<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.0 Transitional//EN"> <HTML><HEAD><TITLE></TITLE> <META http-equiv=Content-Type = content=text/html;charset=ISO-8859-1> <META content="MSHTML 6.00.2800.1400" name=GENERATOR> <STYLE></STYLE> </HEAD> <BODY bgColor=#ffffff> <DIV><FONT face=Arial size=2>Ric,</FONT></DIV> <DIV><FONT face=Arial size=2>thank you very much for your statements = about the pure 12th tuning...</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>15 years after its publication in euro = piano 3/88 ("Stopper tuning - Equally temepered scale based on pure dudecimos = (12th, pure octave + pure 5th) it seems to become accepted. </FONT></DIV> <DIV><FONT face=Arial size=2>At the time i did the publication, = most technicians called me crazy and there were only a few who = understood what my intention was.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Isaac,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>maybe your opinion about the pure 12th = may change if you hear this tuning done by someone who is familiar with tuning it. = I can not agree that the 5ths are more strange than in normal tuning, since they are less sharp than your preferred normal VT = tuning.</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>best regards,</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>Bernhard Stopper</FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <DIV><FONT face=Arial size=2>for more information about the pure = 12th tuning (in german):</FONT></DIV> <DIV> </DIV> <DIV> <FONT face=Arial size=2><A href="http://www.piano-stopper.de/html/stotun.htm">http://www.piano-sto= pper.de/html/stotun.htm</A></FONT></DIV> <DIV><FONT face=Arial size=2></FONT> </DIV> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; = BORDER-LEFT: #000000 2px solid; MARGIN-RIGHT: 0px"> <DIV style="FONT: 10pt arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: = black"><B>From:</B> <A title=Richard.Brekne@grieg.uib.no href="mailto:Richard.Brekne@grieg.uib.no">Richard Brekne</A> </DIV> <DIV style="FONT: 10pt arial"><B>To:</B> <A title=oleg-i@noos.fr href="mailto:oleg-i@noos.fr">oleg-i@noos.fr</A> ; <A = title=pianotech@ptg.org href="mailto:pianotech@ptg.org">Pianotech</A> </DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> Wednesday, May 26, 2004 = 11:05 PM</DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Re: For your Listening = Pleasure - tuning thoughts</DIV> <DIV><BR></DIV>Issac..<BR><BR>I couldnt disagree more with you about = the P 12ths tuning.  The 12th tunings curve results in a very condensed = stretch which has the peculiar effect of sounding as tho it has a greater = stretch then its actual stretch numbers would suggest.  Typically the highest = C is no more then 28 cents stretched... which is about as slight a stretch as = they come. I can hardly see that a more conservative stretch is really = possible without creating narrow 2:1 octaves at some point. <BR><BR>In the = temperament range, this tuning has fourths and fifths that are nearly identical to = the standard temperament. The distance between D3's third and A4's = fundamental is typically narrowed by 0.3 to 0.5 bps for this range. Spread over the = 17 notes of the 12th this is hardly something the human ear can directly = discern. A3's 2nd is placed such that A3 has a comfortable 6:3 relationship with A4, = whilst at the same time maintaining an acceptable narrowness with D3's 3rd... = typically about 0.35 bps... also very very standard stuff.  In = fact... the only real area of significant divergence from a standard tuning = scheme is found in the area around A5- E6 in which octave based tuning curves = usually display a temporal shift in direction for the resulting 12ths.  = The P 12ths tuning results in the most singing and warm treble I have ever = heard from a tuning... as long as one is careful not to allow any error on = the wide side of just 12ths. This is because of the natural warmness of pure = intervals, and because of the resulting calm of the double and triple octaves = this yields.  But beyond the warmth this creates the constancy in = major 10ths and 17ths that also results, and the increased sustain times resulting = from frequent incidence of pure coinciding partials in the octaves AND = 12ths contributes to a clarity in addition to the warmth this tuning imparts.<BR><BR>If you have had strange resulting 5ths from attempting = an aural implementation of this tuning... then you have not succeeded in = tuning it precisely enough  I would guess, as one of the most pleasing = results of this tuning is the resulting 5ths. Jim Coleman  mentioned this = in a private note to me, along with his opinion that resulting octaves in = the fore mentioned range (A5 - E6) were particular illy = pleasing.<BR><BR>Reading through the rest of your comments... it seems to me that you havent = really understood what the P 12ths tuning is all about... as in several spots = you allude to a high stretch factor that simply does not exist in such a tuning.  Anyone tuning double  octaves that are wide enough = to begin to silence triple octaves is contriving a tense and piercing = tuning  indeed, which goes tonally in the opposite direction of the warmth you = indicate below. Not that there are not uses for this approach mind you.<BR><BR>I havent had opportunity to tune with the VT yet, so I = will certainly reserve comment as to the nature of its standard tuning. Tho = I imagine it to be a fine ETD.  <BR><BR>And by the way.... I = personally thought the violinist was from time to time a bit less then on top of = his game intonation wise. What you deemed as fourths slightly smaller then the pianos... I deemed as just plain flat, at least at several instances = sitting in the concert hall.  And I wasnt the only one judging from the discussion afterwards. Perhaps understandable since he was suffering = from a very bad cold.<BR><BR>Cheers<BR>RicB<BR><BR>Isaac OLEG wrote:<BR> <BLOCKQUOTE cite=midMABBLJGEBJDPJHIACJBAOEFDFOAA.oleg-i@noos.fr = type="cite"> <META content="MSHTML 6.00.2800.1400" name=GENERATOR></BLOCKQUOTE><BR><BR></BLOCKQUOTE></BODY></HTML>