Reply to Judith Conrad

Judith Conrad wrote,

>The essence of meantone as I use it isn't that it's quarter comma; it can
>be third-comma or fifth comma or sixth comma (which gets a little silly
>and academic). It's that you come out with a good average approximation
>for the intervals that really matter, and let the wolves howl away on the
>other intervals. Somewhere in the Baroque, people started using wolves for
>fun (Bach, Farewell suite to his brother going on a trip, very youthful
>work), but that was a gimmick, pretty much a sign that meantone had worn
>out its welcome.

>What do you mean by calling these mathematically derived equal emperaments
>'mean tone tunings'? Is it really just the size of the seconds?

It's the size of all the intervals, since they are all generated by the fifth
and the 19-tET fifth and 31-tET fifth are meantone fifths (~695 and ~697 cents,
respectively).

Judith, 19-tET and 31-tET come out with a good average approximation
for the intervals that really matter, and if you only use 12 keys on your
keyboard, the wolves will howl. However, if you extend your keyboard to
19 notes (as Salinas did in the 16th century) or 31 notes (many examples)
you will have tamed all of the wolves, as in 12-tET, but without sacrificing
the good appoximations for the intervals that really matter.

By the way, the "intervals that really matter" are the 5-limit consonances,
and 31-tET also gives you good approximations to 7-limit intervals, which
is why many have heralded 31-tET as a tuning for the past and for the
future.

On 29 Aug 1999 perlich@acadian-asset.com wrote:

> Judith, 19-tET and 31-tET come out with a good average approximation
> for the intervals that really matter, and if you only use 12 keys on your
> keyboard, the wolves will howl. However, if you extend your keyboard to
> 19 notes (as Salinas did in the 16th century)

I know of several 17-note keyboards in the 16th century. With split
accidentals. You tune the C# pure to A, the D-flat pure to F. Nothing
equal tempered about it. Describe this 19-note keyboard of the 16th
century to me.

> or 31 notes (many examples)

I hate to sound belligerent, but, um, historically speaking, name one?

Judy

Judith Conrad wrote,

>> Judith, 19-tET and 31-tET come out with a good average approximation
>> for the intervals that really matter, and if you only use 12 keys on your
>> keyboard, the wolves will howl. However, if you extend your keyboard to
>> 19 notes (as Salinas did in the 16th century)

>I know of several 17-note keyboards in the 16th century. With split
>accidentals. You tune the C# pure to A, the D-flat pure to F. Nothing
>equal tempered about it.

Excellent. In 1/4-comma meantone tuning, these intervals would be pure. I
don't why it's upsetting you, but if you tuned these keyboards to 17 out of
31-tone equal temperament, these intervals would still sound pure, as
31-tone equal temperament and 1/4-comma meantone tuning are aurally
indistinguishable. 1/4-comma meantone is constructed from a chain of
696.6-cent fifths, while 31-tone equal temperament is constructed from a
chain of 696.8-cent fifths. Therefore the major thirds differ by 0.8 cents,
which is negligible by 16th century standards.

>Describe this 19-note keyboard of the 16th
>century to me.

If you tuned a 17-tone keyboard to 1/3-comma meantone temperament, and then
tried to add a key between E and F, you would find that if you tuned it as
E#, a just minor third below G#, it would be within one cent of Fb, a just
minor third above Db. Likewise, a key between B and C could serve as both B#
and Cb. You now kave a complete circle of 19 notes, and can play in 19 keys
with all keys sounding virtually the same. For all intents and purposes,
this is 19-tone equal temperament. Costeley and other early composers
actually wrote music in this system. Salinas himself never mentioned this
property himself, but since he did have a 19-tone keyboard, and was the
first to describe 1/3-comma meantone temperament, it would seem likely that
he hit upon the idea of a closed 19-tone system.

>> or 31 notes (many examples)

>I hate to sound belligerent, but, um, historically speaking, name one?

Besides the examples Daniel Wolf just posted, others have been mentioned on
this list, some with links to photographs. Important modern examples include
the Fokker organ, which has been used to perform the music of Sweelinck and
other Renaissance composers in an authentic tuning, and on which all key
signatures are fingered identically. I believe there were more mentioned on
the web page on organs with subsemitones, but that link has mysteriously
disappeared from John Starrett's page.

Thanks everybody for explaining the 19 and 31 tone 'mean-tone' equal
temperaments. I know about Vicentino's archicembalo, I know about
Salinas. I have found Huygens in the Jorgenson Tuning book and in a
physics text, I fear he is not often referred to in music texts. I think
he was a theoretician. Said, I fear, with a sneer. But ignore me. I play
the things, I tune the things. I do not write footnoted papers about the
things.

What I have not found is this mysterious clavichord-like instrument called
a 'Sambuco'. References, please?

Judith Conrad, Clavichord Player (jconrad@tiac.net)
Music Minister, Calvary Baptist Church, Providence, RI
Director of Fall River Fipple Fluters
Piano and Harpsichord Tuner-Technician

Judith, you asked about using a soundcard for playing different tunings.
If you have a PC running Windows 3.1, (or 95/98), I suggest you download
Graham Breed's MIDI Relay, from:

http://x31eq.com/software.htm

This software sits between your external keyboard and your soundcard,
and lets you achieve any fixed tuning of your choice. It uses pitch
bends, so does not depend upon the quirks of a particular brand of card,
as long as the card is General MIDI compatible.

JdL

> Judith, you asked about using a soundcard for playing different tunings.
> If you have a PC running Windows 3.1, (or 95/98), I suggest you download
> Graham Breed's MIDI Relay

I tried that a year or two ago; It did not work with my dynasonics wave
soundcard and my Roland xp-10. I do have meantone set in the memory of the
xp-10, and space for one other tuning; but the keyboard isn't enough fun
for the space it takes up and I virtually never use it, because it gets
covered with piles of papers.

I'm supposedly about to upgrade from windows 3.11 to win 98, if I can ever
get the system put together. Thanks everybody for the suggestions, which I
am doing my best to decode.

Judy

On Sat, 27 May 2000, Judy wrote about my software:

> I tried that a year or two ago; It did not work with my dynasonics wave
> soundcard and my Roland xp-10. I do have meantone set in the memory of the
> xp-10, and space for one other tuning; but the keyboard isn't enough fun
> for the space it takes up and I virtually never use it, because it gets
> covered with piles of papers.

What didn't work? Does the soundcard not receive pitch bends? I don't
remember getting a bug report.

I tried an XP10 in a shop a while back. I found it had some good bass sounds,
and a smart variable filter but not much else. I ended up leaving
with a Korg X5D which I much prefer. It's got some moderately good presets,
and can be programmed, although I haven't done much of this.

The SoundBlaster Live! also looks promising if I ever get around to programming
it. You can use your own samples and set envelopes and filters and things.
The bad points are that it doesn't support tuning tables (although it responds
well to pitch bends) and has fairly primitive expressive responses. Like you
can't crossfade samples as the velocity changes, or link a filter to a
continuous controller.

That Korg is better in these respects, and has some good effects built in, but
you have to make do with the ROM samples. I don't know to what extent they
improve as you go up the product range.

> I'm supposedly about to upgrade from windows 3.11 to win 98, if I can ever
> get the system put together. Thanks everybody for the suggestions, which I
> am doing my best to decode.

There's a newer version of Midi Relay that'll work with Win98. Although I
don't think it'll solve any show stoppers, but you haven't told me what they
are yet. You didn't download the broken Windows 3.1 upgrade I had on my
website for a while did you?

Graham