Yahoo Tuning Groups Ultimate Backup tuning Ivor Darreg on quartertones

Hi all,

Here's another one of Ivor Darreg's articles worth
a read, a ponder, and maybe some testing -
http://sonic-arts.org/darreg/dar2.htm

It's entitled 'THE QUARTERTONE QUESTION
by Ivor Darreg [1947]'.

Does anyone have anything to add to the picture
that Ivor painted way back then?
Regards,
Yahya

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🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:
>
> Hi all,
>
> Here's another one of Ivor Darreg's articles worth
> a read, a ponder, and maybe some testing -
> http://sonic-arts.org/darreg/dar2.htm
>
> It's entitled 'THE QUARTERTONE QUESTION
> by Ivor Darreg [1947]'.
>
> Does anyone have anything to add to the picture
> that Ivor painted way back then?
> Regards,
> Yahya

"Overtones of higher order are well represented by quartertone
intervals."

This is not really true if the texture is to contain four-part or
larger harmony. The representations fail to fit together the way they
do in JI, which is now referred to as the "inconsistency" of 24-equal
in the 7-limit and above.

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

Hallo again all!

On Sat, 18 Feb, "wallyesterpaulrus" wrote:
>
> --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:
> >
> > Hi all,
> >
> > Here's another one of Ivor Darreg's articles worth
> > a read, a ponder, and maybe some testing -
> > http://sonic-arts.org/darreg/dar2.htm
> >
> > It's entitled 'THE QUARTERTONE QUESTION
> > by Ivor Darreg [1947]'.
> >
> > Does anyone have anything to add to the picture
> > that Ivor painted way back then?
> > Regards,
> > Yahya
>
> "Overtones of higher order are well represented by quartertone
> intervals."
>
> This is not really true if the texture is to contain four-part or
> larger harmony. The representations fail to fit together the way they
> do in JI, which is now referred to as the "inconsistency" of 24-equal
> in the 7-limit and above.

Thanks, Paul.

Actually I dismissed that particular comment (of Ivor's)
on my first reading as an oversimplification. I'm surprised
that you qualify your comment by 'four-part or larger
harmony'. Surely the inconsistencies would also be
noticeable - perhaps more so - with only two or three
voices? Or should I take you to assume that people won't
use the 7-limit with fewer than 4 notes?

As I was disconnected from yahoo for a couple of days
while my emails were bouncing, due to a catastrophic
motherboard failure, I missed a few daily digests of
messages from the tuning (and other) lists. If anyone else
has made any comments on this article on quartertones, I
may have missed them, so please send me another copy
privately. I have been toying with the notion that 24-EDO
may be "good enough" for most of my own musical purposes,
and I'd hate to invest too much energy in following the
wrong path, should it prove to be so.

Regards,
Yahya

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🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:
>
>
> Hallo again all!
>
> On Sat, 18 Feb, "wallyesterpaulrus" wrote:
> >
> > --- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@> wrote:
> > >
> > > Hi all,
> > >
> > > Here's another one of Ivor Darreg's articles worth
> > > a read, a ponder, and maybe some testing -
> > > http://sonic-arts.org/darreg/dar2.htm
> > >
> > > It's entitled 'THE QUARTERTONE QUESTION
> > > by Ivor Darreg [1947]'.
> > >
> > > Does anyone have anything to add to the picture
> > > that Ivor painted way back then?
> > > Regards,
> > > Yahya
> >
> > "Overtones of higher order are well represented by quartertone
> > intervals."
> >
> > This is not really true if the texture is to contain four-part or
> > larger harmony. The representations fail to fit together the way
they
> > do in JI, which is now referred to as the "inconsistency" of 24-
equal
> > in the 7-limit and above.
>
>
> Thanks, Paul.
>
> Actually I dismissed that particular comment (of Ivor's)
> on my first reading as an oversimplification. I'm surprised
> that you qualify your comment by 'four-part or larger
> harmony'. Surely the inconsistencies would also be
> noticeable - perhaps more so - with only two or three
> voices?

Absolutely not. With only 2 voices, there's simply no way for any of
the inconsistencies to come into play. You simply use the best
approximation available for the interval you want between the 2
voices, and you're done with it.

> Or should I take you to assume that people won't
> use the 7-limit with fewer than 4 notes?

No, I certainly don't assume that.

