On tuning and temperament – the beauty of a pure third
I love studying this topic. I think it is very interesting and moreover, it generates a better understanding of the origins of music.
To read this article, you do not need theoretical knowledge of tuning systems, because I speak of general things. Although, to understand the details, it is necessary to study it. Here I will not speak about theoretical background.
Nowadays, most classical musicians play equal temperament (ET), a tuning system that divides the octave in 12 equal parts, resulting in a semitone with irrational root .
In a way, it is strange that we do so, because much of the music we play is not meant to be played in this system. Even the so-called ‘Wohltemperiertes Klavier’ by J.S. Bach is not meant to be played in equal temperament, but in a ‘circular’ temperament that also gives, as in ET, the possibility to play in any key of the circle of fifths.
The difference between this system and ET, is that each key has its specific character, because each key has a different pattern of intervals due to an un-equal compensation of the so-called ‘Wolf-fifth’.
This means that each key has another ‘Affekt’ - to use the original German word. That’s why each key had some kind of affect in the 18th century. For instance d minor is solemn, but f minor is sad, etc…
In ET, where all the keys are an exact transposition of each other, there is no difference between e minor en f minor, to name only one example. One could argue that there is a difference because both keys are on another pitch, but even this is not relevant: there has not been an absolute pitch in music history. An A in 1700 was something like a semitone lower than the current a of 440 Hz and could even vary from region to region. Still there are people who make music in ET and find that A major has another meaning than Es major. To me, it doesn’t make any sense – all major keys are exactly the same and have only a different pitch and relative function, but no different character.
If one does not play in ET, than there IS a difference and there can be a differentiation in affects. There is only one context where this differentiation can be relevant, even in an ET tuning: when we play Frescobaldi for example on a modern keyboard in ET, we can search for the affect that was intended in the original tuning that was used. We can try to search for the same emotional mood, but this is very limited: we cannot make this audible through the inner relationships of the notes, that are – in ET – exactly the same in each major or in each minor key.
With the revival of old music in the seventies of the previous century, great interest has emerged in old tunings as well as in the so-called historically informed practice (see other article about this). Nowadays, nearly all harpsichord players use an old temperament (often some kind of mean tone temperament using pure thirds) suiting better for the Renaissance and Baroque repertoire.
Unfortunately, as guitarists we play a fretted instrument where we are obliged to use ET. When we play old music this is, however, no anachronism, because even in the renaissance lute players were obliged to play in ET (if they hadn’t movable frets).
Finally, if such a sacrifice has to be made, why is ET so popular? It is only from the middle of the 19th century onwards, that ET is generalized in classical music. With the mass industry of keyboard production, ET is a very practical tuning. One could even assume that it incorporates the ‘democratic’ idea of ‘each person (note) has the same rights (value)’ – but this is a philosophical supposition. There is one interval that remains at the border of tolerance in ET: the major third. The fifth is a little too narrow, but the major third is much too wide in ET. Once heard the beauty of a pure third, you can only dream about a perfect musical world where just intonation can be realized… where all intervals are pure according to the harmonic series.
I love studying this topic. I think it is very interesting and moreover, it generates a better understanding of the origins of music.
To read this article, you do not need theoretical knowledge of tuning systems, because I speak of general things. Although, to understand the details, it is necessary to study it. Here I will not speak about theoretical background.
Nowadays, most classical musicians play equal temperament (ET), a tuning system that divides the octave in 12 equal parts, resulting in a semitone with irrational root .
In a way, it is strange that we do so, because much of the music we play is not meant to be played in this system. Even the so-called ‘Wohltemperiertes Klavier’ by J.S. Bach is not meant to be played in equal temperament, but in a ‘circular’ temperament that also gives, as in ET, the possibility to play in any key of the circle of fifths.
The difference between this system and ET, is that each key has its specific character, because each key has a different pattern of intervals due to an un-equal compensation of the so-called ‘Wolf-fifth’.
This means that each key has another ‘Affekt’ - to use the original German word. That’s why each key had some kind of affect in the 18th century. For instance d minor is solemn, but f minor is sad, etc…
In ET, where all the keys are an exact transposition of each other, there is no difference between e minor en f minor, to name only one example. One could argue that there is a difference because both keys are on another pitch, but even this is not relevant: there has not been an absolute pitch in music history. An A in 1700 was something like a semitone lower than the current a of 440 Hz and could even vary from region to region. Still there are people who make music in ET and find that A major has another meaning than Es major. To me, it doesn’t make any sense – all major keys are exactly the same and have only a different pitch and relative function, but no different character.
If one does not play in ET, than there IS a difference and there can be a differentiation in affects. There is only one context where this differentiation can be relevant, even in an ET tuning: when we play Frescobaldi for example on a modern keyboard in ET, we can search for the affect that was intended in the original tuning that was used. We can try to search for the same emotional mood, but this is very limited: we cannot make this audible through the inner relationships of the notes, that are – in ET – exactly the same in each major or in each minor key.
With the revival of old music in the seventies of the previous century, great interest has emerged in old tunings as well as in the so-called historically informed practice (see other article about this). Nowadays, nearly all harpsichord players use an old temperament (often some kind of mean tone temperament using pure thirds) suiting better for the Renaissance and Baroque repertoire.
Unfortunately, as guitarists we play a fretted instrument where we are obliged to use ET. When we play old music this is, however, no anachronism, because even in the renaissance lute players were obliged to play in ET (if they hadn’t movable frets).
Finally, if such a sacrifice has to be made, why is ET so popular? It is only from the middle of the 19th century onwards, that ET is generalized in classical music. With the mass industry of keyboard production, ET is a very practical tuning. One could even assume that it incorporates the ‘democratic’ idea of ‘each person (note) has the same rights (value)’ – but this is a philosophical supposition. There is one interval that remains at the border of tolerance in ET: the major third. The fifth is a little too narrow, but the major third is much too wide in ET. Once heard the beauty of a pure third, you can only dream about a perfect musical world where just intonation can be realized… where all intervals are pure according to the harmonic series.