[Harp-L] re: 17-note and 12-note scales

[Jonathan Ross <jross38@xxxxxxxxxxx>]

I can't seem to find the post Richard Hunter was responding to in the  
archives, but no matter--I'll deal with just what Richard wrote.   
Thus, all quotes below are from Richard except the first one which he  
had quoted:

"<the chromatic or diatonic scale, contrasted with the tonic or equal  
<tempered scale, is a musical scale consisting of 17 notes, where  
each <sharp and each flat differ by approximately 8hz. <snip>)"

What this sounds like is a very odd way of describing a 17TET  
temperament--ie, one where the octave is divided into 17 equally  
spaced notes rather than 12.  You can find more information on 17TET  
here, particularly some sound examples and such: http:// 
xenharmonic.wikispaces.com/SeventeenTonePianoProject .  Also, this is  
a site which can play sound samples of the scales and chords (the  
chords may not be quite correct--Midi can message notes in weird  
ways): http://www.suddensound.com/um/monochord/ .

Now, all the other quotes are Richard's.

"This terminology is definitely not common, and several comments on  
the same web page as the one above note that this is so. I'd like to  
see a picture of a keyboard designed to use this scale. Even better  
if the reference describes how widely used such instruments were."

I know of no instruments historically tuned to 17TET.  There are many  
examples of instruments with split-keys and such for use in non- 
equal, non-circular temperaments, from meantones to more complex  
arrangements.  These were never particularly common, but were  
certainly not unknown in either the harpsichord or organ world.  The  
way this was done was to "split" the black keys into two pieces,  
front and back.  I have pictures, but non online (I suppose I could  
photograph the photo in a book if you want--no scanner)--though I am  
sure there are pictures of such keyboards online if you do a search  
for "split-key" harpsichords or the like.  More recently, some organ  
and harpsichord firms have built both new and replica instruments  
with this feature.  The Fisk Organ Company comes to mind.

"The count of the pipes is not the same as the count of the keys, for  
several reasons. Multiple keys can and do use a single pipe. Various  
mechanical systems are used to switch from one set of pipes to  
another. That's how those old organs produce different tones."

Not really.  We are talking about older organs here, primarily  
Baroque or earlier.  These use a mechanical action and as such it is  
rare that a pipe will be played by more than one key (ignoring  
couplers for the moment).  Now, each key can play more than one pipe,  
and the various sets of different pitch-range and tonal-class pipes  
are usually (though not in the earliest organs) available to be  
switched on-and-off by use of the "stops"--traditionally sliders  
(like a chromatic) which either aligned or mis-aligned a set of holes  
in the slider allowing air through to the pipe from the chest or not  
depending on what you wanted.  It wasn't really until the advent of  
the electric action organ in the late 19th century that truly  
practical means of playing one pipe from several keys was managed.   
And by then, 12TET was not just the norm but dominant.  Thus, a big  
distinction has often been made between what are called "unit" organs  
where one pipe may play at several different pitches and "classic"  
organs were most pipes play at just one pitch and from just one key.   
Theater organs are the most commonly found form of unit organ--though  
often smaller, less expensive instruments of non-theater type are  
made on the unit system, and degrees of "unification" are found on  
many otherwise traditionally designed organs.

More than most wanted to know, I'm sure, but the explanation is a bit  
complex.

"The point of the equal temperament isn't to try and condense 17  
notes into 12; it's to produce a tuning in which all 12 keys sound  
equally good."

Or equally bad.  Really, the point was to not have wolf tones and to  
make playing increasingly chromatic music possible without harsh  
tonalities intervening.  The result was similar to Douglas Tate's  
maxim of playing everything with your worst legato so that you give  
an illusion of greater smoothness than if you were switching  
constantly from a smooth legato to a more harsh one.

"In early medieval temperaments, intervals between notes were tuned  
in such a way that some keys (the ones closest to C) sounded  
fabulously, luminously beautiful, and others (the ones farthest from  
C) sounded absolutely awful. That's why F# was known in medieval  
times as "the devil's key"."

Define "medieval".  The various mean-tones pretty much fall into  
these descriptions, and they were still well in use in the early 19th  
century.  Notably, Wheatstone invented his concertina specifically to  
be tuned in a mean-tone (1/4-comma, I believe).  That's more than a  
bit beyond the "medieval" period--by about a couple, centuries or so.

