TUNING digest 967

>On Fri, 24 Jan 1997, Kami Rousseau wrote:
>
>> I was looking at 7-limit modal scales, and I noticed the weird interval
>> 8/7. My calculator told me that it is 4/3 / 7/6. It is also 9/8 * 64/63.
>>
>> I don't want to sound like I am septimising everything, but could it be
>> a kind submediant of IV? The only other time I saw this interval was in
>> the scale :
>>
>> 7/7 8/7 9/7 10/7 11/7 12/7 13/7 14/7.


A while back, a Pygmie Scale was distributed on this list, for which some
of us composed short pieces:

1/1 8/7 21/16 3/2 7/4

_________________
Adam B. Silverman
153 Cold Spring Street; A3
New Haven, CT 06511
(203) 782-1765

abs22@pantheon.yale.edu



Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Mon, 27 Jan 1997 18:22 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16442; Mon, 27 Jan 1997 18:21:59 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA16498
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id JAA01158; Mon, 27 Jan 1997 09:21:51 -0800
Date: Mon, 27 Jan 1997 09:21:51 -0800
Message-Id: <199701271607.IAB23776@ella.mills.edu>
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu

^^^BTW, the inspiration came from something I recall reading long ago
^^about the frets of the being adjusted and then fixed with
^^wax. [If anyone knows what instrument that is, could you refresh my
^^memory? I want to say sitar, but I don't think that's correct]


The _vina_ has its large frets set in a beeswax mixture. This does not,
however, make the frets very mobile (they are only reset when they fall
out). K.S. Subramanian (in 1983-84) had his frets tuned as follows:

1/1 256/243 9/8 32/27 5/4 4/3 45/32 3/2 128/81 27/16 16/9 15/8



Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Tue, 28 Jan 1997 17:48 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17605; Tue, 28 Jan 1997 17:48:00 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA17550
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id IAA00311; Tue, 28 Jan 1997 08:47:51 -0800
Date: Tue, 28 Jan 1997 08:47:51 -0800
Message-Id: <199701280908_MC2-104A-4D7F@compuserve.com>
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu

Steven's temporary fretting scheme struck me as interesting. Moveable
or removable frets can certainly be a benefit.

But once you've found a tuning you want to explore for a while, a really
good permanent refretting job, is also very gratifying. I recently had the
pleasure of using the official luthiers' tools for the first time in a
refretting job. I learned two lessons in the process: Refretting with the
right equipment makes the process a lot easier, and the right tools don't
really cost a whole lot.

The proper tools are available from the Luthiers Merchatile (800)
477-4437.

Another comment: It's easy to precisely calculate fret positions,
especially for equal temperaments. We've been over this on the list
before, but here's here it goes again:

BASICALLY fret positions can be calculated best measure from the bridge.
The first thing to do is measure the open string length. That varies from
guitar to guitar, but it's typically about 65cm. Next calculate the
frequency multiplier for adjacent steps in your tuning. That is given by
the Nth root of 2, or the 22nd root of 2 for 22TET for example. (That is
also the same as 2 raised to the 1/22 power, by the way, if your calculator
doesn't have a root key.) The first fret position, again measured from the
bridge, is the open string length divided by that frequency multiplier.
The second fret position is the first fret position divided by that same
number. The third fret is the second-fret position divided by that number,
and so forth all the way up the neck.

There is an important complicating factor though: When you press a
string down to the fingerboard, you add tension to it, and that added
tension is greater for higher fret positions, meaning that you get sharper
as go up the neck. To compensate for this, the usual procedure is to
adjust the bridge a little away from the nut. This ensures that higher
frets endure a greater percentage lengthening, and thus flattening, than
lower frets. This has two important ramifications:
1. You can't use the distance from nut to bridge for the open string
length.
You instead have to measure from nut to octave fret and double that to
get the theoretical open-string length.
2. Although it's easiest to CALCULATE the fret positions from the bridge,
you're better off MEASURING them from the nut, since the bridge
position
isn't trustable. To measure them from the nut instead of from the
bridge,
just subtract them from the open-string length.

A footnote to #1 above: If you find that the octave fret mismatches the
octave-fret harmonic by much, you may want to compensate for that so get a
more ideal octave-fret position. If the octave fret plays a little sharp
of the octave harmonic, you need to move the ideal octave-fret position
toward the nut. But be VERY careful of moving it too much, you rarely need
to move it more than a millimeter or two.

Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl
with SMTP-OpenVMS via TCP/IP; Tue, 28 Jan 1997 18:02 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA17678; Tue, 28 Jan 1997 18:02:36 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA17641
Received: from by ella.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI)
for id JAA01413; Tue, 28 Jan 1997 09:02:29 -0800
Date: Tue, 28 Jan 1997 09:02:29 -0800
Message-Id: <199701280908_MC2-104A-4D81@compuserve.com>
Errors-To: madole@mills.edu
Reply-To: tuning@ella.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@ella.mills.edu