<!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 HTML//EN"> <HTML> <HEAD> <META content=text/html;charset=iso-8859-1 = http-equiv=Content-Type><!DOCTYPE HTML PUBLIC "-//W3C//DTD W3 = HTML//EN"> <META content='"MSHTML 4.72.3110.7"' name=GENERATOR> </HEAD> <BODY bgColor=#ffffff> <DIV>Hello group.  This is my first = entry to pianotech.  According to G.C. Klop, in his Harpsichord = Tuning, page 18, in Werckmeister III, also known as the Correct Temperament No. = 1, the four tempered fifths, c-g, g-d, d-a, b-f#, are each 1/4 comma narrow = (Klop calls these "meantone fifths").  The remaining fifths are just.</DIV> <DIV> </DIV> <DIV>This temperament also appears in Jorgensen's The = Equal-Beating Temperaments on page25.  Being an aural tuner, = and not having the tables in front of me, I can't quote the cents deviation from = ET.  I hope this helps.</DIV> <DIV> </DIV> <DIV>Mike</DIV> <BLOCKQUOTE style="BORDER-LEFT: #000000 solid 2px; MARGIN-LEFT: 5px; PADDING-LEFT: = 5px"> <DIV>-----Original = Message----- From: Richard Moody <<A = href="mailto:remoody@easnet.net">remoody@easnet.net</A>> To: = <A href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> <<A = href="mailto:pianotech@ptg.org">pianotech@ptg.org</A>> Date: Thursday, September 02, 1999 1:07 PM Subject: Re: = Werkmeister #3 </DIV>Curious as to his source.  Does he  = mean Kirnberger III? That is mentioned in New Groves. For = Werckmeister they give "For the first four 5ths (C--G, G--D, D--A, B--F#) = he used a tuning slightly tempered by a third of a comma, while the eight = other 5ths remained pure....the 3rds varied from those of a quarter of = a comma to high to others equalling Pythagorean tuning."   = {New Groves} ** Note "the first four 5ths" are not the = first four fifths of the cycle.  A--E, and E--B are passed by so = they must be  of the "eight others"  thus  = pure.  But the order of the eight others is not mentioned.  At any = rate, 1/3 syntonic comma is is a Fifth 7.17 cents narrow from pure. or 5.2 = cents from ET. (695)  That is not exactly "slightly tempered".   The narrowest third -would- seem to be = wide by a quarter comma  as tempering three 5ths by 1/3 comma gives a = full comma (3/3) at A, the third 5th.  Going a pure fifth to = E  to make the C--E third,  would seem to to take it back to = 3/4.  or 1/4 comma wider than pure.(full comma = 4/4 = pure Third when = Fifths are tempered 1/4 comma) HOWEVER when the cents are added up, = The C--E comes out at 386--387 which is a pure Third.  Also the A = makes a pure Third with F within a cent. If they are suppposed to be 1/4 = comma "high" that would make them 391.   On the = aural side, I am wondering if they thought three 1/3 comma Fifths gives a = pure Sixth? 5/3.  Tuning a 5/3 sixth from C, then tuning a pure 5th = up to E, then an octave down should give a 5/4 Third (pure)(this would be C--E).  A pure Fifth from C also works out to a pure Third = at A.  The only  tempering in this scheme is two notes G = and D to "fit" into the 5/3 C--A . The other Fifths with one = execption are pure.  THAT doesn't seem like too bad a = tuning task.  So adding up the cents,  the 1/3 comma fifth is aprox 695 cents.   Three of these minus 1200 gives 885. A 5/3 = Sixth is 884.3587.  Thats "99 1/2 pure" From this A a = pure Fifth (702!!)  (E) gets 885 + 702 - 1200 = 387 cents. (C--E) = again close enough to call it pure. C--F is supposed to be pure, that = would give 498.   885 - 498 = 387. Perhaps I did = some  math wrong, or the assumption is wrong that a pure fifth from = a full comma gives a quarter comma off. I am hoping Dr. Coleman will have = an Rx for my dilemma.---ric ps  A comma (syntonic) is how much = wider from pure a Third is after a series of four pure (Pythagorean) Fifths.  But all tuners know that..... ; ) = ---------- > From: dale  r fox <<A href="mailto:foxpiano@juno.com">foxpiano@juno.com</A>> > = To: <A href="mailto:pianotech@ptg.org">pianotech@ptg.org</A> > = Subject: Werkmeister #3 > Date: Wednesday, September 01, 1999 8:47 = PM > > List,  especially those HT specialists.  I have a = customer who does some > concert work here in town who would = like something similar to a > Werkmeister#3.  Is there a = generic equivalent included on RCT's > historical temperments? > = > Thanks in advance. > > Dale Fox > = > = ___________________________________________________________________ &g= t; Get the Internet just the way you want it. > Free software, = free e-mail, and free Internet access for a month! > Try Juno Web: = <A = href="http://dl.www.juno.com/dynoget/tagj">http://dl.www.juno.com/dynog= et/tagj</A>. > </BLOCKQUOTE></BODY></HTML>