbers. Anything else is 'contrived',
> which doesn't necessarily diminish its value, but which means it just
> ain't natural. Either you grok the node of the powers of 2 and 3 or
> you don't. No one is forcing you.
>
> Peter

You can use the word "natural" for anything you want Peter. But please try
to recognize when you are having an opinion. See Carl's post which preceeds
mine. In spite of what you say, in "natural" I hear a value judgement
"better". If not then why not choose or invent other terms which actually
elucicate the particular strengths of Dodekaphony so you are not forced to
hijack the generic term "natural" for your own purposes. However, if you
are nice, maybe you will earn an entry in Monz's dictionary defining
Sault-natural. ;) For example see Lumma stability.

You could just say instead, such-and-such has the following qualities, or
perhaps even the following strengths. Such words are unpretentious and are
helpful to everyone, particularly if you have found out something new.

Meanwhile I tend to have the *suspicion* that everything you are saying
about Dodekaphony amounts to a single equation in Gene's collection of
thousands. Once you learn the language that is used here, and realize the
breadth of experience that has been touched by this community, I will be
really interested to hear what you have to say about Dodekaphony that is not
old news.

-Kurt

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> There are other nodes of the powers of 2 and 3, such as 17, 19, 29,
> 31, 41, 53. . . But there are also other measures of goodness which
> may be more appropriate, especially beyond the 3-limit, and if you
> pay very close attention around here you might learn about some of
> them.

Or if you want to get into heavier lifting, tuning-math.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >That's what 'natural' is all about. Dodekaphony emerges naturally
> >from the series of natural numbers. Anything else is 'contrived',
> >which doesn't necessarily diminish its value, but which means it
just
> >ain't natural. Either you grok the node of the powers of 2 and 3
or
> >you don't. No one is forcing you.
>
> There are other nodes of the powers of 2 and 3, such as 17, 19, 29,
> 31, 41, 53. . . But there are also other measures of goodness which
> may be more appropriate, especially beyond the 3-limit, and if you
> pay very close attention around here you might learn about some of
> them.
>
> -Carl

What do you mean by 'node' here, Carl?

Peter

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@c...> wrote:
>
> > --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
> >> I notice that Dodekaphony insists on the 81/64 Major third.
> >>
> >> Though incidental I cannot help but quote our man Partch:
> >>
> >> "As the first revelation of the nature of tone among a restless
and
> >> curious people, Pythagoras' 3/2 was a brilliant omen. However,
the
> >> advocate of this ratio seemed to reason that if one 3/2 were
good,
> >> twelve were twelve times good, and after 2500 years we a re still
> >> trying to correct the excesses of his judgement" Genesis of A
> > Music...
> >> p363 (2nd Ed Da Capo)
> >>
> >> I still don't accept that the 'natural' basis of music should
> > limit
> >> its gamut to 12 pitch-classes.
> >>
> >> M
> >
> > Hi Mark
> >
> > That's what 'natural' is all about. Dodekaphony emerges naturally
> > from the series of natural numbers. Anything else is 'contrived',
> > which doesn't necessarily diminish its value, but which means it
just
> > ain't natural. Either you grok the node of the powers of 2 and 3
or
> > you don't. No one is forcing you.
> >
> > Peter
>
> You can use the word "natural" for anything you want Peter. But
please try
> to recognize when you are having an opinion. See Carl's post which
preceeds
> mine. In spite of what you say, in "natural" I hear a value
judgement
> "better".

Kurt

I am pretty precise in my use of words. I did not name the 'series of
natural numbers' nonetheless that is what it is called. It
is 'natural' for water to seek a level. It is 'natural' for entropy
to increase. These are things that just simply happen in 'nature'.
You are wrong to impute false meanings to my words. The rest of
what you said here can safely be ignored.

Peter

> If not then why not choose or invent other terms which actually
> elucicate the particular strengths of Dodekaphony so you are not
forced to
> hijack the generic term "natural" for your own purposes. However,
if you
> are nice, maybe you will earn an entry in Monz's dictionary defining
> Sault-natural. ;) For example see Lumma stability.
>
> You could just say instead, such-and-such has the following
qualities, or
> perhaps even the following strengths. Such words are unpretentious
and are
> helpful to everyone, particularly if you have found out something
new.
>
> Meanwhile I tend to have the *suspicion* that everything you are
saying
> about Dodekaphony amounts to a single equation in Gene's collection
of
> thousands. Once you learn the language that is used here, and
realize the
> breadth of experience that has been touched by this community, I
will be
> really interested to hear what you have to say about Dodekaphony
that is not
> old news.
>
> -Kurt

>> >That's what 'natural' is all about. Dodekaphony emerges naturally
>> >from the series of natural numbers. Anything else is 'contrived',
>> >which doesn't necessarily diminish its value, but which means it
>> >just ain't natural. Either you grok the node of the powers of 2
>> > and 3 or you don't. No one is forcing you.
>>
>> There are other nodes of the powers of 2 and 3, such as 17, 19, 29,
>> 31, 41, 53. . . But there are also other measures of goodness which
>> may be more appropriate, especially beyond the 3-limit, and if you
>> pay very close attention around here you might learn about some of
>> them.
>>
>> -Carl
>
>What do you mean by 'node' here, Carl?
>
>Peter

Near coincidences of the series of base-2 and base-3 numbers. I
thought that's what you meant...

-Carl

Nothing in natural numbers insists on twelve. Twelve is not a holy grail. Of course you are entitled to your thoughts - you are thinking them. But to make the assertion that whoever does not believe you is also wrong, a charlatan, and worse is a failing of the greatest order.

12 is merely the result of pythagoranism. 81/64 is necessarily a worse consonance than 5/4. Better still look at an oscilloscope with sine waves combined in the two proportions.

I have studied acoustics to degree level, and been introduced to psychoacoustics. Sorry Peter, but thousands of studies into the relationships between tones etc are not wrong. Take a look at JASA, and you will see what I mean.

Mark

on 12/14/03 7:57 AM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@c...> wrote:
>>
>>> --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:

>>>> I still don't accept that the 'natural' basis of music should
>>> limit
>>>> its gamut to 12 pitch-classes.
>>>>
>>>> M
>>>
>>> Hi Mark
>>>
>>> That's what 'natural' is all about. Dodekaphony emerges naturally
>>> from the series of natural numbers. Anything else is 'contrived',
>>> which doesn't necessarily diminish its value, but which means it
> just
>>> ain't natural. Either you grok the node of the powers of 2 and 3
> or
>>> you don't. No one is forcing you.
>>>
>>> Peter
>>
>> You can use the word "natural" for anything you want Peter. But
> please try
>> to recognize when you are having an opinion. See Carl's post which
> preceeds
>> mine. In spite of what you say, in "natural" I hear a value
> judgement
>> "better".
>
> Kurt
>
> I am pretty precise in my use of words. I did not name the 'series of
> natural numbers' nonetheless that is what it is called. It
> is 'natural' for water to seek a level. It is 'natural' for entropy
> to increase. These are things that just simply happen in 'nature'.
> You are wrong to impute false meanings to my words. The rest of
> what you said here can safely be ignored.
>
> Peter

Natural numbers are either postive integers, or non-negative integers,
depending on the source and the context. There is nothing special about 12
here.

Ok, I'll bite. You are apparently thinking *something*. So maybe its time
for a guessing game. 12 is a very nice number yes. It probably divides by
more things evenly than any other number before it, while not having gotten
too large yet.

Am I getting warmer?

-Kurt

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 12/14/03 7:57 AM, Peter Wakefield Sault <sault@c...> wrote:
>
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >> on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@c...> wrote:
> >>
> >>> --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...>
wrote:
>
> >>>> I still don't accept that the 'natural' basis of music should
> >>> limit
> >>>> its gamut to 12 pitch-classes.
> >>>>
> >>>> M
> >>>
> >>> Hi Mark
> >>>
> >>> That's what 'natural' is all about. Dodekaphony emerges
naturally
> >>> from the series of natural numbers. Anything else
is 'contrived',
> >>> which doesn't necessarily diminish its value, but which means it
> > just
> >>> ain't natural. Either you grok the node of the powers of 2 and 3
> > or
> >>> you don't. No one is forcing you.
> >>>
> >>> Peter
> >>
> >> You can use the word "natural" for anything you want Peter. But
> > please try
> >> to recognize when you are having an opinion. See Carl's post
which
> > preceeds
> >> mine. In spite of what you say, in "natural" I hear a value
> > judgement
> >> "better".
> >
> > Kurt
> >
> > I am pretty precise in my use of words. I did not name
the 'series of
> > natural numbers' nonetheless that is what it is called. It
> > is 'natural' for water to seek a level. It is 'natural' for
entropy
> > to increase. These are things that just simply happen in 'nature'.
> > You are wrong to impute false meanings to my words. The rest of
> > what you said here can safely be ignored.
> >
> > Peter
>
> Natural numbers are either postive integers, or non-negative
integers,
> depending on the source and the context. There is nothing special
about 12
> here.
>
> Ok, I'll bite. You are apparently thinking *something*. So maybe
its time
> for a guessing game. 12 is a very nice number yes. It probably
divides by
> more things evenly than any other number before it, while not
having gotten
> too large yet.
>
> Am I getting warmer?
>
> -Kurt

Hi Kurt

You are at the South Pole in a t-shirt. You can read the whole story,
which I am not about to reproduce here, at
http://www.odeion.org/atlantis/chapter-1.html

The pattern described is unique to the primes 2 and 3 and does not
occur between any other pair except 2 and 5 which itself reinforces
the augmented triad (interval classes 0, 4 and 8). Natural numbers
may be considered an abstraction of harmonics.

Peter

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> >That's what 'natural' is all about. Dodekaphony emerges
naturally
> >> >from the series of natural numbers. Anything else
is 'contrived',
> >> >which doesn't necessarily diminish its value, but which means it
> >> >just ain't natural. Either you grok the node of the powers of 2
> >> > and 3 or you don't. No one is forcing you.
> >>
> >> There are other nodes of the powers of 2 and 3, such as 17, 19,
29,
> >> 31, 41, 53. . . But there are also other measures of goodness
which
> >> may be more appropriate, especially beyond the 3-limit, and if
you
> >> pay very close attention around here you might learn about some
of
> >> them.
> >>
> >> -Carl
> >
> >What do you mean by 'node' here, Carl?
> >
> >Peter
>
> Near coincidences of the series of base-2 and base-3 numbers. I
> thought that's what you meant...
>
> -Carl

Thanks Carl

I just wanted to be sure we were on the same planet. And the series
of powers of 2 and 3, aside from perfect coincidence at unity, do not
come any closer than the 19th power of 2 and the 12th power of 3. So
the 18th power of 2 and the 12th power of 3 are very nearly an octave
apart. Here the mysterious beauty deepens because although 18 and 12
are the respective exponents of 2 and 3, 18 = 2 x 3^2 and 12 = 2^2 x
3. So this 'octave' spans 2^(2 x 3^2) and 3^(2^2 x 3). Anyone could
be forgiven for thinking that this is "all twos and threes". And of
course the only doubly-perfect number would have to be 6, wouldn't it?

peter

on 12/14/03 1:39 PM, Kurt Bigler <kkb@breathsense.com> wrote:

> on 12/14/03 7:57 AM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:
>
>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>>> on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@c...> wrote:
>>>
>>>> --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
>
>>> You can use the word "natural" for anything you want Peter. But
>> please try
>>> to recognize when you are having an opinion. See Carl's post which
>> preceeds
>>> mine. In spite of what you say, in "natural" I hear a value
>> judgement
>>> "better".
>>
>> Kurt
>>
>> I am pretty precise in my use of words. I did not name the 'series of
>> natural numbers' nonetheless that is what it is called. It
>> is 'natural' for water to seek a level. It is 'natural' for entropy
>> to increase. These are things that just simply happen in 'nature'.
>> You are wrong to impute false meanings to my words. The rest of
>> what you said here can safely be ignored.
>>
>> Peter
>
> Natural numbers are either postive integers, or non-negative integers,
> depending on the source and the context. There is nothing special about 12
> here.
>
> Ok, I'll bite. You are apparently thinking *something*. So maybe its time
> for a guessing game. 12 is a very nice number yes. It probably divides by
> more things evenly than any other number before it, while not having gotten
> too large yet.
>
> Am I getting warmer?
>
> -Kurt
>

Peter,

To further clarify. Lest you take my comments above to be facetious, I was
looking for an intuitive way into the question of what you are talking
about, so the "getting warmer" approach I was hoping might work as a way of
getting us into the ballpark.

It appears to me that you have made a conjecture, that you are sure of it,
and it seems clear that most of the participating community here considers
it to be an undemonstrated conjecture. In that position I think the
responsibility still lies with you to clarify your conjecture, rather than
continuing to refer to it with no further clarification. Your approach so
far has not worked to elucidate anything to us so it would appear that you
have some underlying assumption or reference that is entirely unfamiliar to
the rest of us in spite of being somehow obvious to you.

By the way, I hear the words "The rest of what you said here can safely be
ignored" as dismissive, and I understand being dismissive as a mild form of
agression. This is consistent with what it is to "ignore" someone. You may
not have meant that, and my take on the connotation may seem absurd to you.
In fact perhaps some of my frustration and anger leaked into my message to
which you responded, and I would have been better to acknowledge that
frustration up front. So perhaps I started it by my indirectness.

But for now I don't know of a way to avoid the fact that you are in the
minority, and that by convention the responsibility lies with you to
demonstrate your point about how the word "natural" has a particular
relation to the number "12". Anything further references to it on your part
without further clarification are fruitless, as I see it.

So let me ask another question to try to help the process. Are you
referring to a "naturalness" - something that might be a matter of degree
(and might refer to a function which reaches a maximum at the number 12), or
is it simply a matter of "natural or not" - something that is black and
white?

-Kurt

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
> Nothing in natural numbers insists on twelve. Twelve is not a holy
> grail. Of course you are entitled to your thoughts - you are
thinking
> them. But to make the assertion that whoever does not believe you
is
> also wrong, a charlatan, and worse is a failing of the greatest
order.
>
> 12 is merely the result of pythagoranism. 81/64 is necessarily a
worse
> consonance than 5/4. Better still look at an oscilloscope with sine
> waves combined in the two proportions.
>
> I have studied acoustics to degree level, and been introduced to
> psychoacoustics. Sorry Peter, but thousands of studies into the
> relationships between tones etc are not wrong. Take a look at JASA,
and
> you will see what I mean.
>
> Mark

What I see here is that "There are none so blind as those who will
not see" (English proverb).

What I see here is that you are joining in the sport of gang-
slandering and -libelling Peter Sault with lies and deceits. I have
at no time accused anyone of being a charlatan. However, you are
coming close to earning that title for yourself without any help from
me.

Peter

Peter

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 12/14/03 1:39 PM, Kurt Bigler <kkb@b...> wrote:
>
> > on 12/14/03 7:57 AM, Peter Wakefield Sault <sault@c...> wrote:
> >
> >> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >>> on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@c...> wrote:
> >>>
> >>>> --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...>
wrote:
> >
> >>> You can use the word "natural" for anything you want Peter. But
> >> please try
> >>> to recognize when you are having an opinion. See Carl's post
which
> >> preceeds
> >>> mine. In spite of what you say, in "natural" I hear a value
> >> judgement
> >>> "better".
> >>
> >> Kurt
> >>
> >> I am pretty precise in my use of words. I did not name
the 'series of
> >> natural numbers' nonetheless that is what it is called. It
> >> is 'natural' for water to seek a level. It is 'natural' for
entropy
> >> to increase. These are things that just simply happen
in 'nature'.
> >> You are wrong to impute false meanings to my words. The rest of
> >> what you said here can safely be ignored.
> >>
> >> Peter
> >
> > Natural numbers are either postive integers, or non-negative
integers,
> > depending on the source and the context. There is nothing
special about 12
> > here.
> >
> > Ok, I'll bite. You are apparently thinking *something*. So
maybe its time
> > for a guessing game. 12 is a very nice number yes. It probably
divides by
> > more things evenly than any other number before it, while not
having gotten
> > too large yet.
> >
> > Am I getting warmer?
> >
> > -Kurt
> >
>
> Peter,
>
> To further clarify. Lest you take my comments above to be
facetious, I was
> looking for an intuitive way into the question of what you are
talking
> about, so the "getting warmer" approach I was hoping might work as
a way of
> getting us into the ballpark.
>
> It appears to me that you have made a conjecture, that you are sure
of it,
> and it seems clear that most of the participating community here
considers
> it to be an undemonstrated conjecture. In that position I think the
> responsibility still lies with you to clarify your conjecture,
rather than
> continuing to refer to it with no further clarification. Your
approach so
> far has not worked to elucidate anything to us so it would appear
that you
> have some underlying assumption or reference that is entirely
unfamiliar to
> the rest of us in spite of being somehow obvious to you.
>
> By the way, I hear the words "The rest of what you said here can
safely be
> ignored" as dismissive, and I understand being dismissive as a mild
form of
> agression.

Kurt

You are getting increasingly paranoid and risk losing the respect
that you had previously earned from me. It was *you* who accused me
of equivocation, putting words into my mouth that I had not spoken.
If you choose to ignore the explanations that I have presented to you
rather than deal with them that does not make me wrong - it makes you
an ass. Again I will point you to
http://www.odeion.org/atlantis/chapter-1.html
If you can find any fault in that with regard to the generation of
dodekaphony I would be pleased to hear about it. Otherwise you are
just playing the game of being deliberately obtuse. At some point you
will become what you pretend to be. It is the fate of all liars to
lose the distinction between lies and truth and to get caught out by
an even bigger liar than themselves. You should beware of falling
into that trap because I don't think there is any way out of it.

Peter

This is consistent with what it is to "ignore" someone. You may
> not have meant that, and my take on the connotation may seem absurd
to you.
> In fact perhaps some of my frustration and anger leaked into my
message to
> which you responded, and I would have been better to acknowledge
that
> frustration up front. So perhaps I started it by my indirectness.
>
> But for now I don't know of a way to avoid the fact that you are in
the
> minority, and that by convention the responsibility lies with you to
> demonstrate your point about how the word "natural" has a particular
> relation to the number "12". Anything further references to it on
your part
> without further clarification are fruitless, as I see it.
>
> So let me ask another question to try to help the process. Are you
> referring to a "naturalness" - something that might be a matter of
degree
> (and might refer to a function which reaches a maximum at the
number 12), or
> is it simply a matter of "natural or not" - something that is black
and
> white?
>
> -Kurt

on 12/14/03 3:23 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 12/14/03 1:39 PM, Kurt Bigler <kkb@b...> wrote:
>>
>>> on 12/14/03 7:57 AM, Peter Wakefield Sault <sault@c...> wrote:
>>>
>>>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>>>>> on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@c...> wrote:
>>>>>
>>>>>> --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...>
> wrote:
>>>
>>>>> You can use the word "natural" for anything you want Peter. But
>>>> please try
>>>>> to recognize when you are having an opinion. See Carl's post
> which
>>>> preceeds
>>>>> mine. In spite of what you say, in "natural" I hear a value
>>>> judgement
>>>>> "better".
>>>>
>>>> Kurt
>>>>
>>>> I am pretty precise in my use of words. I did not name
> the 'series of
>>>> natural numbers' nonetheless that is what it is called. It
>>>> is 'natural' for water to seek a level. It is 'natural' for
> entropy
>>>> to increase. These are things that just simply happen
> in 'nature'.
>>>> You are wrong to impute false meanings to my words. The rest of
>>>> what you said here can safely be ignored.
>>>>
>>>> Peter
>>>
>>> Natural numbers are either postive integers, or non-negative
> integers,
>>> depending on the source and the context. There is nothing
> special about 12
>>> here.
>>>
>>> Ok, I'll bite. You are apparently thinking *something*. So
> maybe its time
>>> for a guessing game. 12 is a very nice number yes. It probably
> divides by
>>> more things evenly than any other number before it, while not
> having gotten
>>> too large yet.
>>>
>>> Am I getting warmer?
>>>
>>> -Kurt
>>>
>>
>> Peter,
>>
>> To further clarify. Lest you take my comments above to be
> facetious, I was
>> looking for an intuitive way into the question of what you are
> talking
>> about, so the "getting warmer" approach I was hoping might work as
> a way of
>> getting us into the ballpark.
>>
>> It appears to me that you have made a conjecture, that you are sure
> of it,
>> and it seems clear that most of the participating community here
> considers
>> it to be an undemonstrated conjecture. In that position I think the
>> responsibility still lies with you to clarify your conjecture,
> rather than
>> continuing to refer to it with no further clarification. Your
> approach so
>> far has not worked to elucidate anything to us so it would appear
> that you
>> have some underlying assumption or reference that is entirely
> unfamiliar to
>> the rest of us in spite of being somehow obvious to you.
>>
>> By the way, I hear the words "The rest of what you said here can
> safely be
>> ignored" as dismissive, and I understand being dismissive as a mild
> form of
>> agression.
>
> Kurt
>
> You are getting increasingly paranoid and risk losing the respect
> that you had previously earned from me. It was *you* who accused me
> of equivocation, putting words into my mouth that I had not spoken.
> If you choose to ignore the explanations that I have presented to you
> rather than deal with them that does not make me wrong - it makes you
> an ass. Again I will point you to
> http://www.odeion.org/atlantis/chapter-1.html

My apologies. I had forgotten about this, had not read it at the time, and
then completely misplaced its very existence. It looks like in this case I
was making more trouble for everyone, since even others had read this. So I
was speaking out of an unnecessary confusion.

It is a good lesson for me, and appropriate that it should come at this
time.

> If you can find any fault in that with regard to the generation of
> dodekaphony I would be pleased to hear about it. Otherwise you are
> just playing the game of being deliberately obtuse.

No not that I hope.

> At some point you
> will become what you pretend to be.

Yes, may I pretend well then. And I trust that your admonition about liars
is a warning and not yet an accusation.

-Kurt

> It is the fate of all liars to
> lose the distinction between lies and truth and to get caught out by
> an even bigger liar than themselves. You should beware of falling
> into that trap because I don't think there is any way out of it.
>
> Peter
>
>
> This is consistent with what it is to "ignore" someone. You may
>> not have meant that, and my take on the connotation may seem absurd
> to you.
>> In fact perhaps some of my frustration and anger leaked into my
> message to
>> which you responded, and I would have been better to acknowledge
> that
>> frustration up front. So perhaps I started it by my indirectness.
>>
>> But for now I don't know of a way to avoid the fact that you are in
> the
>> minority, and that by convention the responsibility lies with you to
>> demonstrate your point about how the word "natural" has a particular
>> relation to the number "12". Anything further references to it on
> your part
>> without further clarification are fruitless, as I see it.
>>
>> So let me ask another question to try to help the process. Are you
>> referring to a "naturalness" - something that might be a matter of
> degree
>> (and might refer to a function which reaches a maximum at the
> number 12), or
>> is it simply a matter of "natural or not" - something that is black
> and
>> white?
>>
>> -Kurt

>Thanks Carl
>
>I just wanted to be sure we were on the same planet. And the series
>of powers of 2 and 3, aside from perfect coincidence at unity, do not
>come any closer than the 19th power of 2 and the 12th power of 3.

Let's start with this; it's wrong, whether you measure the absolute
difference between the series or the difference 'per 3'. Measuring
the difference 'per 3' is equivalent to asking about the quality of
approximation to 3:2 in an arbitrary equal temperament. The smallest
equal temperament with better fifths than 12-tET is 29-tET. Verify
that...

3^12 / 2^19 ~ 1.0136432647705078
12th-root-of(1.0136432647705078) ~ 1.0011298906275257

2^46 / 3^29 ~ 1.0253294077568411
29th-root-of(1.0253294077568411) ~ 1.0008629215642235

To find a smaller absolute difference we can go to 41...

2^65 / 3^41 ~ 1.0115288518086085

I would expect improvements in both 'per 3' and absolute differences
to continue as the series goes to infinity, and I'm suspect Gene could
rattle out a proof of that in a few minutes. If I didn't have to
meet a friend now, I'd start by making an analogy with Euclid's proof
that there are infinitely many primes.

-Carl

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> on 12/14/03 3:23 PM, Peter Wakefield Sault <sault@c...> wrote:
>
> > --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >> on 12/14/03 1:39 PM, Kurt Bigler <kkb@b...> wrote:
> >>
> >>> on 12/14/03 7:57 AM, Peter Wakefield Sault <sault@c...> wrote:
> >>>
> >>>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
> >>>>> on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@c...> wrote:
> >>>>>
> >>>>>> --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...>
> > wrote:
> >>>
> >>>>> You can use the word "natural" for anything you want Peter.
But
> >>>> please try
> >>>>> to recognize when you are having an opinion. See Carl's post
> > which
> >>>> preceeds
> >>>>> mine. In spite of what you say, in "natural" I hear a value
> >>>> judgement
> >>>>> "better".
> >>>>
> >>>> Kurt
> >>>>
> >>>> I am pretty precise in my use of words. I did not name
> > the 'series of
> >>>> natural numbers' nonetheless that is what it is called. It
> >>>> is 'natural' for water to seek a level. It is 'natural' for
> > entropy
> >>>> to increase. These are things that just simply happen
> > in 'nature'.
> >>>> You are wrong to impute false meanings to my words. The rest of
> >>>> what you said here can safely be ignored.
> >>>>
> >>>> Peter
> >>>
> >>> Natural numbers are either postive integers, or non-negative
> > integers,
> >>> depending on the source and the context. There is nothing
> > special about 12
> >>> here.
> >>>
> >>> Ok, I'll bite. You are apparently thinking *something*. So
> > maybe its time
> >>> for a guessing game. 12 is a very nice number yes. It probably
> > divides by
> >>> more things evenly than any other number before it, while not
> > having gotten
> >>> too large yet.
> >>>
> >>> Am I getting warmer?
> >>>
> >>> -Kurt
> >>>
> >>
> >> Peter,
> >>
> >> To further clarify. Lest you take my comments above to be
> > facetious, I was
> >> looking for an intuitive way into the question of what you are
> > talking
> >> about, so the "getting warmer" approach I was hoping might work
as
> > a way of
> >> getting us into the ballpark.
> >>
> >> It appears to me that you have made a conjecture, that you are
sure
> > of it,
> >> and it seems clear that most of the participating community here
> > considers
> >> it to be an undemonstrated conjecture. In that position I think
the
> >> responsibility still lies with you to clarify your conjecture,
> > rather than
> >> continuing to refer to it with no further clarification. Your
> > approach so
> >> far has not worked to elucidate anything to us so it would appear
> > that you
> >> have some underlying assumption or reference that is entirely
> > unfamiliar to
> >> the rest of us in spite of being somehow obvious to you.
> >>
> >> By the way, I hear the words "The rest of what you said here can
> > safely be
> >> ignored" as dismissive, and I understand being dismissive as a
mild
> > form of
> >> agression.
> >
> > Kurt
> >
> > You are getting increasingly paranoid and risk losing the respect
> > that you had previously earned from me. It was *you* who accused
me
> > of equivocation, putting words into my mouth that I had not
spoken.
> > If you choose to ignore the explanations that I have presented to
you
> > rather than deal with them that does not make me wrong - it makes
you
> > an ass. Again I will point you to
> > http://www.odeion.org/atlantis/chapter-1.html
>
> My apologies. I had forgotten about this, had not read it at the
time, and
> then completely misplaced its very existence. It looks like in
this case I
> was making more trouble for everyone, since even others had read
this. So I
> was speaking out of an unnecessary confusion.
>

Apology accepted. You have shot back up the respect scale and have
rung the bell at the top. Your prize is my apology for being a
cantankerous old fool. Hopefully I will mellow out and become more
like you. We are all fighting over Helen of Troy when we should be
throwing her to the army.

