 The Clarinet BBoard
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Author: Liquorice
Date: 2006-07-08 09:58
How do YOU tune the 7th in a dominant 7th chord? eg. the F in the chord G-B-D-F. There are differing theories, some tune it high, some tune it low.
I just did an experiment with my clarinet and synthesiser. I got the synthesiser to play sustained tones while I fooled around with various tunings of various notes on my clarinet.
If I get the synthesiser to play a C and I play a flat enough E, then I hear a low-pitched difference tone of a C (two octaves lower, I think?) If I play an Eb sharp enough with the C then I get a difference tone of A-flat, creating an Ab major chord. Getting the difference tones in tune shows me that I've found the "pure" interval.
So, back to the dominant 7th. The people that tune it high say that they are playing a minor 3rd above the 5th. Therefore the F has to be sharp enough to get a pure minor 3rd above D. But this creates a difference tone of B-flat, which clashes with the B in the chord. However, this is not a "resolved" chord, so maybe the clash isn't so bad? In any case, a sharp 7th sounded acceptable to my ears.
Then I tried playing a flat F. If I tuned it low enough (which was extremely low- more than 20 cents below an equal tempered F) then I heard a very faint difference tone of a G, perhaps 2 or 3 octaves lower. This would be great for the chord, but I question whether it is reasonable to expect woodwind instruments to be flexible enough to tune over 20 cents flatter to produce a pure minor 7th. However, this very flat 7th also sounded acceptable to my ears.
Maybe my ears just find anything acceptable??! What do you all think about this?
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Author: clarinetwife
Date: 2006-07-08 17:01
Liquorice wrote:
>
> So, back to the dominant 7th. The people that tune it high say
> that they are playing a minor 3rd above the 5th. Therefore the
> F has to be sharp enough to get a pure minor 3rd above D.
t
I don't know a huge amount about the acoustics of how the pitches work together, but it seems that the interval at the top of the chord depends very much on what you do with the 5th. You might not want the pure minor third at the top of the chord. How did you place your 5th in the major chord? Also, if you are playing the F in the G7 chord and then resolving down a half step to play the E in a C chord, do you want that half step to be larger or smaller? String players seem to work with these complexities as a very basic part of their playing because they have such flexibility in placing notes. They can't get away with the finger and blow (or finger and bow) approach to pitch even at the elementary level.
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Author: clarinetwife
Date: 2006-07-08 17:44
By the way, on a slightly different angle, are there some significant adjustments that string players have to make when they play with piano? I know that some of my husband's more traditionally tuned flutes and whistles are a bit dicey tuning-wise with piano.
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Author: johng ★2017
Date: 2006-07-09 02:40
My understanding is that in Just intonation, where intervals are tuned to a beatless sound, the minor 7th interval would be raised about 18 cents from the expected equal tempered tuning in order to reach just intonation. (Equal temperament tuning means the notes between an octave are divided equally -100 cents apart-, which allows for playing in all keys, although not perfectly in tune) On the other hand, when a dominant seventh chord is played the tendency is to play the seventh a little lower to anticipate the resolution if it resolves to the 3rd of the resolution chord.
The equal temperament of pianos may cause the problems with an instrument tuned for pure intervals. Modern woodwinds are close to equal tempered, but when we play in an ensemble, we want to listen for pure intervals of just intonation.
http://www.jb-linear-music.com/sound_samples/eq%20just%20maj%20chord.wav is a sound file with a major chord first in just tuning and then in equal temperament. For just tuning, the major 3rd is lowered 14 cents and the 5th is raised 2 cents. This doesn't answer Liquorice's question, but it does show the big difference in the quality of the chord when played in just intonation.
John Gibson, Founder of JB Linear Music, www.music4woodwinds.com
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Author: clarinetwife
Date: 2006-07-09 03:07
Thanks, John. That actually helped a lot. I opened up the file in Audacity so I could both see and hear the difference. Very interesting. I think my ear likes the 7th a bit on the high side, although the 18 cents you quote seems like a lot. Maybe my ear and brain want to make room for that resolution.
