reverse well explained (no graphs, only one number)

[Kristinn Leifsson]

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
>
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