[Harp-L] re: Fine Tuning

[Jonathan Ross <jross38@xxxxxxxxxxx>]

Bertram Becher wrote:

"just take a look at this page: http://ohw.se/hca/tntheory.php
Here all the questions are answered in a very comprehensive and  
accurate manner.
Greetings"

I'll agree with comprehensive, but accurate is another matter.  It  
may be just me, but my fine-toothed comb always comes up when there's  
a quite factual error to start things off.

"12TET came into universal use during the latter half of the 18th  
century "

No, it didn't.  12TET was being advocated for at that time, along  
with other temperaments, but it didn't come into common usage until a  
century later--indeed, right around the 1850's or so we see it  
starting to be common in keyboard instruments, and pretty much  
universal by the 1870's (excepting some Brits--let's face it, they  
earned that stodgy reputation by a lot of hard work:).  That's a good  
hundred years later, and you can't understand the previous hundred  
years of classical music without understanding this.

So, let's see.  A minor error is here:

"12TET is characterized by (1) a doubling of the frequency for each  
octave and (2) a division of the octave in twelve equal steps  
(semitones). The first property is common to all temperaments"

While it might be "common" it is not universal.  I do know of a few  
temperaments which do not have pure octaves.  I wouldn't advise  
playing them, but they do exist.

"One alternative to 12TET is the 7-tone just major (7TJM) scale. This  
is..."

A figment of the authors imagination?  I've never heard the term used  
before, perhaps because it doesn't make sense.  There is no such  
thing as the "just major scale".  Rather, there are an infinite  
number of scales which may be derived from the various just  
intonations one wishes to use.  Just intonation is a system, not a  
specific.  You can derive a major scale from 5-limit just intonation  
and it will be different from the one you derive from 7-limit or 19- 
limit (three commonly used just intonations for the standard  
harmonica tuning).  All will be "7-tone just major" scales.  None is  
any more valid than any of the others.

The author begins to correct this here:

"The 7TJM temperament is one of several examples of just  
temperaments. Often, they are loosely referred to as just intonation  
(JI), which also will be used in the following."

But again gets it wrong.  By definition JUST INTONATION IS NOT  
TEMPERED!  Calling something a "just temperament" is not merely an  
oxymoron, it's wrong.  You cannot be both just and tempered--they are  
mutually exclusive.  And there is nothing loose about just  
intonation--again, it is a system of deriving pitches--an old and  
very specific system.  That it is an open-set (ie, infinite) set of  
possible pitches doesn't make it loose.

This misunderstanding of the terminology continues:

"Mainly as an example, we will now design a temperament (tuning scheme)"

A temperament is not the same thing as a "tuning scheme".  A  
temperament is a TYPE of tuning, the difference is extremely  
important.  The word temperament comes from the word "temper", which  
gives the same root as the word "tamper" in English.  It means that  
you are messing with the ideal and thus have to "tamper" with it.   
Not all tuning schemes are "tampered", and again, by definition those  
which are not cannot be called a "temperament", thus you can not have  
a "temperament" in just intonation.  It doesn't make sense.

There is some good information here, but the innacuracies are glaring  
(as is my spelling of that word).  The tuning tables may be of use,  
but frankly when so much of the theory is just plain wrong it makes  
me wonder if any of it is useful.

Again, I refer people to Pat Missin's website ( http:// 
www.patmissin.com/index1.html )  and the links he gives.

Obviously, a lot of effort went into that website, but it would be  
much more impressive if similar effort had gone into understanding  
the underlying issues of temperament and intonation.  Hell,  
understanding what the words mean would have been a good start.




 ()()    JR "Bulldogge" Ross
()  ()   & Snuffy, too:)
`----'