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



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:) `----'







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