Discussion in 'Repertoire' started by pianolady, Jul 26, 2007.
What is tempered tuning?
Our common tuning is the equal temperated tuning. That means that the difference between every note is the same, the distance is mathematically seen the 12th root of 2. That means, after 12 halftones the frequency is doubled, as it is the next octave.
With this tuning system there are no very bad sounding intervalls at all on piano (but one could say also, no very good sounding intervalls). For instance if you play a quinte, you will hear a slight wobbling, maybe every second or so. If you play the quint a half tone higher, and proceed every half tone, you will realize that this wobbling gets contiously more and more, an octave higher the wobbling is doubled. At least that is the case in a perfect tuned piano.
Beside that there are historical temerated tunings with not equal intervals. Some sound worse, some better. Because some intervals have no wobblings, normally received as very strong and powerful chords. Others have so much wobblings that one needs to avoid those keys better.
To me it is problematic to give in the equal temperated tuning different keys a certain character. Because from the temperament all keys are similar (in opposit to the nonequal temperated tunings).
That's why it is problematic (to me) to e.g. associate d major with a festive character (only to mention an example). Already the fact, that some played 300 years ago d major a half tone lower or higher, so that means d flat major or e flat major were the keys in those days which must be associated with the character some refer with d major today.
The different character of different keys come in my opinion more from how often a key is used in general or for certain moods some personal "reference" pieces have in that key, but not from inherent character of a key. Because with equal temperated tuning, there is no certain character anymore of a certain key. By the way, I very much like historical tunings, there are some organs in Germany at which those tunings are used with success for certain baroque music.
Never mind, Terez. I just looked it up. That kind of thing is way over my head.
Here's the long explanation of tempered tuning, or Equal Temperament (link), or perhaps Well Temperament as opposed to Pythagorean Tuning, or perhaps Meantone Temperament. A great deal of Baroque music is written with Pythagorean tuning or meantone temperament in mind, and the differences are fairly slight for the most part, but enough that a certain harpsichord would only be good for certain keys. In , the leading tone of any key should be at a pitch sharper than a 100-cent half step (not sure exactly how many cents would be between the leading tone and the root (i.e., B to C in the key of C) but it's less than the 100-cent distance of every half step in equal temperament tuning.
I don't know a great deal about the differences in tuning, which is why my comment above was a question. lol...it actually seems counter-intuitive to think that tempered tuning would have anything to do with why certain keys sound better on a keyboard with equal temperament (and we all play on equal temperament keyboards). Ah, well....that's why Bach's Well Tempered Clavier was such a revolutionary work, I think - it was meant for a keyboard on which you could play any key! And I think it was the first major work that was intended for such an instrument, though I could of course be wrong.
EDIT: wow, I must be slow - two people posted while I was working on this!
oops - looks like we posted at the exact same time. Thanks for answering but I still don't get it.
Wow! Three people posting at exactly the same time. Now I'll go read Olaf's response.
Also not from what I wrote? If that's the case, what exactly you don't get (indeed 3 posts with same time stamp)?
It's okay, Monica - I don't really get it either!
You guys are too smart for me. Thank you for the explanations, though.
Olaf, off the top of your head, do you know of any piano recordings on the internet that use 'historical tuning' ? (don't waste any more time if you don't know - it's okay)
No, I don't know (have only some CDs for organ music with historical temperaments).
Some digital pianos (like my Kawai MP9500) can change their temperament, so I played for fun some WTC items with historical temperaments, the difference is not that stronge (to my taste), but audible.
People argue for almost 300 years what Bach meant with "Well" temperated clavier. What is well? Must not be necessarily "equal", that's the problem. There would be no discussion about that if he choosed a more exact term :cry:
The Wikipedia article on the Well Tempered Clavier goes into that debate a good bit. It seems obvious that he did not intend strict Pythagorean tuning or meantone temperament, though.
I have wondered about that, myself. But I must have the word 'temperated' wrong, because i thought it was 'tempered', so in that case, and in my simple mind, I just thought of it as meaning the klavier is 'nice'. :lol:
In English, it is "tempered" (I think Olaf made that word up!) but it doesn't mean that the clavier is "nice". :lol: I have seen spoofs called "The Bad Tempered Clavier" and such. :lol:
Hmm, the origin is German, Bach called it "Das Wohltemperierte Klavier". "Temperierung" is now in Germany more or less only in use as something related to the temperature, how warm or how cold it is. You are right, it is translated to "tempered" and not "temperated" in that context.
I think this is neat – here is a link to a website where you can hear different tunings.
The different sounds are fascinating. And at the bottom of that page there is a link to a whole big explanation on tunings. (some of it is even starting to sink in, now - but only a little :? )
Yep, doesn't sound a pure major chord so much stronger than an equal tempered major chord, especially because the thirds are so ugly tempered instead beeing pure (the quint is almost pure, but not 100% pure)?
The old baroque masters knew exactly which intervalls sounded very good and which very bad and avoided the latter on their church organ. So quit a few organs in Germany are put back to original tuning in order to bring the beauty e.g. Buxtehude organ works show in certain keys!
I am also a bit wondering why violinists tune their fiddle to pure quints normally. So they pile 4 pure quints one upon the other. That means the difference between the equal tempered quints on piano is multiplied by 4 at the end. But since quints are very sligthly tempered, even that is of only small importance (maybe also because the empty strings are more seldom used on the fiddle?).
I know as I tuned my guitar in the beginning without electronic tuner I was always wondering why it did not work although I tuned all quarts to pure intervals... Until I realized there must be slightly wobbling between the quarts, because a guitar must also be tuned equal tempered.
Ok, that is very much OT, unfortunately.
I believe it was in the book called 'What to listen for in Mozart' by Robert Harris that I read that perhaps the average listener from the day before equal temperament would more easily 'get' the harmonic changes in say a Mozart sonata. The different keys would have more distinct sounds than they do now, so if the theme re-enters in the 'wrong' key then this would be more intuitively obvious. The listener doesn't necessarily need training to identify this they would just hear that something is different and unsettled. Of course, the good composers of the day would know all about this and perhaps write to make best use of these differences.
I've read the claim that the WTC is best heard in one of the historical 'well' but not 'equal' temperaments. Having never heard anything but either equal (or out of tune equal temperament I have no idea how valid this claim is.
But for some people, the lowest note is an F, or even a C...
Well... I must say that I really don't like major keys. For some reason, they just don't appeal to me.
However, I LOOOOVE minor keys!
My favorite keys are C#, D#, and G# minor. I don't know why, but I just like them.
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