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Heh, I felt I had to write something about temperament after your previous comments on the subject--you know, one of the things about writing these diaries is that I'm learning a lot while searching for pieces, all the info about ratios and temperaments came from that--

Timbre was covered in Part V (a co-production with Greg Whitman.)  You're right about all the things that could be said--these diaries are long but there's a lot I leave out; my idea is that I'll take one track and in the comments others can follow others--widen the range, head in different directions, that kind of thing.

With videos if possible, so that there are sounds to match words (or just sounds!)

I'm planning to do twelve diaries--next up I'm not sure, maybe Ornament, or Form & Function; there's also Major/Minor--

But yeah, I don't want it to all become too technical--more music, less words about music, but I'm also interested in the mechanics of sound production--and have become more so through writing the diaries.  Here's a find I enjoyed but didn't put in the diary--I'm sure you know all this already, so this is just an excuse to post it!

The mythical story of how Pythagoras worked out that sounds came in ratios:

According to legend, the way Pythagoras discovered that musical notes could be translated into mathematical equations was when one day he passed blacksmiths at work, and thought that the sounds emanating from their anvils being hit were beautiful and harmonious and decided that whatever scientific law caused this to happen must be mathematical and could be applied to music. He went to the blacksmiths to learn how this had happened by looking at their tools, he discovered that it was because the anvils were "simple ratios of each other, one was half the size of the first, another was 2/3 the size, and so on."

http://en.wikipedia.org/wiki/Pythagoras#Musical_theories_and_investigations

If you find any videos of pieces played on well-tempered instruments, esp. two different keys on the same instrument--please post them; it would be great to hear the difference (answering the question: "Why do composers talk of the 'mood' of a key?"  My very limited experience with a harpsichord says that E Major is the brightest--)...it would be great to have some video examples to listen to.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Wed Apr 30th, 2008 at 10:34:23 AM EST
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I've just started reading Oliver Sacks' new book "Musicophilia" which is full of stories about people with brain disorders and their relation to music.

In some cases hearing certain music triggers epileptic attacks, in other people hear music during such attacks, etc.

Then there is the whole subject of synesthesia where people see colors in response to music or other cross sensory effects. Scriabin seems to have had this condition and used color with some of his works.

Policies not Politics
---- Daily Landscape

by rdf (robert.feinman@gmail.com) on Wed Apr 30th, 2008 at 11:57:21 AM EST
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The mood issue is problematic. I always think of F major as the happiest of the happy keys. Trevor Horn said that D minor was the best key for pop because D on the bass provided the best foundation. D sharp minor - all the black notes - is slightly spooky.

But all of this would have to depend on A=440 being a standard, and given that A used to wander all over the place, and A=450 or 460 isn't totally unheard of even today - it sounds sharper and more exciting - it's hard to imagine there's any genuine consistency.

According to the perfect pitch courses I've seen, each key has a different subjective experience. From my limited experiments, there seems to be some truth to this. The F sharp in B always honks a little, and you don't seem to get that honk in other keys.

Who knows why?

Meanwhile - the weird chord in the Bach piece is a diminished 7th, which was about as dissonant as things got in those days, and includes the infamous flattened fifth.

It's a nice general purpose chord which can go in any direction, and it adds a bit of drama, so Bach used it quite a bit.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat May 3rd, 2008 at 09:48:23 AM EST
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The way I understand it is that the difference between the keys is related to the root.  If you tune perfect fifths and accurate major thirds to C, it'll have an effect on pieces in F# minor.  If you tune them to F, then whatever note relates to F the way F# relates to C (C?--the raised fourth!) will have (if I've understood correctly) the same feel in relation to the root.  So when the composers talked about the feel of a key, it would always be in relation to C as the root and then the various tuning mechanisms brought out different flavours as the key varied.

With the advent of synthesisers, any relationships can be created and then re-created in realtime as preferred, so the idea of G having a particular feel makes no sense--all the relationships sound the same and as you say, C has moved around so it can't be a strict pitch thing.

With instruments, though (again, if I've understood it right), there do exist notes that are better for the structure--trumpets and trombones are built around specific tones; strings sound different if you tune them more than a tone above or below--the tensions are noticeably different--

If I say I like Es on electrics and Ds on an acoustic, I think that means the way the strings resonate when held down in those patterns with those instruments--

What intrigued me when I played on the harpsichord is that different keys did seem to have a different feel; what Robert has pointed me to and said about temperament made me think that tuning harpsichords a certain way around C does give keys specific flavours--

I came to Bach via the sound of the piano, so the Well-Tempered Clavier had a different meaning to me; the various keys didn't matter much, they just mean playing from different starting points; but I think there are probably lots of enjoyable things Bach was doing for the player and listener that can only be heard when played on correctly tempered instruments.

Don't fight forces, use them R. Buckminster Fuller.

by rg (leopold dot lepster at google mail dot com) on Sat May 3rd, 2008 at 07:40:37 PM EST
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rg:
The way I understand it is that the difference between the keys is related to the root.  If you tune perfect fifths and accurate major thirds to C, it'll have an effect on pieces in F# minor.

No, there should be no difference at all between harmonic ratios for each key in equal temperament. In effect you get exactly the same scale with exactly the same relationships, only it can start on any frequency. Conventionally its tuned to A440, but there's no reason why you couldn't tune it half a semitone above that - around A450 - and in theory the scale should still have the same mood.

Of course if people really have a kind of rudimentary perfect pitch that won't be true. It would be an interesting thing to experiment with.

Synthesizers are usually tuned with equal temperament because even when you get access to the tuning tables, hardly anyone knows how to calculate the ratios needed to use them. Apparently non-Western scales are popular in Arab countries, and synths are regularly tuned to non-Western scales there. But in Europe and the US, equal temperament is usually the default aznd it's rarely changed.

Harpsichords, I don't know - I suspect not. It probably depends how early-music the player is trying to be. There are various tunings with names like Kirnberger and Valloti which are all variations on not-quite-equal temperament, and I'd expect those to sound different away from the home key.

Perfectly tuned keys sound very strange to Western ears. Terry Riley did an album called Shri Camel in perfect intonation and it's not easy to listen to, because all the intervals sound out of tune - at least until you get used to them.

The other thing about equal is that introduces movement. There's a theory that because the intervals all beat slightly, there's a subconscious tendency to want to move on, which means that music speeded up and became busier as temperament moved away from perfect intervals.

I'm not sure how true that is, but it's an interesting idea.

by ThatBritGuy (thatbritguy (at) googlemail.com) on Sat May 3rd, 2008 at 08:54:48 PM EST
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