> It is a good lesson for me, and appropriate that it should come at
this
> time.
>
> > If you can find any fault in that with regard to the generation of
> > dodekaphony I would be pleased to hear about it. Otherwise you are
> > just playing the game of being deliberately obtuse.
>
> No not that I hope.
>
> > At some point you
> > will become what you pretend to be.
>
> Yes, may I pretend well then. And I trust that your admonition
about liars
> is a warning and not yet an accusation.
>
> -Kurt
>
> > It is the fate of all liars to
> > lose the distinction between lies and truth and to get caught out
by
> > an even bigger liar than themselves. You should beware of falling
> > into that trap because I don't think there is any way out of it.
> >
> > Peter
> >
> >
> > This is consistent with what it is to "ignore" someone. You may
> >> not have meant that, and my take on the connotation may seem
absurd
> > to you.
> >> In fact perhaps some of my frustration and anger leaked into my
> > message to
> >> which you responded, and I would have been better to acknowledge
> > that
> >> frustration up front. So perhaps I started it by my
indirectness.
> >>
> >> But for now I don't know of a way to avoid the fact that you are
in
> > the
> >> minority, and that by convention the responsibility lies with
you to
> >> demonstrate your point about how the word "natural" has a
particular
> >> relation to the number "12". Anything further references to it
on
> > your part
> >> without further clarification are fruitless, as I see it.
> >>
> >> So let me ask another question to try to help the process. Are
you
> >> referring to a "naturalness" - something that might be a matter
of
> > degree
> >> (and might refer to a function which reaches a maximum at the
> > number 12), or
> >> is it simply a matter of "natural or not" - something that is
black
> > and
> >> white?
> >>
> >> -Kurt

hi Peter and Carl,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > Thanks Carl
> >
> > I just wanted to be sure we were on the same planet.
> > And the series of powers of 2 and 3, aside from perfect
> > coincidence at unity, do not come any closer than the
> > 19th power of 2 and the 12th power of 3.
>
> Let's start with this; it's wrong, whether you measure
> the absolute difference between the series or the
> difference 'per 3'. Measuring the difference 'per 3'
> is equivalent to asking about the quality of approximation
> to 3:2 in an arbitrary equal temperament. The smallest
> equal temperament with better fifths than 12-tET is 29-tET.
> Verify that...
>
> 3^12 / 2^19 ~ 1.0136432647705078
> 12th-root-of(1.0136432647705078) ~ 1.0011298906275257
>
> 2^46 / 3^29 ~ 1.0253294077568411
> 29th-root-of(1.0253294077568411) ~ 1.0008629215642235
>
> To find a smaller absolute difference we can go to 41...
>
> 2^65 / 3^41 ~ 1.0115288518086085
>
> I would expect improvements in both 'per 3' and absolute
> differences to continue as the series goes to infinity,
> and I'm suspect Gene could rattle out a proof of that in
> a few minutes. If I didn't have to meet a friend now,
> I'd start by making an analogy with Euclid's proof
> that there are infinitely many primes.

i took Peter's comment to refer to the Pythagorean comma.

if the series of powers of 2s and 3s is continued, there
is a smaller comma at 3^53, known as "Mercator's comma",
and a tiny one at 3^665, the "satanic comma".

http://tonalsoft.com/enc/pythag.htm

-monz

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Thanks Carl
> >
> >I just wanted to be sure we were on the same planet. And the
series
> >of powers of 2 and 3, aside from perfect coincidence at unity, do
not
> >come any closer than the 19th power of 2 and the 12th power of 3.
>
> Let's start with this; it's wrong, whether you measure the absolute
> difference between the series or the difference 'per 3'. Measuring
> the difference 'per 3' is equivalent to asking about the quality of
> approximation to 3:2 in an arbitrary equal temperament. The
smallest
> equal temperament with better fifths than 12-tET is 29-tET. Verify
> that...
>
> 3^12 / 2^19 ~ 1.0136432647705078
> 12th-root-of(1.0136432647705078) ~ 1.0011298906275257
>
> 2^46 / 3^29 ~ 1.0253294077568411
> 29th-root-of(1.0253294077568411) ~ 1.0008629215642235
>

Whoa Carl! You are introducing an extra operation into the procedure.
What's with taking the 12th root of the pythagorean comma and the
29th root of the analog?

Also, it does not follow that this leads only to ET. One could
equally well have 29-JI.

> To find a smaller absolute difference we can go to 41...
>
> 2^65 / 3^41 ~ 1.0115288518086085
>

I see you are absolutely right. So (2^19 / 3^12) is simply the second
node (taking unity as the first). What I would like to know is - how
close do the two series have to come for the ratio to be considered a
node? What criterion can be applied to that? Is it purely subjective
or is there some physical law at the root of it? I'm not sure a 41-
fret guitar would be playable, nor a 41 keys/8ve clavier, so perhaps
it's just a practical consideration.

> I would expect improvements in both 'per 3' and absolute differences
> to continue as the series goes to infinity, and I'm suspect Gene
could
> rattle out a proof of that in a few minutes. If I didn't have to
> meet a friend now, I'd start by making an analogy with Euclid's
proof
> that there are infinitely many primes.

So we should divide the octave into an infinite number of intervals.
At least white noise does not contain any detectable discords. Shhhh -
if you don't tell anyone, I won't either. Just give me a snare and a
brush...

>
> -Carl

>> > I just wanted to be sure we were on the same planet.
>> > And the series of powers of 2 and 3, aside from perfect
>> > coincidence at unity, do not come any closer than the
>> > 19th power of 2 and the 12th power of 3.
>>
>> Let's start with this; it's wrong, whether you measure
>> the absolute difference between the series or the
>> difference 'per 3'. Measuring the difference 'per 3'
>> is equivalent to asking about the quality of approximation
>> to 3:2 in an arbitrary equal temperament. The smallest
>> equal temperament with better fifths than 12-tET is 29-tET.
>> Verify that...
>>
>> 3^12 / 2^19 ~ 1.0136432647705078
>> 12th-root-of(1.0136432647705078) ~ 1.0011298906275257
>>
>> 2^46 / 3^29 ~ 1.0253294077568411
>> 29th-root-of(1.0253294077568411) ~ 1.0008629215642235
>>
>> To find a smaller absolute difference we can go to 41...
>>
>> 2^65 / 3^41 ~ 1.0115288518086085
>>
>> I would expect improvements in both 'per 3' and absolute
>> differences to continue as the series goes to infinity,
>> and I'm suspect Gene could rattle out a proof of that in
>> a few minutes. If I didn't have to meet a friend now,
>> I'd start by making an analogy with Euclid's proof
>> that there are infinitely many primes.
>
>
>
>i took Peter's comment to refer to the Pythagorean comma.

Right, that's 1.0136432647705078.

>if the series of powers of 2s and 3s is continued, there
>is a smaller comma at 3^53, known as "Mercator's comma",
>and a tiny one at 3^665, the "satanic comma".
>
>http://tonalsoft.com/enc/pythag.htm

You only need to go to 41 to find a smaller comma. Is
there a name for it?

-Carl

>>>And the series of powers of 2 and 3, aside from perfect coincidence
>>>at unity, do not come any closer than the 19th power of 2 and the
>>>12th power of 3.
>>
>>Let's start with this; it's wrong, whether you measure the absolute
>>difference between the series or the difference 'per 3'. Measuring
>>the difference 'per 3' is equivalent to asking about the quality of
>>approximation to 3:2 in an arbitrary equal temperament. The
>>smallest equal temperament with better fifths than 12-tET is 29-tET.
>>Verify that...
>>
>>3^12 / 2^19 ~ 1.0136432647705078
>>12th-root-of(1.0136432647705078) ~ 1.0011298906275257
>>
>>2^46 / 3^29 ~ 1.0253294077568411
>>29th-root-of(1.0253294077568411) ~ 1.0008629215642235
>
>Whoa Carl! You are introducing an extra operation into the procedure.
>What's with taking the 12th root of the pythagorean comma and the
>29th root of the analog?

That's the 'per 3' difference. It may not be what you're interested
in, but it gives the error of the 5th in the associated equal
temperament, by dividing the comma up over all the fifths in the
system.

>Also, it does not follow that this leads only to ET. One could
>equally well have 29-JI.

My point exactly! Your paradigm of justifying the 12-tone system
could *very well* be applied to another number of tones. I'm not
saying you *should* do this -- it looks like you've got a good
thing going with what you're up to -- but it would be equally as
"natural" as 12.

>> To find a smaller absolute difference we can go to 41...
>>
>> 2^65 / 3^41 ~ 1.0115288518086085
>
>I see you are absolutely right. So (2^19 / 3^12) is simply the second
>node (taking unity as the first). What I would like to know is - how
>close do the two series have to come for the ratio to be considered a
>node? What criterion can be applied to that?

It seems natural to look for successive improvements, where each
node must be at a closer coincidence than the last. Another option
is to 'penalize' by the number of tones in the system, and one could
in principle make a penalty so stiff that only 12 seems acceptable...
but since composers who've tried larger systems seem to have such
great results (to my ear), I cannot conceive of musical justification
for such a stiff penalty.

>Is it purely subjective or is there some physical law at the root of
>it? I'm not sure a 41-fret guitar would be playable, nor a 41
>keys/8ve clavier, so perhaps it's just a practical consideration.

There have been 41-tone clavier designs put forth, and I never
cease to be amazed at what musicians can do. That said, as a
clavier player myself I intend to focus on 31 tones and fewer.

A pipe organ with 31 tones have been proven playable by Fokker
and the Dutch 31-toners. A harpsichord with 29 tones has been
proven playable by Norman Henry.

Try this link...

http://www.xs4all.nl/~huygensf/english/instrum.html

Now this...

http://lumma.org/tuning/norman_henry.jpg

And this will give you an idea of how the notes can be laid
out on one of these babies...

http://lumma.org/tuning/carlos_keyboard.jpg

>> I would expect improvements in both 'per 3' and absolute differences
>> to continue as the series goes to infinity, and I'm suspect Gene
>> could rattle out a proof of that in a few minutes. If I didn't have
>> to meet a friend now, I'd start by making an analogy with Euclid's
>> proof that there are infinitely many primes.
>
>So we should divide the octave into an infinite number of intervals.
>At least white noise does not contain any detectable discords. Shhhh -
>if you don't tell anyone, I won't either. Just give me a snare and a
>brush...

It's an embarrassment of riches, we know. It's our biggest problem
around here. Searching out all these systems and trying to figure
out which ones would be most fruitful musically has been the goal
of many of the 49,000 messages here. Any one of these systems might
take a lifetime to master.

While we've come up with many fascinating results, your dodekaphonic
system is doing pretty well, in my estimation. Therefore if you like
it, you might as well continue full-speed ahead, knowing that you have
my full theoretical blessing.

-Carl

on 12/14/03 3:54 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>> on 12/14/03 3:23 PM, Peter Wakefield Sault <sault@c...> wrote:
>>
>>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>>>> on 12/14/03 1:39 PM, Kurt Bigler <kkb@b...> wrote:
>>>>
>>>>> on 12/14/03 7:57 AM, Peter Wakefield Sault <sault@c...> wrote:
>>>>>
>>>>>> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>>>>>>> on 12/13/03 5:17 PM, Peter Wakefield Sault <sault@c...> wrote:
>>>>>>>
>>>>>>>> --- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...>
>>> wrote:
>>>>>
>>>>>>> You can use the word "natural" for anything you want Peter.
> But
>>>>>> please try
>>>>>>> to recognize when you are having an opinion. See Carl's post
>>> which
>>>>>> preceeds
>>>>>>> mine. In spite of what you say, in "natural" I hear a value
>>>>>> judgement
>>>>>>> "better".
>>>>>>
>>>>>> Kurt
>>>>>>
>>>>>> I am pretty precise in my use of words. I did not name
>>> the 'series of
>>>>>> natural numbers' nonetheless that is what it is called. It
>>>>>> is 'natural' for water to seek a level. It is 'natural' for
>>> entropy
>>>>>> to increase. These are things that just simply happen
>>> in 'nature'.
>>>>>> You are wrong to impute false meanings to my words. The rest of
>>>>>> what you said here can safely be ignored.
>>>>>>
>>>>>> Peter
>>>>>
>>>>> Natural numbers are either postive integers, or non-negative
>>> integers,
>>>>> depending on the source and the context. There is nothing
>>> special about 12
>>>>> here.
>>>>>
>>>>> Ok, I'll bite. You are apparently thinking *something*. So
>>> maybe its time
>>>>> for a guessing game. 12 is a very nice number yes. It probably
>>> divides by
>>>>> more things evenly than any other number before it, while not
>>> having gotten
>>>>> too large yet.
>>>>>
>>>>> Am I getting warmer?
>>>>>
>>>>> -Kurt
>>>>>
>>>>
>>>> Peter,
>>>>
>>>> To further clarify. Lest you take my comments above to be
>>> facetious, I was
>>>> looking for an intuitive way into the question of what you are
>>> talking
>>>> about, so the "getting warmer" approach I was hoping might work
> as
>>> a way of
>>>> getting us into the ballpark.
>>>>
>>>> It appears to me that you have made a conjecture, that you are
> sure
>>> of it,
>>>> and it seems clear that most of the participating community here
>>> considers
>>>> it to be an undemonstrated conjecture. In that position I think
> the
>>>> responsibility still lies with you to clarify your conjecture,
>>> rather than
>>>> continuing to refer to it with no further clarification. Your
>>> approach so
>>>> far has not worked to elucidate anything to us so it would appear
>>> that you
>>>> have some underlying assumption or reference that is entirely
>>> unfamiliar to
>>>> the rest of us in spite of being somehow obvious to you.
>>>>
>>>> By the way, I hear the words "The rest of what you said here can
>>> safely be
>>>> ignored" as dismissive, and I understand being dismissive as a
> mild
>>> form of
>>>> agression.
>>>
>>> Kurt
>>>
>>> You are getting increasingly paranoid and risk losing the respect
>>> that you had previously earned from me. It was *you* who accused
> me
>>> of equivocation, putting words into my mouth that I had not
> spoken.
>>> If you choose to ignore the explanations that I have presented to
> you
>>> rather than deal with them that does not make me wrong - it makes
> you
>>> an ass. Again I will point you to
>>> http://www.odeion.org/atlantis/chapter-1.html
>>
>> My apologies. I had forgotten about this, had not read it at the
> time, and
>> then completely misplaced its very existence. It looks like in
> this case I
>> was making more trouble for everyone, since even others had read
> this. So I
>> was speaking out of an unnecessary confusion.
>>
>
>
> Apology accepted. You have shot back up the respect scale and have
> rung the bell at the top. Your prize is my apology for being a
> cantankerous old fool. Hopefully I will mellow out and become more
> like you. We are all fighting over Helen of Troy when we should be
> throwing her to the army.

I appreciate this and I do wish to continue to earn respect from everyone.
Of course I can not treat your respect scale as an absolute. But I
appreciate your apology and also the humor in it.

If I am going to be offering anything pertaining to clarifying communication
I feel a responsibility bordering on the need to be impeccable. Having made
the mistake I made I have for the moment lost the inclination to give
further input in that vein, until I can be sure again of my own clarity.

-Kurt

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> You are at the South Pole in a t-shirt. You can read the whole
story,
> which I am not about to reproduce here, at
> http://www.odeion.org/atlantis/chapter-1.html
>
> The pattern described is unique to the primes 2 and 3 and does not
> occur between any other pair except 2 and 5 which itself reinforces
> the augmented triad (interval classes 0, 4 and 8). Natural numbers
> may be considered an abstraction of harmonics.

I can find nothing relevant in this chapter. I suggest you either say
what you have to say, giving an argument with specifics, or at least
tell us what the relevant sections are, and why they are relevant.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> A pipe organ with 31 tones have been proven playable by Fokker
> and the Dutch 31-toners.

We hardly needed Fokker to show that; we have centuries of music
which is much better descibed as music for 31-et than music for 12-et,
after all. And no, I'm not getting cranky about Bach. :)

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > You are at the South Pole in a t-shirt. You can read the whole
> story,
> > which I am not about to reproduce here, at
> > http://www.odeion.org/atlantis/chapter-1.html
> >
> > The pattern described is unique to the primes 2 and 3 and does
not
> > occur between any other pair except 2 and 5 which itself
reinforces
> > the augmented triad (interval classes 0, 4 and 8). Natural
numbers
> > may be considered an abstraction of harmonics.
>
> I can find nothing relevant in this chapter. I suggest you either
say
> what you have to say, giving an argument with specifics, or at
least
> tell us what the relevant sections are, and why they are relevant.

Relevant to what, Gene? The South Pole?

Peter

HI everyone. This is mostly for Peter, but I'd hope everyone will
work to clarify the issue at hand.

I been following the discussions and I've read Peter's page, and
I'd like to make this *preliminary* observation:

If we simply delete from the discussion all phrases that are not
directly applicable to understanding something music related,
there seems to still be some confusion. I think Peter's writings
put a possibly unique perspective on the details of 12-tone,
although everyone here already understands the basis of
12-tone scales. Peter's assertion that 12-tone is natural is
certainly not debateable. The assertion however that it is the
only or the ultimate "natural" scale is what is being argued about.

Peter, it seems to me that your site explains very well the strong
argument for 12-tone music. However, there is nothing on your
site that disproves any claim for other tunings to also be
considered "natural." As I see it, various people have both made
such claims as well as provided evidence supporting them. So,
Peter, your next step should be to see if you can DISPROVE the
claims for various other tunings being "natural."

I will say on my part that a good portion of the microtonal stuff I've
heard sounds "unnatural" to me. As I've heard microtonal music
that I've liked that seemed natural as well, my conclusion is that
whatever I hear as "natural" has more to do with the composer's
care in choosing pitch relations over time than with what limit or
what scales end up being used throughout a piece.

"Natural" needs to be defined as to what is meant by the word,
and what qualifies a music system as "natural."

Peter, it'd be great for you to attempt to disprove the "natural"
claim for other tunings like 19-tet, or heptatonic or pentatonic
scales etc. There is a gigantic amount of information available
online about all these different tuning issues. If you actually have
evidence that some scales don't work quite as people have
claimed, it would be a great help to everyone for you to make
such evidence available. But evidence of the significance of
12-tone is simply not evidence *against* other tunings...

Also, maybe I missed it, but is there somewhere that you've
described the actual method used in odien for selecting related
notes?

Thanks,
Aaron Wolf

>> A pipe organ with 31 tones have been proven playable by Fokker
>> and the Dutch 31-toners.
>
>We hardly needed Fokker to show that; we have centuries of music
>which is much better descibed as music for 31-et than music for 12-et,
>after all. And no, I'm not getting cranky about Bach. :)

*Playable*, Gene. The tuning works of course, but the issue of
a workable performance devise is different.

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> I would expect improvements in both 'per 3' and absolute differences
> to continue as the series goes to infinity, and I'm suspect Gene could
> rattle out a proof of that in a few minutes.

Probably it is true that for any k>0,
|log2(3)-p/q| < 1/kq^2 has an infinity of solutions, but the trick for
a mathematician is proving it. Normal people, or physicists, can
assume it. Values of k which are "Lagrange numbers" take us up to k=3,
but this isn't quite good enough to show there are an infinity of q's
beating 12 out. On the other hand, it isn't known if log2(3) has an
irrationality measure greater than 2, which would mean for some d>2 we
would have an infinity of solutions to |log2(3)-p/q|<1/q^d, which
would clean 12's clock quite thouroughly. I wouldn't bank on it.

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...> wrote:

> Relevant to what, Gene? The South Pole?

Relevant to you claim that 12 is tops. You have neither defined what
this claim means, nor supported it with a real argument. If you ever
do, we can discuss it.

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:

Hello Aaron

> HI everyone. This is mostly for Peter, but I'd hope everyone will
> work to clarify the issue at hand.
>
> I been following the discussions and I've read Peter's page, and
> I'd like to make this *preliminary* observation:
>
> If we simply delete from the discussion all phrases that are not
> directly applicable to understanding something music related,
> there seems to still be some confusion. I think Peter's writings
> put a possibly unique perspective on the details of 12-tone,
> although everyone here already understands the basis of
> 12-tone scales. Peter's assertion that 12-tone is natural is
> certainly not debateable. The assertion however that it is the
> only or the ultimate "natural" scale is what is being argued about.
>

That has been cleared up by the discussion of 'nodes' of the series
of powers of 2 and 3. I was previously under the false impression
that the closest values of the two series occurred at 3^12 and 2^19.
Although I have not yet analysed the other nodes (3^41, 3^53 etc.)
for analogous behaviour I will do so just as soon as I get the chance
(in the next month or two I hope).

> Peter, it seems to me that your site explains very well the strong
> argument for 12-tone music. However, there is nothing on your
> site that disproves any claim for other tunings to also be
> considered "natural." As I see it, various people have both made
> such claims as well as provided evidence supporting them. So,
> Peter, your next step should be to see if you can DISPROVE the
> claims for various other tunings being "natural."
>

See my above comment and bear in mind that my primary reason for
describing the derivation of dodekaphony is to demonstrate that it is
non-arbitrary and is in itself the derivation of the Babylonian unit
of rotation, or degree of angle, and also of the minute of time. I
have yet to hear anything which is non-dodekaphonic which moves me in
the way that a good classical symphony does. This may be only because
no one has yet written a symphony for any other division of the
octave. I await the 41-tone Beethoven. So dodekaphony may well
be 'natural' in the sense that it is more keyed into our emotional
responses but here and now we can only speculate.

> I will say on my part that a good portion of the microtonal stuff
I've
> heard sounds "unnatural" to me. As I've heard microtonal music
> that I've liked that seemed natural as well, my conclusion is that
> whatever I hear as "natural" has more to do with the composer's
> care in choosing pitch relations over time than with what limit or
> what scales end up being used throughout a piece.
>

Here we do need to distinguish between pleasing to the ear in an
absolute sense and, on the other hand, as a result of
enculturation. 'Natural' intervals comprising ratios of small whole
numbers seem to qualify in the absolute sense. ET seems to require a
degree of enculturation, or 'getting used to'. It is almost
impossible for us to judge this impartially because we have all been
exposed to 12-ET from an early age.

> "Natural" needs to be defined as to what is meant by the word,
> and what qualifies a music system as "natural."
>
> Peter, it'd be great for you to attempt to disprove the "natural"
> claim for other tunings like 19-tet, or heptatonic or pentatonic
> scales etc. There is a gigantic amount of information available
> online about all these different tuning issues. If you actually
have
> evidence that some scales don't work quite as people have
> claimed, it would be a great help to everyone for you to make
> such evidence available. But evidence of the significance of
> 12-tone is simply not evidence *against* other tunings...
>
> Also, maybe I missed it, but is there somewhere that you've
> described the actual method used in odien for selecting related
> notes?
>

The method is what I call the 'Rule of the Natural Aesthetic',
or 'Path of Natural Intervals'. It may well be equally applicable to
other pitch sets such as 41-JI and 53-JI. I have yet to perform a
full numerical analysis of these alternate systems to discover the
extent to which they too possess a large number of 'correlative
intervals'. The easiest way to understand correlative intervals is to
download my Natural Dodekaphonic Interval Correlator (for Windows
only I am afraid). You can download the installer from:-
http://www.odeion.org/atlantis/natural2.html
This program comes with extensive Help.

The Rule of the Natural Aesthetic depends on the presence of
correlative intervals within a scale. Briefly, a correlative interval
is one between any two pitches, neither of which is the tonic, which
is numerically interval to an interval of the defining set. The
defining set is that specified from the tonic. In ET all intervals
are correlative, so this system only works using JI intervals. A
melody or chord which follows this rule only combines notes whose
relative interval is correlative. All other melodic motion of chord
structures are forbidden.

It has been pointed out to me that I enforce 'inversion symmetry' in
my system and I am planning to allow that to be switchable and will
let everyone know when a new version of the Correlator is available.
I will also make the program extendable to the higher analogs such as
JI-41 and JI-53. We will then see if they are more or less 'natural'
than 12-JI. Using the definitive set
1:1
15:16
8:9
5:6
4:5
3:4
45:64 & 32:45 (i.e. dim5th and aug4th in place of a single tritone)
2:3
5:8
3:5
9:16
8:15
1:2
gives rise to 44 correlative intervals, from a total of 66 relative
intervals. So 2/3 exactly of the intervals are correlative. An
example of a correlative interval is that between pitch 3 and pitch
8, interval class 5 which evaluates to 3:4 which is a definitive
interval as listed above. An example of an irrelative (i.e. non-
correlative) interval is that between pitch 3 and pitch 10. This is
interval class 7 and evaluates to 27:40, which is absent from the set
of definitive intervals. Thus, following the Rule, no melodic motion
can ever take place in either direction between pitches 3 and 10 and
no chord can contain both notes. In ODEION I extend this to include
alternate as well as immediate melodic relations such that, for any
given note of a melody, the preceding note must relate to the
following note in like manner.

If this system turns out also to work with JI-41 or JI-53 etc. then
we have a general case. If not then it means that 12-JI truly is
unique (within this system) because it is a special case with no
higher analog.

> Thanks,
> Aaron Wolf

My pleasure and thankyou for your interest.

Peter S.

hi Peter,

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> I have yet to hear anything which is non-dodekaphonic
> which moves me in the way that a good classical symphony
> does. This may be only because no one has yet written
> a symphony for any other division of the octave.
> I await the 41-tone Beethoven.

after less than a week, you've already forgotton my posts
(directed at you) about Mozart intending his orchestral
music to be tuned to a 19- or 20-tone subset of 55edo?

/tuning/topicId_49031.html#49281
/tuning/topicId_49031.html#49406

you responded that you found my webpage "opaque", but
you never said a word about the audio example of the
beginning of Mozart's 40th (G-minor) Symphony in 55edo.

> > "Natural" needs to be defined as to what is meant by the
> > word, and what qualifies a music system as "natural."
> >
> > Peter, it'd be great for you to attempt to disprove the
> > "natural" claim for other tunings like 19-tet, or
> > heptatonic or pentatonic scales etc. There is a gigantic
> > amount of information available online about all these
> > different tuning issues. If you actually have evidence
> > that some scales don't work quite as people have claimed,
> > it would be a great help to everyone for you to make
> > such evidence available. But evidence of the significance
> > of 12-tone is simply not evidence *against* other tunings...
> >
> > Also, maybe I missed it, but is there somewhere that you've
> > described the actual method used in odien for selecting
> > related notes?
> >
>
>
> The method is what I call the 'Rule of the Natural Aesthetic',
> or 'Path of Natural Intervals'. It may well be equally
> applicable to other pitch sets such as 41-JI and 53-JI.
> I have yet to perform a full numerical analysis of these
> alternate systems to discover the extent to which they too
> possess a large number of 'correlative intervals'. The
> easiest way to understand correlative intervals is to
> download my Natural Dodekaphonic Interval Correlator
> (for Windows only I am afraid). You can download the
> installer from:-
> http://www.odeion.org/atlantis/natural2.html
> This program comes with extensive Help.
>
> <snip>
>
> If this system turns out also to work with JI-41 or JI-53 etc.
> then we have a general case. If not then it means that
> 12-JI truly is unique (within this system) because it
> is a special case with no higher analog.

since you're speaking about JI systems, it seems to me that
what you're doing has ties to Fokker's periodicity-block
theory. you'd probably benefit from Paul Erlich's tutorial
on that, which begins here:

http://tonalsoft.com/td/erlich/intropblock1.htm

utilizing a specific set of unison-vectors, if one arranges
the monzos of those unison-vectors in a matrix, the determinant
of that matrix gives the area (= number of pitches) in the
JI periodicity-block.

there's been a *vast* amount of work done on this subject
on the tuning-math list over the last two years.

-monz

hi Peter,

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

> since you're speaking about JI systems, it seems to me that
> what you're doing has ties to Fokker's periodicity-block
> theory. you'd probably benefit from Paul Erlich's tutorial
> on that, which begins here:
>
> http://tonalsoft.com/td/erlich/intropblock1.htm
>
>
> utilizing a specific set of unison-vectors, if one arranges
> the monzos of those unison-vectors in a matrix, the determinant
> of that matrix gives the area (= number of pitches) in the
> JI periodicity-block.
>
> there's been a *vast* amount of work done on this subject
> on the tuning-math list over the last two years.

you may find these definitions useful:

http://tonalsoft.com/enc/uvector.htm
http://tonalsoft.com/enc/monzo.htm
http://tonalsoft.com/enc/matrix.htm
http://tonalsoft.com/enc/determ.htm

-monz

--- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...> wrote:

> The Rule of the Natural Aesthetic depends on the presence of
> correlative intervals within a scale. Briefly, a correlative interval
> is one between any two pitches, neither of which is the tonic,
which
> is numerically interval to an interval of the defining set. The
> defining set is that specified from the tonic. In ET all intervals
> are correlative, so this system only works using JI intervals. A
> melody or chord which follows this rule only combines notes
whose
> relative interval is correlative. All other melodic motion of chord
> structures are forbidden.
>
> It has been pointed out to me that I enforce 'inversion
symmetry' in
> my system and I am planning to allow that to be switchable
and will
> let everyone know when a new version of the Correlator is
available.
> I will also make the program extendable to the higher analogs
such as
> JI-41 and JI-53. We will then see if they are more or less
'natural'
> than 12-JI. Using the definitive set
> 1:1
> 15:16
> 8:9
> 5:6
> 4:5
> 3:4
> 45:64 & 32:45 (i.e. dim5th and aug4th in place of a single
tritone)
> 2:3
> 5:8
> 3:5
> 9:16
> 8:15
> 1:2
> gives rise to 44 correlative intervals, from a total of 66 relative
> intervals. So 2/3 exactly of the intervals are correlative. An
> example of a correlative interval is that between pitch 3 and
pitch
> 8, interval class 5 which evaluates to 3:4 which is a definitive
> interval as listed above. An example of an irrelative (i.e. non-
> correlative) interval is that between pitch 3 and pitch 10. This is
> interval class 7 and evaluates to 27:40, which is absent from
the set
> of definitive intervals. Thus, following the Rule, no melodic
motion
> can ever take place in either direction between pitches 3 and
10 and
> no chord can contain both notes. In ODEION I extend this to
include
> alternate as well as immediate melodic relations such that, for
any
> given note of a melody, the preceding note must relate to the
> following note in like manner.

Peter, first, unfortunately I have a Mac and can't use your
program. Anyway, I think I am understanding, but let me ask a
question to clarify...

By stating correlative as "numerically interval to an interval of the
defining set" do you mean only those intervals such as exist in
the set from tonic?
I must be missing something, because it would seem from what
I am reading that you could not move from the second scale
degree (pitch 9/8 in the scale) to the third degree (pitch 5/4)
because the interval of 9:10 is not in the defining set. Is this
correct?? That movement is a pretty common and basic
movement in a lot of music, from what I understand...

Aaron

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:

> Peter, it seems to me that your site explains very well the strong
> argument for 12-tone music.

Where? I can find no such argument.

I would like Mr Sault's view on two things:

1. Erno Lendvai's theories based on a symmetric 12 tone universe based on the solmisation tone 'Re'.

Erno Lendvai: Symmetries of Music, Kodaly Institute, Kecksemet, 1993

2. THe Golden Section, and where it fits into his theories. IIRC the parthenon has many golden section properties built into it, and it is regarded as a ratio of some importance, but the only composer to have made systematic use of it is Bartok, whose music forms the basis for much of Lendvai's ideas.

I won't give my opinion of Lendvai's work, as I would like your opinion, Peter, unbiased...

