In 2005 Lehman suggested that the recipe for Bach's well temperament is contained within the squiggles at the top of the Well-Tempered Clavier manuscript's title page(*), if you turn them upside-down, and the idea is that when you turn the page upside-down you get a set of instructions for tuning by the number of squiggles inside the big loops. One gets the sequence 2-2-2-2-2-0-0-0-1-1-1 which tells a tuner by how many twelfths of a Pythagorean comma to make the eleven fifths narrow from a perfect fifth as you go on a circle of fifths starting from C. You can read through his research and hypothesis, and even listen to sound samples, at http://www.larips.com/Alan Carruth wrote:I have to say that I don't remember where the person doing the demonstration got his data on Bach's tuning. This was something I heard on the radio in 1985, on the anniversary of Bach's birth: I remember being struck by the differences, without recalling any of the specifics.
What a spot! I'm sceptical by nature and tend to think these things are more likely to be coincidences, but would love to think this was intentional - and it does fit with Bach having encoded his initials in his music, his fondness for puzzle canons, etc.guitarrista wrote:In 2005 Lehman suggested that the recipe for Bach's well temperament is contained within the squiggles at the top of the Well-Tempered Clavier manuscript's title page(*), if you turn them upside-down, and the idea is that when you turn the page upside-down you get a set of instructions for tuning by the number of squiggles inside the big loops. One gets the sequence 2-2-2-2-2-0-0-0-1-1-1 which tells a tuner by how many twelfths of a Pythagorean comma to make the eleven fifths narrow from a perfect fifth as you go on a circle of fifths starting from C.
It would be great to research this properly / empirically. We know that in an unequal temperament some intervals and progressions will be further out of tune than others, pretty much regardless of how we define "in tune". A good composer - and certainly a great composer like Bach - will avoid the dodgy ones and favour the ones that are closer to the ideal. Thus music composed for a particular well-tempered key may well have a particular character, and it is not surprising if musicians come to associate that character with that key... but is this really due to the temperament? I would say not, or only in the very limited sense that the temperament influenced the actual content of the music by restricting the composer's options. I think the heroic piece would still be heroic if played in ET. As I say, I think it would be very interesting to investigate this empirically, but you would probably have to use music that your subjects weren't already familiar with, otherwise you would just be testing how strong their convictions were. You would also have to find a way to control for the effects of absolute pitch - so not really very practical... which brings us back to our own personal convictions - in my case that we grasp music by relating it to an intuitive pitch structure, and that this mental process has a "snap to grid" function that means that mistunings are ironed out very early on,Alan Carruth wrote:In the recordings of Bach's 'Well Temperament' that heard that was not the case; each major or minor key, while clearly being 'major' or 'minor', had it's own affect. Organists will often say that one or another key is more 'heroic' or 'introspective' or whatever, and that's to be expected with an unequal temperament such as they are used to hearing. All of the semitones are different sizes, and since each semitone is in a fixed position on the keyboard the mis-tunings stack up in different ways depending on which note is your tonic.
It says this: If I ever publish an own composition, I would like to introduce it with "For the Use and Profit of the Musical Youth Desirous of Learningamezcua wrote:What is the translation of the triangle of words below the squiggles ?
That caught my eye as well - what a weird thing to say - unless this was some sort of "popular" article written by a journalist without a musical background.Alan Carruth wrote:"As we know, a circle of 12 fifths begins and ends with the same note. Strangely, however, 12 pure fifths do not really “fit” within the octave, ..."
It's not strange at all.
Sure it can - you just have to give up the idea that Ab and G# are supposed to be exactly the same. It's funny because we insist they are different when it comes to spelling and analysis, but when it comes to tuning we say they are the same because there is only one key on the piano for both.Alan Carruth wrote:Since the interval if the fifth is implicit in musical sound, it makes sense to try to preserve fifths as 'pure' tones, but it can't be done for all fifths.
Well I know you are in good company in holding that view, but for reasons that will be clear from the above, I prefer to see temperament as a compromise that allows one key to be used for what are really several (slightly) different notes.Temperament is the process of shifting the tuning of various intervals to some compromise that is 'close enough' to be satisfactory for the music to be performed, that preserves the octave which must be preserved. As with any compromise, what works for one may not be satisfactory for another.
OK if you don't modulate to a different key. Have a look at (and more importantly listen to) this video illustrating one of the common meantone tunings, 1/6 comma meantone:amezcua wrote:That totally convinced me that the older temperaments were better . Better musically. More expressive. Not getting away with any ugly sounds .120% better in every way .You can`t improve on 120% .
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