different temperaments: empirical test

Gregor _ karlkaputt at hotmail.com
Sun Jul 1 06:29:04 MDT 2007


I am not shure, if empirical tests would show an advantage of one 
temperement over the other, if these both temperaments are somehow 
*similiar*. I don´t know which temperaments in the recent discussion are 
referred to (WT vs ET). But I would love to conduct an experiment with these 
two ET tunings: 12 step per octave (our standard) vs the pure duodecime with 
19 steps (what´s its name?). I think the latter was the topic of the 
discussion with Bernhard Stopper? I assume that both ET´s are somehow 
*similiar* just because they are ET´s. Furthermore, I assume that piano 
tuners are the only persons on this planet who are able to differentiate 
these two temperaments. Remember all your customers who ask: was my piano 
detuned at all (20 years after the last tuning)!

Anyway: there was an empirical test of 4 different temperaments and 4 
different songs. Subjects were music students. The temperaments were: our 
Standard ET and the following temperaments which names I only know in 
German: natürlich-harmonisch (natural harmonic?), phytagoräisch 
(pythagoreian?), mitteltönig (no idea about English word: middle tone?). The 
results were:

subjects were realy bad in hearing differences. In a pairwise comparison, 
they had 3 answer categories: first song was cleaner, second was cleaner, no 
difference. Subjects answered on chance level, when 2 identical temperaments 
were presented one after the other (the same song in the same temperament, a 
*fake pair*):each answer category had about 33 %. And there was poor 
reliability: asked again in a retest, the answers were quiet different. When 
the two temperaments in the pair were different (e.g. ET vs pythagoreian, 
same song) there was a clear tendency to prefer ET.

Other tests with choirs or string ensembles showed that the musicians 
intonated the notes in such a different/idiosyncratic way that a 
classification to *any* temperament was not possible.

My point is: would a musician notice a difference between the two 
temperaments that were discussed the last days? Is that discussion perhaps 
just theory with no practical relevance? Are tuners able to differentiate 
these temperaments when they hear a piece of music?

A theory about listening comes from Gestalt psychology: music has a 
good/proper Gestalt. If there are some deviations from the proper Gestalt, 
one tends to correct the deviation in direction of the Gestalt. The 
deviations from that Gestalt are different for different temperaments, but 
not so great at all.

Gregor

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