Mark

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...>
wrote:
> I would like Mr Sault's view on two things:
>
> 1. Erno Lendvai's theories based on a symmetric 12 tone
universe based
> on the solmisation tone 'Re'.
>
> Erno Lendvai: Symmetries of Music, Kodaly Institute,
Kecksemet, 1993
>
> 2. THe Golden Section, and where it fits into his theories. IIRC
the
> parthenon has many golden section properties built into it, and
it is
> regarded as a ratio of some importance, but the only
composer to have
> made systematic use of it is Bartok, whose music forms the
basis for
> much of Lendvai's ideas.
>
> I won't give my opinion of Lendvai's work, as I would like your
> opinion, Peter, unbiased...
>
> Mark

Mark, to say Bartok is the *only* composer to systematically use
the golden mean is a bit hasty. In addition to the probability that
it has been used more recently by various composers, I know for
a fact that Debussy worked the golden mean into many aspects
of some of his compositions.

-Aaron

--- In tuning@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "backfromthesilo"
> <backfromthesilo@y...> wrote:
>
> > Peter, it seems to me that your site explains very well the
strong
> > argument for 12-tone music.
>
> Where? I can find no such argument.

Gene, I am referring to the fact that his site has various
information showing the mathematical origins of an essentially
12-note system and also its stability both musically and
mathematically. I know his discussion is not complete in that
regard but it is certainly there. What is lacking is any discussion
of how that relates to it being any *more* stable or musically
valuable when compared to other systems, as there are no
mentions of any other systems on his site at all.

Peter, in addition to your new exploration of higher number
tunings like 53, what do you think about music that confines itself
to less than 12 notes, such as pentatonic or heptatonic scales?
Do you think they are less "natural?" or perhaps do you think they
represent an incomplete but functional subset of 12-note
scales? (If the latter, then when you find 53 to be a working
number, couldn't the same be said about 12 as a subset of 53?)
I'm not claiming anything here, just trying to get a more complete
understanding of your ideas by asking questions. I'll refrain from
directly challenging your ideas until I feel I actually know what
they are.

Aaron

--- In tuning@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "backfromthesilo"
> <backfromthesilo@y...> wrote:
>
> > Peter, it seems to me that your site explains very well the
strong
> > argument for 12-tone music.
>
> Where? I can find no such argument.

Gene, I am referring to the fact that his site has various
information showing the mathematical origins of an essentially
12-note system and also its stability both musically and
mathematically. I know his discussion is not complete in that
regard but it is certainly there. What is lacking is any discussion
of how that relates to it being any *more* stable or musically
valuable when compared to other systems, as there are no
mentions of any other systems on his site at all.

Peter, in addition to your new exploration of higher number
tunings like 53, what do you think about music that confines itself
to less than 12 notes, such as pentatonic or heptatonic scales?
Do you think they are less "natural?" or perhaps do you think they
represent an incomplete but functional subset of 12-note
scales? (If the latter, then when you find 53 to be a working
number, couldn't the same be said about 12 as a subset of 53?)
I'm not claiming anything here, just trying to get a more complete
understanding of your ideas by asking questions. I'll refrain from
directly challenging your ideas until I feel I actually know what
they are.

Aaron

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:

> Gene, I am referring to the fact that his site has various
> information showing the mathematical origins of an essentially
> 12-note system and also its stability both musically and
> mathematically. I know his discussion is not complete in that
> regard but it is certainly there.

Sorry to be dense, but I'm not finding it. I find a remark that
checking harmonics up to the seventh does not force a 12 note scale,
which is true. I find a remark that the Pythagorean comma is not
large, and a discussion of the 12 note Pythagorean scale. Does this
relate in some manner to "stability", and what, pray tell, is
stability?

What is lacking is any discussion
> of how that relates to it being any *more* stable or musically
> valuable when compared to other systems, as there are no
> mentions of any other systems on his site at all.

There's no mention of anything much which favors 12 either. There
simply does not seem to be the promised argument. While people have
been assuming that smaller 3-limit commas are better, Sault never
says so, and personally I see a lot to be said for a Pythagorean
scale of 17 notes. Where's the beef?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> While people have
> been assuming that smaller 3-limit commas are better, Sault never
> says so, and personally I see a lot to be said for a Pythagorean
> scale of 17 notes. Where's the beef?

Why might one favor 17-note Pythagorean, which involves a
semiconvergent, but not a convergent, of log2(3) and whose comma is
therefore not as small as the Pythagorean comma?

The 3-limit comma for 17 is c17 = 2^27/3^17, of size 66.765 cents. If
we take its continued fraction, we find 26/25 is a convergent, which
is nice if we want to go to the 13-limit; however 25/24 still is only
two schismas sharper, which is perhaps even nicer. The 17-note
Pythagorean has a wolf fifth of 2^26/3^16, two schismas flatter than
25/16, giving us an excellent augmented triad compounded of two major
thirds each flat by a schisma. It also has eight major triads with the
thirds flat a schisma, and the corresponding eight minor triads with
thirds sharp by a schisma. It even has a some decent septimal
intervals and chords, belonging to septimal schismic with comma basis
225/224 and 3125/3087.

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
> <sault@c...> wrote:
>
> > The Rule of the Natural Aesthetic depends on the presence of
> > correlative intervals within a scale. Briefly, a correlative
interval
> > is one between any two pitches, neither of which is the tonic,
> which
> > is numerically interval to an interval of the defining set. The
> > defining set is that specified from the tonic. In ET all
intervals
> > are correlative, so this system only works using JI intervals. A
> > melody or chord which follows this rule only combines notes
> whose
> > relative interval is correlative. All other melodic motion of
chord
> > structures are forbidden.
> >
> > It has been pointed out to me that I enforce 'inversion
> symmetry' in
> > my system and I am planning to allow that to be switchable
> and will
> > let everyone know when a new version of the Correlator is
> available.
> > I will also make the program extendable to the higher analogs
> such as
> > JI-41 and JI-53. We will then see if they are more or less
> 'natural'
> > than 12-JI. Using the definitive set
> > 1:1
> > 15:16
> > 8:9
> > 5:6
> > 4:5
> > 3:4
> > 45:64 & 32:45 (i.e. dim5th and aug4th in place of a single
> tritone)
> > 2:3
> > 5:8
> > 3:5
> > 9:16
> > 8:15
> > 1:2
> > gives rise to 44 correlative intervals, from a total of 66
relative
> > intervals. So 2/3 exactly of the intervals are correlative. An
> > example of a correlative interval is that between pitch 3 and
> pitch
> > 8, interval class 5 which evaluates to 3:4 which is a definitive
> > interval as listed above. An example of an irrelative (i.e. non-
> > correlative) interval is that between pitch 3 and pitch 10. This
is
> > interval class 7 and evaluates to 27:40, which is absent from
> the set
> > of definitive intervals. Thus, following the Rule, no melodic
> motion
> > can ever take place in either direction between pitches 3 and
> 10 and
> > no chord can contain both notes. In ODEION I extend this to
> include
> > alternate as well as immediate melodic relations such that, for
> any
> > given note of a melody, the preceding note must relate to the
> > following note in like manner.
>
> Peter, first, unfortunately I have a Mac and can't use your
> program. Anyway, I think I am understanding, but let me ask a
> question to clarify...
>
> By stating correlative as "numerically interval to an interval of
the
> defining set" do you mean only those intervals such as exist in
> the set from tonic?
> I must be missing something, because it would seem from what
> I am reading that you could not move from the second scale
> degree (pitch 9/8 in the scale) to the third degree (pitch 5/4)
> because the interval of 9:10 is not in the defining set. Is this
> correct?? That movement is a pretty common and basic
> movement in a lot of music, from what I understand...
>
> Aaron

Hi Aaron

Your understanding is correct on both points. The exclusion of that
step (II to III) remains even if the defining interval itself is
changed to 9:10, as the step from II to III then becomes 8:9.
Nevertheless, that is the rule employed by the ODEION program
in 'Natural Mode' which gave rise to the piece called Natural No.1-
003. (ODEION has 3 modes of operation, which I called, rightly or
wrongly, 'Natural', 'Melodic' and 'Equal'. In 'Melodic', the
allowable steps are user selected and in 'Equal' all possible steps
are allowed. 'Melodic' works well with chordal scales - which amounts
to arpeggiating a chord and 'Equal' does not seem to produce anything
listenable).

Bear in mind as well that that piece in particular does not employ
the Natural Major scale but instead uses the Phrygian Dominant scale
which is identical to mode V of the Harmonic Minor scale. It auto-
modulates, moving the tonic to scale degree IV, whenever scale degree
IV (i.e. pitch class 5) occurs as the first note in a bar (=
US 'measure') in the 'Canto Firmo' (I use the term loosely and by
analogy) which role is held by the bass line in this particular piece.

I have yet to perform a full analysis to determine whether the piece
really is in the key that I, and the ODEION program, think it is in.
What I mean by this is that the actual tonic may not be degree I of
the Phyrygian Dominant scale. It could be that the true scale is in
fact the Harmonic Minor and that, therefore, the tonic actually lies
at what the program thinks is degree V of the Phrygian Dominant scale.

I have also found that ODEION works better (i.e. generates 'better'
melodies) with Mode II ('Dorian') of the Natural Major scale than it
does with Mode I ('Ionian'). This may be for the reason given above
or it may be because the 'Dorian Mode' is symmetrical in terms of the
contained 5ths. Once again, examples of this need tonal analysis to
discover what is really going on.

It is in some ways as much of a mystery to me as it must be to anyone.

Regards
Peter

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "backfromthesilo"
> <backfromthesilo@y...> wrote:
>
> > Peter, it seems to me that your site explains very well the
strong
> > argument for 12-tone music.
>
> Where? I can find no such argument.

Hi Gene

I think the best argument of all is the infectious nature of
dodekaphony. It may well be a case of simple things pleasing simple
minds but, at risk of sounding patronizing towards humanity in
general, simple minds are in the majority. We all have a simple-
minded side. If you do not, which may well be possible, then you are
in a very small and lonely minority. Perhaps the world's acknowledged
best composers were only playing to the crowd - but whatever their
motive they have always stuck to a roughly logarithmic 12-tone
division of the 8ve. Stockhausen, on the other hand, has disappeared
into the depths of obscurity and is of interest only to hardcore
musicologists (myself excluded).

While I do not deny that other possibilities exist, trying to get
people off dodekaphony is a bit like banning alcohol or, for that
matter, maryjane. Ban it and people will gather together in secret to
indulge in it. I cannot imagine that happening for music created with
obscure and esoteric divisions of the 8ve.

Also please note that the central purpose of my analysis titled 'The
Ring of Truth' is not to 'prove' that dodekaphony is the be-all and
end-all of civilization but to demonstrate that symmetric JI is the
most likely source of the Babylonian degree of angle and the Vedic
minute of time and that by extension 360-day solar calendars are
secondary derivations. The ODEION program is merely a spin-off. That
ODEION can produce listenable melodic structures, which just about
everyone else here has concluded for themselves, should give you food
for thought.

Peter

--- In tuning@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:
> I would like Mr Sault's view on two things:
>
> 1. Erno Lendvai's theories based on a symmetric 12 tone universe
based
> on the solmisation tone 'Re'.
>
> Erno Lendvai: Symmetries of Music, Kodaly Institute, Kecksemet, 1993
>
> 2. THe Golden Section, and where it fits into his theories. IIRC
the
> parthenon has many golden section properties built into it, and it
is
> regarded as a ratio of some importance, but the only composer to
have
> made systematic use of it is Bartok, whose music forms the basis
for
> much of Lendvai's ideas.
>
> I won't give my opinion of Lendvai's work, as I would like your
> opinion, Peter, unbiased...
>
> Mark

Hi Mark

I confess to complete ignorance of both Lendvai and his work. Can you
recommend a Web-based reference? In what way(s) did Bartok employ the
Golden Mean?

My personal analytical interest in the Parthenon begins and ends with
the stylobate, which is in proportion 4:9, or 2^2:3^2 and which,
therefore, is unconnected with phi. It is mere coincidence that
Pheidias' nickname was Phiphi. He was responsible solely for the
ornamental sculptures.

Peter

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > I have yet to hear anything which is non-dodekaphonic
> > which moves me in the way that a good classical symphony
> > does. This may be only because no one has yet written
> > a symphony for any other division of the octave.
> > I await the 41-tone Beethoven.
>
>
> after less than a week, you've already forgotton my posts
> (directed at you) about Mozart intending his orchestral
> music to be tuned to a 19- or 20-tone subset of 55edo?
>
> /tuning/topicId_49031.html#49281
> /tuning/topicId_49031.html#49406
>
>

No Joe - I have not forgotten. But you are referring to the tunings
that Mozart intended, not to the scales employed which was still
dodekaphonic by implication at least if the scales are diatonic. If
the music was written, and can be read, on standard staves then it
was dodekaphonic and no matter what tuning was intended for the
dodekaphony.

> you responded that you found my webpage "opaque", but
> you never said a word about the audio example of the
> beginning of Mozart's 40th (G-minor) Symphony in 55edo.
>
>

Your work is a vast and detailed treasure and will take quite a while
for me to assimilate, Joe. Forgive me my slowness, please.
My 'learning curve' is longer than most other peoples' because of the
demands which I place upon myself - I need to understand in the
deepest sense what is being described.

>
> > > "Natural" needs to be defined as to what is meant by the
> > > word, and what qualifies a music system as "natural."
> > >
> > > Peter, it'd be great for you to attempt to disprove the
> > > "natural" claim for other tunings like 19-tet, or
> > > heptatonic or pentatonic scales etc. There is a gigantic
> > > amount of information available online about all these
> > > different tuning issues. If you actually have evidence
> > > that some scales don't work quite as people have claimed,
> > > it would be a great help to everyone for you to make
> > > such evidence available. But evidence of the significance
> > > of 12-tone is simply not evidence *against* other tunings...
> > >
> > > Also, maybe I missed it, but is there somewhere that you've
> > > described the actual method used in odien for selecting
> > > related notes?
> > >
> >
> >
> > The method is what I call the 'Rule of the Natural Aesthetic',
> > or 'Path of Natural Intervals'. It may well be equally
> > applicable to other pitch sets such as 41-JI and 53-JI.
> > I have yet to perform a full numerical analysis of these
> > alternate systems to discover the extent to which they too
> > possess a large number of 'correlative intervals'. The
> > easiest way to understand correlative intervals is to
> > download my Natural Dodekaphonic Interval Correlator
> > (for Windows only I am afraid). You can download the
> > installer from:-
> > http://www.odeion.org/atlantis/natural2.html
> > This program comes with extensive Help.
> >
> > <snip>
> >
> > If this system turns out also to work with JI-41 or JI-53 etc.
> > then we have a general case. If not then it means that
> > 12-JI truly is unique (within this system) because it
> > is a special case with no higher analog.
>
>
>
> since you're speaking about JI systems, it seems to me that
> what you're doing has ties to Fokker's periodicity-block
> theory. you'd probably benefit from Paul Erlich's tutorial
> on that, which begins here:
>
> http://tonalsoft.com/td/erlich/intropblock1.htm
>
>
> utilizing a specific set of unison-vectors, if one arranges
> the monzos of those unison-vectors in a matrix, the determinant
> of that matrix gives the area (= number of pitches) in the
> JI periodicity-block.
>
> there's been a *vast* amount of work done on this subject
> on the tuning-math list over the last two years.
>
>

Firstly I need to learn your language, Joe, before I can absorb what
you are saying. The opacity (to me) of some of your work is rooted in
the fact that at present you may as well be speaking Klingon.

>
> -monz

Give me time and lots of it and I will understand what you are saying
in its fullness.

Peter

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Peter,
>
>
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > since you're speaking about JI systems, it seems to me that
> > what you're doing has ties to Fokker's periodicity-block
> > theory. you'd probably benefit from Paul Erlich's tutorial
> > on that, which begins here:
> >
> > http://tonalsoft.com/td/erlich/intropblock1.htm
> >
> >
> > utilizing a specific set of unison-vectors, if one arranges
> > the monzos of those unison-vectors in a matrix, the determinant
> > of that matrix gives the area (= number of pitches) in the
> > JI periodicity-block.
> >
> > there's been a *vast* amount of work done on this subject
> > on the tuning-math list over the last two years.
>
>
>
> you may find these definitions useful:
>
> http://tonalsoft.com/enc/uvector.htm
> http://tonalsoft.com/enc/monzo.htm
> http://tonalsoft.com/enc/matrix.htm
> http://tonalsoft.com/enc/determ.htm
>
>
>
> -monz

Would it make more sense were I to substitute 'rational'
for 'natural' in my little theory?

Peter

--- In tuning@yahoogroups.com, "backfromthesilo"
<backfromthesilo@y...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith"
> <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "backfromthesilo"
> > <backfromthesilo@y...> wrote:
> >
> > > Peter, it seems to me that your site explains very well the
> strong
> > > argument for 12-tone music.
> >
> > Where? I can find no such argument.
>
> Gene, I am referring to the fact that his site has various
> information showing the mathematical origins of an essentially
> 12-note system and also its stability both musically and
> mathematically. I know his discussion is not complete in that
> regard but it is certainly there. What is lacking is any
discussion
> of how that relates to it being any *more* stable or musically
> valuable when compared to other systems, as there are no
> mentions of any other systems on his site at all.
>
> Peter, in addition to your new exploration of higher number
> tunings like 53, what do you think about music that confines itself
> to less than 12 notes, such as pentatonic or heptatonic scales?
> Do you think they are less "natural?" or perhaps do you think they
> represent an incomplete but functional subset of 12-note
> scales? (If the latter, then when you find 53 to be a working
> number, couldn't the same be said about 12 as a subset of 53?)
> I'm not claiming anything here, just trying to get a more complete
> understanding of your ideas by asking questions. I'll refrain from
> directly challenging your ideas until I feel I actually know what
> they are.
>
> Aaron

Hi Aaron

Pentatonic and heptatonic scales are indeed subsets of dodekaphony.
One could contrive pentaphonic and heptaphonic ET scales as powers of
2^(1/5) and 2^(1/7) respectively but that is another matter.

The 'natural' pentatonic and heptatonic scales are incomplete series
of 5ths. The basic principle of dodekaphony is multiplexed 5ths.

Until I examine 53-phony more closely I cannot comment on which, if
any, intervals map to dodekaphony. Do you understand my concept of a
dodekaphonic virtual (i.e. numerical) comb filter? I must generate a
similar structure for 53-phony in order to find out whether there is
the possibility of common intervals.

Peter

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "backfromthesilo"
> <backfromthesilo@y...> wrote:
>
> > Gene, I am referring to the fact that his site has various
> > information showing the mathematical origins of an essentially
> > 12-note system and also its stability both musically and
> > mathematically. I know his discussion is not complete in that
> > regard but it is certainly there.
>
> Sorry to be dense, but I'm not finding it. I find a remark that
> checking harmonics up to the seventh does not force a 12 note
scale,
> which is true. I find a remark that the Pythagorean comma is not
> large, and a discussion of the 12 note Pythagorean scale. Does this
> relate in some manner to "stability", and what, pray tell, is
> stability?
>
> What is lacking is any discussion
> > of how that relates to it being any *more* stable or musically
> > valuable when compared to other systems, as there are no
> > mentions of any other systems on his site at all.
>
> There's no mention of anything much which favors 12 either. There
> simply does not seem to be the promised argument. While people have
> been assuming that smaller 3-limit commas are better, Sault never
> says so, and personally I see a lot to be said for a Pythagorean
> scale of 17 notes. Where's the beef?

Hi Gene

What's a "3-limit comma"?

Peter

on 12/15/03 3:17 PM, Peter Wakefield Sault <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>> hi Peter,
>>
>>
>> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
>> wrote:
>>
>>> I have yet to hear anything which is non-dodekaphonic
>>> which moves me in the way that a good classical symphony
>>> does. This may be only because no one has yet written
>>> a symphony for any other division of the octave.
>>> I await the 41-tone Beethoven.
>>
>>
>> after less than a week, you've already forgotton my posts
>> (directed at you) about Mozart intending his orchestral
>> music to be tuned to a 19- or 20-tone subset of 55edo?
>>
>> /tuning/topicId_49031.html#49281
>> /tuning/topicId_49031.html#49406
>>
>>
>
>
> No Joe - I have not forgotten. But you are referring to the tunings
> that Mozart intended, not to the scales employed which was still
> dodekaphonic by implication at least if the scales are diatonic. If
> the music was written, and can be read, on standard staves then it
> was dodekaphonic and no matter what tuning was intended for the
> dodekaphony.

That might not be quite true, but there are some ambiguities here. With the
use of accidentals including double-sharp and double-flat, you have the
possibility of 7 nominals times 5 accidental states (double-flat, flat,
natural, sharp, double-sharp), allowing 35 distinct tones to be identified
in a meantone system. For example in a sharp key signature a flat
accidental would permit explicit notation of what in other contexts is
called "the wolf", and I believe people have told me that Mozart did in fact
notate wolf intervals in this way in his music when he wanted them, but I do
not have the facts in my hands.

I think the mention of a 19- or 20-tone subset meant that that entire span
occured in a single piece, presumably even a single movement. It would be
interesting to know the largest tonal subset that occurs within a narrower
scope, perhaps even single measures. One might argue that if
enharmonically-equivalent accidentals do not occur in very close proximity
that dodekaphony still applies. I don't think I've ever seen data on this.

Perhaps Gene or some one has data available on this? The dodekaphony
question aside, I think this would clarify the broader implications of
Mozart's 55edo intention.

-Kurt

>>> after less than a week, you've already forgotton my posts
>>> (directed at you) about Mozart intending his orchestral
>>> music to be tuned to a 19- or 20-tone subset of 55edo?
>>>
>>> /tuning/topicId_49031.html#49281
>>> /tuning/topicId_49031.html#49406
>>>
>>
>> No Joe - I have not forgotten. But you are referring to the tunings
>> that Mozart intended, not to the scales employed

Indeed.

>> which was still
>> dodekaphonic by implication at least if the scales are diatonic.

How does diatonic imply dodekaphonic?

>> If the music was written, and can be read, on standard staves then
>> it was dodekaphonic and no matter what tuning was intended for the
>> dodekaphony.
>
>That might not be quite true, but there are some ambiguities here.
>With the use of accidentals including double-sharp and double-flat,
>you have the possibility of 7 nominals times 5 accidental states
>(double-flat, flat, natural, sharp, double-sharp), allowing 35
>distinct tones to be identified in a meantone system. //

But can you find a single piece of Mozart's music that uses them?

Mozart's music is firmly based on and in the diatonic scale. Much
of his music does not require 12 tones, and much of what does still
spends 90% of its time on the 7 notes of the diatonic key in which
it was scored.

Even in the 20th century there are very few composers who can truly
claim to be using a 12-tone *scale* (even counting serialists, who
are cheaters). The real comb filters of interest to Peter are
probably natural/rational versions of the scales composers use in
12-equal. See...

http://lumma.org/microwave/#2003.06.02

But since picking these out and figuring out how to tune chromatic
tones is a real bother, 12 would seem to be a good practical
minimum for an automatic "comb filter".

-Carl

on 12/15/03 5:40 PM, Carl Lumma <ekin@lumma.org> wrote:

>>>> after less than a week, you've already forgotton my posts
>>>> (directed at you) about Mozart intending his orchestral
>>>> music to be tuned to a 19- or 20-tone subset of 55edo?
>>>>
>>>> /tuning/topicId_49031.html#49281
>>>> /tuning/topicId_49031.html#49406
>>>>
>>>
>>> No Joe - I have not forgotten. But you are referring to the tunings
>>> that Mozart intended, not to the scales employed
>
> Indeed.
>
>>> which was still
>>> dodekaphonic by implication at least if the scales are diatonic.
>
> How does diatonic imply dodekaphonic?
>
>>> If the music was written, and can be read, on standard staves then
>>> it was dodekaphonic and no matter what tuning was intended for the
>>> dodekaphony.
>>
>> That might not be quite true, but there are some ambiguities here.
>> With the use of accidentals including double-sharp and double-flat,
>> you have the possibility of 7 nominals times 5 accidental states
>> (double-flat, flat, natural, sharp, double-sharp), allowing 35
>> distinct tones to be identified in a meantone system. //
>
> But can you find a single piece of Mozart's music that uses them?

Yes, that's exactly what I am asking.

> Mozart's music is firmly based on and in the diatonic scale. Much
> of his music does not require 12 tones, and much of what does still
> spends 90% of its time on the 7 notes of the diatonic key in which
> it was scored.

Well there is the thing about notating the wolf. More to the point: if in
fact an A# and a Bb occurred in the same measure that would be very
interesting to know.

> Even in the 20th century there are very few composers who can truly
> claim to be using a 12-tone *scale* (even counting serialists, who
> are cheaters). The real comb filters of interest to Peter are
> probably natural/rational versions of the scales composers use in
> 12-equal. See...
>
> http://lumma.org/microwave/#2003.06.02
>
> But since picking these out and figuring out how to tune chromatic
> tones is a real bother, 12 would seem to be a good practical
> minimum for an automatic "comb filter".
>
> -Carl

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> Until I examine 53-phony more closely I cannot comment on which, if
> any, intervals map to dodekaphony.

53 gives very much better approximations to your justly tuned
Dodekaphonic scale than 12 does. Isn't that what you want?

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> What's a "3-limit comma"?

In the sense I use the term, a rational number only a bit larger than
one, of the form 2^a 3^b where a and b are integers, considered as an
interval in music. The paradigm case is the Pythagorean comma.

--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> I think the mention of a 19- or 20-tone subset meant that that
entire span
> occured in a single piece, presumably even a single movement. It
would be
> interesting to know the largest tonal subset that occurs within a
narrower
> scope, perhaps even single measures.

I'm not understanding your question; you mean in Mozart? I'm not a
good person to ask, as I use midi files for scoring.

> > What's a "3-limit comma"?
>
> In the sense I use the term, a rational number only a bit larger
> than one, of the form 2^a 3^b where a and b are integers,
> considered as an interval in music. The paradigm case is the
> Pythagorean comma.

Well put, Gene. For the curios, a 5-limit comma would then be:

A rational number only a bit larger than 1, of the form
2^a 3^b 5^c where a, b and c are integers, considered as
an interval in music. The paradigm case is the Syntonic
comma (81/80).

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >>> after less than a week, you've already forgotton my posts
> >>> (directed at you) about Mozart intending his orchestral
> >>> music to be tuned to a 19- or 20-tone subset of 55edo?
> >>>
> >>> /tuning/topicId_49031.html#49281
> >>> /tuning/topicId_49031.html#49406
> >>>
> >>
> >> No Joe - I have not forgotten. But you are referring to the
tunings
> >> that Mozart intended, not to the scales employed
>
> Indeed.
>
> >> which was still
> >> dodekaphonic by implication at least if the scales are diatonic.
>
> How does diatonic imply dodekaphonic?

Hi Carl

It's the full chromatic scale which is dodekaphonic. Diatonic scales
are a subset of that. I think there is some confusion here - when I
say 'dodekaphonic' I am not referring to a type or style of music but
to a scale structure. It is possible to think of diatonic scales in
terms of the notes missing from the full chromatic.

>
> >> If the music was written, and can be read, on standard staves
then
> >> it was dodekaphonic and no matter what tuning was intended for
the
> >> dodekaphony.
> >
> >That might not be quite true, but there are some ambiguities here.
> >With the use of accidentals including double-sharp and double-flat,
> >you have the possibility of 7 nominals times 5 accidental states
> >(double-flat, flat, natural, sharp, double-sharp), allowing 35
> >distinct tones to be identified in a meantone system. //
>
> But can you find a single piece of Mozart's music that uses them?
>
> Mozart's music is firmly based on and in the diatonic scale. Much
> of his music does not require 12 tones, and much of what does still
> spends 90% of its time on the 7 notes of the diatonic key in which
> it was scored.
>

I don't think I was ever disputing that. See what I just said above.

> Even in the 20th century there are very few composers who can truly
> claim to be using a 12-tone *scale* (even counting serialists, who
> are cheaters). The real comb filters of interest to Peter are
> probably natural/rational versions of the scales composers use in
> 12-equal. See...
>
> http://lumma.org/microwave/#2003.06.02
>
> But since picking these out and figuring out how to tune chromatic
> tones is a real bother, 12 would seem to be a good practical
> minimum for an automatic "comb filter".

Again, by 'dodekaphonic comb filter' I do not mean something which
picks out certain notes to form either a melody or a diatonic scale.
The comb filter is a set of 12 equal passbands each the width of a
pythagorean comma. Those passpands determine the limits of ratios
that can be called dodekaphonic. The so-called 'harmonic 7th' (4:7)
is not and can never be a dodekaphonic pitch according to this scheme.

>
> -Carl

Peter

on 12/15/03 7:54 PM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> --- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:
>
>> I think the mention of a 19- or 20-tone subset meant that that
> entire span
>> occured in a single piece, presumably even a single movement. It
> would be
>> interesting to know the largest tonal subset that occurs within a
> narrower
>> scope, perhaps even single measures.
>
> I'm not understanding your question; you mean in Mozart? I'm not a
> good person to ask, as I use midi files for scoring.

Yes, Mozart. You popped out some nice data about chords in Chopin recently,
so I was hoping maybe you would know of a way to get this kind of info out
of a midi file.

-Kurt

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > Until I examine 53-phony more closely I cannot comment on which,
if
> > any, intervals map to dodekaphony.
>
> 53 gives very much better approximations to your justly tuned
> Dodekaphonic scale than 12 does. Isn't that what you want?

