Reply to R. C. Valentine

>
>}> On the list, I believe someone =17 by no means devoid of understanding =
>=17
>}> said that "Gibson's preference for mean-tone temperaments is
>}> well-established" as if there are any others worth discussing (for
>}> long). Well, there is just intonation and Pythagoreanism, but they are
>}> not temperaments. There are 22- 29- 41- & 53-tone equal, but I do hope
>}> that by now I have explained why these 'temperaments' are valueless, for
>}> they cast out the consonant thirds from their tonal fabric as soon as
>}> one tries to preserve the consonant fifths. =20
>
>}I really don't understand this statement "cast out the consonant thirds".
>
>} 12TET 7 M4 =3D=3D 4 P5
>} 19TET 11 M4 =3D=3D 6 P5
>} 53TET 31 M4 =3D=3D 17 P5=20
>
>}Is the "problem" that the 53TET (and others) has a choice of thirds to
>}use depending on context (in this run of 31 M4, we probably came close
>}to a variety of M4 that were diatonically correct to the original root,
>}if we built the equivalent of I, IV, V)?
>
>I can't understand your notation. What is M4? Anyway, Gregg is referring to
>the fact that 22-, 29-, 41-, 53-equal and JI are not meantone temperaments.
>You're going to tie yourself (and the music) in knots if you try to use these
>tunings for traditional diatonic music. Modulations to nearby keys become
>extremely awkward, as do single-key chord progressions such as I-IV-ii-V-I
>and I-vi-ii-V-I.
>
>}Of course, this choice gives you lots of VERY consonant thirds, and,=20
>}using them when it is important harmonically (to fix audible beating)
>}does not mean we really care whether we hit them exactly melodically
>}(since we already have determined that melody can be a lot sloppier
>}than harmony).
>
>JI is perfect harmonically but contains melodic errors of a syntonic comma.
>(The other non-meantone temperaments mentioned are worse than JI in both
>respects). If one treats sustained tones as single pitches (not altering them
>by a comma mid-stream) these melodic errors can accumulate over the course of
>a piece, often landing the piece as much as ten commas below where it
>started. 1/4-comma meantone temperament is perfect melodically but contain
>harmonic errors of no more than 1/4 syntonic comma. These errors do not
>accumulate since consonant intervals of the same type do not combine to form
>other consonant intervals. So the relevant question is not whether melody can
>be a lot sloppier than harmony but whether melody can be four (locally) to
>forty (globally) times sloppier than harmony. I think the answer depends on
>the exact sizes of the errors and, of course, the musical context, but I
>think meantone wins in most cases. Of course, one can write piece
>specifically for JI which avoids most of its disturbing characteristics, but
>the vast majority of classical composers did not do this.
>
>In a performance context one would have to deal with far fewer pitches in a
>meantone rendition. These practical benefits of meantone may have been the
>decisive factor in making meantone the most important tuning in the West from
>1500-1800.
>
>31-equal is close to 1/4-comma meantone; 19-equal is virtually 1/3-comma
>meantone, having harmonic errors no larger than 1/3 comma.
>
>}Ezra Simms is currently advocating 72TET (he approached it from a few
>}other directions) and has articles in Perspectives of New=20
>}Music (vol 29, their microtonal series) and Computer Music Journal
>}in recent years. As a REAL tuning system to advocate vs 12TET, this=20
>}one meets all the tests above.
>
>I do like your argument (deleted). Ezra Sims, though, attributes some ratios
>to 72TET that it cannot express consistently. 72TET is only consistent
>through the 17-limit.
>
>}Regarding 19TET in particular, perhaps it is the last temperment which
>}preserves "sameness" of the "big" and "small" major seconds (9:8, 10:9).
>
>} major scale...
>
>} 12TET : 2 2 1 2 2 2 1
>} 19TET : 3 3 2 3 3 3 2
>} 22TET : 4 3 2 4 3 4 2
>} 29TET : 5 4 3 5 4 5 3
>} 41TET : 7 6 4 7 6 7 4
>} 53TET : 9 8 5 9 8 9 5
>
>}But... is that a good thing? Thanks a lot.
>
>This sameness is what characterizes a meantone temperament, and as I have
>stated above, I think it is a good thing for diatonic music. More:
>
>15TET: 3 2 1 3 2 3 1
>26TET: 4 4 3 4 4 4 3
>31TET: 5 5 3 5 5 5 3
>34TET: 6 5 3 6 5 6 3
>72TET: 12 11 7 12 11 12 7
>
>For one thing, the ii triad is lousy in those of the above "major scales"
>where there are two sizes of major second. It is unfortunate that the best
>meantone scales that 72TET has to offer are the same as 12TET scales. This
>often prevents one from taking advantage of the superb 5:4 of 72TET in a
>diatonic context.
>
>The "major scales" in 15- and 22-equal sound really out-of-tune melodically
>because of the two different sizes of major second. So even if the ii triad
>and modulation are avoided, these tunings will sound weird for diatonic
>music.
>
>I have non-diatonic reasons for liking 22-equal. Blackwood has written about
>good reasons for liking 15- and 16-equal in Perspectives of New Music.
>


