Yahoo Tuning Groups Ultimate Backup tuning Re: [tuning] Digest Number 3521

Hi Jon,

> Boy, you have a future in the diplomatic service! :)

Thanks - I'll give your name as a reference
if I ever apply for one ( :-) joke).

Yes of course I agree that its common
use is as an ordered scale, and that
it is necessary of course to accept that.
It is only once one thinks about
the interval structures of scales
that one may come to think that
an unordered set be a more
appropriate way to think of a scale.

BTW I was thinking, a really clear
case for a scale with no natural ordering on
it would be a 2D (or higher) doubly
infinite scale - well it does
have an infinite ordering of type
omega squared - i.e. so that each
pitch in a row is counted as occurring
before the the one to its right,
and each entire row is counted as
occurring before the next entire row.

It means that if you order the scale
that way you have to accept that there
are some pitches in the scale
that can never be reached in a finite
number of steps by just walking up through
its notes in increasing order.
Rather than think of a scale in
that way one might prefer to think
of it as not having a fixed
natural ordering.

In this case it doesn't help at all
to try ordering the notes in increasing
order, that only makes the problem
worse as in some cases
the scale may very well end
up being dense, so that you can't
even get from 1/1 to 5/4 or
get anywhere in it at all
in a finite number of steps.
Particularly if the scale is
an ordering of all possible
ratios as some infinite scales are
- then it is easy to see that once
they are put in ascending order then
the result is dense.

Robert

----- Original Message ----- From: <tuning@yahoogroups.com>
To: <tuning@yahoogroups.com>
Sent: Friday, May 20, 2005 11:54 AM
Subject: [tuning] Digest Number 3521

>
> There are 2 messages in this issue.
>
> Topics in this digest:
>
> 1. joe's samba--fretless guitar solo
> From: "daniel_anthony_stearns" > <daniel_anthony_stearns@yahoo.com>
> 2. question about just intonation scales
> From: "ahoningh2000" <ahoningh@science.uva.nl>
>
>
> ________________________________________________________________________
> ________________________________________________________________________
>
> Message: 1
> Date: Fri, 20 May 2005 00:58:51 -0000
> From: "daniel_anthony_stearns" <daniel_anthony_stearns@yahoo.com>
> Subject: joe's samba--fretless guitar solo
>
> For anyone who might be interested... I sometimes contribute to a jazz
> guitar forum and some members occasionally post backing tracks for the
> other intrepid members to try to solo over. In a best case scenario
> this is a kind of healthy, hands-on problem solving exercise,
> unfortunately no one ever seems to have put an art-first approach to
> the idea of a backing track and so far they've all been pretty, err,
> Love Boat! Oh well, usually I'd approach a samba or a bossa nova hoping
> for something a little more interactive. But this sort of
> canned ,clockwork jazz-in-a-box track obviates any attempt in that
> direction, so I just hada little fun laying waaaaay back and roughing
> up the changes and the time--and the intonation--a bit .
>
> http://zebox.com/daniel_anthony_stearns/
>
> joe'Samba
> (bottom of page
>
>
>
>
>
> ________________________________________________________________________
> ________________________________________________________________________
>
> Message: 2
> Date: Fri, 20 May 2005 08:27:45 -0000
> From: "ahoningh2000" <ahoningh@science.uva.nl>
> Subject: question about just intonation scales
>
> Dear all,
>
> I was wondering what makes a sequence of notes a (just intonation)
> scale. Maybe somebody can tell me about properties of just intonation
> scales, like conditions they have to satisfy?
> In the Encyclopaedia of Tuning I did find some properties of scales.
> Under 'scale' is written: "Scales often, but not always, exhibit
> tetrachordal similarity, and other properties such as MOS, propriety,
> distributional evenness, etc."
> However, all these properties are only valid for equal tempered scales
> (or am I wrong?).
> Are there similar properties for just intonation scales? I hope
> somebody can help me. Thanks in advance.
>
> Best regards,
> Aline Honingh
>
>
>
>
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Re: [tuning] Digest Number 3521

🔗Robert Walker <robertwalker@ntlworld.com>

🔗Gene Ward Smith <gwsmith@svpal.org>