Equal Tempered & Well Tempered

[paolo]

I was delving into Changs book & was fasicnated by the following quote
"You will see a dramatic demonstration of this if you can listen to the last movement of Beethoven’s Waldstein played in ET and WT"
Has anyone got any samples of music played with both ET & WT?

[faulty_damper]

Umm, what's the difference?

[r.schaefer]

I tried a few temperaments :-) with my stage piano.  The well-tempered ones (Kirnberger 3 and Werckmeister) really sound better for the Waldstein! I also noticed a big difference in Mozart's sonata facile.

Good information page: https://www.kirnberger.fsnet.co.uk/

[faulty_damper]

You mean just intonment vs. equal temperament?

I guess not.  I thought well-tempered and equal tempered refered to the same thing.  So are pianos most commonly tuned equally?  I tune my own piano and this is new to me.

[r.schaefer]

You mean just intonment vs. equal temperament?

I guess not.  I thought well-tempered and equal tempered refered to the same thing.  So are pianos most commonly tuned equally?  I tune my own piano and this is new to me.

Well-tempered tunings are unequal (the comma of Pythgoras is NOT
distributed equally among all the keys). These were in use from the late seventeenth century to well into the nineteenth century.

[Lance Morrison]

it is a common misbelief that equal tempered and well tempered are the same. in well temperment, the intervals are *not* equal, and this gives the keys that are further away from the key of C a different character. these systems of tuning were developed so that more key signitures could be used.

[pianonut]

beethoven must have been going for the equal temperament since the Walstein is all over the place.  also, he wanted the C's to be especially ringing - so this was probably the easiest for a tuner to pull off ( i think - i don't tune pianos).  notice he uses the high c area as a contrast (very effective - played lightly as one would hear overtones).  how did he think of all this?  guess that geniuses think about many things at one time.

[pianonut]

in the new harvard dictionary, under temperament, it explains that practical compromises are made in desiring acoustical purity (and that for musical transposition or modulation) that is not compatible in a closed system.  if the fifths are kept acoustically pure (as in pythagorean tuning), then enharmonic pitch classes such a Ab and G# will differ by an amount known as the pythagorean or ditonic comma, equivalent to 23.5 cents.  mozart utilized these positively (as with the violin - playing in a sharp key toward the higher end - and a flat key toward the lower end).  BUT, i think Beethoven was looking ahead farther (though he still obviously liked overtones)

in the twentieth century, a temperament with 12 part equal distribution has predominated.  in this, each of the pythagorean scale's fifths is diminished by about two cents so as to eliminate over the sum of 12 fifths the accumulation of the nearly 24 cents of the pythagorean comma. 

just intonation replaced the pythagorean scale and equally distributed the syntonic comma. 

for irregular and enequal distributions (still thought to be more equally tuned - than the well tempered system of bach)  was the temperaments of Johann Georg Neidhart (probably read by Beethoven). his model temperament #3 (1732) distributes the pythagorean comma unequally: fifths on Eb and Gb are 1/12 of a comma (two cents) flat; on C and G, 1/6 of a comma (four cents) flat; and on D and A, 1/4 of a comma (six cents) flat.  Neidhartdt's own favorite temperament distrubutes the comma unequally to nine fifths in the scale.  Those on Bb, A, B, F#, C#, and G# are 1/12 of a comma flat; thos on C, G, and D are 1/6 of a comma flat.  Doesn't it seem like Beethoven experimented with those very same keys in the Walstein.

[pianonut]

found an article on temperament entitled 'good vibrations' by ruth franklin.  it's a good read when you have time:

www.tnr.com/121001/franklin121001_print.html

[xvimbi]

found an article on temperament entitled 'good vibrations' by ruth franklin.  it's a good read when you have time:

www.tnr.com/121001/franklin121001_print.html

I have Isacoff's book. It's a nice read on a rainy day, but it is rather shallow and leaves the investigative mind dissatisfied. It nevertheless gives some impression about the issues and is written in a way that keeps laypeople interested but compromises accuracy and depth.

[Lance Morrison]

i wish i could hear the WTC in well temperment...

[jim_24601]

I tried a few temperatures with my stage piano.  The well-tempered ones (Kirnberger 3 and Werckmeister) really sound better for the Waldstein! I also noticed a big difference in Mozart's sonata facile.

Good information page: https://www.kirnberger.fsnet.co.uk/

Temperaments, R, not temperatures But thank you for the link to that very interesting site. I put my stage piano in mean tone temperament, played a "wolf" 5th G#-D# and actually said "ow" out loud. I may start using some well temperaments for baroque stuff in future, though.

[theodopolis]

My favourite temperament would definitely be Werckmeister III, to which my harpsichord is tuned. Its especially good when playing in C major. There is nothing quite like a pure third in a final chord, an unfortunately rare occurence nowadays.

There are experiments in Europe with dividing the scale into 36 seperate notes instead of 12, and playing through a silent keyboard into three pianos, all tuned diferently to encompass this array of 264 notes instead of 88. In between the pianos is a computer which chooses the tone which is tued purest in relation to the note being played.
It allows the purity of mean-tone with no wolf... and equal temperament as well.
Someone should make a Baroque recording on this instrument
https://vms.cc.wmich.edu/~code/groven/

Listen to the sound samples - They really higlight the shortcomings and impotence which equal-temperament poses.
(Who likes playing in G-sharp anyway )