Looking for advice

Hi,

I'm currently running a PPC 603e (Mac).

I would like recommendations on the best cards and/or synths and/or
software for doing alternate tunings. I'm looking for something that is
relatively easy to use as I'm a beginner in these waters.

Thanks in advance,
Sanford

PS - Is there a tuning editor for the Roland JV 880?

On Mon, 21 Sep 1998, Robin Perry wrote:
> It involves generating two sets of ratios (as outlined below) then
> finding the intersection of the two.
>
> In this case, the set to the right is exactly 3/2 of the set to the
> left. I stopped where I have because I have not found any more common
> ratios beyond this point.

[snip lists of ratios separated from 3/2 and 1/1 by superparticulars]

There shouldn't be any more. The first few superparticulars (those
larger than 8/7) don't bring you closer than a 16/15 to the central
pair, so once your list of superparticulars goes beyond 16/15 there
won't be any more overlap possible.

What a very interesting method of generating a scale, BTW. 3/2s and
superparticulars both seem to be very pleasing, and this method
guarantees a lot of them.

> The intersection of these two is:
>
> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 12/7 7/4 9/5 15/8 2/1

Here's lattice diagram for the scale. Given the method of generation,
it's not suprising that the resulting shape is very symmetrical.

5/3 --- 5/4 ---15/8
/ \ / \ / \
/ \ / \ / \
/ \ / 7/4 \ / \
4/3 --- 1/1 --- 3/2 --- 9/8
\ / \12/7 / \ /
\ / \ / \ /
\ / \ / \ /
8/5 --- 6/5 --- 9/5

The scale can also be described as all the 5-limit pitches that form
(5-limit) consonances with either 1/1 and 3/2, plus the two 7-limit
pitches that form (7-limit) consonances with _both_ 1/1 and 3/2.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

>> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 12/7 7/4 9/5 15/8 2/1

Bob Lee wrote,

>That leaves the 12/7 and 7/4. Can you form beatless harmonies with
these
>and other notes of the scale? I'm having a hard time imaging their
use,
>maybe because I'm basically a 5-limit player.

7/4 of course figures in the "barbershop" dominant seventh chord or
"otonal tetrad" 1/1:5/4:3/2:7/4 (or 4:5:6:7). This is a relatively
beatless harmony (but even a just 5-limit triad has some beats among the
higher partials) and unequivocally implies a fundamental two octaves
below the root. If the 12/7 is transposed down an octave to 6/7, it
combines with 1/1:6/5:3/2 to form a sort of half-diminished seventh
chord or "utonal tetrad" (1/7:1/6:1/5:1/4) which at low volumes is as
beatless as the otonal one but is more ambiguous as to its fundamental.
However, in this latter chord all tones have a clear common overtone two
octaves above the 3/2, which, if attention is drawn to it, should be
easily audible (for tuning purposes, if nothing else) unless the
intonation is too exact and phase cancellation occurs.

Paul Hahn wrote,

>The scale can also be described as all the 5-limit pitches that form
>(5-limit) consonances with either 1/1 [or] 3/2, plus the two 7-limit
>pitches that form (7-limit) consonances with _both_ 1/1 and 3/2.

In other words, this is the scale of the most consonant notes against a
1/1-3/2 drone. I once tried tuning several guitar strings to such a
drone and found that I could generally tune a remaining string to any
pitch that formed a 7-limit consonance with either 1/1 or 3/2, or an
11-limit consonance with both 1/1 and 3/2. (This is sort of mentioned in
my 22-tET paper.) The resulting scale:

1/1 21/20 15/14 12/11 9/8 8/7 7/6 6/5 5/4 9/7 21/16 4/3 11/8 7/5 10/7
3/2 8/5 5/3 12/7 7/4 9/5 15/8 (2/1)

Coincidentally, this scale has 22 notes while Robin Perry's has 12.

The smallest scale I could find which is a superset of Perry's scale is a
19-tone JI-scale by Max Meyer.

