dear stewart - staggering. i didn't mean for you (or jon) to compose anything so comprehensive and thorough. while i'm sure you meant this for general edification i'd like to say thank you all very much from me.
i wouldn't be even remotely interested in going to one of these but i understand there are oud camps in the us for people who want to immerse themselves in arabic music. one of the introductory exercises is spent inching your fingers up and down the neck while listening out for the infinite subtleties which can be produced on a stringed instrument without frets. i tune my instruments with a digital auto tuner, designed for a guitar and while the little light may indicate that i'm in perfect tune, my ear often tells me otherwise. i've often wondered if "being in perfect tune" was a purely subjective consideration dependent on such things as what song was playing when the radio alarm went off; what the weather is like outside and barometric pressure and no q-tips left in the bathroom. i understand what you say and it all sounds to be a bit of a mystery. maybe the hillbilly prelude to some song or other in the key of "...round 'bout 'c'..." may be the best that any of us can hope for. thanks again stewart. i continue to be amazed at all the things i don't know and very, very grateful to those people who do. sincerely - bill On Gioved�, lug 22, 2004, at 15:03 Europe/Rome, Stewart McCoy wrote: > Dear Jon and Bill, > > I am no mathematician, so I cannot give a detailed account of sixth > comma meantone. You will find the relevant information in books like > Mark Lindley, _Lutes, Viols & Temperaments_ (Cambridge: Cambridge > University Press, 1984). I'll try to explain how I understand it, > without going into all the maths. A few simple sums are inevitable > though. > > The first thing to realise is that lutes, like all other > instruments, cannot be tuned perfectly. The sums don't add up. We > have to compromise, so, when we tune an instrument, we put up with > slightly squiffy intervals between notes, hopefully so slight that > no-one notices that anything is amiss. > > When you start to learn a string instrument, tuning may seem easy, > because you tolerate all sorts of bad tuning. As you get better at > it, your ear becomes more perceptive, and you find tuning more > difficult, because you get to be more fussy. Eventually, in despair, > you get so good, that you simply cannot get the ****** instrument in > tune. Mercifully modern tuning boxes can help one cope with a task > which ultimately is theoretically impossible. > > Equal temperament > > Equal temperament is used nowadays on the piano. The piano tuner > will tune all the semitones the same distance apart - hence "equal" > temperament, but it means that the major thirds (e.g. C+E, E+G#, > etc.) are much wider than pure. (Pure = perfectly in tune.) The > human ear can cope with this, but any wider, and you'd say the notes > were out of tune. At the same time the piano tuner will tune all the > fifths (e.g. C+G, E+B, etc.) very slightly narrower than they would > be if they were perfectly in tune. Again, the human ear can cope > with slightly narrow fifths, because the difference between those > fifths and pure fifths is hardly noticeable. > > The advantage of equal temperament is that you can play in any key > you like, and it will all sound OK. Vincenzo Galilei argued in > favour of equal temperament for the lute. I think equal temperament > is essential for the baroque guitar. Mark Lindley presents much of > the evidence we have from the past, but he seems to conclude that > equal temperament was more commonly used with some fretted > instruments than I think he should. > > Meantone tunings > > The idea of a meantone temperament is to get the major thirds > narrower than they are with equal temperament, so that they are > better in tune, and will sound sweeter. You can do this for some > major thirds, but it is impossible to do so with all of them. The > trick is to favour the common thirds (e.g. C+E, F+A, etc.), and have > horrible out-of-tune intervals for the thirds you are unlikely to > need (e.g. F#+A#, B+D#, etc.). > > The most extreme meantone tuning is quarter comma meantone, which > was commonly used for early keyboard instruments. In this > temperament all the common major thirds are pure. This works well > for keyboard instruments, which have separate strings for each note, > but it is a bit risky on fretted instruments like lutes, which use > the same string (fretted) for many different notes. Discrepancies > may creep in with lutes for all kinds of reasons, and you don't want > to risk having a major third less than pure. > > Fifth comma and sixth comma meantone are compromises, with the good > major thirds tuned somewhere between pure and equal. Sixth comma > meantone is closer to equal temperament, and seems to work well for > most renaissance lute music. Occasionally you might have to move a > fret or two, if you want to play in an extreme key, which is what we > know some vihuela players did. > > The evidence supplied by surviving citterns is very important in > knowing what temperament may have been used for fretted instruments > in the past. According to Peter Forrester, who has examined > virtually all surviving citterns, the cittern fretting system is > closest to sixth comma meantone. He has told me that later > instruments tend to move towards equal, but they never actually make > it. Perhaps it is because it is so easy to distort the pitch of the > short wire strings, but equal temperament just doesn't work for > citterns. There has to be some move in a meantone direction for them > to sound any good. > > People in the past argued about the suitability of different > temperaments, just as they do now. We all have our preferences. Mine > is sixth comma meantone for renaissance lutes and citterns. > > The syntonic comma > > A comma is a discrepancy arising from the fact that the figures > don't add up. The syntonic comma is the amount the 1st and 6th > courses of the lute would be out, if