source file: mills2.txt Date: Sat, 4 Jan 1997 09:54:00 -0800 Subject: Early Music, Temperaments, Logs From: John Chalmers I saw this on rec.music.early. Does anyone know anything more about this and the music played? (Johnny?). rec.music.early #16829 (0 + 17 more) From: mccomb@best.com (Todd Michel McComb) [2] Re: alternative tunings in 16th century + music Date: Fri Jan 03 13:49:47 PST 1997 In article <2184@purr.demon.co.uk>, Jack Campin wrote: >A few years ago I heard an astonishing broadcast (on BBC Radio 3) of 16th >century Neapolitan harpsichord music written for microtonal insytruments - >the concert was part of an International Festival of Microtonal Music mainly >centred around contemporary works. Does anybody out there know what I'm >talking about? Who was the performer, and has he or she toured this stuff >or put it on a published recording? I don't know anything about this particular performance, but the repertory is fairly well-known to EM keyboardists. Definitely, as far as recordings go, the one to hear is Alan Curtis' on Nuova Era 7177 http://www.medieval.org/emfaq/cds/nuo7177.htm Todd McComb mccomb@medieval.org BTW, I was re-reading Bosanquet's 1876 book "An Elementary Treatist on Musical Intervals and Temperament" in which he describes his famous generalized keyboard. What caught my attention was a section where he calculates musical logarithms, in this case the semitone measure of ratios (equivalent to cents divided by 100). Bosanquet computes his own logs from a series expansion approximation rather than using tables and implies that the proofs of such expansions were commonly given in 19th century trig books. Anyway, a longer discussion which illuminated the method of Ellis, which I posted to the tuning list last Spring (or so). The method appears less to have been pulled out of thin air than it does in Ellis's exposition in Helmholtz. I, for one, would like to see David Feldman's table of "isotempered" interval pairs. Alas, I have an old, small screen Mac and would need the reformatted or a hardcopy version. By using Brun's algorithm, it was easy to show that Feldman is correct in that the series of relations of the degrees of the fifth Q to those in the octave T: Q\T ~3\5, 4\7, 7\12, 10\17, 17\29, 24\41, 31\53, 55\94 corresponds to the number of degrees of the 13/9 in the equal divisions of the 15/8. One might describe this as series of compressed octaves which in which the relative size of the 13/9 corresponds to the relative size of the 3/2 in the original series of octaval ET's. I also played around with another, but related, problem of finding optimal ET's for sets of all 4 numbers, in this case 2/1, 15/8, 3/2 and 13/9. Using Viggo Brun's version of the euclidean algorithm, I got the following N-tone ET's: 10, 19, 24, 43, 53, 72, 125, 178...(only those which distinguish all 4 ratios are listed). Selmer's version oscillates a bit, but finds 20, 21, 12, 26, 34, 46, 33, 41, 54, 75, 62, 87, 162. Pipping's ramified version gave erratic results, though it works fine for 3 terms. --John Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sat, 4 Jan 1997 20:11 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA01169; Sat, 4 Jan 1997 20:13:52 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA01167 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id LAA12790; Sat, 4 Jan 1997 11:13:49 -0800 Date: Sat, 4 Jan 1997 11:13:49 -0800 Message-Id: <009ADE03C0567240.0557@vbv40.ezh.nl> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu