<HTML style="FONT-SIZE: x-small; FONT-FAMILY: MS Sans Serif"><HEAD> <META charset=US-ASCII http-equiv=Content-Type content="text/html; charset=US-ASCII"> <META content="MSHTML 6.00.2900.3199" name=GENERATOR></HEAD> <BODY style="FONT-SIZE: 10pt; FONT-FAMILY: Arial; BACKGROUND-COLOR: #ffffff"> <DIV> <DIV> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">>Why is equal temperament the only way to solve the dividing of octaves?<?xml:namespace prefix = o ns = "urn:schemas-microsoft-com:office:office" /><o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">It is not the only way.<SPAN style="mso-spacerun: yes">  </SPAN>In modern music we have made it the only way we know and use, but historically there have been other, better ways.<o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">>I know that the beautifully mathematical solution on paper <EM>sounds and works</EM> fine, but what if >there a way we could be missing out on something, such as better sounding music?<o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">We ARE missing out on something, quite a lot, actually!<SPAN style="mso-spacerun: yes">  </SPAN>I have not read the book recommended<SPAN style="mso-spacerun: yes">  </SPAN>by Paul Bruesch, but it sounds fascinating.<SPAN style="mso-spacerun: yes">  </SPAN>I must read it myself.<SPAN style="mso-spacerun: yes">  </SPAN>My comments may be outdated by more recent research, but I can tell you of my experience with historical temperaments, although I have moved on to other things in my more recent work experience.<SPAN style="mso-spacerun: yes">  </SPAN><o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">Years ago, I assisted Owen Jorgensen in preparing a dozen keyboard instruments for his “temperament recital” at a university where I worked at the time.<SPAN style="mso-spacerun: yes">  </SPAN>In his recital, among other things, he played selections in every major and minor key from Bach’s Well-Tempered Clavier.<SPAN style="mso-spacerun: yes">  </SPAN>In the lecture portion of the recital, Owen made reference to the writings of early musicians and composers who expressed their particular preferences for certain keys.<SPAN style="mso-spacerun: yes">  </SPAN>This has long been puzzling to modern musicians, who know no temperament other than ET, in which the only difference from one key to another is the fundament frequency of the tonic in each key, upon which all of the other tones of the scale are built on precisely the same pitch relationships.<SPAN style="mso-spacerun: yes">  </SPAN>This is certainly not the case in any temperament other than ET.<SPAN style="mso-spacerun: yes">  </SPAN>Prior to Owen Jorgensen’s research, and probably to this day, most musicologists believe(d) that Bach’s Well-Tempered Clavier was a promotion of ET, as the only temperament which would allow for pre-tuning an instrument which could then be played in all keys, and that the earlier temperaments, mean-tone temperaments, could be used in only a few keys.<SPAN style="mso-spacerun: yes">  </SPAN>Owen contradicted this notion with his argument that there was an entire class of temperaments that had been overlooked by musicologists.<SPAN style="mso-spacerun: yes">  </SPAN>This class of temperament was called Well Tempered scales, which, by the was, was prescribed by Bach in the title of his work, The Well-Tempered Clavier.<SPAN style="mso-spacerun: yes">  </SPAN>What distinguished well tempered scales from the others, is that the division of the octave allowed for performing in all keys, but, unlike ET, preserved distinctively different sounds in the various keys.<SPAN style="mso-spacerun: yes">  </SPAN><o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">Returning to your question, “are we missing out on something,” I would say, for one, we are missing out on a fair measure of the genius that is Bach.<SPAN style="mso-spacerun: yes">  </SPAN>His writing in the key of C emphasizes and “shows off” the beauty of the clean Major 3<SUP>rd</SUP> intervals, while his writing in the key of C# plays off of the raucous, disturbing sound of the rough 3rds.<SPAN style="mso-spacerun: yes">  </SPAN>The character of his writing matches the inherent character of the key, but only when an appropriate tuning is used.<SPAN style="mso-spacerun: yes">  </SPAN>I am sure other examples can be found, if sought out, in the works of other early composers.<o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">>Haven’t we manipulated string lengths and diameters to force E.T. to sound well?<o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial"> <o:p></o:p></SPAN></P> <P class=MsoNormal style="MARGIN: 0mm 0mm 0pt"><SPAN style="FONT-SIZE: 10pt; FONT-FAMILY: Arial">Well, I wouldn’t say that.<SPAN style="mso-spacerun: yes">  </SPAN>The scale design of pianos has evolved over the centuries to accommodate different pitch standards, higher tensions, and a more powerful sound, but not necessarily to accommodate a particular temperament, although ET has been assumed to be the only choice for many decades.<SPAN style="mso-spacerun: yes">  </SPAN>The sound quality of a modern piano may suffer from tuning to a lower pitch, but the subtle difference in the overall balance of things, that occurs with temperaments other than ET, do not detectably alter the sounds of individual notes, in isolation.<SPAN style="mso-spacerun: yes">  </SPAN>Of course, there are markedly audible differences in intervallic relationships.<SPAN style="mso-spacerun: yes">  </SPAN>Although there is much to be said for playing “period” music on “period” instruments, tuned to “period” temperaments, one can legitimately tune a modern instrument to an early temperament, and recapture much of the composers original intent for his music.<o:p></o:p></SPAN></P></DIV> <DIV> </DIV> <DIV> <DIV>Frank Emerson</DIV> <DIV> </DIV></DIV></DIV> <DIV> </DIV> <BLOCKQUOTE style="PADDING-RIGHT: 0px; PADDING-LEFT: 5px; MARGIN-LEFT: 5px; BORDER-LEFT: #000000 2px solid"> <DIV style="FONT: 10pt Arial">----- Original Message ----- </DIV> <DIV style="BACKGROUND: #e4e4e4; FONT: 10pt arial; font-color: black"><B>From:</B> <A title=KeyKat88@aol.com href="mailto:KeyKat88@aol.com"></A></DIV> <DIV style="FONT: 10pt arial"><B>To: </B><A title=pianotech@ptg.org href="mailto:pianotech@ptg.org">pianotech@ptg.org</A></DIV> <DIV style="FONT: 10pt arial"><B>Sent:</B> 10/21/2007 12:39:36 PM </DIV> <DIV style="FONT: 10pt arial"><B>Subject:</B> Who says E.T. is the best way to solve octave divisions?</DIV> <DIV><BR></DIV><FONT size=2> <DIV>Greetings,</DIV> <DIV> </DIV> <DIV>         Why is equal temperament the only way to solve the dividing of octaves? I know that the beautifully mathematical solution on paper <EM>sounds and works</EM> fine, but what if there a way we could be missing out on something, such as better sounding music? Havent we manipulated string lengths and diameters to force E.T. to sound well? What information am I missing here?</DIV> <DIV> </DIV> <DIV>Julia Gottshall</DIV> <DIV>Reading, PA  </DIV><BR><BR><BR> <DIV><FONT style="FONT: 10pt ARIAL, SAN-SERIF; COLOR: black"> <HR style="MARGIN-TOP: 10px"> See what's new at <A title=http://www.aol.com?NCID=AOLCMP00300000001170 href="http://www.aol.com?NCID=AOLCMP00300000001170" target=_blank>AOL.com</A> and <A title=http://www.aol.com/mksplash.adp?NCID=AOLCMP00300000001169 href="http://www.aol.com/mksplash.adp?NCID=AOLCMP00300000001169" target=_blank>Make AOL Your Homepage</A>.</FONT></DIV></FONT></BLOCKQUOTE></BODY></HTML>