For me to generate a 53-phony analog of my model of dodekaphony I
must first define a 53-passband comb filter, where each passband is
the width of the 53-comma by mapping a series of 53 ascending 5ths
against a series of 53 descending 5ths. Now I already know that the
intervals of 53-ET will all pass through the filter. However, for 53-
JI I must firstly find ratios of whole numbers which will pass
through, and then I must find the particular combination of such
ratios which maximizes the number of correlative intervals. In the
case of 12-phony and the set of ratios which I have found maximize
this quantity, there are 44 intervals out of 66 which are
correlative. I have already modified my 12-phonic interval correlator
to allow assymmetric inversions, and when I use 5:6 for a minor 7th
(retaining 8:9 for a tone), the total number of correlative intervals
falls to 35. I am just now bringing the helpfile up to date and then
I will upload the installer for version 2.01 of the correlator.

Peter

hi Peter (and Carl and Kurt),

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >>> after less than a week, you've already forgotton my posts
> > >>> (directed at you) about Mozart intending his orchestral
> > >>> music to be tuned to a 19- or 20-tone subset of 55edo?
> > >>>
> > >>> /tuning/topicId_49031.html#49281
> > >>> /tuning/topicId_49031.html#49406
> > >>>
> > >>
> > >> No Joe - I have not forgotten. But you are referring to the
> tunings
> > >> that Mozart intended, not to the scales employed
> >
> > Indeed.
> >
> > >> which was still
> > >> dodekaphonic by implication at least if the scales are
diatonic.
> >
> > How does diatonic imply dodekaphonic?
>
>
> Hi Carl
>
> It's the full chromatic scale which is dodekaphonic.
> Diatonic scales are a subset of that. I think there is
> some confusion here - when I say 'dodekaphonic' I am not
> referring to a type or style of music but to a scale
> structure. It is possible to think of diatonic scales
> in terms of the notes missing from the full chromatic.

but the argument that Carl, Kurt, and myself are presenting
to you (Peter) is that Mozart, in his orchestral music
(not his keyboard works, which are 12-tone and well-tempered)
manifestly did *not* intend his 7-tone diatonic scales to be
subsets of a "dodekaphonic" (12-tone) gamut, but rather,
subsets of a 20-tone tuning in which flats differ from sharps,
which in turn was intended to be a subset of 55edo.

if you read my webpage in its entirety, including the
quotations from Attwood's notebooks, you'll see this.

you're trying to force Mozart's orchestral tuning into
your dodekaphonic straight-jacket and that's not what
it's supposed to be.

-monz

hi Peter and Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:

> --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
> <sault@c...> wrote:
>
> > Until I examine 53-phony more closely I cannot comment
> > on which, if any, intervals map to dodekaphony.
>
> 53 gives very much better approximations to your justly tuned
> Dodekaphonic scale than 12 does. Isn't that what you want?

in fact, 12edo does not give a good approximation to the
"natural" JI intervals at all, since it tempers out the
syntonic comma.

53 does indeed give an excellent approximation to 5-limit JI.

take a look at it here:

http://tonalsoft.com/enc/bingo.htm

-monz

>Would it make more sense were I to substitute 'rational'
>for 'natural' in my little theory?

Undoubtedly.

-C.

-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Dienstag, 16. Dezember 2003 06:59
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Dodekaphony

hi Peter (and Carl and Kurt),

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >>> after less than a week, you've already forgotton my posts
> > >>> (directed at you) about Mozart intending his orchestral
> > >>> music to be tuned to a 19- or 20-tone subset of 55edo?
> > >>>
> > >>> /tuning/topicId_49031.html#49281
> > >>> /tuning/topicId_49031.html#49406
> > >>>
> > >> No Joe - I have not forgotten. But you are referring to the
> tunings
> > >> that Mozart intended, not to the scales employed
> > Indeed.
> > >> which was still
> > >> dodekaphonic by implication at least if the scales are
diatonic.
> >
> > How does diatonic imply dodekaphonic?
>
> Hi Carl
>
> It's the full chromatic scale which is dodekaphonic.
> Diatonic scales are a subset of that. I think there is
> some confusion here - when I say 'dodekaphonic' I am not
> referring to a type or style of music but to a scale
> structure. It is possible to think of diatonic scales
> in terms of the notes missing from the full chromatic.

but the argument that Carl, Kurt, and myself are presenting
to you (Peter) is that Mozart, in his orchestral music
(not his keyboard works, which are 12-tone and well-tempered)
manifestly did *not* intend his 7-tone diatonic scales to be
subsets of a "dodekaphonic" (12-tone) gamut, but rather,
subsets of a 20-tone tuning in which flats differ from sharps,
which in turn was intended to be a subset of 55edo.

if you read my webpage in its entirety, including the
quotations from Attwood's notebooks, you'll see this.

you're trying to force Mozart's orchestral tuning into
your dodekaphonic straight-jacket and that's not what
it's supposed to be.

-monz

May it be allowed to say that Mozart had the idea of a special
tuning model in his mind when he was writing a composition?
Indeed, we have reasons to believe that he knew the possibilities and
limits
of contemporary keyboards which have been almost tuned near to. E.T., but:
He (as well as other composers) oftenly transcribed his compositions from
orchestra to piano, from piano to string quartet or harmony music and
inverse.
If his keyboard works "are 12 tone and well-tempered" every
transcribtion
would have been a treason to the "original work tuning idea".
Mozart would laugh at such ideas.
Or did I misunderstand something?

Werner

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--- In tuning@yahoogroups.com, Kurt Bigler <kkb@b...> wrote:

> Yes, Mozart. You popped out some nice data about chords in Chopin
recently,
> so I was hoping maybe you would know of a way to get this kind of
info out
> of a midi file.

I use a couple of freeware programs--midchord, followed by NoteTab
Lite to do the counting.

>Hi Carl
>
>It's the full chromatic scale which is dodekaphonic. Diatonic scales
>are a subset of that. I think there is some confusion here - when I
>say 'dodekaphonic' I am not referring to a type or style of music but
>to a scale structure.

Yes and I am disputing your claim that 'anything written on the
standard staff is dodekaphonic'.

>> Even in the 20th century there are very few composers who can truly
>> claim to be using a 12-tone *scale* (even counting serialists, who
>> are cheaters). The real comb filters of interest to Peter are
>> probably natural/rational versions of the scales composers use in
>> 12-equal. See...
>>
>> http://lumma.org/microwave/#2003.06.02
>>
>> But since picking these out and figuring out how to tune chromatic
>> tones is a real bother, 12 would seem to be a good practical
>> minimum for an automatic "comb filter".
>
>Again, by 'dodekaphonic comb filter' I do not mean something which
>picks out certain notes to form either a melody or a diatonic scale.
>The comb filter is a set of 12 equal passbands each the width of a
>pythagorean comma. Those passpands determine the limits of ratios
>that can be called dodekaphonic. The so-called 'harmonic 7th' (4:7)
>is not and can never be a dodekaphonic pitch according to this scheme.

Right, and I think it's a good scheme. One could do the same with the
syntonic comma and a 7-note scale...

-Carl

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
> -----Ursprüngliche Nachricht-----
> Von: monz [mailto:monz@a...]
> Gesendet: Dienstag, 16. Dezember 2003 06:59
> An: tuning@yahoogroups.com
> Betreff: [tuning] Re: Dodekaphony
>
>
> hi Peter (and Carl and Kurt),
>
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> wrote:
>
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > >>> after less than a week, you've already forgotton my posts
> > > >>> (directed at you) about Mozart intending his orchestral
> > > >>> music to be tuned to a 19- or 20-tone subset of 55edo?
> > > >>>
> > > >>> /tuning/topicId_49031.html#49281
> > > >>> /tuning/topicId_49031.html#49406
> > > >>>
> > > >> No Joe - I have not forgotten. But you are referring to the
> > tunings
> > > >> that Mozart intended, not to the scales employed
> > > Indeed.
> > > >> which was still
> > > >> dodekaphonic by implication at least if the scales are
> diatonic.
> > >
> > > How does diatonic imply dodekaphonic?
> >
> > Hi Carl
> >
> > It's the full chromatic scale which is dodekaphonic.
> > Diatonic scales are a subset of that. I think there is
> > some confusion here - when I say 'dodekaphonic' I am not
> > referring to a type or style of music but to a scale
> > structure. It is possible to think of diatonic scales
> > in terms of the notes missing from the full chromatic.
>
> but the argument that Carl, Kurt, and myself are presenting
> to you (Peter) is that Mozart, in his orchestral music
> (not his keyboard works, which are 12-tone and well-tempered)
> manifestly did *not* intend his 7-tone diatonic scales to be
> subsets of a "dodekaphonic" (12-tone) gamut, but rather,
> subsets of a 20-tone tuning in which flats differ from sharps,
> which in turn was intended to be a subset of 55edo.
>
> if you read my webpage in its entirety, including the
> quotations from Attwood's notebooks, you'll see this.
>
> you're trying to force Mozart's orchestral tuning into
> your dodekaphonic straight-jacket and that's not what
> it's supposed to be.
>
> -monz
>
> May it be allowed to say that Mozart had the idea of a
> special tuning model in his mind when he was writing a
> composition?
> Indeed, we have reasons to believe that he knew the
> possibilities and limits of contemporary keyboards which
> have been almost tuned near to. E.T., but:
> He (as well as other composers) oftenly transcribed his
> compositions from orchestra to piano, from piano to
> string quartet or harmony music and inverse.
> If his keyboard works "are 12 tone and well-tempered"
> every transcribtion would have been a treason to the
> "original work tuning idea". Mozart would laugh at such
> ideas.
> Or did I misunderstand something?

Mozart's teaching to Attwood clearly indicates that he
wanted 55edo as his tuning basis. the flats are supposed
to be "one comma" higher than their enharmonically equivalent
sharps.

if he really transcribed pieces from piano to orchestra,
then clearly he had a flexible view of intonation, because
the keyboard's 12-tone weel-temperament behaves differently
from the orchestra's 20-tone subset of 55edo.

there are also instances of enharmonic modulation in Mozart,
which also clearly indicates that in some instances, flats
and sharps in his compositions are supposed to be "the same".

(i'm not necessarily claiming that they are tuned to exactly
the same frequency, but the context of his usage indicates
equivalence.)

-monz

Hi Werner,

>May it be allowed to say that Mozart had the idea of a special
>tuning model in his mind when he was writing a composition?

Indeed, it may not. Mozart may simply have been less up-tight
about tuning as some of us here.

-Carl

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
>
> > What's a "3-limit comma"?
>
> In the sense I use the term, a rational number only a bit larger
than
> one, of the form 2^a 3^b where a and b are integers, considered as
an
> interval in music. The paradigm case is the Pythagorean comma.

Thanks for that, Gene. I'm still struggling to understand your
objections so you'll have to forgive me if I don't have an answer for
you yet.

Peter

-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Dienstag, 16. Dezember 2003 08:25
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
> -----Urspr�ngliche Nachricht-----
> Von: monz [mailto:monz@a...]
> Gesendet: Dienstag, 16. Dezember 2003 06:59
> An: tuning@yahoogroups.com
> Betreff: [tuning] Re: Dodekaphony
>
>
> hi Peter (and Carl and Kurt),
>
>
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault"
<sault@c...>
> wrote:
>
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > > >>> after less than a week, you've already forgotton my posts
> > > >>> (directed at you) about Mozart intending his orchestral
> > > >>> music to be tuned to a 19- or 20-tone subset of 55edo?
> > > >>>
> > > >>> /tuning/topicId_49031.html#49281
> > > >>> /tuning/topicId_49031.html#49406
> > > >>>
> > > >> No Joe - I have not forgotten. But you are referring to the
> > tunings
> > > >> that Mozart intended, not to the scales employed
> > > Indeed.
> > > >> which was still
> > > >> dodekaphonic by implication at least if the scales are
> diatonic.
> > >
> > > How does diatonic imply dodekaphonic?
> >
> > Hi Carl
> >
> > It's the full chromatic scale which is dodekaphonic.
> > Diatonic scales are a subset of that. I think there is
> > some confusion here - when I say 'dodekaphonic' I am not
> > referring to a type or style of music but to a scale
> > structure. It is possible to think of diatonic scales
> > in terms of the notes missing from the full chromatic.
>
> but the argument that Carl, Kurt, and myself are presenting
> to you (Peter) is that Mozart, in his orchestral music
> (not his keyboard works, which are 12-tone and well-tempered)
> manifestly did *not* intend his 7-tone diatonic scales to be
> subsets of a "dodekaphonic" (12-tone) gamut, but rather,
> subsets of a 20-tone tuning in which flats differ from sharps,
> which in turn was intended to be a subset of 55edo.
>
> if you read my webpage in its entirety, including the
> quotations from Attwood's notebooks, you'll see this.
>
> you're trying to force Mozart's orchestral tuning into
> your dodekaphonic straight-jacket and that's not what
> it's supposed to be.
>
> -monz
>
> May it be allowed to say that Mozart had the idea of a
> special tuning model in his mind when he was writing a
> composition?
> Indeed, we have reasons to believe that he knew the
> possibilities and limits of contemporary keyboards which
> have been almost tuned near to. E.T., but:
> He (as well as other composers) oftenly transcribed his
> compositions from orchestra to piano, from piano to
> string quartet or harmony music and inverse.
> If his keyboard works "are 12 tone and well-tempered"
> every transcribtion would have been a treason to the
> "original work tuning idea". Mozart would laugh at such
> ideas.
> Or did I misunderstand something?

Mozart's teaching to Attwood clearly indicates that he
wanted 55edo as his tuning basis. the flats are supposed
to be "one comma" higher than their enharmonically equivalent
sharps.

if he really transcribed pieces from piano to orchestra,
then clearly he had a flexible view of intonation, because
the keyboard's 12-tone weel-temperament behaves differently
from the orchestra's 20-tone subset of 55edo.

there are also instances of enharmonic modulation in Mozart,
which also clearly indicates that in some instances, flats
and sharps in his compositions are supposed to be "the same".

(i'm not necessarily claiming that they are tuned to exactly
the same frequency, but the context of his usage indicates
equivalence.)

-monz

Hi monz,

I agree that in Mozart's compositions the sharps and flats
seem to be used and performed best with the same or nearly
the same frequency. But this does every well educated
orchestra or chamber music group, too, nevertheless
they are doing this with flexible intonation and performing
the chords and harmonic structures according to - or near to -
just intonation.
Is this a contradiction in terms? Not for people who have
been sitting in orchestras and chamber music groups. On the
one hand they adjust their frequencies in the actual harmonic
situation near to just intonation, on the other hand the average
level of a virtual equal tempered level of mastertune is
remembered in the background, so that the actual tuning level
doesn't drift too much away from this line. And a major chord
F#-A#-C# for an orchestra will be performed in almost the same
tuning level like Gb-Bb-Db
But I assume: You know this as well as I do?

The problem by discussing in this forum is: Depending of our
musical origin we are thinking in different categories.
An orchestra musician thinks in flexible frequencies adjusted
near to. E.T.
A keyboarder thinks perhaps in a 1/4 comma meantone system where
the difference between G# and Ab is by about 41 Cents.
A "just intonation creator" as they are represented by a lot of
members of this list sets perhaps the difference between F# and Gb
to 24 Cents (pythagorean comma) or 22 Cents (syntonic comma) or....,
depending on his own or preferred system.
(As I am a "creator of just intonation", too, I want to add,
that for my system F#-A#-C# and Gb-Bb-Db will be the same in default).
What I want to say: It is hard for everyone, even for me, to change
his thinking structures and to understand the other. Or to listen
attentive to him.

Well, I don't understand the term "20-tone subset of 55edo"
and my problem is: I have a in advance an aversion against an
idea pressing orchestral or choral music in a fix raster of
frequencies.
But maybe I am erroneous? Wher do I find informations in this
"20-tone subset of 55edo" system?

But I want to contradict the idea that composers are
fixed to tuning systems by their composition's ideas.
This would mean that the young Bach would have composed in
Meantone categories, the old Bach in well-tempered categories,
Liszt in equal tempered categories, 12-tone compositors in
equal tempered categories.
Indeed: It was may opinion that for 12 tone music equal
temperament will be the adequate temperament. But at a discussion
with a 12 tone composer (Huber) he told me that when he is
writing a third interval he has the idea that this has to be
performed in just intonaton "if possible".

regards
Werner

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-----Urspr�ngliche Nachricht-----
Von: Carl Lumma [mailto:ekin@lumma.org]
Gesendet: Dienstag, 16. Dezember 2003 10:07
An: tuning@yahoogroups.com
Betreff: Re: AW: [tuning] Re: Mozart's ideas

Hi Werner,

>May it be allowed to say that Mozart had the idea of a special
>tuning model in his mind when he was writing a composition?

Indeed, it may not. Mozart may simply have been less up-tight
about tuning as some of us here.

-Carl

Carl,

I like you and I agree. But it stops the discussion... Sometimes I like
more
to dispute...

Werner

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> >Would it make more sense were I to substitute 'rational'
> >for 'natural' in my little theory?
>

The term "dodekaphony" is also confusing, because it is already an
accepted term for something else, namely Schoenberg's 12-tone
technique. (In some languages, the cognate of "dodekaphony" is the
only term for 12-tone technique. In the Brockhaus Riemann Lexikon,
for example, "Dodekaphonie" directs the reader to "Zwoelftontechnik".

Priority is important to you, why not call it "Sault's technique"?

Gabor

In a message dated 12/16/03 4:46:53 AM Eastern Standard Time,
wmohrlok@hermode.com writes:

> Wher do I find informations in this
> "20-tone subset of 55edo" system?
>

It was well laid out by Telemann, when Mozart was quite young. Telemann's
analysis of tuning has fully been explored on this List.

> But I want to contradict the idea that composers are
> fixed to tuning systems by their composition's ideas.
>

Composers are fixed to specific tuning, but their compositions may not be
enough to determine what they are. With enough study and performance there opens
clear patterns of tuning preference, always completely supported by era and
geography cultural values.

best, Johnny Reinhard

In a message dated 12/15/2003 8:14:01 PM Eastern Standard Time,
sault@cyberware.co.uk writes:

> Hi Gene
>
> What's a "3-limit comma"?
>
> Peter
>

Gene, could we also have a musical definition? Mathematical definitions are
fine as well, but we are talking about music, are we not? Maybe you could try
your hand at fashioning musical definitions that are mathematically accurate?
It will be of great service.

best, Johnny

In a message dated 12/16/2003 7:23:49 AM Eastern Standard Time,
alternativetuning@yahoo.com writes:

> Priority is important to you, why not call it "Sault's technique"?
>
> Gabor
>

Are you being sarcastic, Gabor?

Professor Reinhard

In a message dated 12/16/2003 1:31:42 AM Eastern Standard Time,
wmohrlok@hermode.com writes:

> He (as well as other composers) oftenly transcribed his compositions from
> orchestra to piano, from piano to string quartet or harmony music and
> inverse.
> If his keyboard works "are 12 tone and well-tempered" every transcribtion
>
> would have been a treason to the "original work tuning idea".
> Mozart would laugh at such ideas.
> Or did I misunderstand something?
>
> Werner
>

Mozart, like Bach, could hear everything in his mind before setting it down
to paper. This precision of thought works when there is no confusion of tuning
in the mind. A composer could certainly transcribe between musical forces,
and across different tunings. An example is Bach's transcriptions for keyboard
the string pieces of Vivaldi (certainly in a different tuning than Bach's
keyboard tuning).

Rather than guess at what Mozart would laugh at, a careful study reveals that
he was a creature of his time, all the more so because of his being brought
up as a musical prodigy. That Mozart should have a different reference for his
notation that modern times is certainly no laughing matter to modern
musicians continuing in their mission to best represent the intentions of great
composers of the past.

best, Johnny Reinhard

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> Indeed: It was may opinion that for 12 tone music equal
> temperament will be the adequate temperament. But at a discussion
> with a 12 tone composer (Huber) he told me that when he is
> writing a third interval he has the idea that this has to be
> performed in just intonaton "if possible".

Sounds like a candidate for adaptive tuning!

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Gene, could we also have a musical definition?

Probably it would be best to see if Carl or Paul or one of the other
tuning-math denizens can produce what you are looking for.

Anyone want to take a shot at this?

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Rather than guess at what Mozart would laugh at, a careful study
reveals that
> he was a creature of his time, all the more so because of his being
brought
> up as a musical prodigy.

It's more than just being a creature of his time. Mozart is much more
a meantone composer than Haydn, for example.

-----Urspr�ngliche Nachricht-----
Von: Afmmjr@aol.com [mailto:Afmmjr@aol.com]
Gesendet: Dienstag, 16. Dezember 2003 16:38
An: tuning@yahoogroups.com
Betreff: Re: AW: [tuning] Re: Mozart's ideas

In a message dated 12/16/2003 1:31:42 AM Eastern Standard Time,
wmohrlok@hermode.com writes:

He (as well as other composers) oftenly transcribed his compositions
from
orchestra to piano, from piano to string quartet or harmony music and
inverse.
If his keyboard works "are 12 tone and well-tempered" every
transcribtion
would have been a treason to the "original work tuning idea".
Mozart would laugh at such ideas.
Or did I misunderstand something?

Werner

Mozart, like Bach, could hear everything in his mind before setting it
down to paper. This precision of thought works when there is no confusion
of tuning in the mind. A composer could certainly transcribe between
musical forces, and across different tunings. An example is Bach's
transcriptions for keyboard the string pieces of Vivaldi (certainly in a
different tuning than Bach's keyboard tuning).

Rather than guess at what Mozart would laugh at, a careful study reveals
that he was a creature of his time, all the more so because of his being
brought up as a musical prodigy. That Mozart should have a different
reference for his notation that modern times is certainly no laughing matter
to modern musicians continuing in their mission to best represent the
intentions of great composers of the past.

best, Johnny Reinhard

Johnny,

as I already said: In such a group there is a high risk of
misunderstanding. I didn't say that Mozart or Bach
or any other composer, even you, couldn't hear their compositions in their
mind before setting it down to paper.
I only wanted to say that in their mind as well as in your mind there was
or is an "idea of the compostion on
itself" before writing it down. I believe that composers have in their
mind the "ideal of a fifth
or a third" and not a fifth or a third in any tuning model or temperament.
And I repeat: Mozart would laugh at the idea that he called over different
tuning models in his
mind when composing either for a piano or on the other hand for a string
quartet.
(Indeed, he certainly knew the different result in acoustic, but this was
not the question).
And you should not be shocked by the idea of a laughing Mozart...

Besides, we are all creature of our time, nevertheless actually (at our
time) there are "musical creatures"
who believe that a "well tempered" tuning model (and not knowing what
this term means) is the best tuning
for all kinds of music. And there are others, no "creatures", but the
members of this list who are looking
for the best tools
- either to perform traditional music with adequate tuning models
- or looking for new tuning models for experimental music.
I belong mainly to the traditional group and have developed tools for
this. But I possess also tools
for experimental tunings.
You belong to both groups.
We all - or at least most of us - follow this idea, sometimes by different
models, but this doesn't matter.
In this way there is no reason for a fundamental dissension.

Regarding the "20-tone subset of 55edo" system of Telemann: Maybe I will
find the precise information
in this list, but I think I will look for it in german sites. I will
understand it quicker.
And you are right: Before discussing a subject one should look for
informations.

All the best from bassoon to bassoon

Werner

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-----Urspr�ngliche Nachricht-----
Von: gwsmith@svpal.org [mailto:gwsmith@svpal.org]
Gesendet: Dienstag, 16. Dezember 2003 18:13
An: tuning@yahoogroups.com
Betreff: [tuning] Adaptive tuning of serialism

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> Indeed: It was may opinion that for 12 tone music equal
> temperament will be the adequate temperament. But at a discussion
> with a 12 tone composer (Huber) he told me that when he is
> writing a third interval he has the idea that this has to be
> performed in just intonaton "if possible".

Sounds like a candidate for adaptive tuning!

Ask him. His website is:
www.klaushuber.com

Werner

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-----Urspr�ngliche Nachricht-----
Von: gwsmith@svpal.org [mailto:gwsmith@svpal.org]
Gesendet: Dienstag, 16. Dezember 2003 18:25
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> Rather than guess at what Mozart would laugh at, a careful study
reveals that
> he was a creature of his time, all the more so because of his being
brought
> up as a musical prodigy.

It's more than just being a creature of his time. Mozart is much more
a meantone composer than Haydn, for example.

Much more... maybe. It is not my intention to oppose.
But he wrote a lot of pieces in his operas in Eb major. Why? As these
pieces are equipped with clarinets in B and Horns in Eb. And for horns at
that time
Eb major was a very comfortable key.
Eb major against this is impossible in a standard meantone temperament
because
of the "wolf" Ab-Eb.
If you agree that Mozart probably knew a lot in the different tuning
possibilities of
keyboards and orchestras we can make "shakehands".

Werner

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In a message dated 12/16/2003 12:38:10 PM Eastern Standard Time,
wmohrlok@hermode.com writes:

> Much more... maybe. It is not my intention to oppose.
> But he wrote a lot of pieces in his operas in Eb major. Why? As these
> pieces are equipped with clarinets in B and Horns in Eb. And for horns at
> that time
> Eb major was a very comfortable key.
> Eb major against this is impossible in a standard meantone temperament
> because
> of the "wolf" Ab-Eb.
> If you agree that Mozart probably knew a lot in the different tuning
> possibilities of
> keyboards and orchestras we can make "shakehands".
>
> Werner

Hi Werner, you are correct that I am interested in several different
perspectives on this list, including early music performance. For Mozart to use
"uncomfortable" keys is to get a fresh sound, no? Besides, there was no wolf in
the extended meantone paradigm.

re Telemann: I do have the German urtext. It really is fascinating that
Telemann should have thought out extended sixth-comma meantone at the end of his
life. Maybe he had this worked out much sooner, waiting until bedridden before
he wrote down the detail.

best, Johnny

In a message dated 12/16/2003 12:29:02 PM Eastern Standard Time,
wmohrlok@hermode.com writes:

> . I believe that composers have in their mind the "ideal of a fifth
> or a third" and not a fifth or a third in any tuning model or temperament.
> And I repeat: Mozart would laugh at the idea that he called over different
> tuning models in his
> mind when composing either for a piano or on the other hand for a string
> quartet.
> (Indeed, he certainly knew the different result in acoustic, but this was
> not the question).
> And you should not be shocked by the idea of a laughing Mozart...
>

Bach would choose very carefully to use a quarter-comma flat "perfect fifth"
when designing a motive. Of course, this is based on Bach using Werckmeister
III as his "chromatic" tuning. There is much material on this subject.

Considering there are only four flattened "perfect fifths" in Werckmeister
III, as opposed to eight 3/2 (702 cents) perfect fifths, it is astounding how
Bach avoids the pure ones in the opening motives to his pieces. You are welcome
to check this for yourself.

I am not shocked by a laughing Mozart, only at the idea of what he might be
laughing about.

>
> Besides, we are all creature of our time, nevertheless actually (at our
> time) there are "musical creatures"
> who believe that a "well tempered" tuning model (and not knowing what this
> term means) is the best tuning
> for all kinds of music. And there are others, no "creatures", but the
> members of this list who are looking
> for the best tools
> - either to perform traditional music with adequate tuning models
> - or looking for new tuning models for experimental music.
> I belong mainly to the traditional group and have developed tools for
> this. But I possess also tools
> for experimental tunings.
> You belong to both groups.
> We all - or at least most of us - follow this idea, sometimes by different
> models, but this doesn't matter.
> In this way there is no reason for a fundamental dissension.

agreed.

> All the best from bassoon to bassoon
>
> Werner
>

best, Johnny

>Priority is important to you, why not call it "Sault's technique"?

It's not usually cool to name something after oneself.

-C.

Peter,

I dissagree to a couple of semantics aspects with regards to your
point of view in this discussion, but I do respect your ideas and
efforts. However, I must make a (funny) point here:

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:

> I think the best argument of all is the infectious nature of
> dodekaphony. It may well be a case of simple things pleasing simple
> minds but, at risk of sounding patronizing towards humanity in
> general, simple minds are in the majority. We all have a simple-
> minded side. If you do not, which may well be possible, then you
are
> in a very small and lonely minority. Perhaps the world's
acknowledged
> best composers were only playing to the crowd - but whatever their
> motive they have always stuck to a roughly logarithmic 12-tone
> division of the 8ve. Stockhausen, on the other hand, has
disappeared
> into the depths of obscurity and is of interest only to hardcore
> musicologists (myself excluded).
>

Dodekaphony is certainly not for simple minds. Just give'em
heptatonic, or even more plain music.

> While I do not deny that other possibilities exist, trying to get
> people off dodekaphony is a bit like banning alcohol or, for that
> matter, maryjane. Ban it and people will gather together in secret
to
> indulge in it. I cannot imagine that happening for music created
with
> obscure and esoteric divisions of the 8ve.
>

If heptatonicy is maryjane, dodekaphony is horse. And don't even try
31-eq. There's no coming back... ;)
Max.

> Also please note that the central purpose of my analysis
titled 'The
> Ring of Truth' is not to 'prove' that dodekaphony is the be-all and
> end-all of civilization but to demonstrate that symmetric JI is the
> most likely source of the Babylonian degree of angle and the Vedic
> minute of time and that by extension 360-day solar calendars are
> secondary derivations. The ODEION program is merely a spin-off.
That
> ODEION can produce listenable melodic structures, which just about
> everyone else here has concluded for themselves, should give you
food
> for thought.
>
> Peter

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
> Hi monz,
>
> I agree that in Mozart's compositions the sharps and flats
> seem to be used and performed best with the same or nearly
> the same frequency. But this does every well educated
> orchestra or chamber music group, too, nevertheless
> they are doing this with flexible intonation and performing
> the chords and harmonic structures according to - or near to -
> just intonation.
> Is this a contradiction in terms? Not for people who have
> been sitting in orchestras and chamber music groups. On the
> one hand they adjust their frequencies in the actual harmonic
> situation near to just intonation, on the other hand the average
> level of a virtual equal tempered level of mastertune is
> remembered in the background, so that the actual tuning level
> doesn't drift too much away from this line. And a major chord
> F#-A#-C# for an orchestra will be performed in almost the same
> tuning level like Gb-Bb-Db
> But I assume: You know this as well as I do?

yes. my early musical training was as an orchestral and
band woodwind player (clarinet, oboe, sax, bassoon).

however, you are stating what is probably modern practice.
this is not how the music was played in Mozart's time.

the main evidence i have for Mozart intending to use 55edo
(or another similar meantone) in his orchestral music
is: 1) his own comments to his student Thomas Attwood
(Attwood's notebooks have been preserved and published,
with comments in Mozart's handwriting), and 2) his father
Leopold's violin method.

