Semitone systems - the size of a semitone

A tuning blade, hook or lever shortens the length of the vibrating part of the string and raises its pitch by one semitone. The amount by which the string is shortened is determined by means of a simple calculation based upon the well-tempered scale invented by J.S. Bach, which is now universally recognised.

Folk music of eastern countries does not follow this chromatic scale, and bagpipe music does not follow it either ... that is why there are people who find it difficult to appreciate bagpipe music. They consider that it is completely out of tune, but they are wrong.

It seems Gildas is referring to Scots highland pipes here:I certainly haven't heard people who think the scales of Lowland Scots or the Irish or Northumbrian pipes sound out of tune, nor indeed those of other countries.

To clear up some common misunderstandings:

- it is an acoustical fact that when properly in tune, the various steps between notes in the western scale are different sizes in different contexts: to produce these different notes accurately in tune involves endless complications - Handel is said to have had a harpsichord made with 52 notes to the octave rather than the normal 12 - and the practical solution has always been to compromise, using a fewer number of keys and 'adjusting' or "tempering" the tuning by using notes which are deliberately just a little out-of-tune: there are many systems which, if they're used consistently are close enough for most people's ears, but there have always been different opinions about what compromises are acceptable, and where they should be made

- from Gildas' words we might think that the expression 'well-tempered' was a general term used throughout the history of music for a specific scale or tuning system: this isn't the case, the name is a translation from German from a title used by J.S. Bach for a particular collection of pieces

- many people today understand 'well-tempered' to mean the compromise where all the steps and half-steps are the same size: but the appropriate name for such a scale is 'equal-tempered': 'well-tempered' in baroque times didn't refer to an 'equal-tempered ' scale, but one where you could play in all keys without retuning - in Baroque tuning systems the distances between the semitones are actually all different, so each key sounds objectively different and has its own distinct character - for example C#-major is much more out-of-tune that C-major, but it's still just about usable: and this essential aspect of the sound of Baroque music is lost if you use equal temperament

- Bach invented neither the equal-tempered scale nor the idea of a collection of pieces in all the different keys: both were established long before his time, and however much he may be seen as great and influential today, I haven't seen anything to suggest that during his own time his music influenced other musicians, or was even widely known, outside of his own circle

- equal temperament wasn't commonly used until long after Bach's time

- sure, equal temperament is used for most pre-tuned instruments today, like accordions and pianos: but that doesn't mean it's universally used, even if it's universally recognised. In an orchestra, for instance, it's the model for the wood-wind instruments, but the brass work according to a different system, while violins are tuned using yet another. For anyone who plays mediaeval, renaissance or baroque music, it's well-worth recognising the difference between the basic tunings which were used in these three periods: the historical tunings are much easier to tune, and the music really only makes its proper effect when the tuning matches

I've written a piece which explains this properly and demonstrates it, putting it on the Web is on my list of jobs, and it'll get higher priority if you let me know you're interested ...


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 | strings  | sources
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