Misc 3

James Kukula
------------

>Equal tempered scales have the property that each note has the same set of
>intervals available.

In many ways an important limitation! In many ways an advantage.

>Conventional ET is not the only system with interval symmetry.

Very true!

>One can have multiple generating intervals instead of just one.

And they can be just!

>If I understand how the "k-limit" term is used, it might be useful to make a
>finer distinction. Suppose I take a set of notes (2**n)(3**m)(5**p) where n
>and m are unbounded but p is constrained to be 0 or 1. My understanding is
>that this scale would be called 5-limit. The scale where p is also allowed
>unbounded values would also be 5-limit. Perhaps the case of unbounded
>exponents is not of sufficient interest to merit a new term?

Maybe it is! The question would maybe be smoother if it contained a
suggestion...

Terms like "compound" and "secondary", as opposed to "primary", have already
been used to identify such cases. See my post to Tunging Digest 1221 for a
brief discussion of this.

One thing is for sure: Deciding how many of your limits are bounded, and
how far they are bounded is a real important choice! Especially when you
get into the higher limits! The JI Primer gives a good treatment of this --
besides Genesis of a Music, the only treatment that I know of.

-----------
Paul Erlich
-----------

[for escaping the diatonic hegemony, 22TET]

>may be our only hope.

I am on my knees! You cannot believe this, Paul! You just can't! There
must be a million and one good ways to escape diatonic hegemony! That they
might not meet the same criteria you use to make 22TET good does not
dis-qualify them!

MHO, with nothing against your criteria for 22TET.

---------------
David Beardsley
---------------

>I don't think so. 7, 11 & 13 limit ji tunings do more for me
>then all the Xtet, mean tone and well tunings put together.

No wonder, considering the number of times more information that can be
stored in the 7-limit than in any root of 2 temperament with up to 2 times
the number of pitches.

I'm not sure JI tunings do more for me than all the others put together
(since no implimentaions of strong JI exist to my knowledge), but at least I
can't say they don't do SOMETHING!

------------
Gregg Gibson
------------

>In melody however, which is the primary means by which harmony is produced
(at >least ideally) the critical limen of intervallic perception is on the
order of >55-60 cents

Ridiculous. Your vocabulary will reach the limet of perception before any
intervals will.

>My comments on the intervals of 19-tone equal at the limit of human
>perception seem to have provoked some disbelief. I am indeed serious. Of
>course anyone can distinguish between tones as little as 5-10 cents
>apart in successive hearings. But if one substitutes one such tone for
>the other in a given melody, not one person in a thousand will identify
>that _melody_ as different.

I suggest that your usage of the term "melody" is very un-good. But I've
got a comparo for you anyhow...

1. Play a melody using 100 cent steps.
2. Play a melody using 88 cent steps.
3. Not a bigger difference to be found.

>has induced many to doubt that any standard tuning system should exist.
This is >emphatically not the attitude of the great artists of the past...

1. Who cares?
2. How do you know?

>Music which innovates too radically is somewhat in the case of poetry which
>should adopt so many new words that the sense is obscured.

1. Music that innovates what?
2. Your analogy depends on a relationship between sound and words that
doesn't exist.

>I have observed that rock singers use a great many third tones; there is
>seldom a popular melody nowadays without them. This perhaps is what
>makes rock melody so much more pleasing to the masses than the 12-tone
>melodies of the last century, which are now almost wholly disregarded. I
>suspect that if 12-tone equal is ever dethroned, it will be by rock
>instrumentalists wishing to reproduce the subtler, necessarily 19-tone
>melodies of their vocalists.

I was a melody freak once... I think I know where you're coming from.
Believe me, what you call melody is an arbitrary and limiting thing. When
you give it up, what you call the best melodies will pop out of the sink in
the morning.

Carl


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From: A440A
Subject: re:Chestnut help
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> Without knowing how to accurately measure the width of a third, it would
>be very difficult to tune a 12TET on a strung keyboard instrument.

That's not surprising, and you of course know more about the topic than I do.

But considering that what brought up the topic was playing in tune with
lutes, wouldn't a lute provide a very effective equal-temperament tuning
reference? Since clavichords and harpsichords require such frequent
retuning, wouldn't it make sense to, in the scenario of playing with a
lute, tune to that lute for that session?

Then again, best I can remember, keyboards playing with fretted strings
was, and still is, a comparatively unusual scenario (in the classical-music
tradition that is - it is of course fairly common in modern-day popular
music).


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From: Brian Belet
Subject: Re: Steel Guitar Tuning
PostedDate: 10-12-97 17:58:16
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J.S. Bach's reputation was to empower the cello as opposed to fretted
gamba continuo useage. This is besides the special and historic attention
Bach gave the cello in the 6 Suites for Cello.

While learning of Bach's championing of the fretless cello, with his
gunning apart from the status quo, I concluded it must have something to
do with the ease with which the cello could perfrom in the myriad of
well-temperament constellations.

Gallileo's father Vincenzo Gallilei's musical sponsor Bardi
described how due to temperament, lute players (of whom Vincenzo was an
arch-lute virtuoso) did not play with keyboard players because the
sound was painful. (Read Bardi in Strunk, The Renaissance in Source
Material). Keyboards kept different friends than lutes, apparently.

