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Did equal temperament really ruin harmony
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October 23, 2016 - 10:59 pm
Member Since: October 16, 2016
Forum Posts: 12
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Having this book in mind

I will copy a commentary read in The Guardian


For the most striking anomaly in the world of music is that the notes of the musical scale do not, so to speak, add up. If you progress in a cycle of pure fifths (where the notes have a ratio of 3:2, as imagined, say, by the length of the strings plucked) from a starting note of C, when you next end up at a C, you end up a quarter of a semitone too high. This might not seem too disastrous, but it doesn't sound good - "an excruciating discrepancy", as Professor Duffin puts it.

He knows that he is dealing with what may superficially look like an abstruse subject. And, looked at one way, it is: for the past 200 years or so, musicians have been nudged towards the orthodoxy of Equal Temperament (ET), until its almost complete ubiquity in the 20th century. Most audiences of the western canon (and this means pretty much everything we hear in Britain apart from some of the more far-flung world music on Radio 3) are hearing notes played from a scale where everything has been flattened ever so slightly in order to even out the differences. So it is, in a sense, a non-problem - in the way that the elephant, safely ignored in the corner of the living room, is also a non-problem.

But look at the fingerboard diagram from Peter Prelleur's The Modern Musick-Master (1730-31) and you will notice that C sharp comes before D flat; and E sharp is pitched higher than F flat. (We don't even have a note called F flat any more.) In 1797, another fingerboard diagram is still saying that F sharp is higher pitched than G flat, and so on. For a piano to work without ET, it would have had to have split-key accidentals: 17 keys to the octave rather than the 12 we are familiar with.

I used to have a very glancing acquaintance with this problem, but assumed, like many others, that the business had been sorted out around the time when Bach composed The Well-Tempered Clavier. Wasn't that what the very title of his work meant? No, says Duffin: it was written for an irregular temperament that worked in a wide variety of keys, and one which meant you didn't have to retune the instrument whenever you changed keys - but it was not ET. (Duffin cites evidence that Bach's son Johann Christian was importing split-key pianos in 1766, which suggests that his father had not abandoned them.)

Haydn, in 1802, made an explicit note in the autograph score for his Op 77 No 2 Quartet that a cello's E flat is to be played as if it were a D sharp - more evidence that this was by no means common practice. And when Beethoven started going deaf, was he still hearing his compositions in the old style, or in newfangled ET?

As I say, you might find this an abstruse subject, but Duffin goes out of his way to make it accessible to as many people as possible: short, punchy, and interspersed with potted biographies of musicologists and, should you need them, cartoons.

If I may propose an analogy of my own: ET is like pasteurised cheese, which means it's easier to make and more people can eat it; but it doesn't have as rich a flavour. Similarly, ET was born from the need to supply the expanding middle class with instruments they could play among themselves with the minimum of difficulty. (And the increasing use of vibrato may well have been used to mask some of the ensuing small crashes of harmony when string players accompanied keyboard instruments.)



I am by no means familiar with just intonation or others temperaments, I have only read about on wikipedia or other books. I'm curious if the change is really drastic enough to have someone claim that equal temperament has ruined harmony.


Are other temperaments used often?

Jeffersonville, VT
October 24, 2016 - 1:06 pm
Member Since: April 25, 2016
Forum Posts: 43
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Wow. That is a terrific video. Maybe the violin's ability (and challenge) of having an almost infinite range of pitches is to a large extent why we like it so much. 

I have a very good book on music theory called Edly's Music Theory for Practical People by Ed Roseman. In it he talks about the Melodic Minor Scale where the descending scale is different than the ascending scale. The purpose is "to make the harmonic minor scale smoother melodically." I think that is what the speaker in the video was also talking about at the beginning. This is all over my head, so I'm not sure.

The C Melodic Minor Scale:

     C  D  Eb  F  G  A  B  (C)  Bb  Ab  G  F  Eb  D  C


One of the statements in the video that most surprised me was that "the most difficult art form for intonation on stringed instruments is the string quartet." I would have guessed that it would be easier if everyone is playing a fretless instrument. But again it's the connection between harmony and melody that needs to be worked out.

Very interesting video.

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