you tuned all the intervals > between the courses pure. This is how it works: > > Simple sums for simple intervals > > To get different intervals you multiply with simple numbers. For > example, to get a note an octave higher, you multiply by 2. If > middle C = 256, C an octave higher = 512. > > Let's think of 6-course renaissance lutes and the five intervals > between the six courses. The 6th course is tuned to G. Let's say > (for the sake of argument) that it vibrates at 81 cycles per second. > To get a note a fourth higher (the 5th course C), you multiply by > 4/3: > > If G = 81, C = (81x4/3) = 108 > > You do the same to get the 4th course: > > If C = 108, F = (108x4/3) = 144 > > To get a major third higher for the 3rd course you multiply by 5/4: > > If F = 144, A = (144x5/4) = 180 > > The 2nd course is a fourth higher, so you multiply by 4/3: > > If A = 180, D = 240 > > Finally, for the 1st course you multiply again by 4/3: > > If D = 240, G = 320 > > We should now have ended up two octaves higher than the 6th course. > We started with G = 81. To get an octave higher we multiply by 2, so > to get two octaves higher we have to multiply by 4: > > If G (6th course) = 81, G (1st course) = (81x4) = 324. > > Unfortunately that's not the same as the 320 we got earlier, by > calculating from one course to the next across the neck of the lute. > The difference between 320 (four intervals of a fourth + one major > third) and 324 (two octaves) is called the syntonic comma. Somehow > or other we have to stretch our intervals, so that 320 can become > 324. We can do this many ways: > > 1) Pythagorean temperament > > Keep the four intervals of a fourth (G+C, C+F, A+D, D+G) the same > (pure), and widen the major third between F and A. This means that > all fourths (and consequently fifths) are pure, but the major third > is pretty foul. This sort of temperament was used for mediaeval > music, when there were lots of fourths and fifths in the harmony, > and when they understandably avoided bad-sounding thirds and sixths. > > 2) Quarter comma meantone > > Keep the major third between F and A the same (pure), and widen the > other intervals (the four fourths). This is quarter comma meantone, > because you have divided the syntonic comma into four, and shared it > out amongst the four fourths (between G+C, C+F, A+D, D+G). > > 3) Fifth comma meantone > > Divide the syntonic comma into five, and spread the discrepancy > amongst all the intervals between the strings. The four fourths will > be slightly wider than pure, and the major third between F and A > will also be a little wider than pure. > > 4) Sixth comma meantone > > Again, share the discrepancy out between all the strings, but this > time divide the comma into six portions. Each of the four fourths > will be very slightly closer to pure than with fifth comma meantone, > and the third between F and A will be very slightly wider. In sixth > comma meantone the major third is quite wide, but not as wide as it > would be with equal temperament. > > I think that's how it all works. Any comments or corrections will be > welcome. > > All the best, > > Stewart. > > > ----- Original Message ----- > From: "Jon Murphy" <[EMAIL PROTECTED]> > To: "Stewart McCoy" <[EMAIL PROTECTED]>; "bill" > <[EMAIL PROTECTED]> > Cc: "Lute Net" <[EMAIL PROTECTED]> > Sent: Thursday, July 22, 2004 8:37 AM > Subject: Re: Sorry, help me....what to buy???? > > >> bill, >> >> The cittern was originally designed for amateurs (according to my > books), >> the pros preferred the lute. And I heard one played with a harp > this weekend >> (a commercial cittern, it had to be, as the pegs were guitar style >> machines). But the cittern wasn't intended to be a lute. >> >> As to the 6th comma meantone, Stewart will explain that. But there > are many >> tunings for our western scale that are all compromises. If you > want it I'll >> scan a pictorial of the various compromises, and their > relationship to the >> pure tones, and send it. I haven't the vaguest idea what the "6th > comma" is, >> but I do know the Pythagorean comma. Pythagoras made a board with > a string >> (perhaps several, I don't know how good his pitch memory was - > never met the >> man). >> >> The natural overtone scale has a few fractions in it. They confuse > the >> issue. In a tempered scale the octaves which are primary should > come to the >> same result as the fifths (the half lengths). (And if I'm a bit > off in >> saying the details, let the overall principal apply). The half > should add to >> the total, but it doesn't. Five octaves and eight fifths don't > come to the >> same pitch - and the difference is called the Pythgorean comma. So > whatever >> the 6th comma is, it is a compromise in the scale. There are a > number of >> ways to do it, the orchestral piano has fixed pitches, as does the > harp. The >> lute family may not, although once you have set your frets you > have chosen a >> temperament, but on the violin or any unfretted instrument that > can vary. >> Meantone is one choice (and there are several meantones, depending > on >> whether you want to make the fifths closer to the natural, or the > thirds - >> you can never do both). The standard solution is to divide the > octave into >> twelve equal parts by frequency, and this is a compromise. Twelve > hundred >> "cents" to the octave, each half tone worth one hundred "cents". > Works well >> for digital tuners, but it is not the only solution. >> >> Best, Jon >> >> ----- Original Message ----- >> From: "bill" <[EMAIL PROTECTED]> >> To: "Stewart McCoy" <[EMAIL PROTECTED]> >> Cc: "Lute Net" <[EMAIL PROTECTED]> >> Sent: Thursday, July 22, 2004 2:37 AM >> Subject: Re: Sorry, help me....what to buy???? >> >> >> >> On Gioved�, lug 22, 2004, at 00:46 Europe/Rome, Stewart McCoy > wrote: >> >>> the grooves for the frets were already >>> made, and they aren't at 6th-comma meantone >> >> dear stewart - >> >> i've tried to imagine what this might mean but haven't a clue. > sounds >> intriguing. would you please explain? >> >> sincerely - bill > > >
