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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