Author Topic: Explanation of how composers used temperament effects to enhance their music  (Read 2894 times)

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David Pinnegar

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Following discussions about the interference of "beat frequencies" which we hear when tuning, in pipe chambers at high sound pressure levels, and on electronic organs with loud stops, it's apparent that temperament and frequency differences, heard directly or unconsciously perceived are greatly interrelated and significantly important to the character and spirit of the tonalities of what we hear in music. is a particularly interesting video. It shows how higher sounds resonate in the bass strings, but because in equal temperament the notes are not harmonically tuned, they resonate less. In Unequal Temperament some notes are wide of their harmonic counterparts and won't resonate at all, giving a skating on thin ice to those keys, whilst notes which are on the harmonic series of their counterparts in the bass will be beautifully resonant and "solid", "firm", "sure" and certain.

I have put together a video in which, if you play it through your computer speakers at high enough volume, you might be able to hear these beat notes and how they coincide, or otherwise.

Looking at the opening bars of Chopin's Funeral March, we can see how he was concurrently using two effects - both the disconcerting effect of following a Rooted chord (one where the notes all interrelate back to a root harmonic fundamental note) by an Unrooted chord (one where the difference frequencies of the notes are so wide of the fundamental note that they have no harmonic foundation and are perceived as sounds without meaning in their interrelationships), as well as using a chord which has a bell-like inharmonic aliquote or "partial" tone, actually heard in a vibrating ringing way to represent the bell tolling for the funeral.

This is possibly the most startling example of use of temperament and the effect is always to add emotion, often subliminally. In the case of the piano, perhaps being nearer to the instrument and therefore the higher sound pressures necessary to catalyse the perception of beat notes, the performer is more directly aware of the resonances, harmonies and rootlessness. If sensitive to them the performer will react to them. But the audience too, although not necessarily hearing the beat frequencies directly will be aware of a fullness or an emptiness in the chords which will therefore be thrown into three dimensions, some harmonies coming to the fore or receding.

The instrument and the performer through the composer can therefore be compared to projecting a hologram through to the audience, of which the performer and instrument tuner may be more aware of the patterns of waves on the holographic plate than the members of the audience. Just because the audience aren't directly aware of those wave patterns on the holographic plate does not mean that they won't receive the image of the hologram. In fact they do, and, both in theory and from tests by Adolfo Barabino and myself in making recordings in unequal and equal temperaments, music projected in unequal temperaments leaves a more emotional imact on the audience than when equal temperament is used.

When students have the opportunity of playing an instrument in unequal temperament, sometimes it can be very revealing as to the composers intentions and conveyed meaning. An example of this is in Chopin's 4th Ballade in which the waves of arpeggios focus and climax in a series of bar long chords in the centre, these chords having particular effects, harmonies leading to consonance in unequal temperament.

People often argue as to the "correct" temperament to use, but "well temperaments" in general followed on from Werkmeister who modified away from Meantone where all white note keys from C-A are essentially harmonious and all black note keys were on the basis of "venture here if you dare".

(From this historical perspective only a singular very recently proposed temperament is the odd man out and should not be included in the academic repertoire)

Best wishes

David P


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