 The Clarinet BBoard
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Author: Robert
Date: 2002-10-14 15:41
I have a question regarding the tuning of the dominant seventh note (e.g. the F in a G7 chord). I've been reading Larry Guy's book "Intonation Training for Clarinetists". He says that thirds in major chords sound best a tiny bit flat, and thirds in minor chords sound best a tiny bit sharp. But then he goes on to say that the seventh in a V7 chord should be a bit flat. I always thought it was the other way around, because the 7th forms a minor 3rd above the 5th. If we're talking about "just intonation", shouldn't the dominant 7th be sharper than it is in equal temperament?
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Author: Don Berger
Date: 2002-10-14 16:01
I'm too unaccomplished to discuss musical theory, BUT, IMHExperience, when a well-tuned-up group plays scales, most of the notes EXCEPT for the [savage] 7th are reasonably well "agreeded upon" ! Suggestions. please. Don
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Author: Alphie
Date: 2002-10-14 16:20
It's correct that a minor 7th shall be tuned flat. By 27 cents. It's a lot but correct. Somebody who know their matematics around acoustics better than I do can maybe explain the pure spots within a minor third. I've learned 27 cents flat for a 7th and about 10 cents sharp for a minor third. Keep in mind that the 5th is already a few cents sharp already when it harmonize with the flat 7th so the gap is between the 5th and the 7th is really small.
Alphie
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Author: Robert
Date: 2002-10-14 17:21
Thanks Alphie and Don.
I tried to measure the intervals by listening to the difference tones. I found that major 3rds shoudl be about 14 cents lower than equal temperament, and minor 3rd about 14 cents higher. (Not scientific measuring, just listening!!) I find the 5th must be about 2 cents higher. But my question remains- if the minor 7th is a minor 3rd above the 5th, then shouldn't it be much higher? That would be something like:
2 cents (for the 5th) + 14 cents (for the minor 3rd)= 16 cents
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Author: Kat
Date: 2002-10-14 17:24
Ultimately, you're not tuning the 7th to the fifth, but to the root of the chord. That's why it needs to be flat. All of the notes in the chord need to "come" from the root...
Katrina
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Author: Alphie
Date: 2002-10-14 17:46
Kat is right that you always tune to the root/tonic of a chord. But each note also relate to every other note within the same chord. The interval 5th-7th is indeed a minor 3rd. But within the mi.3rd are at least two pure spots, one narrow and one that is wider.
Alphie
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Author: Craig
Date: 2002-10-16 11:06
A dominant 7th chord cannot be tuned with all pure intervals. That is why it was regarded as a severe discord in earliers times (ie.the eigteenth century when it first came into uses in western music).
The seventh can be obtained by adding 2 pure fourths, whereby it will be 4 cents flatter than equal temp. (2 cents for each fourth). It can also be obtained as a pure minor 3rd from the fifth, making it quite a lot sharper. (by about 18 cents).
It therefore depends on the voicing of the chord what will sound best. And many fine musicians will sense this diffently. If for example the fifth is very strongly scored a high 7th may sound best. If the chord is in close position (ie. the seventh is inverted to a 2nd) then a lower 7th will probably sound better (otherwise the tone will sound painfully narrow.)
Since fully scored chords in close position are often part of the orchestral texture, low sevenths are mostly preferred by orchestral players. In the chamber context, with more open scorings, sensitive musicians may find more alternatives.
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Author: Robert
Date: 2002-10-16 16:17
Craig- thanks a lot for the information. I never thought about tuning the V7 as two perfect 4ths.
I once played in a youthorchestra and we were coached by one of the Concertgebouw woodwind pricipals. He told us to tune the V7 sharper than equal temperament, which is why I've always done it this way.
But as you say, it is regarded as a severe discord. I suppose it's whatever sounds best. It's just that my colleagues and I don't always agree on this!
Robert
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Author: diz
Date: 2002-10-18 00:15
Alphie said:
"It's correct that a minor 7th shall be tuned flat. By 27 cents. It's a lot but correct."
what?? and if you happen to be playing with a fixed tunning instrument (piano, organ, whatever), then what??
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Author: Zack Best
Date: 2002-10-18 17:31
"Just" intonation has the ratio of the frequencies
at simple fractions. This results in minimum dissonance
and beat. Whether this sounds good or not is a matter
of artistic judgement.
For a dominant seventh the ratios would be 4:5:6:7.
With equal ratio tuning an octive is divided into
1200 "cents" where an octive is a factor of two in frequency.
So to calculate an interval in cents that has a frequency
ratio of R, use the following formula:
C = 1200 * log(R) / log(2)
for R=7/4 you get C = 969.
Note that 969 is 31 cents flat of the normal 1000 for a
minor seventh. (I not sure why my answer does not agree
with the 27 mentioned perviously.)
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Author: Robert
Date: 2002-10-18 21:49
Diz wrote:
"what?? and if you happen to be playing with a fixed tunning instrument (piano, organ, whatever), then what??"
We've been discussing "just intonation" on this thread, not tempered tuning of a fixed tuning instrument.
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