🔗Yahya Abdal-Aziz <yahya@melbpc.org.au>

On Sat, 18 Feb, "wallyesterpaulrus" wrote:

[snip]
> > > "Overtones of higher order are well represented by quartertone
> > > intervals."
> > >
> > > This is not really true if the texture is to contain four-part or
> > > larger harmony. The representations fail to fit together the way
> > > they do in JI, which is now referred to as the "inconsistency" of
> > > 24-equal in the 7-limit and above.
> >
> >
> > Thanks, Paul.
> >
> > Actually I dismissed that particular comment (of Ivor's)
> > on my first reading as an oversimplification. I'm surprised
> > that you qualify your comment by 'four-part or larger
> > harmony'. Surely the inconsistencies would also be
> > noticeable - perhaps more so - with only two or three
> > voices?
>
> Absolutely not. With only 2 voices, there's simply no way for any of
> the inconsistencies to come into play. You simply use the best
> approximation available for the interval you want between the 2
> voices, and you're done with it.

Okay ... and with three voices?

Regards,
Yahya

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🔗Keenan Pepper <keenanpepper@gmail.com>

[...]
> > Actually I dismissed that particular comment (of Ivor's)
> > on my first reading as an oversimplification. I'm surprised
> > that you qualify your comment by 'four-part or larger
> > harmony'. Surely the inconsistencies would also be
> > noticeable - perhaps more so - with only two or three
> > voices?
>
> Absolutely not. With only 2 voices, there's simply no way for any of
> the inconsistencies to come into play. You simply use the best
> approximation available for the interval you want between the 2
> voices, and you're done with it.

I disagree. For one thing, you're ignoring melodic intervals. For
another, if you use the best approximation for each interval you can
end up on a different pitch from the one you started on. For example,
consider this two-part harmony:

3/2-7/4-----3/2----
1/1-----5/4-----1/1

If each vertical interval is tuned to the best approximation in
24-edo, the last 1/1 is a quarter-tone lower than the first 1/1.

Keenan

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> [...]
> > > Actually I dismissed that particular comment (of Ivor's)
> > > on my first reading as an oversimplification. I'm surprised
> > > that you qualify your comment by 'four-part or larger
> > > harmony'. Surely the inconsistencies would also be
> > > noticeable - perhaps more so - with only two or three
> > > voices?
> >
> > Absolutely not. With only 2 voices, there's simply no way for any of
> > the inconsistencies to come into play. You simply use the best
> > approximation available for the interval you want between the 2
> > voices, and you're done with it.
>
> I disagree. For one thing, you're ignoring melodic intervals. For
> another, if you use the best approximation for each interval you can
> end up on a different pitch from the one you started on. For example,
> consider this two-part harmony:
>
> 3/2-7/4-----3/2----
> 1/1-----5/4-----1/1
>
> If each vertical interval is tuned to the best approximation in
> 24-edo, the last 1/1 is a quarter-tone lower than the first 1/1.
>
> Keenan
>
You're right. I forgot that I'd made the very same point to John Chalmers.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

Yes, triads are always sufficient, and necessary, to display inconsistency.

--- In tuning@yahoogroups.com, "Yahya Abdal-Aziz" <yahya@...> wrote:
>
>
> On Sat, 18 Feb, "wallyesterpaulrus" wrote:
>
> [snip]
> > > > "Overtones of higher order are well represented by quartertone
> > > > intervals."
> > > >
> > > > This is not really true if the texture is to contain four-part or
> > > > larger harmony. The representations fail to fit together the way
> > > > they do in JI, which is now referred to as the "inconsistency" of
> > > > 24-equal in the 7-limit and above.
> > >
> > >
> > > Thanks, Paul.
> > >
> > > Actually I dismissed that particular comment (of Ivor's)
> > > on my first reading as an oversimplification. I'm surprised
> > > that you qualify your comment by 'four-part or larger
> > > harmony'. Surely the inconsistencies would also be
> > > noticeable - perhaps more so - with only two or three
> > > voices?
> >
> > Absolutely not. With only 2 voices, there's simply no way for any of
> > the inconsistencies to come into play. You simply use the best
> > approximation available for the interval you want between the 2
> > voices, and you're done with it.
>
> Okay ... and with three voices?
>
>
> Regards,
> Yahya
>
> --
> No virus found in this outgoing message.
> Checked by AVG Free Edition.
> Version: 7.1.375 / Virus Database: 267.15.11/264 - Release Date: 17/2/06
>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

Yes, triads are always sufficient, and necessary, to display inconsistency.