> Well, I don't understand the term "20-tone subset of 55edo"
> and my problem is: I have a in advance an aversion against an
> idea pressing orchestral or choral music in a fix raster of
> frequencies.
> But maybe I am erroneous? Wher do I find informations in this
> "20-tone subset of 55edo" system?

http://tonalsoft.com/monzo/55edo/55edo.htm

-monz

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >Priority is important to you, why not call it "Sault's technique"?
>
> It's not usually cool to name something after oneself.

It is, however, cool for anyone else to name something after the
person who invented it.

On Mon, 15 Dec 2003 12:48:20 -0000 Monz wrote

>you responded that you found my webpage "opaque", but
>you never said a word about the audio example of the
>beginning of Mozart's 40th (G-minor) Symphony in 55edo.

Do you have more of that anywhere, please?

Peter
www.midicode.com

No, I am serious and want to avoid confusion between Sault's idea and
an existing term. Are you being sarcastic?

Gabor Bernath

-- In tuning@yahoogroups.com, Afmmjr@a... wrote:
> In a message dated 12/16/2003 7:23:49 AM Eastern Standard Time,
> alternativetuning@y... writes:
>
> > Priority is important to you, why not call it "Sault's technique"?
> >
> > Gabor
> >
>
> Are you being sarcastic, Gabor?
>
> Professor Reinhard

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
...
> It's the full chromatic scale which is dodekaphonic. Diatonic
scales
> are a subset of that. I think there is some confusion here - when I
> say 'dodekaphonic' I am not referring to a type or style of music
but
> to a scale structure. It is possible to think of diatonic scales
in
> terms of the notes missing from the full chromatic.

> Peter

Indeed, i would put it the other way round. It's possible to think of
a chromatic dodecaphonical scale as an extension of an heptatonical
diatonic one.

In its origin, Western music is heptatonical more than
dodecaphonical. And if a dodecaphonical extension is admited, why
stop at 12 (besides Sault's acceptable but exclusive considerations)?
Why couldn't we have a F# as well as a Gb, whether phytagorian,
meantone, etc.?

Another point I think needs clarification from Peter is the essential
5-limit approach. What's wrong with 7/4, for instance? Apart from
filosophical stuff (dualism, orphic miths, Phytagorianism, etc.),
from a MUSICAL point of view there's nothing intrinsically akward
with such rationes. And in this way, 12ism had deprived our ears of
so many consonances.

Max.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > I would expect improvements in both 'per 3' and absolute differences
> > to continue as the series goes to infinity, and I'm suspect Gene could
> > rattle out a proof of that in a few minutes.

> Probably it is true that for any k>0,
> |log2(3)-p/q| < 1/kq^2 has an infinity of solutions, but the trick for
> a mathematician is proving it.

On looking at this again, Carl seems to be asking both for relative
and absolute answers. In other words, are there an infinite number of
equal divisions whose 3-limit comma is less than the Pythagorean comma
in terms of relative cents? The answer to that is "probably", but it
leads into the deep waters of my previous posting. However, it is
trivial from the fact that there are an infinity convergents of the
continued fraction for log2(3) that there will be an infinite number
of solutions to the problem of finding ets whose 3-limit comma is
absolutely less than the Pythagorean comma. In fact, a certain fixed
percentage of ets will beat 12 in absolute terms. A certain fixed
percentage will even manage to beat 665 in absolute terms.

Here are the convergents of log2(3) and the size of the associated
comma in cents:

3/2 203.91
8/5 90.225
19/12 23.460
65/41 19.845
84/53 3.615
485/306 1.770
1054/665 0.076
24727/15601 0.0315
.
.
.

--- In tuning@yahoogroups.com, Peter Frazer <paf@e...> wrote:
> On Mon, 15 Dec 2003 12:48:20 -0000 Monz wrote
>
> >you responded that you found my webpage "opaque", but
> >you never said a word about the audio example of the
> >beginning of Mozart's 40th (G-minor) Symphony in 55edo.
>
> Do you have more of that anywhere, please?
>
> Peter
> www.midicode.com

nope ... only got as far as the end of the main theme
of the first movement, all of which opens with the webpage.

Manuel sent me a version of the entire symphony retuned
to 55edo, done by Scala, but it uses only a 12-tone subset,
which does not reflect Mozart's notation or intentions.

-monz

--- In tuning@yahoogroups.com, alternativetuning@y... wrote:
>
> > >Would it make more sense were I to substitute 'rational'
> > >for 'natural' in my little theory?
> >
>
> The term "dodekaphony" is also confusing, because it is already an
> accepted term for something else, namely Schoenberg's 12-tone
> technique. (In some languages, the cognate of "dodekaphony" is the
> only term for 12-tone technique. In the Brockhaus Riemann Lexikon,
> for example, "Dodekaphonie" directs the reader
to "Zwoelftontechnik".
>

It would seem that I have indeed been misusing the
word 'dodekaphonic', hence the mighty confusion that has arisen here.
I must express my gratitude to all concerned who have pointed this
out to me - and must revise my text accordingly. Apparently I should
be using the term 'Chromatic Scale'. The reasons I did not use that
in the first place was that the term 'chromatic' did not necessarily,
to my mind, indicate a specifically 12-tone octave and that I had
perceived the possibility of N-tone chromatic scales based on
divisions of the octave according to 2^(1/N) steps, where N is not
equal to 12, and wanted to be absolutely clear about my intent. Also
the term 'Chromaticism' has other, prior, meanings that I was already
aware of.

> Priority is important to you, why not call it "Sault's technique"?

That's a bit too personal and I did not invent music but thanks for
the thought. How about 'Dodekachrome' (noun) and 'Dodekachromatic'
(adj.)? Or else it could be 'Dodekatone' and 'Dodekatonic' but these
do not, to my mind, indicate equal value steps. All opinions welcomed.

And priority is surely important to everyone except the Pythagoreans,
who wrote everything in the name of Pythagoras. Would you have asked
Mozart to forego the right to put his own name to his own music?

>
> Gabor

--- In tuning@yahoogroups.com, gwsmith@s... wrote:
> --- In tuning@yahoogroups.com, Afmmjr@a... wrote:
>
> > Gene, could we also have a musical definition?
>
> Probably it would be best to see if Carl or Paul or one of the
other
> tuning-math denizens can produce what you are looking for.
>
> Anyone want to take a shot at this?

I think I have finally understood what is meant in this group (and
presumably more widely) by 3-limit and 5-limit scales and commas. The
numbers refer to the highest prime used to define rational
(my 'natural') intervals.

The musical expression of the mathematics is in the sounds of the
intervals. Music is unconscious, direct-experience mathematics.

--- In tuning@yahoogroups.com, giordanobruno76@y... wrote:
> --- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
> wrote:
> ...
> > It's the full chromatic scale which is dodekaphonic. Diatonic
> scales
> > are a subset of that. I think there is some confusion here - when
I
> > say 'dodekaphonic' I am not referring to a type or style of music
> but
> > to a scale structure. It is possible to think of diatonic scales
> in
> > terms of the notes missing from the full chromatic.
>
> > Peter
>
> Indeed, i would put it the other way round. It's possible to think
of
> a chromatic dodecaphonical scale as an extension of an heptatonical
> diatonic one.
>
> In its origin, Western music is heptatonical more than
> dodecaphonical. And if a dodecaphonical extension is admited, why
> stop at 12 (besides Sault's acceptable but exclusive
considerations)?
> Why couldn't we have a F# as well as a Gb, whether phytagorian,
> meantone, etc.?
>
> Another point I think needs clarification from Peter is the
essential
> 5-limit approach. What's wrong with 7/4, for instance? Apart from
> filosophical stuff (dualism, orphic miths, Phytagorianism, etc.),
> from a MUSICAL point of view there's nothing intrinsically akward
> with such rationes. And in this way, 12ism had deprived our ears of
> so many consonances.
>
> Max.

Hi Max

You need to read my previous posts on this, for example
/tuning/topicId_49980.html#49998

4:7 is excluded because it falls in the region of a dodekachromatic
stopband.

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

/tuning/topicId_49814.html#49991

I believe that composers have in their
> mind the "ideal of a fifth
> or a third" and not a fifth or a third in any tuning model or
temperament.

***Well, of course, Werner you mean in systems that *have* fifths and
thirds! Other more "experimental" systems may not, or may have
many "varieties" of them and that's why I believe it's important that
composers work right with the sound material on a xenharmonic
keyboard, since some of it can be so unfamiliar...

J. Pehrson

-----Urspr�ngliche Nachricht-----
Von: Afmmjr@aol.com [mailto:Afmmjr@aol.com]
Gesendet: Dienstag, 16. Dezember 2003 19:23
An: tuning@yahoogroups.com
Betreff: Re: AW: [tuning] Re: Mozart's ideas

In a message dated 12/16/2003 12:38:10 PM Eastern Standard Time,
wmohrlok@hermode.com writes:

Much more... maybe. It is not my intention to oppose.
But he wrote a lot of pieces in his operas in Eb major. Why? As these
pieces are equipped with clarinets in B and Horns in Eb. And for horns
at that time
Eb major was a very comfortable key.
Eb major against this is impossible in a standard meantone temperament
because
of the "wolf" Ab-Eb.
If you agree that Mozart probably knew a lot in the different tuning
possibilities of
keyboards and orchestras we can make "shakehands".

Werner

Hi Werner, you are correct that I am interested in several different
perspectives on this list, including early music performance. For Mozart to
use "uncomfortable" keys is to get a fresh sound, no? Besides, there was no
wolf in the extended meantone paradigm.

re Telemann: I do have the German urtext. It really is fascinating that
Telemann should have thought out extended sixth-comma meantone at the end of
his life. Maybe he had this worked out much sooner, waiting until bedridden
before he wrote down the detail.

best, Johnny

Hi Johnny,
regarding the pieces in Eb major in Mozarts operas or, on the other hand
for instance
the Eb major symphony: I know them all by musical interpretations near to
just intonation. I don't
believe that these pieces will be morer authentic in a "sharp tuned"
interpretation.
In other case my own personal efforts in orchestras and chamber music,
combined with
many hours of tuning discussions in these groups and combined with hard
work to be
"in tune" would have been absurd.
But I am speaking for myself and not "ex cathedra". Everyone is free to
have his own idea
of this.

Regarding Telemann: I cannot answer before have studied him. I know that
he was very
interested in tuning problems and I know that he tested a "klavier" with
much more keys than
12 per octave. And he was enthusiasm on it. The original one (or a replica
?) is, I believe,
to find at the "Deutsches Museum"
in M�nchen.

I have to add something:
In one of my last messages I wrote "Mozart would have laughed at...." as I
wanted to translate
the german term "lachen �ber.." which means somehow "to be amused"
(without any negative
touch). Now my dictionary says to me that this english term is the
translation of the german
term "auslachen" which is a negative one, discriminating the opposite
person.
This was not my intention and I apologize for this.

best, Werner

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-----Urspr�ngliche Nachricht-----
Von: monz@attglobal.net [mailto:monz@attglobal.net]
Gesendet: Dienstag, 16. Dezember 2003 21:19
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
> Hi monz,
>
> I agree that in Mozart's compositions the sharps and flats
> seem to be used and performed best with the same or nearly
> the same frequency. But this does every well educated
> orchestra or chamber music group, too, nevertheless
> they are doing this with flexible intonation and performing
> the chords and harmonic structures according to - or near to -
> just intonation.
> Is this a contradiction in terms? Not for people who have
> been sitting in orchestras and chamber music groups. On the
> one hand they adjust their frequencies in the actual harmonic
> situation near to just intonation, on the other hand the average
> level of a virtual equal tempered level of mastertune is
> remembered in the background, so that the actual tuning level
> doesn't drift too much away from this line. And a major chord
> F#-A#-C# for an orchestra will be performed in almost the same
> tuning level like Gb-Bb-Db
> But I assume: You know this as well as I do?

yes. my early musical training was as an orchestral and
band woodwind player (clarinet, oboe, sax, bassoon).

however, you are stating what is probably modern practice.
this is not how the music was played in Mozart's time.

the main evidence i have for Mozart intending to use 55edo
(or another similar meantone) in his orchestral music
is: 1) his own comments to his student Thomas Attwood
(Attwood's notebooks have been preserved and published,
with comments in Mozart's handwriting), and 2) his father
Leopold's violin method.

> Well, I don't understand the term "20-tone subset of 55edo"
> and my problem is: I have a in advance an aversion against an
> idea pressing orchestral or choral music in a fix raster of
> frequencies.
> But maybe I am erroneous? Wher do I find informations in this
> "20-tone subset of 55edo" system?

http://tonalsoft.com/monzo/55edo/55edo.htm

-monz

Thank you for your reference.

Regarding modern and historic practice in orchestra's intonation: I don't
believe that at
historic times string and wind instrument players liked to perform fifths
by detuned meantone
frequency ratios. "Menatone" is a keyboard tool for the approach to just
intonation, requiring
narrow fifths in order to get better tuned major thirds.
There is no practical reason, neither in Bach's nor Mozart's times and not
actually for the
tuning behavior in an orchestra to perform such narrow fifths. And it is
much easy to
control pure fifths by ear, but very difficult to perform exact weighted
beats of
- for instance - 1/4 comma meantone fifths?
Why should string and wind instruments follow the intonation problems of
keyboards?
By having pity with them?

Best
Werner

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-----Urspr�ngliche Nachricht-----
Von: giordanobruno76@yahoo.com.ar [mailto:giordanobruno76@yahoo.com.ar]
Gesendet: Dienstag, 16. Dezember 2003 23:20
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Dodekaphony

--- In tuning@yahoogroups.com, "Peter Wakefield Sault" <sault@c...>
wrote:
...
> It's the full chromatic scale which is dodekaphonic. Diatonic
scales
> are a subset of that. I think there is some confusion here - when I
> say 'dodekaphonic' I am not referring to a type or style of music
but
> to a scale structure. It is possible to think of diatonic scales
in
> terms of the notes missing from the full chromatic.

> Peter

Indeed, i would put it the other way round. It's possible to think of
a chromatic dodecaphonical scale as an extension of an heptatonical
diatonic one.

In its origin, Western music is heptatonical more than
dodecaphonical. And if a dodecaphonical extension is admited, why
stop at 12 (besides Sault's acceptable but exclusive considerations)?
Why couldn't we have a F# as well as a Gb, whether phytagorian,
meantone, etc.?

Another point I think needs clarification from Peter is the essential
5-limit approach. What's wrong with 7/4, for instance? Apart from
filosophical stuff (dualism, orphic miths, Phytagorianism, etc.),
from a MUSICAL point of view there's nothing intrinsically akward
with such rationes. And in this way, 12ism had deprived our ears of
so many consonances.

Max.

I like the 7/4 natural sept. In principle. But at a chord sequence legato
from D-A-C-F to
D-G-B-F in polyphonic music as it is to find for example in compositions
of Bach,
it will cause an misplaced retuning effects. As to my opinion.
Nevertheless I already discussed with well educated musicians who liked
such
retuning effects.
This means: One has to weight where it may be opportune or not - and if
you like it
nobody can contradict you. It is an aesthetic question and not an
objective one.

Best
Werner
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-----Urspr�ngliche Nachricht-----
Von: jpehrson@rcn.com [mailto:jpehrson@rcn.com]
Gesendet: Mittwoch, 17. Dezember 2003 04:13
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

/tuning/topicId_49814.html#49991

I believe that composers have in their
> mind the "ideal of a fifth
> or a third" and not a fifth or a third in any tuning model or
temperament.

***Well, of course, Werner you mean in systems that *have* fifths and
thirds! Other more "experimental" systems may not, or may have
many "varieties" of them and that's why I believe it's important that
composers work right with the sound material on a xenharmonic
keyboard, since some of it can be so unfamiliar...

J. Pehrson

Indeed, thank you for the clarification.

Werner

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hi Peter,

--- In tuning@yahoogroups.com, sault@c... wrote:

> I think I have finally understood what is meant in this
> group (and presumably more widely) by 3-limit and 5-limit
> scales and commas. The numbers refer to the highest prime
> used to define rational (my 'natural') intervals.

yes, that's correct.

in fact, just two weeks ago paul erlich helped me with
a great update of my "limit" definition:

http://tonalsoft.com/enc/limit.htm

note particularly that "limit", unqualified, may mean
either "odd-limit" or "prime-limit" ... i'm hoping to
establish a trend towards using the "odd" or "prime"
qualifier to help keep things clearer.

the use of "limit" originates with Harry Partch. it's
used fairly widely these days in the tuning community,
but not otherwise (so far) by music-theorists.

Kraig Grady prefers to use the term "cap" instead of "limit",
and a handful of other composers and theorists follow his lead.

-monz

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
> > Von: monz@a... [mailto:monz@a...]
> > Gesendet: Dienstag, 16. Dezember 2003 21:19
> > An: tuning@yahoogroups.com
> > Betreff: [tuning] Re: Mozart's ideas
> >
> > <snip>
> >
> > http://tonalsoft.com/monzo/55edo/55edo.htm
> >
>
> Thank you for your reference.
>
> Regarding modern and historic practice in orchestra's
> intonation: I don't believe that at historic times string
> and wind instrument players liked to perform fifths
> by detuned meantone frequency ratios. "Menatone" is a
> keyboard tool for the approach to just intonation,
> requiring narrow fifths in order to get better tuned
> major thirds.
> There is no practical reason, neither in Bach's nor
> Mozart's times and not actually for the tuning behavior
> in an orchestra to perform such narrow fifths. And it is
> much easy to control pure fifths by ear, but very difficult
> to perform exact weighted beats of - for instance - 1/4 comma
> meantone fifths?
> Why should string and wind instruments follow the
> intonation problems of keyboards?
> By having pity with them?

well, sorry to disagree with you, but you will have to
change your beliefs. :)

Leopold Mozart's violin method clearly illustrates the
use of "9 commas per whole-tone", "5 commas per diatonic
semitone", and "4 commas per chromatic semitone".
and of course the syntonic comma is supposed to be
tempered out.

as i state on my webpage, the only tuning which gives
these results is 55edo.

the point i'm making is that this type of meantone
was *explicitly* taught to orchestral musicians.
it has nothing at all to do with keyboards, which by
Mozart's time were nearly universally tuned to a 12-tone
"circulating" well-temperament (excluding organs, which
were also still tuned to meantone).

perhaps i can offer a simplified historical view:

the tuning paradigms for European "art" music were historically:

500 AD - 1500: Pythagorean
1500s: 1/4-comma meantone (and its relative 31edo)
1600s: 1/5-comma meantone (and its relative 43edo)
1700s: 1/6-comma meantone (and its relative 55edo)
1800 - 2000: 12edo (i.e., 1/11-comma meantone)

... with the exception that 12-tone "circulating"
well-temperaments became standard on harpsichords, clavichords,
and pianos during the 1700s, and 1/4-comma meantone
persisted on organs as late as 1850.

-monz

--- In tuning@yahoogroups.com, sault@c... wrote:
> --- In tuning@yahoogroups.com, giordanobruno76@y... wrote:
> > Another point I think needs clarification from Peter is the
> essential
> > 5-limit approach. What's wrong with 7/4, for instance? Apart from
> > filosophical stuff (dualism, orphic miths, Phytagorianism, etc.),
> > from a MUSICAL point of view there's nothing intrinsically akward
> > with such rationes. And in this way, 12ism had deprived our ears
of
> > so many consonances.
> >
> > Max.
>
> Hi Max
>
> You need to read my previous posts on this, for example
> /tuning/topicId_49980.html#49998
>
> 4:7 is excluded because it falls in the region of a dodekachromatic
> stopband.

Of course I know about your procedure, and I'm fully aware of your
method excluding such thing like 7/4. And, as you have previously
pointed out, it is rather difficult for a 12-tone octave to admit
such ratio.

Let me rephrase my question: Do you feel that a method that excludes
such rationes is completely acceptable? Don't you feel there's
something missing?

I bet you'll answer YES & NO respectively, and that's fine. It's only
I'd answer NO & YES instead, but that's me.

Max.

In a message dated 12/17/2003 1:42:09 AM Eastern Standard Time,
wmohrlok@hermode.com writes:

> Regarding modern and historic practice in orchestra's intonation: I don't
> believe that at
> historic times string and wind instrument players liked to perform fifths
> by detuned meantone
> frequency ratios. "Menatone" is a keyboard tool for the approach to just
> intonation, requiring
> narrow fifths in order to get better tuned major thirds.
> There is no practical reason, neither in Bach's nor Mozart's times and not
> actually for the
> tuning behavior in an orchestra to perform such narrow fifths. And it is
> much easy to
> control pure fifths by ear, but very difficult to perform exact weighted
> beats of
> - for instance - 1/4 comma meantone fifths?
> Why should string and wind instruments follow the intonation problems of
> keyboards?
> By having pity with them?
>
> Best
> Werner
>

Dear Werner,

I understand what it must be like for your musical beliefs to be
reconsidered, but I think it is necessary regarding early tuning.

Baroque music always has a keyboard all other instruments must indeed have
pity on them. Hearing an exact tempered fifth of any kind is easily repeatable.
I have done so with other musicians for decades. The bassoon can play any
single tuning system, besides.

When you say Mozart, I say Bach. Why? Because I really know the details for
Bach, and only learned of Mozart's tuning practices later. Bach in just
intonation is awful. The master of temperament is thus eviscerated, indeed
castrated.

Also, narrow fifths may be necessary if there is modulation involved as in
Mozart. Werner, your bias for "reine stimmung" is showning. But I hope you
have the patience to sift through early music a second time in your lifetime to
account for tuning practices that are poorly advertised to today's musicians.

best, Johnny Reinhard

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

> note particularly that "limit", unqualified, may mean
> either "odd-limit" or "prime-limit" ... i'm hoping to
> establish a trend towards using the "odd" or "prime"
> qualifier to help keep things clearer.

I'm hoping to start a trend for people to say "consonances" when they
mean odd-limit; it would make a lot more sense.

> Kraig Grady prefers to use the term "cap" instead of "limit",
> and a handful of other composers and theorists follow his lead.

We could use "limit" for one, and "cap" for the other.

--- In tuning@yahoogroups.com, giordanobruno76@y... wrote:
> --- In tuning@yahoogroups.com, sault@c... wrote:
> > --- In tuning@yahoogroups.com, giordanobruno76@y... wrote:
> > > Another point I think needs clarification from Peter is the
> > essential
> > > 5-limit approach. What's wrong with 7/4, for instance? Apart
from
> > > filosophical stuff (dualism, orphic miths, Phytagorianism,
etc.),
> > > from a MUSICAL point of view there's nothing intrinsically
akward
> > > with such rationes. And in this way, 12ism had deprived our
ears
> of
> > > so many consonances.
> > >
> > > Max.
> >
> > Hi Max
> >
> > You need to read my previous posts on this, for example
> > /tuning/topicId_49980.html#49998
> >
> > 4:7 is excluded because it falls in the region of a
dodekachromatic
> > stopband.
>
> Of course I know about your procedure, and I'm fully aware of your
> method excluding such thing like 7/4. And, as you have previously
> pointed out, it is rather difficult for a 12-tone octave to admit
> such ratio.
>
> Let me rephrase my question: Do you feel that a method that
excludes
> such rationes is completely acceptable? Don't you feel there's
> something missing?
>
> I bet you'll answer YES & NO respectively, and that's fine. It's
only
> I'd answer NO & YES instead, but that's me.
>
> Max.

Instead I'll ask you a few questions, Max. Would you eat apple pie
with gravy? Would you eat roast beef with custard? Would you wear a
dinner jacket with beach shorts? I'll bet you'll answer NO, NO and
NO, in which case WHAT HAVE YOU GOT AGAINST APPLE PIE, BUDDY???

Peter

-----Urspr�ngliche Nachricht-----
Von: monz@attglobal.net [mailto:monz@attglobal.net]
Gesendet: Mittwoch, 17. Dezember 2003 11:17
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
> > Von: monz@a... [mailto:monz@a...]
> > Gesendet: Dienstag, 16. Dezember 2003 21:19
> > An: tuning@yahoogroups.com
> > Betreff: [tuning] Re: Mozart's ideas
> >
> > <snip>
> >
> > http://tonalsoft.com/monzo/55edo/55edo.htm
> >
>
> Thank you for your reference.
>
> Regarding modern and historic practice in orchestra's
> intonation: I don't believe
> that at historic times string
> and wind instrument playe rs liked to perform fifths
> by detuned meantone frequency ratios. "Meantone" is a
> keyboard tool for the approach to just intonation,
> requiring narrow fifths in order to get better tuned
> major thirds.
> There is no practical reason, neither in Bach's nor
> Mozart's times and not actually for the tuning behavior
> in an orchestra to perform such narrow fifths. And it is
> much easy to control pure fifths by ear, but very difficult
> to perform exact weighted beats of - for instance - 1/4 comma
> meantone fifths?
> Why should string and wind instruments follow the
> intonation problems of keyboards?
> By having pity with them?

> well, sorry to disagree with you, but you will have to
> change your beliefs. :)

> Leopold Mozart's violin method clearly illustrates the
> use of "9 commas per whole-tone", "5 commas per diatonic
> semitone", and "4 commas per chromatic semitone".
> and of course the syntonic comma is supposed to be
> tempered out.

Well, than the question will be whether the orchestras
have followed Leopold Mozart and have tuned their fifths
incorrect. You know (I repeat) that it is simple (in
comparision) to perform fifths in just intonation against
an abstract method of reducing the interval by a part
of a comma and to weight this correctly. This seems
impossible to me.

> as i state on my webpage, the only tuning which gives
> these results is 55edo.

I will study it.

> the point i'm making is that this type of meantone
> was *explicitly* taught to orchestral musicians.
> it has nothing at all to do with keyboards, which by
> Mozart's time were nearly universally tuned to a 12-tone
> "circulating" well-temperament (excluding organs, which
> were also still tuned to meantone).

> Perhaps i can offer a simplified historical view:

> the tuning paradigms for European "art" music were historically:

> 500 AD - 1500: Pythagorean
> 1500s: 1/4-comma meantone (and its relative 31edo)
> 1600s: 1/5-comma meantone (and its relative 43edo)
> 1700s: 1/6-comma meantone (and its relative 55edo)
> 1800 - 2000: 12edo (i.e., 1/11-comma meantone)

> ... with the exception that 12-tone "circulating"
> well-temperaments became standard on harpsichords, clavichords,
> and pianos during the 1700s, and 1/4-comma meantone
> persisted on organs as late as 1850.

-monz

Okay, I would set the beginning of the ideas of the third as
an independend interval and as a result of this the beginning
of the meantone discussions to the end of the 14th or to the
beginning of 15th century.
And we both know that the ideas of tuning models near to ET
are much older as with the 18th century - as lute instruments
couldn't be tuned to meantone models. Additionally a temperament
model for keyboards(!) of Arnolt Schlick of 1511(!!!) shows
already a closen (circulating) somehow "well-tempered" system,
and all tuning values of it nearer to E.T. as for instance with
Kirnberger III.
But please, actually we should not start a discussion
in the history of tuning models.

Best-

Werner

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-----Urspr�ngliche Nachricht-----
Von: Afmmjr@aol.com [mailto:Afmmjr@aol.com]
Gesendet: Mittwoch, 17. Dezember 2003 17:51
An: tuning@yahoogroups.com
Betreff: Re: AW: [tuning] Re: Mozart's ideas

In a message dated 12/17/2003 1:42:09 AM Eastern Standard Time,
wmohrlok@hermode.com writes:

Regarding modern and historic practice in orchestra's intonation: I
don't believe that at
historic times string and wind instrument players liked to perform
fifths by detuned meantone
frequency ratios. "Menatone" is a keyboard tool for the approach to just
intonation, requiring
narrow fifths in order to get better tuned major thirds.
There is no practical reason, neither in Bach's nor Mozart's times and
not actually for the
tuning behavior in an orchestra to perform such narrow fifths. And it is
much easy to
control pure fifths by ear, but very difficult to perform exact weighted
beats of
- for instance - 1/4 comma meantone fifths?
Why should string and wind instruments follow the intonation problems of
keyboards?
By having pity with them?

Best
Werner

> Dear Werner,

> I understand what it must be like for your musical beliefs to be
reconsidered,
> but I think it is necessary regarding early tuning.

> Baroque music always has a keyboard all other instruments must indeed
have
> pity on them. Hearing an exact tempered fifth of any kind is easily
repeatable.
> I have done so with other musicians for decades. > The bassoon can play
any
> single tuning system, besides.

Yes, it can, but it is always a hard battle...

> When you say Mozart, I say Bach. Why? Because I really know the
details for Bach,
> and only learned of Mozart's tuning practices later. Bach in just
intonation is awful.

I agree. But for most other traditional music, written with third and
fifth intervals it
is awful, too.

> The master of temperament is thus eviscerated, indeed castrated.

> Also, narrow fifths may be necessary if there is modulation involved
as in Mozart.
> Werner, your bias for "reine stimmung" is showning.
If you would say: "your bias for a better approach to just intonation..."
I can agree.

