Joe's Blog


March 2, 2017

Originally Posted on Facebook on 2.23.16

In a previous post we showed:

1. that pitch is how the brain interprets loudness, when the peaks of the loudness occur many times per second.

2. We have also shown that the combination of pitch and loudnesses among the overtones of a note is interpreted by the brain as tone color or timbre.

3. Lastly we showed that changes in loudness between notes in a phrase, if subtle* enough, is interpreted by the brain as a ‘shape’ being given to the phrase, in which the performer figuratively acts as sculptress, and ‘molds’ a series of notes.

Our starting point today is the third of these conclusions.

* we noted that changes in loudness between notes in a phrase can be interpreted by the brain in one of two ways. If the changes are large enough, we are aware that the loudness is changing. If the changes are just below the threshold of our awareness, we no longer hear at all changes in loudness, but say that the phrase “has a shape”.

Consider the following thought experiment. We ask a question. How much increase in the measurable amplitude (loudness) of a sound wave has there to cause the brain to say: this sound is “twice” as loud as the sound before. Would it be if the sound altered so as to have exactly twice the amplitude it had before? Might it just as possibly be if the sound has a half times the amplitude of the previous sound wave? Or three times the previous amplitude in the wave?

There is no one-to-one correspondence when between a measurable increase in the amplitude of a physical sound wave, and with the brain’s judgment of change in the intensity (“loudness”) of a sound.

The physical correlative to our subjective assessment of double the loudness may physically be due in one case to a change of one and a half times in the amplitude of the sound wave, and in another case due to an amplitude ratio of three to one. Such may be the case if the pitches of the two sounds are different, or the initial loudness of the two sounds are different.

All that counts in ‘shaping’ a phrase is the subjective appreciation of loudness, the conscious judgment of loudness. What we are looking for in phrase “shaping” are differences in loudness that lie just below the threshold of awareness. We are aware of these changes but no longer as obvious changes in loudness, but instead as if a string of notes was just given a “shape”.

A relevant question to ask is how ‘many’ changes of amplitude, that are just below the threshold of awareness*, is the performer capable of producing when playing one note
and then another in a musical phrase.

* by paying particular attention to two sounds, one can remove the sense of ‘shape’ and become aware that there is a difference, though a small one, in loudness. It is an issue of attention and the way we listen.

We might state the question using the more figurative terms used in music to describe loudness: pianissimo, piano, mezzo piano, mezzo forte, forte and fortissimo. Thus we might ask many such subliminal increments in loudness are there between piano and mezzo piano. Is it the same number as exist between forte and fortissimo? My experiments on the subject have yielded the following interesting relationship. There are more degrees of getting louder or softer between piano and mezzo piano than there are between mezzo piano and mezzo forte. And more between the latter two than between mezzo forte and forte. And so on. In other words, the softer we are playing in general, the more differences in dynamics that we can create. If the ‘shape’ of a phrase depends on having command over a larger number of barely subliminal loudness changes, then the pianist whose general level of ‘loudness’ is ‘softer’, will be able to create more obvious and sculptured shapes to his phrases.

The ‘shape’ of each phrase must be a direct expression of one’s understanding of the piece. The shape created should be designed to provide the most information possible about the inner meaning of the piece at that point.

We might borrow a term from the singers, who describe the statistically average pitch of a song as the tessitura. Two different songs can both contain the same lowest pitch and the same highest pitch, but an averaging for all the notes in the song could yield a different tessitura. One song may stay more in a lower range than in the high range, the other might stay more in the higher range than the lower range, and thus the first has a lower tessitura, and the second a higher. The performer who creates the more rounded and shaped phrase is operating at a softer tessitura.

The ‘softer’ our ‘tessitura’ the more room there is for the subtle changes in loudness (from note to note) that result in what the listener calls “shape”. Phrase ‘shaping’ has a lot to do with our concept of ‘beauty’ in a performance. It also enables us to define the boundaries of the larger* elements that are put together in a movement or entire piece.

* last longer as measured usually in minutes.




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