The Intonational Preferences of Irish Setters

With all the judgement being passed on music unheard, based solely on
the materials chosen for a mere *one* of its many organizing
principles, and all the howling being done, about sour tunings causing
ear damage to canines, I thought I'd conduct a little research:

I asked my dog what he thought of the various tunings I've been
playing with.

Now, he couldn't, of course, answer me with numbers, and theroretical
discussions about the canine melodic lemondrop, and I don't have the
equipment necessary to pitch analize *his* singing [the tail is
definately in 2/2 time :)] but, judging by his habit of sleeping next
to me while I'm practicing, and the contented look on his face, I feel
fairly confident that he really doesn't care one bit what tuning I
happen to be using. He's quite happy to know that I am finding some
fulfillment in my attempts at self expression. I'm making music,
which makes me happy, which makes him happy, and the world is richer
all around. What more need he say?

It makes me wonder whether good ol' Boo has something to teach the
human population?

That being said...

I sincerely wish everyone on the list a happy, peaceful and musical
holiday... however you tune it. ;-)


Steve


SMTPOriginator: tuning@eartha.mills.edu
From: Robert C Valentine
Subject: 19, 22, 29, 41, 53 : 12 and multiples
PostedDate: 23-12-97 11:42:24
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On Tue, 23 Dec 1997, Robert C Valentine wrote:
> Regarding 19TET in particular, perhaps it is the last temperment which
> preserves "sameness" of the "big" and "small" major seconds (9:8, 10:9).

Um, what? The nearness of 31, 43, and 55 TET to quarter, fifth, and
sixth comma meantone has been known for hundreds of years. 31 is
level-3 consistent through the 7-limit.

72TET is level 2 consistent through the 11 limit, BTW, and is used not
only by Sims but by the Richter-Herf crowd.

Wendy Carlos uses 144TET on Beauty In The Beast for her "Super-Just"
13-limit scale. On a theoretical basis, I would have preferred 270TET
for a highly modulatory piece like she wrote, since 270 is the first
tuning that is level-2 consistent through the 13-limit, but of course at
such high numbers the difference is far too small for me to notice.

--pH http://library.wustl.edu/~manynote
O
/\ "Do you like to gamble, Eddie?
-\-\-- o Gamble money on pool games?"

NOTE: dehyphenate address to remove spamblock. <*>


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From: Robert C Valentine
Subject: 19, 22, 29, 41, 53 : 12 and multiples
PostedDate: 23-12-97 13:14:54
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----- Forwarded message from Robert C Valentine -----

>From bval Tue Dec 23 12:39:54 1997
Subject: 19, 22, 29, 41, 53 : 12 and multiples
To: tuning@eartha.mills.edu
Date: Tue, 23 Dec 1997 12:39:54 +0200 (IST)
From: Robert C Valentine
Cc: bval (Bob Valentine)
In-Reply-To: from "tuning@eartha.mills.edu" at "Dec 20, 97
07:39:57 am"
X-Mailer: ELM [version 2.4ME+ PL17 (25)]
Content-Length: 5866


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

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

First, regarding the importance of the 55~60 cent melodic
identification concept. There have been maney good points made
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.

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

That said, it seems that the differences that are important
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.

>
> On the list, I believe someone  by no means devoid of understanding 
> 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.

I really don't understand this statement "cast out the consonant thirds".

12TET 7 M4 == 4 P5
19TET 11 M4 == 6 P5
53TET 31 M4 == 17 P5

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,
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  our own, Western people especially  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.
>

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

Since my intended society is "Western", a simple example is
instructive: "hey, lets try it up a half step".
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
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
deficiencies of 12TET are,
1) bad major thirds
(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
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
"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
Music (vol 29, their microtonal series) and Computer Music Journal
in recent years. As a REAL tuning system to advocate vs 12TET, this
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

----- End of forwarded message from Robert C Valentine -----


SMTPOriginator: tuning@eartha.mills.edu
From: "Paul H. Erlich"
Subject: RE: Gibson digest 1274
PostedDate: 23-12-97 14:43:21
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Paul Hahn writes:

> On Tue, 23 Dec 1997, Robert C Valentine wrote:
> > Regarding 19TET in particular, perhaps it is the last temperment which
> > preserves "sameness" of the "big" and "small" major seconds (9:8, 10:9).
>
> Um, what? The nearness of 31, 43, and 55 TET to quarter, fifth, and
> sixth comma meantone has been known for hundreds of years. 31 is
> level-3 consistent through the 7-limit.
>
> 72TET is level 2 consistent through the 11 limit, BTW, and is used not
> only by Sims but by the Richter-Herf crowd.