> But I hope you have the patience to sift through early music a second
time in your
> lifetime to account for tuning practices that are poorly advertised to
today's musicians.

Johnny, you are right and please believe me: I am no analphabet regarding
the history
of tuning and temperament. But I don't believe all what I am reading as,
too in
historical times, the ideas differed and so one has to weight carfully
what should be
regarded as a subjective opinion of an author and what as generally
accepted.

Best
Werner

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> A pipe organ with 31 tones have been proven playable by Fokker
> >> and the Dutch 31-toners.
> >
> >We hardly needed Fokker to show that; we have centuries of music
> >which is much better descibed as music for 31-et than music for 12-
et,
> >after all. And no, I'm not getting cranky about Bach. :)
>
> *Playable*, Gene. The tuning works of course, but the issue of
> a workable performance devise is different.
>
> -Carl

Carl, have you forgotten about the "bedsheet" experiment I mentioned
a while back:

/tuning/topicId_39323.html#39407

Taking into account the amount of time it takes to learn a keyboard,
any keyboard having homogeneous fingering patterns in all keys is
more workable than 7-white-5-black. I haven't spent more than a few
minutes trying out a Fokker keyboard (on an Archiphone), but I can
vouch that the generalized keyboard employed on the Scalatron was
much more comfortable right from the start.

To say that negotiating 31-ET on the GK Scalatron is "workable" would
be an understatement -- in my opinion it's easier than playing 12-ET
on a conventional keyboard.

--George

[Werner wrote...]
>Well, than the question will be whether the orchestras
>have followed Leopold Mozart and have tuned their fifths
>incorrect. You know (I repeat) that it is simple (in
>comparision) to perform fifths in just intonation against
>an abstract method of reducing the interval by a part
>of a comma and to weight this correctly. This seems
>impossible to me.

Werner,

We are in complete agreement on this matter.

>But please, actually we should not start a discussion
>in the history of tuning models.

Indeed, this subject is so very tired.

-Carl

>Carl, have you forgotten about the "bedsheet" experiment I mentioned
>a while back:
>
>/tuning/topicId_39323.html#39407
>
>Taking into account the amount of time it takes to learn a keyboard,
>any keyboard having homogeneous fingering patterns in all keys is
>more workable than 7-white-5-black. I haven't spent more than a few
>minutes trying out a Fokker keyboard (on an Archiphone), but I can
>vouch that the generalized keyboard employed on the Scalatron was
>much more comfortable right from the start.

I have not forgotten, and you'll see I was defending multiphonic
keyboards in this thread. I was simply letting Gene in on what
was being discussed -- keyboards, not tunings.

>To say that negotiating 31-ET on the GK Scalatron is "workable" would
>be an understatement -- in my opinion it's easier than playing 12-ET
>on a conventional keyboard.

I've never played your scalatron, but I'm afraid I cannot agree with
your statement. More notes and more harmonic relationships are in
some sense harder, even if there were a cultural construct to support
them. But there isn't, and we are completely in the dark. If it is
so easy, please share with us your 31-tone music.

As for playing standard repertoire on a generalized keyboard, I do
not doubt it is easier. But for me it is still harder, at least at
first, since I have already gotten over so much of the halberstadt
learning curve.

-Carl

In a message dated 12/17/03 6:08:07 PM Eastern Standard Time, ekin@lumma.org
writes:

> This seems
> >impossible to me.
>
> Werner,
>
> We are in complete agreement on this matter.
>
> >But please, actually we should not start a discussion
> >in the history of tuning models.
>
> Indeed, this subject is so very tired.
>
> -Carl
>

Carl, you are wrong about this. and yet...you find the subject tired. How
ironic.

best, Johnny

-----Urspr�ngliche Nachricht-----
Von: monz@attglobal.net [mailto:monz@attglobal.net]
Gesendet: Mittwoch, 17. Dezember 2003 11:17
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
> > Von: monz@a... [mailto:monz@a...]
> > Gesendet: Dienstag, 16. Dezember 2003 21:19
> > An: tuning@yahoogroups.com
> > Betreff: [tuning] Re: Mozart's ideas
> >
> > <snip>
> >
> > http://tonalsoft.com/monzo/55edo/55edo.htm
> >
> > -monz

Hi Monz,

indeed, how many words for such a simple subject:
"A 55 EDO is an E qual D istance O ctave with 55 steps".
With such words I would have understood it immediately.

Now we know the following models of EDOs:

12 steps = Equal Temperament, Steps = ETHs (E T Halftones)
31 Steps = Fokker/Huygens, Steps = Fokkers
55 Steps = Telemann/Mozart(?), Steps = Teles
624 Steps = Superpythagorean System, Steps = SPPs
1200 Steps = Cent calculation, Steps = Cents
3072 Steps = 12 Bytes, Steps = Stenz

Most names are my proposals, if you will find better suggestions,
please correct me.
I have to explain the term "Stenz" at the "12 bytes model":
"Stenz" is a neckname of a collegue who proposed to calculate
immediately in Bytes as this is will be the simplest way
for electronic musical instruments. Therefore, in order to
understand each better, we called this unit "Stenz".

The first three calculation units may be also regarded as
proposals for keyboards with 12, 31 or 55 Keys per octave,
the last three are only calculation suggestions.

The approach to a major third
in just intonation (decimal 1.25)
and to a fifth in just intonation (decimal 1.5) is,
depending on the different systems:

Equal temperament:
major third = 4 ETHs = 1.2599
Fifth = 7 ETHs = 1.4983

Fokker/Huygens:
major third = 10 Fokkers = 1.2505
fifth = 18 Fokkers = 1.4955

55EDO
major third = 18 Teles = 1.2546
fifth = 32 Teles = 1.4967

Superpythagorean System
major third = 201 SPS = 1.2500
fifth = 365 SPS = 1.500

Cent calculaton:
major third = 386 Cents = 1.2497
fifth = 702 Cents = 1.500

12 Byte system:
major third = 989 Stenz = 1.2500
fifth = 1797 Stenz = 1.5000

Fokkers 31 Steps (a near - to - 1/4 - Comma System)
is not worse than the 55 EDO system, and requires
14 steps or keys less per octave.

Best:
Werner

on 12/16/03 3:59 PM, sault@cyberware.co.uk <sault@cyberware.co.uk> wrote:

> --- In tuning@yahoogroups.com, alternativetuning@y... wrote:
>>
>>>> Would it make more sense were I to substitute 'rational'
>>>> for 'natural' in my little theory?
>>>
>>
>> The term "dodekaphony" is also confusing, because it is already an
>> accepted term for something else, namely Schoenberg's 12-tone
>> technique. (In some languages, the cognate of "dodekaphony" is the
>> only term for 12-tone technique. In the Brockhaus Riemann Lexikon,
>> for example, "Dodekaphonie" directs the reader
> to "Zwoelftontechnik".
>>
>
>
> It would seem that I have indeed been misusing the
> word 'dodekaphonic', hence the mighty confusion that has arisen here.
> I must express my gratitude to all concerned who have pointed this
> out to me - and must revise my text accordingly. Apparently I should
> be using the term 'Chromatic Scale'. The reasons I did not use that
> in the first place was that the term 'chromatic' did not necessarily,
> to my mind, indicate a specifically 12-tone octave and that I had
> perceived the possibility of N-tone chromatic scales based on
> divisions of the octave according to 2^(1/N) steps, where N is not
> equal to 12, and wanted to be absolutely clear about my intent. Also
> the term 'Chromaticism' has other, prior, meanings that I was already
> aware of.

Hmm. Now coming back and rereading this post (after having just posted a
reply to "Re: [tuning] Re: Dodekachrome - Gene" regarding "chromatic"), I'm
wondering to what degree equal-temperament figures into your sense of what
"chromatic" means.

-Kurt

>
>> Priority is important to you, why not call it "Sault's technique"?
>
>
> That's a bit too personal and I did not invent music but thanks for
> the thought. How about 'Dodekachrome' (noun) and 'Dodekachromatic'
> (adj.)? Or else it could be 'Dodekatone' and 'Dodekatonic' but these
> do not, to my mind, indicate equal value steps. All opinions welcomed.
>
> And priority is surely important to everyone except the Pythagoreans,
> who wrote everything in the name of Pythagoras. Would you have asked
> Mozart to forego the right to put his own name to his own music?
>
>
>>
>> Gabor
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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>
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>
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>
>

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> Now we know the following models of EDOs:
>
> 12 steps = Equal Temperament, Steps = ETHs (E T Halftones)
> 31 Steps = Fokker/Huygens, Steps = Fokkers
> 55 Steps = Telemann/Mozart(?), Steps = Teles
> 624 Steps = Superpythagorean System, Steps = SPPs
> 1200 Steps = Cent calculation, Steps = Cents
> 3072 Steps = 12 Bytes, Steps = Stenz
>
> Most names are my proposals, if you will find better
> suggestions, please correct me.
> I have to explain the term "Stenz" at the "12 bytes model":
> "Stenz" is a neckname of a collegue who proposed to calculate
> immediately in Bytes as this is will be the simplest way
> for electronic musical instruments. Therefore, in order to
> understand each better, we called this unit "Stenz".

you might want to take a look at the whole set of "...mu"
terms that several of us together coined over the summer,
to designate the various tuning resolutions available in MIDI.

http://tonalsoft.com/enc/mu.htm

-monz

>>>This seems impossible to me.
>>
>>Werner,
>>
>>We are in complete agreement on this matter.
>>
>>>But please, actually we should not start a discussion in the
>>>history of tuning models.
>>
>>Indeed, this subject is so very tired.
>>
>>-Carl
>
>Carl, you are wrong about this. and yet...you find the subject
>tired. How ironic.

I find it tired because we hash over the same arguments every
time. You state your opinion and I state mine. But I have never
directly reacted to any of your opinions unless pushed, by Paul
in one case, by yourself in others. I have never voluntarily
given a bad review of anyone on this list, but I will speak
plainly if provoked. By now everyone here knows that I think you
have no clue what you're talking about, so why provoke? Time and
time again you refuse to provide any sound recordings at all to
illustrate any of your esoteric ideas. I've seen you perform live
on several occasions and I have your album Raven and I claim the
advertised accuracy of 1 cent everywhere is not even remotely
demonstrated. Now you have another chance to provide an mp3 or
something to back up your ego-crazed claims.

Incidentally, I witnessed you and ensemble give an outstanding
performance of Wyschnegradsky once. And though I haven't listened
in years I thought your Universe Symphony, for which I happily
paid $50, was really great. I have contributed these positive
comments here several times in the past.

The AFMM has done lots of amazing work, which would be far better
served by a more modest approach to theory.

-Carl

-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Donnerstag, 18. Dezember 2003 07:58
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> Now we know the following models of EDOs:
>
> 12 steps = Equal Temperament, Steps = ETHs (E T Halftones)
> 31 Steps = Fokker/Huygens, Steps = Fokkers
> 55 Steps = Telemann/Mozart(?), Steps = Teles
> 624 Steps = Superpythagorean System, Steps = SPPs
> 1200 Steps = Cent calculation, Steps = Cents
> 3072 Steps = 12 Bytes, Steps = Stenz
>
> Most names are my proposals, if you will find better
> suggestions, please correct me.
> I have to explain the term "Stenz" at the "12 bytes model":
> "Stenz" is a neckname of a collegue who proposed to calculate
> immediately in Bytes as this is will be the simplest way
> for electronic musical instruments. Therefore, in order to
> understand each better, we called this unit "Stenz".

> you might want to take a look at the whole set of "...mu"
> terms that several of us together coined over the summer,
> to designate the various tuning resolutions available in MIDI.

http://tonalsoft.com/enc/mu.htm

-monz

Very interesting. Thak you for your reference to this.

Werner

-----Urspr�ngliche Nachricht-----
Von: monz@attglobal.net [mailto:monz@attglobal.net]
Gesendet: Mittwoch, 17. Dezember 2003 11:17
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
> > Von: monz@a... [mailto:monz@a...]
> > Gesendet: Dienstag, 16. Dezember 2003 21:19
> > An: tuning@yahoogroups.com
> > Betreff: [tuning] Re: Mozart's ideas
> >
> > <snip>
> >
> > http://tonalsoft.com/monzo/55edo/55edo.htm
> >
>
> > Thank you for your reference.
>
>> Regarding modern and historic practice in orchestra's
>> intonation: I don't believe that at historic times string
>> and wind instrument players liked to perform fifths
> > by detuned meantone frequency ratios. "Menatone" is a
> > keyboard tool for the approach to just intonation,
> > requiring narrow fifths in order to get better tuned
> > major thirds.
> > There is no practical reason, neither in Bach's nor
> > Mozart's times and not actually for the tuning behavior
> > in an orchestra to perform such narrow fifths. And it is
> > much easy to control pure fifths by ear, but very difficult
> > to perform exact weighted beats of - for instance - 1/4 comma
> > meantone fifths?
> > Why should string and wind instruments follow the
> > intonation problems of keyboards?
> > By having pity with them?

> well, sorry to disagree with you, but you will have to
> change your beliefs. :)

> Leopold Mozart's violin method clearly illustrates the
> use of "9 commas per whole-tone", "5 commas per diatonic
> semitone", and "4 commas per chromatic semitone".
> and of course the syntonic comma is supposed to be
> tempered out.

(Snip)

> -monz

Hi monz,

still an additional answer to this message:

Regarding Mozart I am sure that you are right and I have
changed my mind. My problem is: I like Mozart (the son) but
I don't like the 55EDO or 31 EDO or any other EDO for the
purpose how to handle the subject of perfect or
almost rich tuning in orchestras. As to my opinion
(repeating my argumentation) such systems are rigid and not
adequate for orchestral music. Besides, it is not necessary
to follow the poor fifths of meantone models.
Maybe you or Mozart or others believe(d) that by a
accompaignment of a keyboard the orchestra should follow
precisely the tuning of the keyboard?
No, this is an error. The orchestra may tune to better
frequency ratios than performed with the keyboard, Such a
mix sounds better than an "all the same" meantone or equal
or other temperament.
At least as long the orchestra will move in somehow (!)
the same pitch.
Never heared?
Listen to any piano concert.
Or: On our websites:
www.hermode.com
at the "examples" to the "Charpentier" music. First presented
with horns in just intonation with the accompaignment of a
harpsichord in E.T., than both in E.T. Which sounds better?
Convinced?

Nevertheless I will continue to like Mozart and to like
you for your patience

Best -
Werner

In a message dated 12/18/03 7:46:31 AM Eastern Standard Time,
wmohrlok@hermode.com writes:

> The orchestra may tune to better
> frequency ratios than performed with the keyboard, Such a
> mix sounds better than an "all the same" meantone or equal
> or other temperament.
> At least as long the orchestra will move in somehow (!)
>

But Werner, are saying that for every melodic purpose a pure 702 cent perfect
fifth is better than an a flattened fifth? I don't think music works that
way.

best, Johnny

hi Werner,

> Von: monz [mailto:monz@a...]
> Gesendet: Donnerstag, 18. Dezember 2003 07:58
>
>
> --- In tuning@yahoogroups.com, "Werner Mohrlok"
> <wmohrlok@h...> wrote:
>
> > Now we know the following models of EDOs:
> >
> > 12 steps = Equal Temperament, Steps = ETHs (E T Halftones)
> > 31 Steps = Fokker/Huygens, Steps = Fokkers
> > 55 Steps = Telemann/Mozart(?), Steps = Teles
> > 624 Steps = Superpythagorean System, Steps = SPPs
> > 1200 Steps = Cent calculation, Steps = Cents
> > 3072 Steps = 12 Bytes, Steps = Stenz
> >
> > Most names are my proposals, if you will find better
> > suggestions, please correct me.
> > I have to explain the term "Stenz" at the "12 bytes model":
> > "Stenz" is a neckname of a collegue who proposed to calculate
> > immediately in Bytes as this is will be the simplest way
> > for electronic musical instruments. Therefore, in order to
> > understand each better, we called this unit "Stenz".
>
>
> you might want to take a look at the whole set of "...mu"
> terms that several of us together coined over the summer,
> to designate the various tuning resolutions available in MIDI.
>
> http://tonalsoft.com/enc/mu.htm

the one you call an "ETH" is already widely known as a
"semitone", and i specifically use a capital S for it
(and have been for 10 years):

http://tonalsoft.com/enc/semi.htm

the one you call a "Fokker" was called "diesis" by Fokker
himself:

http://tonalsoft.com/enc/diesis.htm
(definition number 3)

(both terms, "semitone" and "diesis", unfortunately already
have several different meanings, as you can see from my
definitions. so perhaps it *is* a good idea to give them
new names.)

the ones that you call a "Tele" and an "SPP" have never
been named before, AFAIK.

i don't see where the SPP comes from. 624, prime-factored,
is 2^4 * 3 * 13 . it gives 52 units per 12edo Semitone.
can you explain?

we all already know about "cents".

the one you call a "Stenz" is what we have dubbed an "oktamu":
7 bits (= 256 units) per semitone = 3072 units per 8ve.

http://tonalsoft.com/enc/oktamu.htm

-monz

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> Regarding Mozart I am sure that you [monz] are right and I have
> changed my mind. My problem is: I like Mozart (the son) but
> I don't like the 55EDO or 31 EDO or any other EDO for the
> purpose how to handle the subject of perfect or
> almost rich tuning in orchestras. As to my opinion
> (repeating my argumentation) such systems are rigid and not
> adequate for orchestral music. Besides, it is not necessary
> to follow the poor fifths of meantone models.
> Maybe you or Mozart or others believe(d) that by a
> accompaignment of a keyboard the orchestra should follow
> precisely the tuning of the keyboard?
> No, this is an error. The orchestra may tune to better
> frequency ratios than performed with the keyboard, Such a
> mix sounds better than an "all the same" meantone or equal
> or other temperament.
> At least as long the orchestra will move in somehow (!)
> the same pitch.
> Never heared?
> Listen to any piano concert.
> Or: On our websites:
> www.hermode.com
> at the "examples" to the "Charpentier" music. First presented
> with horns in just intonation with the accompaignment of a
> harpsichord in E.T., than both in E.T. Which sounds better?
> Convinced?
>
> Nevertheless I will continue to like Mozart and to like
> you for your patience

actually, we are in closer agreement than it may appear.

you already know that my background is as an orchestral
musician, and i have been emphasizing on this list for years
that the orchestra is capable of very flexible intonation.

i *do* agree that, regardless of which tuning is "supposed"
to be used, good orchestral musicians will not be able to
resist the inclination to make vertical sonorities approach JI
as closely as possible.

(i'm speaking here of highly trained professionals ... of
course orchestras of a more amateur nature will have a much
wider variety of intonation simply because the musicians
have not had as much ear-training. there should be a number
of high-school concerts ocurring this week which would provide
excellent examples of this!)

but the point i am arguing with you is that musicians in
Mozart's day were *trained* to produce 55edo ... and the more
important point i am making is that we have lost sight of
that fact during the 1900s, which means that the sound of
Mozart's music has changed from what he meant it to be.

of course, this is true in other ways as well. it is
widely known that Mozart loved the sound of the clarinet,
but the instrument he wrote for is not the usual Boehm-system
clarinet used today, or even the common Albert-system, but
rather a very different instrument which only had 5 or 6 keys.

so anyway, all i'm trying to do is set the record straight.

the key-signatures which are available in standard
meantone-based musical notation specify 24 different
notes, as shown here:

http://tonalsoft.com/enc/minor.htm

orchestral musicians during the late 1700s were expected to
aim at performing in a subset of 55edo, which gives a meantone
chain in which there are separate instances of sharps and flats:

Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx

composers would in turn use only a subset of this --
frequently only a 12-note subset, but very often larger
than that, usually around 19 notes. the subset chosen
would depend primarily on the overall tonic-note of
the piece.

-monz

--- In tuning@yahoogroups.com, sault@c... wrote:

> Instead I'll ask you a few questions, Max. Would you eat apple pie
> with gravy? Would you eat roast beef with custard? Would you wear a
> dinner jacket with beach shorts? I'll bet you'll answer NO, NO and
> NO, in which case WHAT HAVE YOU GOT AGAINST APPLE PIE, BUDDY???
>
> Peter

:( OOPS, did I miss something? Is the apple pie a consonance? ;)

I was just pointing a fact. Namely, that the advantage something like
31-eq has against 12-eq is that the former can approximate certain 7-
limit rationes the latter can't, period. Don't get too overdefensive.

You may discard this fact. Indeed, I have a bass and a guitar at
home: Neither has 31 frets per octave, and I feel happy playing them.
Of course I love to experiment with something like 31-eq, or anything
else. But feel free to have your own opinions.

I'm not here to discourage anyone from expressing her arguments and
musical ideas.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >Carl, have you forgotten about the "bedsheet" experiment I
mentioned
> >a while back:
> >
> >/tuning/topicId_39323.html#39407
> >
> >Taking into account the amount of time it takes to learn a
keyboard,
> >any keyboard having homogeneous fingering patterns in all keys is
> >more workable than 7-white-5-black. I haven't spent more than a
few
> >minutes trying out a Fokker keyboard (on an Archiphone), but I can
> >vouch that the generalized keyboard employed on the Scalatron was
> >much more comfortable right from the start.
>
> I have not forgotten, and you'll see I was defending multiphonic
> keyboards in this thread. I was simply letting Gene in on what
> was being discussed -- keyboards, not tunings.
>
> >To say that negotiating 31-ET on the GK Scalatron is "workable"
would
> >be an understatement -- in my opinion it's easier than playing 12-
ET
> >on a conventional keyboard.
>
> I've never played your scalatron, but I'm afraid I cannot agree with
> your statement. More notes and more harmonic relationships are in
> some sense harder,

True, but I have found that the amount of time and effort required to
learn a multitude of patterns to play the same things in different
keys on the conventional keyboard is greater than what is required to
learn new notes and relationships on the generalized keyboard. As a
matter of fact, the generalized keyboard makes it unnecessary to
memorize, for example, the particular tone that's a (slightly
tempered) harmonic seventh above an E-semiflat in 31-ET. All I have
to do is locate the E-semiflat on the keyboard (the blue E key) and
play a harmonic 7th interval, and my finger naturally falls on D-
flat. I can do it almost without thinking, because the intervals are
learned kinesthethically (as well as visually and aurally).

> even if there were a cultural construct to support
> them. But there isn't, and we are completely in the dark. If it is
> so easy, please share with us your 31-tone music.

I never wrote anything in 31-ET, but I spent a lot of time at the
keyboard just trying various things out on it (I guess you could call
it improvising). The ease with which I could play whatever
intervals, chords, and melodic patterns that came to mind (in
whatever key I happened to be in) made it pretty obvious to me that
this sort of keyboard is *highly* workable.

I did record a couple of short compositions in 31-ET (by Fokker and
Mandelbaum) on half-track open-reel tape, and I could make mp3 files
of those and send them to you, if you wish (for your personal use).
Unfortunately, the instrument is now in disrepair, so I would not be
able to record anything else on it at this time. I can still use it
to explore tunings, but only by working around the problems.

--George

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

> i *do* agree that, regardless of which tuning is "supposed"
> to be used, good orchestral musicians will not be able to
> resist the inclination to make vertical sonorities approach JI
> as closely as possible.

Do you really think the BPO creeps towards JI? I have noticed no such
inclination.

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > i *do* agree that, regardless of which tuning is "supposed"
> > to be used, good orchestral musicians will not be able to
> > resist the inclination to make vertical sonorities approach
> > JI as closely as possible.
>
> Do you really think the BPO creeps towards JI? I have
> noticed no such inclination.

well, i wrote that quickly and knew that *someone* would
call me on it.

of course, it all depends on the musical context. in a
slow, very tonal, very diatonic, very harmonic piece with
lots of sustained chords (a good example might be the
slow movement from Bruckner's 7th Symphony), yes, i think
what i said holds true.

but for other styles, no, the musicians would be more likely
to stick more closely to the 12edo/meantone/well-tempered
paradigm.

-monz

>I did record a couple of short compositions in 31-ET (by Fokker and
>Mandelbaum) on half-track open-reel tape, and I could make mp3 files
>of those and send them to you, if you wish (for your personal use).

If you have the time, I'm sure history would thank you. Of course
I do not intend to sell it! (?) And of course I hope you meant, for
"our" personal use. (?)

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >I did record a couple of short compositions in 31-ET (by Fokker
and
> >Mandelbaum) on half-track open-reel tape, and I could make mp3
files
> >of those and send them to you, if you wish (for your personal use).
>
> If you have the time, I'm sure history would thank you. Of course
> I do not intend to sell it! (?)

I just wanted to clarify that I'm not the composer(s), only the
performer. (!)

> And of course I hope you meant, for
> "our" personal use. (?)
>
> -Carl

By "our", were you then referring to "you and me", or to everyone in
the group? In which latter case, okay; where would these files be
put so everyone can listen?

--George

>By "our", were you then referring to "you and me", or to everyone in
>the group? In which latter case, okay; where would these files be
>put so everyone can listen?

The latter. You are welcome to host them at lumma.org, or perhaps
tuning_files has room.

-Carl

-----Urspr�ngliche Nachricht-----
Von: Afmmjr@aol.com [mailto:Afmmjr@aol.com]
Gesendet: Donnerstag, 18. Dezember 2003 14:19
An: tuning@yahoogroups.com
Betreff: Re: AW: [tuning] Re: Mozart's ideas

In a message dated 12/18/03 7:46:31 AM Eastern Standard Time,
wmohrlok@hermode.com writes:

The orchestra may tune to better
frequency ratios than performed with the keyboard, Such a
mix sounds better than an "all the same" meantone or equal
or other temperament.
At least as long the orchestra will move in somehow (!)

> But Werner, are saying that for every melodic purpose a pure 702 cent
>perfect fifth is better than an a flattened fifth? I don't think music
works that way.

> best, Johnny

Johnny,

When I am speaking of fifths sounding better when being tuned
as near as possible to 2 : 3, I am speaking of vertical harmonic
situations.
Indeed, for the melodic progress ( I hope, this is the correct term)
it doesn't matter whether the fifths will show sometimes a distance
to this ideal position.
Really, it isn't possible to create a reasonable system
of rich tuned thirds without changing the tuning ratios of the fifths.
The problem is: We both are thinking in different systems or categories.
I hope you will understand my ideas better as soon a my describtion
of Hermode Tuning will be finished.

Or you plug (stick?) your nose into my websites. I sticked the mine
already in yours...

best
Werner

-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Donnerstag, 18. Dezember 2003 15:58
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

hi Werner,

> Von: monz [mailto:monz@a...]
> Gesendet: Donnerstag, 18. Dezember 2003 07:58
>
>
> --- In tuning@yahoogroups.com, "Werner Mohrlok"
> <wmohrlok@h...> wrote:
>
> > Now we know the following models of EDOs:
> >
> > 12 steps = Equal Temperament, Steps = ETHs (E T Halftones)
> > 31 Steps = Fokker/Huygens, Steps = Fokkers
> > 55 Steps = Telemann/Mozart(?), Steps = Teles
> > 624 Steps = Superpythagorean System, Steps = SPPs
> > 1200 Steps = Cent calculation, Steps = Cents
> > 3072 Steps = 12 Bytes, Steps = Stenz
> >
> > Most names are my proposals, if you will find better
> > suggestions, please correct me.
> > I have to explain the term "Stenz" at the "12 bytes model":
> > "Stenz" is a neckname of a collegue who proposed to calculate
> > immediately in Bytes as this is will be the simplest way
> > for electronic musical instruments. Therefore, in order to
> > understand each better, we called this unit "Stenz".
>
>
> you might want to take a look at the whole set of "...mu"
> terms that several of us together coined over the summer,
> to designate the various tuning resolutions available in MIDI.
>
> http://tonalsoft.com/enc/mu.htm

> the one you call an "ETH" is already widely known as a
> "semitone", and i specifically use a capital S for it
> (and have been for 10 years):

> http://tonalsoft.com/enc/semi.htm

> the one you call a "Fokker" was called "diesis" by Fokker
> himself: http://tonalsoft.com/enc/diesis.htm
> (definition number 3)

> (both terms, "semitone" and "diesis", unfortunately already
> have several different meanings, as you can see from my
> definitions. so perhaps it *is* a good idea to give them
> new names.)

> the ones that you call a "Tele" and an "SPP" have never
> been named before, AFAIK.

> i don't see where the SPP comes from. 624, prime-factored,
> is 2^4 * 3 * 13 . it gives 52 units per 12edo Semitone.
> can you explain?

> we all already know about "cents".

> the one you call a "Stenz" is what we have dubbed an "oktamu":
> 7 bits (= 256 units) per semitone = 3072 units per 8ve.

http://tonalsoft.com/enc/oktamu.htm

> -monz

Hi monz,

I made these proposals as I like abbreviations as well as you
and well as the other members of this list. When using them
it will give us a touch of belonging to the initiates.
So it is for instance possible to write "55 ETO" instead
of a an "equal tempered octave of 55 steps"
as this last term could be immediately understood.
(You will be aware that I am sometimes resentful, but I
will forgive you now).
But it was 02:00 a.m. when I invented these terms and
I feeled that my I.Q. had sunk down. This is the reason
why I asked for other an perhaps better proposals.
Thank you for your help.

1. "Semitone" - Says nothing about the size
of this step. I wanted to characterise the "equal tempered
semitone".

2. "Diesis" - You are right, this calls confusions.

3. "Teles" - Indeed... where is a better suggestion?

4. "SPPs" - I will look whether the inventors of
this system have created an own term. I am sure, they have,
but at that time I had no time to look for it.

5. "Stenz" - It will be hard for me to change it,
as it is a very nice term. What is "oktamu" against this?

Regarding the Superpythagorean System".

