On Feb 26, 2009, at 12:17 PM, Jim Busby wrote: > Hi Don, > > Maybe Fred, the Eds (Aren’t you the same? ;-) or someone else could > answer this as well, but is there any source that lays out bearing > setting for these aurally, w/o offsets? Maybe a “HT for Dummies” > booklet? Maybe I missed it in all the many posts. > > Thanks. > > Jim Busby Hi Jim, Actually Jorgensen's "Big Red" isn't very useful for finding historical "tuning recipes." It is mostly taken up with his argument about 19th century tuning practice, and most of the tuning instructions are from that point of view - things published in the 1800s - early 1900s in England. His earlier book (1977), Tuning the Historical Temperaments by Ear, is much more useful, if you can manage to decipher the extraordinarily long and convoluted titles he gives the tunings. This one we've been discussing would be in the chapter "Tuning the Theoretically Correct Jean Baptiste Romieu 1/7 Syntonic Meantone Temperament in the Acoustic Tonality of C Major and A Minor." (There is also another book, "Equal-Beating Temperaments," that I have never seen, which may have more recipes.) Or you can open the attachment Aaron Bousel just sent, which gives beat rates for 4ths, 5ths and M3s. I doubt you'll find 1/7 comma much of anywhere else, other than as a set of cents offsets, as it seems to have been based on just a single mention in the theoretical work of one person. Here is what Murray Barbour wrote: "Romieu mentioned temperaments of 1/7, 1/8, 1/9, and 1/10 commas, but did not consider them sufficiently important to dis- cuss." (Barbour's book is available as a free text or pdf download, and in various formats to read on line: http://www.archive.org/details/turningandtemper027139mbp) . So essentially these are a 20th (and 21st) century phenomenon, with no real historical practice connection. All that said, the way I would tune it aurally follows: Starting with A, tune 5ths in each direction. ADGCFB-flatE-flat and AEBF#C#G#. All 5ths should be half again as large in deviation as ET (IOW, about 1 bps) and 4ths the same (about 1.5 bps). As you create M3s from these strings of 5ths, they should beat at about 2/3 the rate of ET (if it was 6 bps, it should be 4). The final, wolf 5th, E-flatG# should be wide, beating between 3 and 4 bps. As a final verification, check stacked M3s. There will be 4 wolf M3s, spelled as diminished 4ths: F#B- flat, G#C, BE-flat, C#F. These will beat about 1 2/3 times their rate in ET (and the same as "Pythagorean M3s", or M3s produced when you tune 4 consecutive pure 5ths). And when you play series of contiguous M3s (including the "wolves"), the wolves should beat about 2x the rate of the "true" M3s (though the proportion will vary depending whether they are "low or high" in the sequence). Again, I'll put in a plug for Thomas Donahue's A Guide to Musical Temperament. Among other things, it has instructions for a very useful spreadsheet, into which you can insert cents offset, or comma proportions in cents, or another way of expressing cents (based on C as 0 and counting all notes up from there, as done in Barbour, Helmholtz and others), and come up with beat rates for 4ths, 5ths, M3s, m3s and M6s, as well as other parameters like hertz for each note. So that way, faced with something like this, you can do research on the web, find a set of offsets, and generate beat rate tables. Then all you have to to do is use your brain to come up with an aural tuning sequence that makes sense. His spreadsheet gives the same numbers (within a couple tenths of a cent) as Jorgensen or what Rousel posted from Farley, with the addition of intervals they don't include. That's the best I can do in terms of HT for Dummies. (I have entered Donahue's figures in a spreadsheet, which I posted on this list maybe a year or so ago. I have since found that one of the worksheets seems to have a problem, and I haven't yet looked into it - I probably entered a formula wrong into one of the cells - or more than one. The first two work seem to work fine, though). Regards, Fred Sturm University of New Mexico fssturm at unm.edu -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/caut_ptg.org/attachments/20090226/f0577d0d/attachment-0001.html>
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