ASA 16 - Stretched And Compressed Scales


This demonstration, for which we are indebted to E.Terhardt, illustrates that to many listeners an over-stretched intonation, such as case (b) is acceptable, whereas a compressed intonation (a) is not. Terhardt has found that about 40% of a large audience will judge intonation (b) superior to the other two. The program is as follows:

a) intonation compressed by a semitone (bass in C, melody in B);

b) intonation stretched by a semitone (bass in C, melody in C#);

c) intonation "mathematically correct" (bass and melody in C).


E.Terhardt and M.Zick (1975), "Evaluation of the tempered tone scale in normal, stretched, and contracted intonation," Acustica 32, 268-74.

E.M.Burns and W.D.Ward (1982), "Intervals, scales, and tuning," in The Psychology of Music, ed. D.Deutsch (Academic Press, New York) pp. 241-69.

Time Delay


You will hear a melody played in a high register with an accompaniment in a low register. Which of the three presentations sounds best in tune?

In case you wish to sing along, here are some words to go with the melody:

In Munchen steht ein Hofbrauhaus, eins, zwei gsuffa

Da lauft so manches Wasserl aus, eins, zwei, gsuffa

Da hat so mancher brave Mann, eins, zwei, gsuffa

Gezeigt was er vertragen kann,

Schon fruh am Morgen fangt er an

Und spat am Abend hort er auf

So schon ist's im Hofbrauhaus!

(authenticity not guaranteed)