I will look for written references as I learned it by a
lecture. The idea is: A pythagorean tuning will be nearly
closen after 52 octaves. So one can calculate with this raster
not only fifths but also thirds near to just intonation.
Still better than with Cents in integers.
Besides it seems to me that it is an invention of
late Pythagoreans who want to reconcile the integers
2, 3 and 5.

Best

Werner

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
> Regarding the Superpythagorean System".
>
> I will look for written references as I learned it by a
> lecture. The idea is: A pythagorean tuning will be nearly
> closen after 52 octaves. So one can calculate with this raster
> not only fifths but also thirds near to just intonation.
> Still better than with Cents in integers.
> Besides it seems to me that it is an invention of
> late Pythagoreans who want to reconcile the integers
> 2, 3 and 5.

ah, thanks for explaining that, now i understand.

however, you're really thinking of *53*edo, not 52.

53edo gives outstanding approximations of 3-limit
Pythagorean tuning, and also excellent approximations
of 5-limit JI.

see
http://tonalsoft.com/enc/pythag.htm

about 2/3 of the way down the page.

-monz

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> I will look for written references as I learned it by a
> lecture. The idea is: A pythagorean tuning will be nearly
> closen after 52 octaves. So one can calculate with this raster
> not only fifths but also thirds near to just intonation.

If you want to do that, you should use 612 notes to the octave, not
624. For that the measure is skismas, or sk for short.

--- In tuning@yahoogroups.com, "Maximiliano G. Miranda Zanetti"
<giordanobruno76@y...> wrote:
> --- In tuning@yahoogroups.com, sault@c... wrote:
>
>
> > Instead I'll ask you a few questions, Max. Would you eat apple
pie
> > with gravy? Would you eat roast beef with custard? Would you wear
a
> > dinner jacket with beach shorts? I'll bet you'll answer NO, NO
and
> > NO, in which case WHAT HAVE YOU GOT AGAINST APPLE PIE, BUDDY???
> >
> > Peter
>
> :( OOPS, did I miss something? Is the apple pie a consonance? ;)
>
> I was just pointing a fact. Namely, that the advantage something
like
> 31-eq has against 12-eq is that the former can approximate certain
7-
> limit rationes the latter can't, period. Don't get too
overdefensive.
>
> You may discard this fact. Indeed, I have a bass and a guitar at
> home: Neither has 31 frets per octave, and I feel happy playing
them.
> Of course I love to experiment with something like 31-eq, or
anything
> else. But feel free to have your own opinions.
>
> I'm not here to discourage anyone from expressing her arguments and
> musical ideas.

Max,

What you say is perfectly true. However, it has precisely nothing to
do with either your original question or my response to it.

In case you've forgotten, your question was "What's wrong with 7/4,
for instance [in the context of dodekaphony]?". Now if you think
about my response in that context, perhaps the matter will come clear
to you. Otherwise please don't let me stop you from eating your
favorite meal of roast beef and custard whilst wearing a dinner
jacket with beach shorts. Why don't you add a bit of tomato ketchup
just to complete the INCONGRUITY of it all?

Peter

-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Donnerstag, 18. Dezember 2003 16:36
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> Regarding Mozart I am sure that you [monz] are right and I have
> changed my mind. My problem is: I like Mozart (the son) but
> I don't like the 55EDO or 31 EDO or any other EDO for the
> purpose how to handle the subject of perfect or
> almost rich tuning in orchestras. As to my opinion
> (Snip)

> actually, we are in closer agreement than it may appear.

> you already know that my background is as an orchestral
> musician, and i have been emphasizing on this list for years
> that the orchestra is capable of very flexible intonation.

> i *do* agree that, regardless of which tuning is "supposed"
> to be used, good orchestral musicians will not be able to
> resist the inclination to make vertical sonorities approach JI
> as closely as possible.

> (i'm speaking here of highly trained professionals ... of
> course orchestras of a more amateur nature will have a much
> wider variety of intonation simply because the musicians
> have not had as much ear-training. there should be a number
> of high-school concerts ocurring this week which would provide
> excellent examples of this!)

> but the point i am arguing with you is that musicians in
> Mozart's day were *trained* to produce 55edo ... and the more
> important point i am making is that we have lost sight of
> that fact during the 1900s, which means that the sound of
> Mozart's music has changed from what he meant it to be.

> of course, this is true in other ways as well. it is
> widely known that Mozart loved the sound of the clarinet,
> but the instrument he wrote for is not the usual Boehm-system
> clarinet used today, or even the common Albert-system, but
> rather a very different instrument which only had 5 or 6 keys.

> so anyway, all i'm trying to do is set the record straight.

> the key-signatures which are available in standard
> meantone-based musical notation specify 24 different
> notes, as shown here:

http://tonalsoft.com/enc/minor.htm

> orchestral musicians during the late 1700s were expected to
> aim at performing in a subset of 55edo, which gives a meantone
> chain in which there are separate instances of sharps and flats:

> Fb Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx Cx Gx

> composers would in turn use only a subset of this --
> frequently only a 12-note subset, but very often larger
> than that, usually around 19 notes. the subset chosen
> would depend primarily on the overall tonic-note of
> the piece.

> -monz

Hi monz,

indeed, we are less far as on the beginning of our discussion.
But we shouldn't blur the points in which we opposite.
You know a lot of informations in the abstract behavior of
orchestra instrumentalists in historic orchestras.
And I say: I don't believe that the theories, mentioned
above, could become completely transposed in orchestra
situations. Even not at that times.
1. What did the lutes? Setting a meantone temperament on a lute
is impossible.
2. You say: "I *do* agree that, regardless of which tuning is
"supposed" to be used, good orchestral musicians will not be
able to resist the inclination to make vertical sonorities
approach JI as closely as possible".
- But I said the opposite: "It is easy (in comparison) to
tune near to JI, but difficult to weight precisely the beats
for meantone fifths".
3. A harpsichord can be retuned very easily so that the
idea of an extented meantone temperament can be followed.
I know this by own experience.
But what was the ideal for an orchestra when beeing in
accompaniment by a pipe orgen in meantone temperament and
by only 12 keys per octave? Following the fifth and
third wolfes of this instrument? Or avoiding these chords?
But some composers didn't weight the limitations of
such instruments.

I agree: Since the invention of the major third in the 13th
or 14th century there exist people who try to realize this
in the best way. And we both follow the same idea. As well
as most of this tuning list. And I like all temperaments
for keyboards which bring the tuning to better-than-ET.
But the best way depends on the instrumental situation
and on the actual performed music.
And I mistrust the written traditions. Scientists of music
are almost thinking in keyboard categories. But the major
third hasn't been invented by keyboarders or scientists
of music. These have only adopted this idea and try to
follow it as best as possible by their (keyboard) tuning
constructions.
Nobody can do more than "as best as possible" but as an
orchestra can do it better than a keyboard I doubt that
even in the 17th or 18th century all orchestra
instrumentalists liked to follow the keyboard restrictions.

Best
Werner

-----Urspr�ngliche Nachricht-----
Von: Gene Ward Smith [mailto:gwsmith@svpal.org]
Gesendet: Samstag, 20. Dezember 2003 00:48
An: tuning@yahoogroups.com
Betreff: [tuning] Re: ET Octaves with different steps (former: Mozart's
ideas)

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> > I will look for written references as I learned it by a
> > lecture. The idea is: A pythagorean tuning will be nearly
> > closen after 52 octaves. So one can calculate with this raster
> > not only fifths but also thirds near to just intonation.

> If you want to do that, you should use 612 notes to the octave, not
> 624. For that the measure is skismas, or sk for short.

Hi Gene

Indeed, It was not a 52 EDO. But it also was not the 51 EDO. It
was the 53 EDO which was called by the lecturer (Rolf Maedel, Austria)
a "Superpythagorean system".

Nevertheless, thank you for your kind information.

Werner

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-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Samstag, 20. Dezember 2003 00:35
An: tuning@yahoogroups.com
Betreff: [tuning] Re: ET Octaves with different steps (former: Mozart's
ideas)

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
> >
> > Regarding the Superpythagorean System".
> >
> > I will look for written references as I learned it by a
> > lecture. The idea is: A pythagorean tuning will be nearly
> > closen after 52 octaves. So one can calculate with this
> > raster
> > not only fifths but also thirds near to just intonation.
> > Still better than with Cents in integers.
> > Besides it seems to me that it is an invention of
> > late Pythagoreans who want to reconcile the integers
> > 2, 3 and 5.

> ah, thanks for explaining that, now i understand.

> however, you're really thinking of *53*edo, not 52.

> 53edo gives outstanding approximations of 3-limit
> Pythagorean tuning, and also excellent approximations
> of 5-limit JI.

> Monz -

you are right. But what a romantic name: "Superpythagorean"
and what a prosaic one: 53EDO".
The lecturer was Rolf Maedel, Austria.

Werner

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> And I say: I don't believe that the theories, mentioned
> above, could become completely transposed in orchestra
> situations. Even not at that times.

indeed. i'm simply saying that there was an *ideal*
of 55edo for non-keyboard instrumental music in the 1700's.
i'm *not* saying that that's what the listener would
actually end up hearing, since the variability of
orchestral tuning is so great and so much at the whim
and ability of the individual performers.

however, i'm trying to emphasize that musicians of
that time were *trained* to produce music that follows
standard staff-notation with sharps/flats, as tuned in
a subset of 55edo -- typically a chain of "5ths" stretching
to 12, 17, or 19 notes.

how closely they achieved this at the time, or even
how closely it can be done today, are subjects for
further research.

but if musicians routinely were taught to play in a
subset of 55edo (which they were), then i'd expect that
composers "heard" their pieces in their minds in 55edo
as well. it would be nice for *us* to hear them in that
tuning now too.

> 1. What did the lutes? Setting a meantone temperament
> on a lute is impossible.

it's easiest to tune all the fretted string instruments
to an equal-temperament, as Peter has been saying again
and again for several days.

the lute was typically tuned to 12edo or at least a
close approximation to it, altho one striking lute tuning
which i view as basically an extended well-temperament
is the one advocated in 1610 by John Dowland:

http://tonalsoft.com/monzo/fngrbds/dowland/dowland.htm

> 2. You say: "I *do* agree that, regardless of which tuning is
> "supposed" to be used, good orchestral musicians will not be
> able to resist the inclination to make vertical sonorities
> approach JI as closely as possible".
> - But I said the opposite: "It is easy (in comparison) to
> tune near to JI, but difficult to weight precisely the beats
> for meantone fifths".

fair enough. i admit that it would be difficult to
*some* degree, since the musician's inclination would
be to adjust towards JI. but again i reiterate that
profession musicians undergo a *training* which is
largely responsible for the intonational choices, and
Mozart's musicians would play 55edo.

> And I mistrust the written traditions. Scientists of music
> are almost thinking in keyboard categories. But the major
> third hasn't been invented by keyboarders or scientists
> of music. These have only adopted this idea and try to
> follow it as best as possible by their (keyboard) tuning
> constructions.

actually, for over a century, investigators into tuning
have been doing much research into the tuning and acoustics
of orchestral instruments. the literature is full of
papers on this.

> Nobody can do more than "as best as possible" but as an
> orchestra can do it better than a keyboard I doubt that
> even in the 17th or 18th century all orchestra
> instrumentalists liked to follow the keyboard restrictions.

but Werner, as i've already said, instrumentalists of
Mozart's time would *not* be following the intonation
of the keyboard unless the piece had a keyboard in it.

by then, keyboards were generally tuned to a circulating
well-temperament which more-or-less-closely resembles
12edo. the instrumental music was generally a ~19-tone
chain-of-5ths subset of 55edo.

-monz

-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Samstag, 20. Dezember 2003 10:51
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

> hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> > And I say: I don't believe that the theories, mentioned
> > above, could become completely transposed in orchestra
> > situations. Even not at that times.

> indeed. i'm simply saying that there was an *ideal*
> of 55edo for non-keyboard instrumental music in the 1700's.
> i'm *not* saying that that's what the listener would
> actually end up hearing, since the variability of
> orchestral tuning is so great and so much at the whim
> and ability of the individual performers.

> however, i'm trying to emphasize that musicians of
> that time were *trained* to produce music that follows
> standard staff-notation with sharps/flats, as tuned in
> a subset of 55edo -- typically a chain of "5ths" stretching
> to 12, 17, or 19 notes.

> how closely they achieved this at the time, or even
> how closely it can be done today, are subjects for
> further research.

> but if musicians routinely were taught to play in a
> subset of 55edo (which they were), then i'd expect that
> composers "heard" their pieces in their minds in 55edo
> as well. it would be nice for *us* to hear them in that
> tuning now too.

This is not only an aesthetic but also historic approach
and even if my personal ideas differ a little to this model
I can and will follow you entirely.

> > 1. What did the lutes? Setting a meantone temperament
> > on a lute is impossible.

> the lute was typically tuned to 12edo or at least a
> close approximation to it, altho one striking lute tuning
> which i view as basically an extended well-temperament
> is the one advocated in 1610 by John Dowland ...

You didn't understand my question. This was
and I am now speaking of the 16th/ 17th century):
If the string and wind instruments generally had to follow
an ideal of meantone temperament of about 1/4 - 1-6 comma)
they had a new conflict when the keyboard was
substituted by lutes, tuned near to. E.T.
At actual concerts we have nearly the same situation with
piano concerts accompained by an orchestra.
In todays orchestras the instrumentalists
(as to my experience) regard the pianos tuning as
a "reference" height, nevertheless the orchestra groups
follow more or less the idea of chords in just intonation.
They don't follow the E.T, as this would sound poor
and they don't follow a meantone model of 12 tones
in fixed tuned heights, as the deviation of some notes
like Eb or G# from E.T. could be too large.
I like this more flexible model and I don't believe that
musicians of the 16th or 17th century in such
situations have been less flexible and have followed
their internal meantone raster instead of weighting
the lute's tuning height.
It was never the question that with a keyboard
tuned to any meantone model the orchestra instruments
have to follow the tuning of a keyboard "as best
as possible".
The dissens between us is: You believe that
they did it with a tuning raster of 55ETO, not only
in their mind but also concrete(!) and I say:
The tuning behavior in an actual orchestra is
more flexible. I cannot believe that in ancient
times they would have been less flexible.
But you don't need to follow me. Even
I don't follow you. Nevertheless I pay
respect to your knowledge and to your kind informations.

> > 2. You say: "I *do* agree that, regardless of which tuning is
> > "supposed" to be used, good orchestral musicians will not be
> > able to resist the inclination to make vertical sonorities
> > approach JI as closely as possible".
> > - But I said the opposite: "It is easy (in comparison) to
> > tune near to JI, but difficult to weight precisely the beats
> > for meantone fifths".

> fair enough. i admit that it would be difficult to
> *some* degree, since the musician's inclination would
> be to adjust towards JI. but again i reiterate that
> profession musicians undergo a *training* which is
> largely responsible for the intonational choices, and
> Mozart's musicians would play 55edo.

Regarding your historical based approach to this subject
I can agree.

> > And I mistrust the written traditions.

> actually, for over a century, investigators into tuning
> have been doing much research into the tuning and acoustics
> of orchestral instruments. the literature is full of
> papers on this.

I don't mistrust all. But as I already have awared evident
errors and opposite ideas, I repeat: one should keep a
little bit of mistrust.

> > Nobody can do more than "as best as possible" but as an
> > orchestra can do it better than a keyboard I doubt that
> > even in the 17th or 18th century all orchestra
> > instrumentalists liked to follow the keyboard restrictions.

> but Werner, as i've already said, instrumentalists of
> Mozart's time would *not* be following the intonation
> of the keyboard unless the piece had a keyboard in it.
> by then, keyboards were generally tuned to a circulating
> well-temperament which more-or-less-closely resembles
> 12edo. the instrumental music was generally a ~19-tone
> chain-of-5ths subset of 55edo.

> monz

but Monz, 17th and 18th century is not Mozart. But this is not
the subject. You believe in a fixed tuning raster in their mind
as it is written down by science of music and "h�las" too by
the Mozarts's.
I say: Maybe, regarding the fixed tuning raster in all
minds I am very sceptic.

You say: This idea was not only in their mind but also
followed and in consequence the poor fifths of such
tuning models have been followed as an ideal.
I say: In this point I cannot follow. *I don't want to follow*.
But this is more or less my problem.

Nevertheless, I thank you again for all the informations
regarding the Mozart's as I didn't know them until now.

And no doubt, I like a 55ETO model much more than an
12ETO model.

Werner

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> > > And I mistrust the written traditions.
>
> > actually, for over a century, investigators into tuning
> > have been doing much research into the tuning and acoustics
> > of orchestral instruments. the literature is full of
> > papers on this.
>
> I don't mistrust all. But as I already have awared evident
> errors and opposite ideas, I repeat: one should keep a
> little bit of mistrust.

stay as critical as you are! that's a *good* thing!!

... the only reason i was receptive to microtonality in
the first place was because i couldn't accept that 12-tone
serialism was really "atonal".

when i was trying to learn how to write serial music at
the conservatory, i kept "feeling" tonality, and was
unsuccessful at writing "atonal" serial pieces.

when i began to understand Partch's theoretical ideas
a year later, they made a lot of sense to me.

> And no doubt, I like a 55ETO model much more than an
> 12ETO model.

i'm interested in your opinion of the sound of the Mozart
example which opens with my webpage (the beginning of the
G-minor 40th Symphony).

http://tonalsoft.com/monzo/55edo/55edo.htm

i've posted before about this but not since we've been
having this discussion: i used to have a very old recording
of this symphony, one of the first electronic recordings,
dating from the early 1920s.

it sounded *exactly* like my 55edo MIDI version, and no
modern recording i've heard has sounded quite like that one.
i was shocked when i finished my 55edo MIDI version, to
hear that it sounded just like that old recording of actual
musicians playing.

apparently there really *was* a tradition of orchestral
playing in something approximating 55edo.

-monz

> > And no doubt, I like a 55ETO model much more than an
> > 12ETO model.

> i'm interested in your opinion of the sound of the Mozart
> example which opens with my webpage (the beginning of the
> G-minor 40th Symphony).

http://tonalsoft.com/monzo/55edo/55edo.htm

> i've posted before about this but not since we've been
> having this discussion: i used to have a very old recording
> of this symphony, one of the first electronic recordings,
> dating from the early 1920s.

> it sounded *exactly* like my 55edo MIDI version, and no
> modern recording i've heard has sounded quite like that one.
> i was shocked when i finished my 55edo MIDI version, to
> hear that it sounded just like that old recording of actual
> musicians playing.

> apparently there really *was* a tradition of orchestral
> playing in something approximating 55edo.

> -monz

Hi monz,

I opened this site but I didn't find the musical example itself.
How should I handle this? I am very interested to hear it.
Besides, I assume that both we couldn't distinguish the acoustic
result of such music when created on the one hand by 55EDO or on
the other hand by the Hermode Tuning mode "horizontal3/5".
I will explain this mode: It is one with thirds and fifths
(no natural septs) tuned as near as possible to just intonation,
and weighting attentively inaudible retuning steps and a tight
approach of the effective frequency positions to 12ET.
Maybe we could distinguish both examples at the 10th or 12th
repetition by counting the fifths beats (if possible)
But indeed: The not perfect frequency ratio of the fifths
is no big aesthetic criterion.
I hope you will not be astonished at the last sentence as I always
said: "I don't like meantone fifths in orchestras", but (I repeat)
"... as it is in orchetral music not necessary to set the fifths
to meantone ratios".

I like your sites as they show many ideas in the science of music by
loving diagrams and explanations. Our "historical" sites inverse are
more didactic, written for beginners.

The two main difference between the 55EDO (or comparable systems)
to Hermode Tuning is that music with such EDOs should be created by
hand or at least by temporary additional messages of the user.
Hermode Tuning inverse runs automatically.
The second one is that these EDO's lead to more distance to
equal temperament and this may be a harder problem
for practical aims.

Reflecting our different approach to this subject I believe
you are much more diligent than I am. I am rather an idler and
therefore created a somehow "automatic tuning gearbox".

Best

Werner

hi Werner,

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> I opened this site but I didn't find the musical example itself.
> How should I handle this? I am very interested to hear it.

the webpage "Mozart's tuning: 55-EDO" should open with
the MIDI of my retuned version of the 40th Symphony
automatically playing.

if it's not working, you can just download the MIDI itself:

http://tonalsoft.com/monzo/55edo/55k550-1bg.mid

(be warned in advance: i am a strong believer in _rubato_,
and i use very flexible tempos in my MIDI-files. not
everyone likes that as much as me.)

-monz

> the webpage "Mozart's tuning: 55-EDO" should open with
> the MIDI of my retuned version of the 40th Symphony
> automatically playing.

> if it's not working, you can just download the MIDI itself:

> http://tonalsoft.com/monzo/55edo/55k550-1bg.mid

> (be warned in advance: i am a strong believer in _rubato_,
> and i use very flexible tempos in my MIDI-files. not
> everyone likes that as much as me.)

> -monz

Hi Monz,

sorry for not having answered until now concerning your
musical example. But my soundcard (or its driver) actually
refuses to play any midi file.
As soon as I can listened to it, you will get my answer.

Werner

Monz:
>> (be warned in advance: i am a strong believer in _rubato_,
> > and i use very flexible tempos in my MIDI-files. not
> > everyone likes that as much as me.)

hear hear I agree mos' heartily ;)
must be sum-t'ing ta due widt me Asian/Sino-Brit backwash ;)
::waves lethal-lookin' heavy-duty bamboo backscratcher::

ObligaTUNING: talkin o' bamboo... anybody got any data on tube zithers and
modes of vibration i.e. a metallic tube 120 cm long, 10-11 cm diametre, or
formulae for obtaining such inharmonical beatifulness (in step-by-step,
colour-by-numbers "Xenotonality for Dummies" format/style, mega-pwetty-sweet-pwease)?

---|-----|--------|-------------|---------------------|
Hanuman Zhang

"For twenty-five centuries, Western knowledge has tried to look upon the
world. It has failed to understand that the world is not for the beholding. It
is for the hearing. It is not legible, but audible. ... Music is a herald,
for change is inscribed in noise faster than it transforms society. ...
Listening to music is listening to all noise, realizing that its appropriation and
control is a reflection of power, that is essentially political." - Jacques
Attali, _Noise: The Political Economy of Music_

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> You say: This idea was not only in their mind but also
> followed and in consequence the poor fifths of such
> tuning models have been followed as an ideal.
> I say: In this point I cannot follow. *I don't want to follow*.
> But this is more or less my problem.

Perhaps the experience of string players tuning their open strings in
pure fifths is so common today that it's difficult to imagine
anything else.

However, this practice was not considered correct in Mozart's day and
for centuries before that. As Peter W. S. correctly points out, what
today is called "meantone tuning" was then simply called "correct
tuning" or even -- blasphemy of blasphemies -- "just tuning". The
tempering of fifths was then one of the most basic parts of a
musician's education, and in the 16th-18th centuries, only a
rather 'rustic' string player would tune the open strings to pure
fifths.

Nevertheless, Werner, you may be quite right that non-keyboard
musicians in those times would *adaptively* adjust all the fifths
toward purity. As I've argued before, this would only require shifts
of a couple of cents -- essentially imperceptible -- from an
underlying meantone grid. However, I find that, contrary to your
assertions, the most highly respected ensembles today fail to adjust
their thirds and sixths away from 12-equal and toward purity more
often than they do do so -- therefore I would not be suprised if the
different "entrenched standard" of meantone in the Renaissance-
Baroque-Classical periods indeed showed up in ensemble playing more
than you seem willing to admit -- especially when open strings were
called for.

In a message dated 12/30/2003 1:09:14 PM Eastern Standard Time,
paul@stretch-music.com writes:

> Baroque-Classical periods indeed showed up in ensemble playing more
> than you seem willing to admit -- especially when open strings were
> called for.
>

Actually, modern string players are encouraged not to use open strings when
playing in the orchestra.

Johnny

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> > You say: This idea was not only in their mind but also
> > followed and in consequence the poor fifths of such
> > tuning models have been followed as an ideal.
> > I say: In this point I cannot follow. *I don't want to follow*.
> > But this is more or less my problem.

> Perhaps the experience of string players tuning their open strings in
> pure fifths is so common today that it's difficult to imagine
> anything else.

> However, this practice was not considered correct in Mozart's day and
> for centuries before that. As Peter W. S. correctly points out, what
> today is called "meantone tuning" was then simply called "correct
> tuning" or even -- blasphemy of blasphemies -- "just tuning". The
> tempering of fifths was then one of the most basic parts of a
> musician's education, and in the 16th-18th centuries, only a
> rather 'rustic' string player would tune the open strings to pure
> fifths.

> Nevertheless, Werner, you may be quite right that non-keyboard
> musicians in those times would *adaptively* adjust all the fifths
> toward purity. As I've argued before, this would only require shifts
> of a couple of cents -- essentially imperceptible -- from an
> underlying meantone grid. However, I find that, contrary to your
> assertions, the most highly respected ensembles today fail to adjust
> their thirds and sixths away from 12-equal and toward purity more
> often than they do do so -- therefore I would not be suprised if the
> different "entrenched standard" of meantone in the Renaissance-
> Baroque-Classical periods indeed showed up in ensemble playing more
> than you seem willing to admit -- especially when open strings were
> called for.

Paul,

you are speaking of fifths and not of thirds, therefore I am uncertain
whether you did understand me.
I started this discussion as I know by my own experience in orchestra
and chamber music that it is actually usual by well educated musicians
to tune not only the fifths but too the thirds (!!!) to just intonation.
In this way there is no dissens betwen us.
But: For people who are thinking in fix tuning models this means a
meantone tuning model. String and wind instrument players and singers
against this almost don't think in such categories. It is in abstract no
problem for them to tune for instance major chords to perfect thirds and
fifths. Indeed, in practice it failures sometimes, but with actual
orchestras and choirs of high quality one can hear that this their ideal
tuning.
The compromise that one has to follow with such tuning ideal is:
One has to set sometimes the melodic steps more or less different to just
intonation and indeed, the melodic fifths will show often the ratios of
"meantone" steps.
I say an example, as it is typical for this kind of intonation and too for
Hermode Tuning:
D-F-A to Bb-D-F
Cent values as deviation from ET:
D -6, F +10, A -4 to Bb +5, D -9, F +11
The step F to B is 695 Cents, a typical meantone step.
And this point is the only one in which we may differ: You and some other
members of this list follow in their ideas a static model of meantone and
I
follow a more dynamic model. And Mozart, I had to learn by "monz", did
follow this static model. This dissens between Mozart and me is sad
for me, but I have to live with it.

best
Werner

-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Montag, 22. Dezember 2003 08:55
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

> the webpage "Mozart's tuning: 55-EDO" should open with
> the MIDI of my retuned version of the 40th Symphony
> automatically playing.

> if it's not working, you can just download the MIDI itself:

> http://tonalsoft.com/monzo/55edo/55k550-1bg.mid

> (be warned in advance: i am a strong believer in _rubato_,
> and i use very flexible tempos in my MIDI-files. not
> everyone likes that as much as me.)

> -monz

Hi monz,

I opened it, but the synth of my PC performs it with terrible
sounds, so I cannot judge the quality of this musical example.
Besides: It seems to me that my synth is playing in ET.
Indeed, I cannot imagine that it supports tuning messages.
If ever you will possess an audio file, please send it to me,
I have DSL so that the size of the file may be large.
Thanks in advance

Werner

Werner

You do not need web access to participate. You may subscribe through
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Hi Werner.

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
>
> --- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...>
wrote:
>
> > > You say: This idea was not only in their mind but also
> > > followed and in consequence the poor fifths of such
> > > tuning models have been followed as an ideal.
> > > I say: In this point I cannot follow. *I don't want to
follow*.
> > > But this is more or less my problem.
>
> > Perhaps the experience of string players tuning their open
strings in
> > pure fifths is so common today that it's difficult to imagine
> > anything else.
>
> > However, this practice was not considered correct in Mozart's
day and
> > for centuries before that. As Peter W. S. correctly points
out, what
> > today is called "meantone tuning" was then simply
called "correct
> > tuning" or even -- blasphemy of blasphemies -- "just tuning".
The
> > tempering of fifths was then one of the most basic parts of a
> > musician's education, and in the 16th-18th centuries, only a
> > rather 'rustic' string player would tune the open strings to
pure
> > fifths.
>
> > Nevertheless, Werner, you may be quite right that non-keyboard
> > musicians in those times would *adaptively* adjust all the
fifths
> > toward purity. As I've argued before, this would only require
shifts
> > of a couple of cents -- essentially imperceptible -- from an
> > underlying meantone grid. However, I find that, contrary to
your
> > assertions, the most highly respected ensembles today fail to
adjust
> > their thirds and sixths away from 12-equal and toward purity
more
> > often than they do do so -- therefore I would not be suprised
if the
> > different "entrenched standard" of meantone in the Renaissance-
> > Baroque-Classical periods indeed showed up in ensemble playing
more
> > than you seem willing to admit -- especially when open strings
were
> > called for.
>
> Paul,
>
> you are speaking of fifths and not of thirds, therefore I am
uncertain
> whether you did understand me.
> I started this discussion as I know by my own experience in
orchestra
> and chamber music that it is actually usual by well educated
musicians
> to tune not only the fifths but too the thirds (!!!) to just
intonation.

I understood this, but my experience has been quite different. Though
some well educated musicians do do this, quite a few, even at the top
of the chamber music field, show no tendency to adjust their thirds
to just intonation. In fact, the latter appears to be more the rule
than the exception these days, and Kyle Gann has attested to having
had similar experience.

> In this way there is no dissens betwen us.

No, it seems that we differ on this.

> But: For people who are thinking in fix tuning models this means
a
> meantone tuning model.

