<p>Julia-<br>For a good graphical view of the meantone temperaments and their differences from well temperaments, please visit my website <a href="http://www.rollingball.com/TemperamentsFrames.htm">http://www.rollingball.com/TemperamentsFrames.htm</a>. There are also excellent descriptions answering your questions by: <br> Pierre Lewis at <a href="http://pages.globetrotter.net/roule/temper.htm">http://pages.globetrotter.net/roule/temper.htm</a> <br>Terry Blackburn at <a href="http://www.terryblackburn.us/music/temperament/index.html">http://www.terryblackburn.us/music/temperament/index.html</a><br> Stephen Bicknell at <a href="http://www.albany.edu/piporg-l/tmprment.html">http://www.albany.edu/piporg-l/tmprment.html</a><br>Kyle Gann at <a href="http://www.kylegann.com/histune.html">http://www.kylegann.com/histune.html</a><br> Ed Foote at <a href="http://www.uk-piano.org/edfoote/">http://www.uk-piano.org/edfoote/</a></p> <p>Meantone tuning favored the thirds; "more in tune" meant pure or nearly pure thirds, instead of our thirds that are expanded by 13.7 cents each. Pure, zero-beating thirds could be achieved in eight keys (generally Eb-Bb-F-C-G-D-A-E). But -- for example take the CE major third. This is created by a series of four fifths -- CGAE. If the fifths were perfect, the resulting major third would be expanded by almost 22 cents. For the major third to be perfect, those four fifths have to be contracted enough to take up all 22 cents; so they are all contracted by 5.5 cents, a lot more than our ET fifths which are contracted by 1.9 cents. The Aaron meantone temperament has eleven of the twelve fifths contracted by 5.5 cents, and the last fifth is expanded by almost 36 cents, a horrible sound called the "wolf".<br> Most Meantone tunings resulted in eight pure or nearly pure M3s; the remaining four M3s are expanded beyond tolerability (41 cents in the Aaron) meaning that the keys of B, F#, C# and Ab were unusable.<br>The graphs on my website show these relationships much more clearly than words or columns of numbers.</p> <div>Tuning your old upright to a meantone is feasible but beware the extreme offsets. If you try to keep it at A=440 then your Eb has to be tuned more than 20 cents sharp, for example. You would be better setting A to 435 and then using the offsets for the Aaron meantone, which you will find on my website or at <a href="http://www.pianolit.com/tuning/">http://www.pianolit.com/tuning/</a> <br> </div> <div>Cordially</div> <div>Jason<br><br></div> <div class="gmail_quote">On Sat, Apr 5, 2008 at 2:06 PM, <<a href="mailto:KeyKat88@aol.com">KeyKat88@aol.com</a>> wrote:<br> <blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid"> <div style="FONT-SIZE: 10pt; FONT-FAMILY: Arial; BACKGROUND-COLOR: #ffffff"> <div>Greetings,</div> <div> </div> <div>           In the Alfred edition of the <u>Bach's Well Tempered Clavier</u>, edited by Willard A. Palmer, it states the following:</div> <div> </div> <div>          "<em>Meantone temperament</em>, the system in general use before the adoption of the <em>well-temperament</em>, favored specific keys. A sharp could not function as a flat and vise-versa. ... Meantone temperament is actually more in tune in the keys it favors than our present day system (E.T.) in any key."</div> <div> </div> <div>          If this is true, then how can this be?</div> <div> </div> <div>1.  Are the intervals of the approx 1BPS for the 4ths and the 3:5BPS for 5ths different in meantone?              How does he mean "more in tune" than our present day system? </div> <div> </div> <div>2. Does this "more in tune-ness" have to do manipulating the comma differently in some keys?</div> <div> </div> <div>2. Are there any books to read that will set me straight on this subject?    </div> <div> </div> <div>3. Can I tune my old upright to meantone to hear this sort of thing, or will the "modern" scale design of it not allow a meantone tuning to be properly executed and heard as true? </div> <div> </div> <div>Thank You,</div> <div>Julia Gottshall</div> <div>Reading, PA</div> <div> </div> <div> </div> <div>  </div><br><br><br> <div><font style="FONT: 10pt ARIAL, SAN-SERIF; COLOR: black"> <hr style="MARGIN-TOP: 10px"> Planning your summer road trip? Check out <a title="http://travel.aol.com/travel-guide/united-states?ncid=aoltrv00030000000016" href="http://travel.aol.com/travel-guide/united-states?ncid=aoltrv00030000000016" target="_blank">AOL Travel Guides</a>.</font></div> </div></blockquote></div><br><br clear="all"><br>-- <br>| || ||| || ||| || ||| || ||| || ||| || ||| || |||<br>jason's cell 425 830 1561