response to Margo (was: "major" and "minor")

Hello, Margo!

> From: M. Schulter <MSCHULTER@VALUE.NET>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, January 30, 2002 9:32 PM
> Subject: [tuning] Re: "major" and "minor"
>
>
> Hello, there, Monz, and what a delight to be exchanging messages with
> you about Boethius, semiditones, 18:17:16 divisions, and the like.
>
> Your mention of Vincenzo Galileo's use of 18:17 to approach a 12-EDO
> semitone, actually more accurate on a lute than the logarithmically
> correct fret spacing according to Mark Lindley because of fretting
> pressure, ...

Hmmm ... I just mentioned a few hours ago in another post (I think
on tuning-math) the ISMA conference I attended in Italy in September.
There were a lot of presentations on the acoustics of plucked strings
(and even more on bowed strings), and some of them explored the
specifics of pitch alterations due to fretting pressure. I was
*particularly* interested in this, because my presentation at that
conference concerned John Dowland's unusual lute fretting, and explored
some of the bizarre beating dissonances Dowland stipulated in his
tablature scores.

I think I mentioned here before that the conference proceedings are
available from the publisher (in Venice) for 90 Euro (about $90 US)
-- expensive, but worth it if you're seriously interested in this
kind of thing. Or perhaps you have access to a library that has
it, or maybe they can be talked into purchasing it if they don't.

> ... reminds me of my idea for a 21st-century fretting solution:
> just use successive ratios of 25:24. However, I'll refrain from
> calling this "JI"; formal RI plus a bit of octave stretching is more
> like it.

So where d stands for degree, and each step is (25/24)^d,

d ~cents

17 1201.43
16 1130.76
15 1060.09
14 989.41
13 918.74
12 848.07
11 777.40
10 706.72
9 636.05
8 565.38
7 494.71
6 424.03
5 353.36
4 282.69
3 212.02
2 141.34
1 70.67

Well, aren't you clever! That deviates from 17-EDO by no more
than ~1.43 cents, so it's no surprise to me that *you* like it,
Margo! I like it -- a simple ratio like that makes it easy to fret.

> While I much regret not mentioning Dave Keenan's definition in my
> earlier post on "What is JI," I'm delighted that my omission prompted
> others to remedy this fault, calling attention to a viewpoint that
> deserves to be noticed whenever this topic comes up.

Yes, as I've said, I'd like to add much from what Dave posted back then
to my definition. But that would take some time.

> For now, while I consider a longer post on "What JI means to me,"
> please let me add that you have frequently made it clear that you set
> no arbitrary limits on JI, literally or figuratively, but like me have
> been intrigued by writers such as Fabio Colonna who discuss higher
> primes and integer ratios.

And don't forget that I'm also intrigued by La Monte Young's music,
which explores even higher primes in actual sound, and which I've
had the good fortune to be able to experience in his Dream House.
(Thanks to David Beardsley for inviting me there several times.)

> Recently I have felt a special wonder at reading Kathleen Schlesinger,
> and seeing her mention many of my favorite ratios -- in 1939. Maybe
> I'd compare her treatise on _The Greek Aulos_ to some late
> 16th-century Italian efforts to achieve a dramatic music along Greek
> lines -- the origins of the opera, of course.

Yes, I too am fascinated with Schlesinger's work. Unfortunately,
I still haven't read all of her book, having continuously gotten
hung up on various particular aspects of her theories which I then
explored further on my own.

In one roundabout case (via research into Greek musical notation)
this further exploration resulted in what I consider one of my most
important papers: "An Examination of a Possible 5-Limit System of
Boethius", which is still as yet unpublished.

I think it would be fantastic if you could provide a summary of
_The Greek Aulos_ to the list. It would help me when I eventually
get back to reading it.

> Anyway, this is mainly to say thanks, for your most recent reply and
> your many contributions.
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@value.net

What a warm response! Thank you, Margo. It's always such a pleasure
when the two of us engage in dialog here that I wish it would happen
more often.

... And discussions with you help pull me a bit away from the
math, and more into the history, which is really even more
fascinating to me and what I do much better anyway.

The main reason I've gotten so wrapped up in tuning math (which
I don't even really understand all that well) is my interest in
applying it visually in my software project. I'd really like
to get the software finished and then *use* it to create terrific
animated-with-audio webpages which explore the *history* of tuning.

>
> P.S. Aside to Jon Wild: the distinction you report in Aristoxenos between
> the simple and composite use of an interval such as the ditone or major
> third very much reminds me of the Vicentino-Lusitano controversy (does any
> use of a melodic minor or major third represent an element of the
> chromatic or enharmonic genus, so that almost all music is actually
> "mixed" rather than diatonic?). Here Lusitano and later Zarlino took the
> position you report, arguing that the chromatic semitone and enharmonic
> diesis are characteristic of these genera, while major and minor thirds
> are also routine as composite intervals in the diatonic.

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