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From: Gregg Gibson
Subject: More on Just Intonation 2
PostedDate: 23-12-97 23:44:53
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Gregg Gibson wrote:

> To pretend that a singer can
> accurately produce an interval four or five perfect fifths above the
> tonic is nonsense; this is a commatic disjunct dissonance, and not
> accurately singable.

There's an assumtion Gregg makes here that goes to the heart
of his argument, and I hope I won't be accused of carping by
pointing it out. It is that temperament has something to do
with singing. Certainly, singers temper intervals.
However, they do not require an explicit system to do so.

Actually, four fifths octave reduce to two major tones. I
wouldn't be at all surprised if it were possible to sing them
both accurately. 9/8 functions as a melodic consonance, but
this is lost in 19 equal. However, this is not worth arguing
about. More to the point, I would not expect the average singer
to produce accurate intervals from an equal temperament.
It is not unreasonable, however, to expect a guitarist to
tune her five strings to five just fifths. A temperament
that takes this into account does have advantages.

Now, to get to the heart of the matter. What difference
does it make to a singer if I play a chord sequence on my
keyboard in schismic temperament, comma shifts and all? I
wouldn't expect any variable pitch instrument to follow
instructions to more precision than 12 pitch classes. If
the harmony makes sense, it shouldn't be too difficult to
sing in tune with it. As the commas are well below the
melodic limen, they shouldn't cause any confusion.

> These matters are widely known ? they are also widely ignored or denied
> or imperfectly known. The ignorant very typically imagine that We Clever
> Moderns have invented a new music in which all the Stupid Old Ideas of
> the dead past don't matter.

Firstly, Gregg, there's a character there that comes out
as a filled in rectangle on my screen. Can you try keeping
to strict ASCII?

Secondly, I consider myself to be post-modern.

Thirdly, the important point. No musician before the 1950s
had a digital computer. Theorists before this date, therefore,
did not need to consider the tuning of an instrument that can
produce a very large number of notes to a high degree of
precision, but that nevertheless requires each pitch to be
specified numerically. You can bet singers in the 16th century
produced an enormous variety of intervals, but there was neither
a reason to write them all down, nor the ability to do so.
Despite all this, schismic temperament is at least implicit in
medieval Islamic theory, which is where I got the idea from.
So, there's nothing new there.

It is in no way arrogant to say that I have an instrument of
hitherto undreamt of resources. I intend to use those resources
to the utmost of my abilities, in order to make up for it's
deficiencies relative to an acoustic instrument. Part of that
means explicitly specifying intervals of less than 50 cents.
Also, using septimal harmony.

The advantages of using meantone (or mesotonic -- a better
word, but I'm not used to it) need not be stated, as anyone
who subscribes to this mailing list must be aware of them. I
expect most people will tune fixed pitch instruments to such
a temperament, if they wish to play harmonic music, and they
will be missing very little. That doesn't stop me using any
tuning I feel like using. I can't be held responsible for a
whole culture.


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PostedDate: 25-12-97 17:37:14
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