Paul,

If you'll pardon my asking what is most likely an FAQ, could you
offer a quick explanation of what level-n consistancy is all
about? I *think* I understand the basic concept of a scale being
[level 1?] consistant, but this is something that I'm not sure
about. Then again, maybe it's obvious, but I don't have the
concepts right.

Either way, an explanatory footnote would be greatly appreciated.

Thanks,

Steve


SMTPOriginator: tuning@eartha.mills.edu
From: Stephen Soderberg
Subject: HABA! (...now that I have your attention)
PostedDate: 23-12-97 18:36:12
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On Tue, 23 Dec 1997, Steven Rezsutek wrote:
> If you'll pardon my asking what is most likely an FAQ, could you
> offer a quick explanation of what level-n consistancy is all
> about?

Level 1 consistency, or just consistency, at some limit x is what you
have when all triads within the x-limit can be consistently represented,
e.g. the tuning's closest approximation of the larger interval is the
sum of the closest approximations of the two smaller intervals.
Example: in 24TET, 5/4 is about 8 steps and 7/5 is about 12 steps, but
7/4 is closer to 19 steps than 20. Ergo, 24TET is not consistent at the
7-limit, because you can't tune a 4:5:7 triad so that all intervals are
represented as accurately as the tuning allows.

For higher consistency levels, consistent representations exist not only
for all the x-limit intervals, but also combinations of up to n of them.
Example: 12TET is level 3 consistent at the 5-limit because even a stack
of three of the interval which is represented with the greatest error,
the 6/5 (that is, 6/5 x 6/5 x 6/5 = 216/125) is represented
consistently: the closest 12TET approximation to 216/125 is 9 steps,
which equals 3 times the 3-step interval which best approximates the
6/5.

You can find tables of consistency levels at

http://library.wustl.edu/~manynote/consist.txt

and

http://library.wustl.edu/~manynote/consist2.txt

The first is simply all the consistency levels at all the relevant
limits up to 1200TET; the second only includes an ET if there is some
limit at which it exhibits a higher consistency level than any smaller
numbered ET, going up to 10000TET. (A period signifies level 1
consistency.)

Incidentally, I think this may relate to why Haba isn't thought of much
these days: as you can see by examining the tables cited above, simply
subdividing the semitones of 12TET doesn't really yield you very good
representations of harmonic intervals until you get up to 72TET which is
level 2 consistent at the 11-limit, but that's a bit too big of a jump
for some people; too many notes. ("--Herr Mozart." 8-)> ) Most of us
find it quite daunting enough trying develop something that makes sense
down in the 19/22/31 range.

--pH http://library.wustl.edu/~manynote
O
/\ "Do you like to gamble, Eddie?
-\-\-- o Gamble money on pool games?"

NOTE: dehyphenate address to remove spamblock. <*>


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From: alves@orion.ac.hmc.edu (Bill Alves)
Subject: Re: Danielou, Touma
PostedDate: 23-12-97 19:48:51
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> Regarding 19TET in particular, perhaps it is the last temperment which
> preserves "sameness" of the "big" and "small" major seconds (9:8, 10:9).

Perhaps this isn't very important (or maybe it is), but this strikes me
as a strange way to think of it. The historical and probably
psychoacoustic basis of Western tuning is Ptolemaic JI, which has two
different sizes of whole step. There is therefore no meaning to preserving
an abstraction that represents those two intervals identically. You can't
preserve something ahistorical.

Forgive me however, if I'm nitpicking an off-the-cuff phraseology of
just a little side thought. If on the other hand this is closer to a
succinct and carefully-chosen summary of a basic tuning philosophy, then I
suggest rethinking that idea.


SMTPOriginator: tuning@eartha.mills.edu
From: mr88cet@texas.net (Gary Morrison)
Subject: Re: Tuning Standards?
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