19, 22, 29, 41, 53 : 12 and multiples

I've been saving (without reading) the Tuning Digest for quite=20
awhile. Thank you ALL for being an inspired group,=20
and willing to share so much information and opinion. [And=20
thanks for the music too, those few of you I have heard
in JIT recordings.]

That said, I have some comments regarding the recent=20
discussions with Gregg Gibson.=20

First, regarding the importance of the 55~60 cent melodic
identification concept. There have been maney good points made=20
about it, pointing out that larger values can also be ignored
(Bill Alves example of Happy Birthday in minor), smaller values
can be detected (88cet experiment showing contour or "aboveness"
and "belowness"), and I'll add my own experiment which is that,
at this time of year, I'll bet you many of the masses would
recognize "Jingle Bells" played by hitting two sticks together.

It seems that psychacoustically, the human listener is quite
willing and able to fix rather major tuning errors to "hear" a
melody properly.=20

However, the example of the high school band member playing=20
some notes thirty cents off shows that, despite his melody=20
being "recognizeable", when it is placed in a harmonic=20
context, these differences are very important.=20

That said, it seems that the differences that are important=20
harmonically are smaller than those in a melodic context. I
don't know the cent value or fraction of a tone, and, it is
sensitive to training and expectations as well.

Now to directly address some of Mr Gibson's comments.

>=20
> 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)?

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).

> Finally, I wish to state again that the masses, although seemingly
> ignorant of and indifferent to tuning questions, are, like it or not,
> our masters. The most imperious dictator who ever lived, the haughtiest
> aristocrat who ever breathed, lives in nightmarish fear of popular
> ridicule. The people =17 our own, Western people especially =17 exert a
> potent influence, via popular melody and musical instrument makers (to
> name just two influences) on the choice of tuning, and on all music.
> Those who refuse to decide on a universal tuning, and consider the
> notion tyrannical, closed-minded, limiting, etc will merely have the
> choice of a universal tuning made _for_ them, most probably in favor of
> 12-tone equal, but one day, most probably, in favor of 19-tone equal.
> The latter should prima facie interest microtonalists more than the
> former.=20
>=20

If one is going to advocate new tunings to the real
world, I am afraid that ANY tuning which cannot play with the=20
traditional instruments of the intended society in a manner
acceptable to that societies common practice will have a long=20
road to travel until adoption.=20

Since my intended society is "Western", a simple example is=20
instructive: "hey, lets try it up a half step".=20
A "new system of temperment" which has to retune the instrument
to meet this challenge won't make it in the "real world".

Similarly, there is a great deal of harmonically-oriented
music from the past two centuries which takes such advantage of
the capabilities of 12-tones per octave, that a real, viable new
tuning should be able to "add" to that body in a meaningful=20
manner, without asking the existing literature be changed.

This suggests a "new tuning" be a subdivisions of 12TET. I will go
ahead and choose some, given that I believe that the primary=20
deficiencies of 12TET are,
1) bad major thirds=20
(I don't mind 12TET minor thirds, probably
because they are very close to 19:16...)
2) important tones missing from the overtone series (bad=20
approximations to 7's and 11's)

Improvements to the major third (vs 12TET) occur with 48, 60, and 72TET,
and for no subdivision before. This is ture for the minor third as well.
The 7:4 and 11:8 improve immediately even in quarter tones, but=20
"excellent 7's" occur with 36TET.

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.



..On the other hand, I'm not trying to change the "real world" to
use a "new tuning", but rather am interested in the sounds mentioned
above which are lacking in 12TET.

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.

Bob Valentine


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Subject: Re: 19, 22, 29, 41, 53 : 12 and multiples
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