Max Meyer, see Doty, David, 1/1 August 1992 (7:4) p.1 and 10-14

16/15 10/9 9/8 8/7 7/6 6/5 5/4 4/3 7/5 10/7 3/2 8/5 5/3 12/7 7/4 16/9 9/5
15/8 2/1

This scale is inversionally symmetric so if Perry's scale is made
symmetrical
by adding the missing octave inverted tones then the resulting 17-tone
scale is
also a subset of this scale.
16/15 10/9 9/8 8/7 7/6 6/5 5/4 4/3 3/2 8/5 5/3 12/7 7/4 16/9 9/5 15/8 2/1
I wrote a Scala program for creating Perry's scale:

harmonic 1 16
collapse
copy 0 1
invert
reverse
merge 1
copy 0 1
move 3/2
normalize
swap 1
normalize
intersect 1
clear 1
show

This program can be parametrised as follows:
! perry.cmd
echo Create a Perry-scale, an intersection of two harmonic/subharmonic
scales
echo Enter first and last harmonic
harmonic ? ?
collapse
copy 0 1
invert
reverse
merge 1
copy 0 1
echo Enter intersection interval
move ?
normalize
swap 1
normalize
intersect 1
clear 1
show

Manuel Op de Coul coul@ezh.nl

On Wed, 23 Sep 1998, Paul H. Erlich wrote:
> I once tried tuning several guitar strings to such a
> drone and found that I could generally tune a remaining string to any
> pitch that formed a 7-limit consonance with either 1/1 or 3/2, or an
> 11-limit consonance with both 1/1 and 3/2. (This is sort of mentioned in
> my 22-tET paper.) The resulting scale:
>
> 1/1 21/20 15/14 12/11 9/8 8/7 7/6 6/5 5/4 9/7 21/16 4/3 11/8 7/5 10/7
> 3/2 8/5 5/3 12/7 7/4 9/5 15/8 (2/1)
>
> Coincidentally, this scale has 22 notes while Robin Perry's has 12.

Umm, do you not consider 11/9 an 11-limit consonance? (I know we have
periodic wars on this subject on the list, at least when Brian is
contributing.) If you do, then 11/6 and 18/11 also fit your criteria,
which makes it a 24-note scale instead of 22.

--pH http://library.wustl.edu/~manynote
O
/\ "Churchill? Can he run a hundred balls?"
-\-\-- o
NOTE: dehyphenate node to remove spamblock. <*>

I wrote,

>> I once tried tuning several guitar strings to such a
>> drone and found that I could generally tune a remaining string to any
>> pitch that formed a 7-limit consonance with either 1/1 or 3/2, or an
>> 11-limit consonance with both 1/1 and 3/2. (This is sort of mentioned
in
>> my 22-tET paper.) The resulting scale:
>>
>> 1/1 21/20 15/14 12/11 9/8 8/7 7/6 6/5 5/4 9/7 21/16 4/3 11/8 7/5 10/7
>> 3/2 8/5 5/3 12/7 7/4 9/5 15/8 (2/1)
>>
>> Coincidentally, this scale has 22 notes while Robin Perry's has 12.

Paul Hahn wrote,

>Umm, do you not consider 11/9 an 11-limit consonance? (I know we have
>periodic wars on this subject on the list, at least when Brian is
>contributing.) If you do, then 11/6 and 18/11 also fit your criteria,
>which makes it a 24-note scale instead of 22.

Paul, you're right, and my paper is wrong. I guess 11/9 is often harder
to hear than some other ratios of 11, and I was too eager to provide a
simple mathematical description of what I heard. I should trash all of
page 20 (in the .pdf version) of my paper, as well as two columns of
table 5. Although it's too late for Xenharmonikon, perhaps if Carl Lumma
reppears we can revise the .pdf version accordingly. Aaargh!!!

Do you mean Brian McLaren? I don't remember those days too well.