It rather seems to me that today, if there is a fixed tuning model in
use among a plurality of chamber ensembles, it is 12-equal rather
than meantone. And since 12-equal has impure thirds and sixths, which
are all too readily produced and heard by chamber groups today, I see
no reason why 16th-18th century musicians wouldn't similarly show
some tendency, however small, toward tempered fifths and fourths.

> String and wind instrument players and singers
> against this almost don't think in such categories.

But many of them have been *trained* to produce the set of possible
intervals as they occur in 12-equal, through constant exposure to the
piano, etc.

> It is in abstract no
> problem for them to tune for instance major chords to perfect
thirds and
> fifths. Indeed, in practice it failures sometimes, but with actual
> orchestras and choirs of high quality one can hear that this their
ideal
> tuning.

I might agree, but then I would have to dismiss many of the most
renowned orchestras and choirs as being "of low quality", since they
show no such tendency -- and this observation has been corroborated
by scientific measurements.

> The compromise that one has to follow with such tuning ideal is:
> One has to set sometimes the melodic steps more or less different
to just
> intonation and indeed, the melodic fifths will show often the
ratios of
> "meantone" steps.
> I say an example, as it is typical for this kind of intonation
and too for
> Hermode Tuning:
> D-F-A to Bb-D-F
> Cent values as deviation from ET:
> D -6, F +10, A -4 to Bb +5, D -9, F +11
> The step F to B is 695 Cents, a typical meantone step.
> And this point is the only one in which we may differ: You and
some other
> members of this list follow in their ideas a static model of
meantone and
> I
> follow a more dynamic model.

The 'static' model of meantone is only useful as a guide to the
*tendencies* that might have been exhibited in the performance of
intervals by 16th-18th century musicians. Of course I don't believe
that a chamber group or orchestra would have produced a static
meantone tuning. In fact, I've made countless posts to this list
about how a dynamic conception of meantone can sit very well with
such tendencies, departing from them only minutely, and still be able
to acheive vertical just intonation in major and minor triads. See,
for example:

http://www.tonalsoft.com/enc/adaptiveji.htm
http://www.sonic-arts.org/monzo/vicentino/vicentino.htm
(the tonalsoft url for the latter page is not working)

Hoping we're moving toward a better understanding of one another,
Paul

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:

> I opened it, but the synth of my PC performs it with terrible
> sounds, so I cannot judge the quality of this musical example.
> Besides: It seems to me that my synth is playing in ET.

Joe: should I put up an ogg file of this?

-----Urspr�ngliche Nachricht-----
Von: Paul Erlich [mailto:paul@stretch-music.com]
Gesendet: Dienstag, 30. Dezember 2003 22:30
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

Hi Paul,

> Hi Werner.

(Snip)
> > you are speaking of fifths and not of thirds, therefore I am
>> uncertain whether you did understand me.
>> I started this discussion as I know by my own experience in
>> orchestra and chamber music that it is actually usual by well
>> educated musicians to tune not only the fifths but too the
>> thirds (!!!) to just
>> intonation.

> I understood this, but my experience has been quite different. Though
> some well educated musicians do do this, quite a few, even at the top
> of the chamber music field, show no tendency to adjust their thirds
> to just intonation. In fact, the latter appears to be more the rule
> than the exception these days, and Kyle Gann has attested to having
> had similar experience.

> > In this way there is no dissens betwen us.

> No, it seems that we differ on this.

Okay then we differ, but as there are orchestras of different quality, the
result
is different. Nevertheless, I know by my own discussions in orchestras
and chamber music groups that the perfect tuning of thirds and fifths at
least
is astrived for - and not only in the best ones.

(Snip)

> > String and wind instrument players and singers
> > against this almost don't think in such categories.

> But many of them have been *trained* to produce the set of possible
> intervals as they occur in 12-equal, through constant exposure to the
> piano, etc.

No, no, and I don't know any qualified professor or teacher
pleading for such tuning behavior.
And I cannot believe that Europe is more progressive than
America.
Nevertheless I believe that the country with the best education
in tuning is England.
A nice example, if you can get it:
The "Hannover Band" with Beethovens Symphony No. 2.

> > It is in abstract no
> > problem for them to tune for instance major
>> chords to perfect thirds and > fifths. Indeed, in practice
>> it failures sometimes, but with actual
> > orchestras and choirs of high quality one can hear that
>> this their ideal tuning.

> > I might agree, but then I would have to dismiss many of the
>> most renowned orchestras and choirs as being "of low quality",
>> since they show no such tendency -- and this observation has
>> been corroborated by scientific measurements.

>I mistrust such measurements as long as I don't
>know how it was done and how it was controlled.
>I believe, it is nearly impossible to measure the
>frequencies in an orchestra in action.

(Snip)
>> And this point is the only one in which we may differ:
>> You and s ome other members of this list follow in their
>> ideas a static model of
>> meantone and I follow a more dynamic model.

> The 'static' model of meantone is only useful as a guide to the
> *tendencies* that might have been exhibited in the performance of
> intervals by 16th-18th century musicians. Of course I don't believe
> that a chamber group or orchestra would have produced a static
> meantone tuning. In fact, I've made countless posts to this list
> about how a dynamic conception of meantone can sit very well with
> such tendencies, departing from them only minutely, and still be able
> to acheive vertical just intonation in major and minor triads. See,
> for example:

http://www.tonalsoft.com/enc/adaptiveji.htm
http://www.sonic-arts.org/monzo/vicentino/vicentino.htm
> (the tonalsoft url for the latter page is not working)

> Hoping we're moving toward a better understanding of one another,
> Paul

I hope so, too.
Best
Werner

>> No, it seems that we differ on this.
>
> Okay then we differ, but as there are orchestras of different
> quality, the result is different. Nevertheless, I know by my
> own discussions in orchestras and chamber music groups that the
> perfect tuning of thirds and fifths at least is astrived for -
> and not only in the best ones.

Werner and I agree on this point.

> > > String and wind instrument players and singers
> > > against this almost don't think in such categories.
>
> > But many of them have been *trained* to produce the set of
> > possible intervals as they occur in 12-equal, through constant
> > exposure to the piano, etc.
>
>No, no, and I don't know any qualified professor or teacher
>pleading for such tuning behavior.

Some do, some don't.

>And I cannot believe that Europe is more progressive than
>America.

America did suffer much more of the serialist music theory
than Europe, which tends to stress the perfection of 12.

Still, it has not been my experience that any modern orchestral
brass section is pulled toward 12-tET. Especially in those
German orchestras still using rotary-valve trumpets, the sound
is very often headed toward JI.

The intonation of string sections is generally pretty poor in
my experience. Even the unisons. Perhaps for this reason I
do not often love orchestral strings. There are exceptions,
such as the MET orchestra (Metropolitan Opera in New York).

>A nice example, if you can get it:
>The "Hannover Band" with Beethovens Symphony No. 2.

A wind band? I love wind bands; I will see if I can get it!

-Carl

-----Urspr�ngliche Nachricht-----
Von: Carl Lumma [mailto:ekin@lumma.org]
Gesendet: Mittwoch, 31. Dezember 2003 00:08
An: tuning@yahoogroups.com
Betreff: Re: AW: [tuning] Re: Mozart's ideas

> > Okay then we differ, but as there are orchestras of different
> > quality, the result is different. Nevertheless, I know by my
> > own discussions in orchestras and chamber music groups that the
> > perfect tuning of thirds and fifths at least is astrived for -
> > and not only in the best ones.

> Werner and I agree on this point.

Thank you for your assistance

> > > String and wind instrument players and singers
> > > against this almost don't think in such categories.
>
> > But many of them have been *trained* to produce the set of
> > possible intervals as they occur in 12-equal, through constant
> > exposure to the piano, etc.
>
> >No, no, and I don't know any qualified professor or teacher
> >pleading for such tuning behavior.

> Some do, some don't.

Carl, you are right. One cannot say "all" or "no one", but I know
much more of the first and better group.

> >And I cannot believe that Europe is more progressive than
> >America.

> America did suffer much more of the serialist music theory
> than Europe, which tends to stress the perfection of 12.

> Still, it has not been my experience that any modern orchestral
> brass section is pulled toward 12-tET. Especially in those
> German orchestras still using rotary-valve trumpets, the sound
> is very often headed toward JI.

> The intonation of string sections is generally pretty poor in
> my experience. Even the unisons. Perhaps for this reason I
> do not often love orchestral strings. There are exceptions,
> such as the MET orchestra (Metropolitan Opera in New York).

> >A nice example, if you can get it:
> >The "Hannover Band" with Beethovens Symphony No. 2.

> A wind band? I love wind bands; I will see if I can get it!

> -Carl

No. it is a traditional symphony orchestra. "Traditional" means:
Equipped with instruments built in the style of about 1800.
But the particular merit is not the ancient sound. It is the
intonation without vibrato, but with nearly perfect thirds
and fifths. If you will compare it with Karajan or Boehm
it is a completely different world. In the first moment very
strange, but than a very exciting interpretation.

Werner

hi Werner,

you know, what i really need to do is just
make an mp3 of it. i will, when i get a chance,
and i'll put that on the webpage.

-monz

--- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...> wrote:
>
> -----Ursprüngliche Nachricht-----
> Von: monz [mailto:monz@a...]
> Gesendet: Montag, 22. Dezember 2003 08:55
> An: tuning@yahoogroups.com
> Betreff: [tuning] Re: Mozart's ideas
>
>
> > the webpage "Mozart's tuning: 55-EDO" should open with
> > the MIDI of my retuned version of the 40th Symphony
> > automatically playing.
>
> > if it's not working, you can just download the MIDI itself:
>
> > http://tonalsoft.com/monzo/55edo/55k550-1bg.mid
>
>
> > (be warned in advance: i am a strong believer in _rubato_,
> > and i use very flexible tempos in my MIDI-files. not
> > everyone likes that as much as me.)
>
> > -monz
>
> Hi monz,
>
> I opened it, but the synth of my PC performs it with terrible
> sounds, so I cannot judge the quality of this musical example.
> Besides: It seems to me that my synth is playing in ET.
> Indeed, I cannot imagine that it supports tuning messages.
> If ever you will possess an audio file, please send it to me,
> I have DSL so that the size of the file may be large.
> Thanks in advance
>
> Werner
>
> Werner
>
>
>
>
>
>
>
>
>
>
>
>
> You do not need web access to participate. You may subscribe
through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the
tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery
on hold
> for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to
daily digest
> mode.
> tuning-normal@yahoogroups.com - change your subscription to
individual
> emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
>
>
>
> --------------------------------------------------------------------
--------
> --
>
> Yahoo! Groups Links
>
> a.. To visit your group on the web, go to:
> /tuning/
>
> b.. To unsubscribe from this group, send an email to:
> tuning-unsubscribe@yahoogroups.com
>
> c.. Your use of Yahoo! Groups is subject to the Yahoo! Terms of
Service.

hi paaul,

In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

> ... Of course I don't believe
> that a chamber group or orchestra would have produced
> a static meantone tuning. In fact, I've made countless
> posts to this list about how a dynamic conception of
> meantone can sit very well with such tendencies, departing
> from them only minutely, and still be able to acheive
> vertical just intonation in major and minor triads. See,
> for example:
>
> http://www.tonalsoft.com/enc/adaptiveji.htm
> http://www.sonic-arts.org/monzo/vicentino/vicentino.htm
> (the tonalsoft url for the latter page is not working)

thanks. it's working now.

http://tonalsoft.com/monzo/vicentino/vicentino.htm

-monz

hi Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> --- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...>
wrote:
>
> > I opened it, but the synth of my PC performs it with terrible
> > sounds, so I cannot judge the quality of this musical example.
> > Besides: It seems to me that my synth is playing in ET.
>
> Joe: should I put up an ogg file of this?

yes, if you can, please do! thanks!!

(the musical quality of your .oggs has been better
than that of my MIDIs, and it's easy for me to convert
your .oggs into .mp3s.)

-monz

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

> (the musical quality of your .oggs has been better
> than that of my MIDIs, and it's easy for me to convert
> your .oggs into .mp3s.)

If you want an mp3 I'll make one directly. What sort of mp3 do you
favor?

-----Urspr�ngliche Nachricht-----
Von: monz [mailto:monz@attglobal.net]
Gesendet: Mittwoch, 31. Dezember 2003 09:04
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

> hi Werner,

> you know, what i really need to do is just
> make an mp3 of it. i will, when i get a chance,
> and i'll put that on the webpage.

> -monz

Thank you in advance.

Werner

> > (be warned in advance: i am a strong believer in _rubato_,
> > and i use very flexible tempos in my MIDI-files. not
> > everyone likes that as much as me.)
>
> > -monz
>
> > Hi monz,
>
> > I opened it, but the synth of my PC performs it with terrible
> > sounds, so I cannot judge the quality of this musical example.
> > Besides: It seems to me that my synth is playing in ET.
> > Indeed, I cannot imagine that it supports tuning messages.
> > If ever you will possess an audio file, please send it to me,
> > I have DSL so that the size of the file may be large.
> > Thanks in advance
>
> > Werner
>

Hello,

Why don't you just get an OGG player or plug-in? You will probably
lose some quality in converting and OGG is a good format by several
measures.

Gabor

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> hi Gene,
>
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> > --- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...>
> wrote:
> >
> > > I opened it, but the synth of my PC performs it with terrible
> > > sounds, so I cannot judge the quality of this musical example.
> > > Besides: It seems to me that my synth is playing in ET.
> >
> > Joe: should I put up an ogg file of this?
>
>
>
> yes, if you can, please do! thanks!!
>
> (the musical quality of your .oggs has been better
> than that of my MIDIs, and it's easy for me to convert
> your .oggs into .mp3s.)
>
>
>
> -monz

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

/tuning/topicId_49814.html#50683

> >> No, it seems that we differ on this.
> >
> > Okay then we differ, but as there are orchestras of different
> > quality, the result is different. Nevertheless, I know by my
> > own discussions in orchestras and chamber music groups that the
> > perfect tuning of thirds and fifths at least is astrived for -
> > and not only in the best ones.
>
> Werner and I agree on this point.
>
> > > > String and wind instrument players and singers
> > > > against this almost don't think in such categories.
> >
> > > But many of them have been *trained* to produce the set of
> > > possible intervals as they occur in 12-equal, through constant
> > > exposure to the piano, etc.
> >
> >No, no, and I don't know any qualified professor or teacher
> >pleading for such tuning behavior.
>
> Some do, some don't.
>
> >And I cannot believe that Europe is more progressive than
> >America.
>
> America did suffer much more of the serialist music theory
> than Europe, which tends to stress the perfection of 12.
>

***Hi Carl,

Are you certain of this? Serialism was *invented* in Europe and
European composers are still writing in that system, much more than
here in America, it seems...

J. Pehrson

hi Gabor,

--- In tuning@yahoogroups.com, "alternativetuning"
<alternativetuning@y...> wrote:

> Hello,
>
> Why don't you just get an OGG player or plug-in? You
> will probably lose some quality in converting and OGG
> is a good format by several measures.
>
> Gabor

yes, i agree. the OGG files Gene has already made of
my Mahler 7th MIDIs sound much better than any of the
mp3's i've made.

i been sticking with mp3 because it seems to me to be
a more universal format. can OGG files be played in
those stand-alone mp3 players?

but if the new website has enough space, perhaps i can
start offering my audio files in both formats.

-monz

>> America did suffer much more of the serialist music theory
>> than Europe, which tends to stress the perfection of 12.
>>
>
>***Hi Carl,
>
>Are you certain of this? Serialism was *invented* in Europe and
>European composers are still writing in that system, much more than
>here in America, it seems...
>
>J. Pehrson

No, I'm not. But I've heard there was a time (like, the 50's) when
it was impossible to do anything but serialism in America while the
same was never true in Europe.

-Carl

>i been sticking with mp3 because it seems to me to be
>a more universal format. can OGG files be played in
>those stand-alone mp3 players?

Only certain ones.

I even use mp3 myself, and I'm an 'early adopter' extreme-
Vitalis member of the Secret Order of early adoption, I am. :)

Happy New Year!

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> No, it seems that we differ on this.
> >
> > Okay then we differ, but as there are orchestras of different
> > quality, the result is different. Nevertheless, I know by my
> > own discussions in orchestras and chamber music groups that the
> > perfect tuning of thirds and fifths at least is astrived for -
> > and not only in the best ones.
>
> Werner and I agree on this point.

Well, I don't know what orchestras and chamber groups you guys have
been listening to. It's evident to me that among the most famous and
most highly respected groups, a huge number, perhaps even a majority,
show no tendency to mutate their harmonies toward just intonation.

> > > > String and wind instrument players and singers
> > > > against this almost don't think in such categories.
> >
> > > But many of them have been *trained* to produce the set of
> > > possible intervals as they occur in 12-equal, through constant
> > > exposure to the piano, etc.
> >
> >No, no, and I don't know any qualified professor or teacher
> >pleading for such tuning behavior.
>
> Some do, some don't.

Exactly. In fact, at least in the United States, despite being
the "home of Just Intonation" in microtonal circles, it's rare to
find a professor or teacher who works to diminsh the emphasis on the
piano and to explicitly encourage those deviations which will yield
more just harmonies.

> Still, it has not been my experience that any modern orchestral
> brass section is pulled toward 12-tET. Especially in those
> German orchestras still using rotary-valve trumpets, the sound
> is very often headed toward JI.

All-brass chamber ensembles have usually sounded most like they were
adapting toward JI (to me).

> The intonation of string sections is generally pretty poor in
> my experience. Even the unisons.

All-string chamber ensembles have usually sounded least like they
were adapting toward JI (to me), despite the fact that flexible
intonation (such as is required for adaptive JI) should be easiest
for them.

>> > Okay then we differ, but as there are orchestras of different
>> > quality, the result is different. Nevertheless, I know by my
>> > own discussions in orchestras and chamber music groups that the
>> > perfect tuning of thirds and fifths at least is astrived for -
>> > and not only in the best ones.
>>
>> Werner and I agree on this point.
>
>Well, I don't know what orchestras and chamber groups you guys have
>been listening to. It's evident to me that among the most famous and
>most highly respected groups, a huge number, perhaps even a majority,
>show no tendency to mutate their harmonies toward just intonation.

I've mentioned a number of groups here. Virtually any early music
group will show this tendency. Modern string quartets, big bands,
etc. not as often. Meanwhile amateur (as opposed to highly-respected)
groups are a great example... their intonation is often very poor,
yet the vertical harmonies are drawn to JI.

>> Still, it has not been my experience that any modern orchestral
>> brass section is pulled toward 12-tET. Especially in those
>> German orchestras still using rotary-valve trumpets, the sound
>> is very often headed toward JI.
>
>All-brass chamber ensembles have usually sounded most like they were
>adapting toward JI (to me).

Yes, of course. But also in an orchestra the brass section can
do this, especially in Mahler where the brass is often given a
rather independant voice (not to mention solos).

>> The intonation of string sections is generally pretty poor in
>> my experience. Even the unisons.
>
>All-string chamber ensembles have usually sounded least like they
>were adapting toward JI (to me), despite the fact that flexible
>intonation (such as is required for adaptive JI) should be easiest
>for them.

I've heard string quartets go both ways. I've heard Mozart with
some nice 5-limit JI. OTOH I often hear more 12-tET (especially
in works where the writing does not stress 5-limit sonorities).

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> > Okay then we differ, but as there are orchestras of different
> >> > quality, the result is different. Nevertheless, I know by my
> >> > own discussions in orchestras and chamber music groups that the
> >> > perfect tuning of thirds and fifths at least is astrived for -
> >> > and not only in the best ones.
> >>
> >> Werner and I agree on this point.
> >
> >Well, I don't know what orchestras and chamber groups you guys
have
> >been listening to. It's evident to me that among the most famous
and
> >most highly respected groups, a huge number, perhaps even a
majority,
> >show no tendency to mutate their harmonies toward just intonation.
>
> I've mentioned a number of groups here. Virtually any early music
> group will show this tendency.

Yes, they are more likely to be trained this way, or at least to be
listening to a meantone reference, which will get them a lot closer
to achieving adaptive JI than 12-equal would, and sounds more like JI
than 12-equal does to begin with.

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

> i been sticking with mp3 because it seems to me to be
> a more universal format. can OGG files be played in
> those stand-alone mp3 players?

That depends on which ones you try it with. It won't work with any
but some of the newest.

--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Werner Mohrlok" <wmohrlok@h...>
wrote:
>
> > You say: This idea was not only in their mind but also
> > followed and in consequence the poor fifths of such
> > tuning models have been followed as an ideal.
> > I say: In this point I cannot follow. *I don't want to follow*.
> > But this is more or less my problem.
>
> Perhaps the experience of string players tuning their open strings
in
> pure fifths is so common today that it's difficult to imagine
> anything else.
>
> However, this practice was not considered correct in Mozart's day
and
> for centuries before that. As Peter W. S. correctly points out,
what
> today is called "meantone tuning" was then simply called "correct
> tuning" or even -- blasphemy of blasphemies -- "just tuning". The
> tempering of fifths was then one of the most basic parts of a
> musician's education, and in the 16th-18th centuries, only a
> rather 'rustic' string player would tune the open strings to pure
> fifths.
>
> Nevertheless, Werner, you may be quite right that non-keyboard
> musicians in those times would *adaptively* adjust all the fifths
> toward purity. As I've argued before, this would only require
shifts
> of a couple of cents -- essentially imperceptible -- from an
> underlying meantone grid. However, I find that, contrary to your
> assertions, the most highly respected ensembles today fail to
adjust
> their thirds and sixths away from 12-equal and toward purity more
> often than they do do so -- therefore I would not be suprised if
the
> different "entrenched standard" of meantone in the Renaissance-
> Baroque-Classical periods indeed showed up in ensemble playing
more
> than you seem willing to admit -- especially when open strings
were
> called for.

Yes, entrenched. Johann Joachim Quantz (On Playing the Flute, 1753)
has an interestingly precise tuning instruction. I gave away my
last copy but maybe in chapter 4, where the fingering charts are, he
says that the difference between a sharp and the enharmonic flat is
one ninth of a whole tone. That is exactly the subset of 55edo,
where c-c# is the 55th root of 2 to the 4th, c#-d the same to the
5th, but Db-D again only to the 4th, etc. This is approximately
enough, 6th comma meantone, and in fact splits the difference
between the commas of Pythagoras and Didymus. Quantz gives compleat
fingerings for 18 or 19 steps per octave, not theory but practice.
He was entirely mainstream since he served in King Frederick's
orchestra with Emmanuel Bach, and their writings underpin Classical
music. He and Bach emphasize good taste and style. I take it that
this degree of control over intonation was required. I hadn't seen
the information on Mozart's opinions to Attwood before, so my thanks
to our contributors, Monz, Werner, et al. On the matter of
intonation, the musical education establishment is degenerate. I
gave my copies of Bach and Quantz to my niece, who is currently
negotiating the university cirriculum, may her ears be opened.

On St. Paul Sunday I heard Kronos Quartet play Harry Partch, sorry
for no title. Funny to hear them talk afterwards about the plus and
minus signs on the notes (their transcription I guess), and "playing
in the cracks". Their fingerboards have cracks? Sounded good to me.

Carl Lumma wrote:
>>>America did suffer much more of the serialist music theory
>>>than Europe, which tends to stress the perfection of 12.
>>>

and:

> > > No, I'm not. But I've heard there was a time (like, the 50's) when
> it was impossible to do anything but serialism in America while the
> same was never true in Europe.

I haven't looked into this deeply, but my impression is the opposite of the latter statement while I concur with the first. The US have always (talking about the 2nd half of the last century) had a greater stylistic variety in newly composed music. Part of the reason is surely the lack of subsidies for orchestras, which cries for pieces that do not deviate too much from common practice. But even then, you had Varese, Cage, Luening/Ussachevsky, Howard Hanson, ... In Europe, Darmstadt and Donaueschingen (plus many other radio-related events and performing entities) were totally taken over by the serialists. Nobody performed e.g. Karl Amadeus Hartmann (who might have served as a stylistic link to pre-wwar non-serial music) after the forties. Orff may be the only exception; he was performed widely in german operas.

I need to be germanocentric here and can't say much about the scene in Spain, Portugal, GB, but Darmstadt and Donaueschingen did include what happened in France and Italy. (Name me a few composers who studied with Naka Boulanger. Where do they come from?) And serialist procedures were a de rigeur subversive gesture in the communist countries - but the same eastern composers were the ones who eventually softened the serial paradigm.

Serialist theory, on the other hand, was invented singlehandedly by Milton Babbit and taken further by Allen Forte and George Perle. They showed the properties of the system, whereas the publications in the Reihe (for instance) generally are child's play in comparison, rediscovering Babbitt's procedures and describing rules used by individual composers for individual pieces.

And possibly a composer's curriculum in the academy was indeed more conservative in Europe (you c/should still go to Darmstadt in summer), while in the US, serial theory was taught to a greater extent than many thought necessary.

klaus

p.s. to cover the off-topicality: I like the "eastern" use of quartertones to thicken the sound.

-----Urspr�ngliche Nachricht-----
Von: Jeff Olliff [mailto:jolliff@dslnorthwest.net]
Gesendet: Donnerstag, 1. Januar 2004 05:23
An: tuning@yahoogroups.com
Betreff: [tuning] Re: Mozart's ideas

> Yes, entrenched. Johann Joachim Quantz (On Playing the Flute, 1753)
> has an interestingly precise tuning instruction. I gave away my
> last copy but maybe in chapter 4, where the fingering charts are, he
> says that the difference between a sharp and the enharmonic flat is
> one ninth of a whole tone. That is exactly the subset of 55edo,
> where c-c# is the 55th root of 2 to the 4th, c#-d the same to the
> 5th, but Db-D again only to the 4th, etc. This is approximately
> enough, 6th comma meantone, and in fact splits the difference
> between the commas of Pythagoras and Didymus. Quantz gives compleat
> fingerings for 18 or 19 steps per octave, not theory but practice.
> He was entirely mainstream since he served in King Frederick's
> orchestra with Emmanuel Bach, and their writings underpin Classical
> music. He and Bach emphasize good taste and style. I take it that
> this degree of control over intonation was required. I hadn't seen
> the information on Mozart's opinions to Attwood before, so my thanks
> to our contributors, Monz, Werner, et al. On the matter of
> intonation, the musical education establishment is degenerate. I
> gave my copies of Bach and Quantz to my niece, who is currently
> negotiating the university cirriculum, may her ears be opened.

> On St. Paul Sunday I heard Kronos Quartet play Harry Partch, sorry
> for no title. Funny to hear them talk afterwards about the plus and
> minus signs on the notes (their transcription I guess), and "playing
> in the cracks". Their fingerboards have cracks? Sounded good to me.

Hi Jeff,

These signs (almost arrows): Higher, a little higher, deeper,
a little deeper, have to be understood as *in comparision to ET*.
They are common in use in chamber music ensembles with strings
and/ or wind instruments.
Indeed, there exist, too, a lot of detailed signs, created by
scientists of music, but these follow more or less abstract ideas
and I never found them in the notes of an orchestra.
In chamber music trials there is always an intensive discussion
in correct tuning: How to tune fifths and thirds as best as possible?
In chamber music this requires about 30 % of the trial time.
Indeed, I can only say this for these ensembles in which I was a
member or for others, whose members I know personally.
In orchestras the problem is different. There is no time to discuss
the subject of tuning in full-length. There it is the task of the
members itself and off the different "Stimmf�hrer" (this means the
leader of an instrumental groups) to discuss it briefly at the
trial itself or by short repetitions with the instrumental group
at the rest.
In orchestras there is a additional difficulty:
Tuning a major chord near to just intonation is simple for a musician
as he can control just intonation by the disappearing of the beats.
This means, one hasn't to follow any abstract idea, one may only
follow the acoustic result.
But for minor chords there exist two different frequency ratios for
*just* intonation:
The first one is
root : minor third : fifth = 10 : 12 : 15,
(with the same third frequency ratios like major chords in
just intonation).
The second one is
root : minor third : fifth = 16 : 19 : 14,
which is very near to ET. It sounds as good as the first one.
It is recommandable to follow the ratios of the first example as
with the second one the changes from a major chord
to its minor parallel chord - or inverse - would cause frequency
jumpings.
But one has to learn this. This means: At minor chords
one cannot only "trust the ears", one has to follow knowingly
one of this both ideas.
And indeed, I sometimes realise that at stops and fermates
with a minor chord there exist two groups in the orchestra,
one of them following the first and one of them
following the other idea.

An additional difficulty is: A string instrument player
can change the position of the referring finger on the chord.
For wind instrument players there exist other means. Some as
described above (with the Quantz example), others by changing
the frequency by different embouchment and breath support.
Nevertheless not all tones of a wind instrument are flexible.
Some are few flexible and others have a tendence
to be "high" or "deep".
Therefore a well educated musician never may say: "I am correct,
it is not my problem whether my neighbor will tune deeper or higher
than to the ideal ferquency". A well educated musician will
additionally weight the height of the tones tones of his neighbour
or his neighbourship. Indeed, a result of this may be that
in this way the better instrumentalist will follow the weak one.

Conclusion: Paul may be right when criticizing that many
orchestras are not following an all embracing *just intonation*,
nevertheless I maintain my opinion: The idea of tuning
in most of the actual ensembles are perfect fifths and(!)thirds
and at least at major chords one can hear this and one doesn't
need to measure it.

Werner

On Thu, 01 Jan 2004 02:11:31 -0000, "Gene Ward Smith" <gwsmith@svpal.org>
wrote:

>--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
>> i been sticking with mp3 because it seems to me to be
>> a more universal format. can OGG files be played in
>> those stand-alone mp3 players?
>
>That depends on which ones you try it with. It won't work with any
>but some of the newest.

I have Winamp 2.81, and I haven't had any problem with OGG files.