"The equal temperament was designed to solve this problem, and it did  
so by compromising pure intervals to produce a set of 12 keys that  
all sounded pretty good. "

As were and are dozens of other temperaments.  12-Tone Equal  
Temperament was just one of the many competing systems out there  
until it became increasingly adopted during the chromatic revolution  
of the mid-Romantic period in the 19th century.  And, there are an  
infinite number of "equal temperaments", not just 12TET--any number  
can be used, really.  Indeed, 19TET has often been suggested by many  
as both a more harmonious temperament and a more accurate  
representation of Western theory (I'd agree with the later, though  
not necessarily the former--it's still an equal temperament, and it's  
just different things are better and worse than 12TET).

"That's why J.S. Bach wrote "The Well Tempered Clavier", which is a  
set of pieces in every major and minor key for keyboard -- to show  
how good EVERY key sounded with an equal temperament."

As I've pointed out here many times before, there is really minimal  
evidence Bach wrote the WTC for 12TET.  Indeed, I'm pretty convinced  
he didn't, but to be fair the scholarship is pretty much open to  
debate: whether Bach wrote for 12TET in general or wrote the WTC for  
12TET is not at all a settled issue by any stretch of the  
imagination.  It was long considered to be the case, but much of the  
reasoning for that was the massive bias for 12TET from the heavily  
chromatic late-Romantic and the atonal modernism (both fairly  
strongly associated with 12TET in their musical theories).  During  
Bach's time not only was mean-tone still present (though he most  
likely didn't use it much) but there were many versions of "well"  
temperaments which attempted to solve the problem in much different  
ways than 12TET.  Bach would have known all of these, and he  
certainly could have used the German word for "equal" or even  
"circular" in his treatise, but he didn't.  That, of course, isn't  
evidence of what he used, but it should help point out that the  
matter is not at all settled.  Moreover, the world post-Bach didn't  
change all that much in terms of temperament until the Romantics--to  
go back to organs, most organs weren't being tuned in 12TET in the US  
until the 1850's or so--England was later and France probably about  
the same as the US, there were too many different traditions in the  
German areas to say any singular trend.  Thus, Mozart was probably  
not working in 12TET, for instance.

"Again: it had nothing to do with a change from 17 notes to 12. By  
Bach's time, keyboards were designed for an octave with 12 notes."

Well before then, actually.  Still, the 7/5 white/black 12-note  
arrangement doesn't indicate temperament, as it was in use long  
before 12TET became popular.  Besides which, harpsichords and the  
like are both easy enough to retune and unstable enough in terms of  
holding a tuning that many players probably used whatever temperament  
was best for the given piece (and would have had to know how to set  
them).  Organs are much harder to tune, so they helped lead the way  
in terms of finding a settled, singular and catholic temperament-- 
similarly, as tension increased on pianos they became both harder to  
tune and more stable, thus increasing a need for a singular  
temperament for all pieces.  12TET eventually became the solution, in  
part because of the rise in chromatic music--had music gone another  
way, things might have been different.

"The piano forte was regarded as a "barbaric bastard of an  
instrument?" I really need to see some scholarly references for that  
one. The piano forte was a relatively late invention too, well after  
the harpsichord and organ, both of which had the same physical  
limitation in terms of keyboard design."

And for most of the harpsichord's lifetime (ie, before it's essential  
death in the 19th century) it would have been rare to find one in  
12TET--similarly for organs during that time.

"In any case, I'm sure of one thing: the vast majority of western  
musicians haven't been writing music for a 17-note scale for hundreds  
of years. For that matter, most modern instruments couldn't easily  
play such music."

I doubt any historic music has been really written for a 17-note  
scale--it was written for the more flexible theory before 12TET took  
over and enharmonic notes became the norm.  Now, much music has been  
written for 12TET, but most could be interpreted in other forms,  
sometimes with wonderful results and sometimes with horrible  
results.  17TET would be fairly easy to play on a properly set-up  
instrument.  You mention that problem in the end: most instruments  
are designed for 12TET, so have trouble playing other things.  That  
is because there was a conscious movement towards 12TET.  If, for  
whatever reason, there was a conscious movement to some other  
standardized temperament, the situation would be different (won't  
happen, but it could).

But, so what?  From a harmonica perspective you could probably  
integrate a 17TET (or 19TET for that matter) instrument into the  
various modern genres.  Indeed, harmonica players often integrate a  
non-12TET diatonic system into musics where most of the other  
instruments are decidedly in 12TET (piano, guitar, bass, etc..).  It  
may be difficult in some ways, but then, it is something the  
harmonica could actually do more easily than some other instruments.




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