To hear some strinking lute temperament, with a choice of possible C's and
other notes, listen to Irish-born composer John Dowland played in the
tuning insisted upon by his son, lutenist Robert. Wim Hoogewerf of Paris
played Renaissance-era Dowland exquisitely on a microtonally-designed
guitar (each string had individual fretlets). Hearing Dowland performed
in this added dimension is the proper preparation for Bach in Werckmeister
III.

Johnny Reinhard
Director
American Festival of Microtonal Music
318 East 70th Street, Suite 5FW
New York, New York 10021 USA
(212)517-3550/fax (212) 517-5495
reinhard@idt.net
http://www.echonyc.com/~jhhl/AFMM


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From: alves@orion.ac.hmc.edu (Bill Alves)
Subject: re:Chestnut help
PostedDate: 10-12-97 19:06:57
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> Then again, best I can remember, keyboards playing with fretted strings
>was, and still is, a comparatively unusual scenario (in the classical-music
>tradition that is - it is of course fairly common in modern-day popular
>music).

I don't think this is necessarily true. The archlute or theorbo were common
bass continuo instruments and thus were often paired with a harpsichord.

But in regards to this question and Neil Haverstick's original question
about Bach jamming with Weiss, let's do a brief reality check. Given what
we know about tuning practices of the time, which did not include counting
beats, as Ed Foote reminds us, there was undoubtedly a significant margin
of error for any tuning, let alone some circulating temperament with no
pure intervals other than the octave.

Leaving aside the special case of the organ, these were workaday musicians
who probably "touched up" the tuning of their harpsichords pretty much
every day. I can tell you from experience that you're not going to spend 45
minutes every day getting every interval at the top end of the keyboard
exact (if indeed that were possible). The story that Bach could tune his
harpsichord in 15 minutes is thus completely believable though still
impressive.

Now, the difference between pure and ET thirds is about 15 cents. If you
consider that most thirds in most temperaments of the period are going to
be compromised in the direction of ET, they are going to be frequently in
the range of 5 to 10 cents away. In a treble register, this is within the
margin of error of even good singers, fretless strings, and woodwinds.
(Remember that these are not modern woodwinds, either.) The margin of error
grows, of course, with the size of the ensemble and speed of the piece. (By
the way, the seeming beat-spotlighting character of the long consonances in
slow movements is mostly an illusion: performers at that time would
improvise filler and ornaments in such occasions.)

In this context, the practical differences between temperaments like some
of Neidhardt's and Marpurg's and ET are angels dancing on the head of pin.

This is not to say that temperament was not important to Bach or that he
couldn't hear the difference, but that it is a matter of degree of
acceptability in practical music making. If I had been present when he and
Weiss jammed, I'm sure that, in the wonder of the music of the moment, a
few acoustical beats here or there would probably be the last thing on my
mind.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
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From: Pat Missin
Subject: Tuning program
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>I don't think this is necessarily true. The archlute or theorbo were common
>bass continuo instruments and thus were often paired with a harpsichord.

Interesting. I've never heard them on any recordings (e.g., Hogwood's).
It's almost always either 'cello, v.d.gamba, or occasionally bass. And I
have, come to think of it, heard bassoon used as the bass of a continuo at
least once.

Can you point me to some recordings of archlute used as the bass of a
continuo?


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From: gbreed@cix.compulink.co.uk (Graham Breed)
Subject: Those srutis again
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>>I don't think this is necessarily true. The archlute or theorbo were common
>>bass continuo instruments and thus were often paired with a harpsichord.
>
> Interesting. I've never heard them on any recordings (e.g., Hogwood's).
>It's almost always either 'cello, v.d.gamba, or occasionally bass. And I
>have, come to think of it, heard bassoon used as the bass of a continuo at
>least once.
>
> Can you point me to some recordings of archlute used as the bass of a
>continuo?

I'm sorry it took me long to reply. A quick check through my CDs did not
turn up a recording as you requested. However, I have heard it plenty of
times, most recently on the Purcell concert on PBS I mentioned earlier. I
have also heard it in live performance, and on other recordings I either
don't own or can't locate right now. I'll keep an eye out.

I would also like to point out that the viola da gamba is a fretted
instrument, and thus would also most likely be in equal temperament. I have
also heard the bassoon and the harp used as continuo instruments. The bass,
I should point out, would normally only be used only in octaves with
another continuo instrument, such as the cello (obviously), gamba, or
bassoon.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)607-7600 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^


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From: "Bob Lee"
Subject: Re: aliens who actually like worthless lemons
PostedDate: 21-12-97 02:05:25
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>The bass,
>I should point out, would normally only be used only in octaves with
>another continuo instrument, such as the cello (obviously), gamba, or
>bassoon.

I have a recording of the bassoon sonatas by J.B. deBoismortier
performed with bass in the continuo. (I thought it a wonderful
performance, by the way; Kim Walker is the bassoonist.) That's the only
case I know of right off the top of my head of bass in continuo.


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From: Didier ASCHOUR
Subject: errata
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