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Author: JoueJolie
Date: 2006-07-09 04:44
I really find just intonation interesting. Can anyone suggest threads, articles, or books to learn more about the specifics? Thanks.
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Author: Steve Epstein
Date: 2006-07-09 07:02
JoueJolie wrote:
> I really find just intonation interesting. Can anyone suggest
> threads, articles, or books to learn more about the specifics?
> Thanks.
"Lies My Music Teacher Told Me: Music Theory for Grown-ups", by Gerald Eskelin. On Amazon.
Steve Epstein
Post Edited (2006-07-09 07:04)
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Author: Tony Pay ★2017
Date: 2006-07-09 07:04
JoueJolie wrote:
>> I really find just intonation interesting. Can anyone suggest threads, articles, or books to learn more about the specifics?>>
I suggest a fascinating article, called "A journey into musical hyperspace", by my friend Michael McIntyre:
http://www.atm.damtp.cam.ac.uk/people/mem/papers/LHCE/lucidity-note-58.pdf
Many of the ideas in this article warrant further discussion.
Tony
Post Edited (2006-07-09 07:36)
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Author: johng ★2017
Date: 2006-07-09 14:38
JoueJolie wrote:
>> I really find just intonation interesting. Can anyone suggest threads, articles, or books to learn more about the specifics?>>
I am working on a method book for clarinet intonation and here are some of the better sources I used for just intonation:
Frazer: The Development of Music Tuning Systems www.midicode.com/tunings/index.sthml
Folkers: Playing in Tune on a Baroque Flute http://traverso.baroqueflute.com/
West: Woodwind Intonation Clinic (handout) www.people.vcu.edu/~bhammel/winds/intonation_vmea_2002.pdf
johng
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Author: Tyler
Date: 2006-07-09 22:24
I know basically nothing about scale temperament, but I would GUESS that tuning low would be a good bet.
Here's what I'm basing this guess on: if the dominant 7th chord should lead to the tonic chord as strongly as possible, and if we're in C major with the dominant 7th chord being GBDF, the minor 7th (the F) is close to both the E and the G but it is closer to the E because it is only the distance of a half step away whereas the distance to the next 'C major chord note' in the opposite direction (G) is a whole step. Therefore, to strongly lead the G7 to a C, the F (maybe) should be tuned low.
THEN AGAIN, maybe a dissonance between the in-tune G and the low-pitched F would occur................ fun stuff!....
-Tyler
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Author: David Peacham
Date: 2006-07-17 10:41
In just intonation, if you play a C major scale then the intervals are as follows:
C to D = 9/8
D to E = 10/9
E to F = 16/15
F to G = 9/8
G to A = 10/9
A to B = 9/8
B to C = 16/15
If you multiply all these ratios together, you get 2/1, as you'd expect.
Now it seems to me that a dominant 7th chord of G belongs fairly and squarely in C major, so you should play all its notes to be in tune in C major. The ratios will then be as follows:
G to B = 5/4
B to D = 6/5
D to F = 32/27
Writing these in cents instead of as ratios, we can see whether each interval is narrow or wide with respect to equal temperament:
G to B = 386 (14 cents narrow)
B to D = 316 (16 cents wide)
D to F = 294 (6 cents narrow)
This argues for playing the D-F interval slightly narrow.
Now how do we reconcile this with Liquorice's statement "The people that tune it high say that they are playing a minor 3rd above the 5th. Therefore the F has to be sharp enough to get a pure minor 3rd above D."
The reason for the contradiction is that there are two sorts of "pure minor third". A minor third is a tone plus a semitone. A semitone is always 16/15. But there are two sorts of tone: 9/8 and 10/9. Minor thirds that include a 9/8 tone are wide. Minor thirds that include a 10/9 tone are narrow.
Caveat: the above is derived from an analysis of the maths, not from the use of a discerning musical ear.
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If there are so many people on this board unwilling or unable to have a civil and balanced discussion about important issues, then I shan't bother to post here any more.
To the great relief of many of you, no doubt.
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