Great incentive Ron, thank you. I would have expected the sparring parties to have cleared this up a long time ago. This was just what I needed... since I share Conrad´s daftness in regard to die Blinkenlights :) Ja gut, Kristinn Leifsson, Reykjavík, Iceland P.S. Die Blinkenlights! I´ll give that name to my garage band (that doesn´t really exist). "Und jetzt, die Blinkenlights vil play for uns zer nu Hevi Metall Hitt Singul; die Flügelmaus! At 16:21 25.10.2000 +0000, you wrote: >Ok, ladies and gents, let’s see if I can shed some light here…. > >No graphs, I promise. > >In equal temperament, all like intervals measure the same, so in theory, >all major thirds will measure 13.7 cents wide of pure. We say that all >thirds are the same, but we hear beats, not cents, so they don’t SOUND the >same. >In theory, (again in equal temperament) if one were to play major thirds >ascending by half steps, the speed of the thirds increases equally at each >step. Here is where tuners can get mixed up. Even if a tuning has the >thirds all increasing in speed, if they don't increase evenly from note to >note, it isn't equal temperament. Now, pianos don’t like to conform to >theories, so mathematical models, and aural tunings digress from each >other in certain areas of the piano. > >What we expect to hear in a well temperament, is that the speed of the >chromatic major thirds will increase AND decrease in speed as the thirds >are played. In a Young’s temperament, the differences are large, and easy >to hear. In others, like the DiVeroli almost equal, there are groups of >thirds that will progress like equal temperament, so the differences are >not so easy to hear. There is a pattern to the differences, and the >pattern relates to the circle of fifths. This musical chart shows the >relationship of the different keys available in Western music. C is at >the top and progresses down to F#/Gb at the bottom. The Well tempered >tunings space the narrower (more pure sounding) thirds at the top of the >circle, with the wider (less pure sounding) thirds at the bottom of the circle. > >So to ‘test’ a well tempered tuning start with a C-E major third, and then >play G,D,A,E,B,F#,Db,Ab,Eb,Bb,F,C progression of thirds. The intensity >of thirds should increase to the middle and then decrease back to C. Or, >played up by half steps, C will beat slower than C#, which will beat >quicker than D, which should be slower, or the same as Eb, which will be >slower than E, which should be quicker than F, and so on. > >A Reverse well would be just the opposite, with the key of C showing the >most intensity, and F# being more pure sounding. But the differences will >not be obvious, because the reverse well will not be as ‘strong’ as >something like the Young’s temperament. > >To do a quick check for a reverse well temperament (check yourself!) play >major thirds ascending and see if C is a little more ‘busy’ than C#, or >even equal to C#, instead of an even increasing of the beats. Check if >the sharp/flat keys aren’t a little out of progression, instead of being >exactly even in progression. > >Of course, once you add the third note of each triad, there is a major >third, a minor third, and a fifth all beating together (beats within >beats) and influencing each other. Sometimes all those beats together >causes the chord which was predicted to sound very busy (just looking at >the major third alone) to sound unexpectedly pure. That’s what the equal >beating temperaments try to use to their advantage. > >I do know that the more I tuned in mild, unequal temperaments; the more I >could hear the differences between the speed of the thirds. I became very >sensitive to how small of a difference it takes to make a very real >difference in the progression of thirds in a tuning. > >I would urge tuners to not only stick with the Young, or the Vallotti >Young in experimenting, because both are pretty strong. A more mild >temperament provides some tone color without the ‘jolts’ that can be found >in those historic temperaments. > >Hope this helps! > >Ron Koval > >Chicagoland > >_________________________________________________________________________ >Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. > >Share information about yourself, create your own public profile at >http://profiles.msn.com. >
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