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I would like to play in tune. I'm having difficulty understanding what this means, and I would greatly appreciate hearing from those of you who do understand. Here's a summary of what I think I know, and what difficulties and questions I have.

Equal temperament is how pianos and my electronic tuners present correct pitches. So I can tune my individual tones to the tuner by achieving 0 cents, and to reference tones from a piano or synthesizer by eliminating the beats. By extension I can play equal tempered scales "in tune" with the tuner and piano.

Just tuning on the other hand is what we strive for in harmony. With some reference tone playing, we play an octave or a fifth or a third, and get it into just tuning by eliminating beats between the two tones. I think everybody here knows just tuning and equal temperament tuning are different, and maybe everybody knows without looking it up that, for example, a just tuning third is 14 cents lower than an equal temperament third.

This means that one horn in equal temperament tune with a piano C, and another horn in equal temperament tune with a piano E, will be 14 cents out of just tuning with each other. Or the other way around, two instruments playing C and E in just tuning will clash significantly with the piano playing the same notes.

Assuming I've got that all correct, are the following conclusions correct?

1. To play "in tune" against an equal temperament instrument or within an equal temperament context such as an orchestra perhaps, we must be able to match the equal temperament reference pitches.

2. To play "in tune" within a just tuning context, such as in a duet of two saxophones, we must be able to alter any single pitch as much as 17 cents plus or minus away from the equal temperament pitch -- 17 cents being the extreme difference in equal temperament versus just tuning, that being for an augmented fourth. We have to be able to go plus or minus depending on the voicing.

In a trio of two horns and a piano, it seems the horns will have to continuously adjust pitches in order to achieve a best compromise of tuning between each other and with the piano. Is there some rule for how to accomplish this? Something to do with the predominant harmony or melody line, for example?

In a duet of two saxophones, if one horn plays the equal temperament pitches, the other horn will have to play other than equal temperament pitches - excepting unisons and octaves - in order to be in just tuning. Is there some rule for which horn should play the equal temperament pitches and which should adjust? For example, the predominant melody line should be in the equal temperament pitches? Lacking a predominant melody line, is it the upper tone perhaps?

I realize these are 300 year old problems and they must have solutions that I haven't found yet. I know that when I hear a violinist playing double stop harmonies in a sonata with keyboard and cello, the tuning seems just lovely. How do they overcome these problems?
 

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I would like to play in tune. I'm having difficulty understanding what this means, and I would greatly appreciate hearing from those of you who do understand.
Well in fact you seem to know rather a lot. :)

Doesn't it all boil down to listening and trying to make things sound good? I mean that quite seriously.
 

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...This means that one horn in equal temperament tune with a piano C, and another horn in equal temperament tune with a piano E, will be 14 cents out of just tuning with each other. Or the other way around, two instruments playing C and E in just tuning will clash significantly with the piano playing the same notes...
I don't understand this. Do you mean pianos are tuned in ET and saxes are tuned in JI? I thought most instruments are tuned in ET.
 

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I believe a functional guideline could be stated simply that when playing with a keyboard accompaniment that the equal tempered pitches be used by all of the wind and stringed instruments. When winds and strings are playing without a keyboard accompaniment or are not playing a unison passage with a mallet percussion instrument then performers should strive for just tuning when playing 3rd's, 6th's, and 7th's on all harmonies that are held long enough that the intonation is critical to a skilled listener of the piece.
 

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Discussion Starter #6
Thanks to all. This is useful and reassuring. The link from hakukani to the essay on string quartet tuning opens up a rich vein of info. Makes me excited about hooking up with a sax quartet some day, and also about listening better to chamber groups.
 

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Discussion Starter #7
I don't understand this. Do you mean pianos are tuned in ET and saxes are tuned in JI? I thought most instruments are tuned in ET.
I'm far from an expert but I can offer what I've read from some of the master players such as Londeix, Sinta, and Rascher for example, and from technical wizards, that no saxophone is ever more than approximately "in tune." The player must learn to imagine or pre-hear good intonation and then learn how to produce that through the instrument. Some have said that the saxophone may be the most flexible musical instrument. It seems clear its flexibility includes intonation. Both equal temperament tuning and just intonation tuning are well within the scope of what can be accomplished with a saxophone. Someone more expert than I am would have to speak to whether the saxophone is designed to better support equal temperament or just tuning.
 

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@jaspire: Thanks for your answer.
The scenario I got from your initial question is that saxes must be tuned in JI, thus not compatible with normally ET-tuned piano.
Maybe I can input a few things...
a) ET and JI are two different tuning systems, but for two or more instruments to play in tune, I think they simply have to use the same (or at least compatible) system.
b) I agree that it's the player who plays in tune, not the sax. As you mentioned both ET and JI are accomplishable with a sax. So I think if two saxes are to be played with a piano tuned in ET, the players should tune the saxes in ET, not JI.
c) I really think modern saxes are designed to be tuned in ET - to make it easiest to tune in ET. Whether they're successful or not is another issue.

I hope I could offer some help.

R.-
 

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I think what it really comes down to is using your ear. Easier said than done, of course.
 

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I think what it really comes down to is using your ear. Easier said than done, of course.
JL - you and Rooty hit it dead on. All the "book-learnin" :) in the world won't help here. Just keep plugging away at playing in tune, and it will pay off. "Critical listening" to any music will help too. Also simple matching your tuning to a tone will help but somehow that sounds a bit too much like work...
 

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JL - you and Rooty hit it dead on. All the "book-learnin" :) in the world won't help here. Just keep plugging away at playing in tune, and it will pay off. "Critical listening" to any music will help too. Also simple matching your tuning to a tone will help but somehow that sounds a bit too much like work...
Play ballads with lots of long notes in front of a tuner?
 

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Play ballads with lots of long notes in front of a tuner?
No, this is not a useful thing to do IMO. Play ballads with lots of long notes with your ears open is better.
 

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No, this is not a useful thing to do IMO. Play ballads with lots of long notes with your ears open is better.
Regarding tuners and open ears, maybe it will be interesting to tell some background that led me to start this thread. In the first part of my daily practice I work an hour or two on long tones, intonation, and altissimo. For a year or so I would play a reference tone-of-the-day and then play unisons, octaves, fourths and fifths, all the while both listening hard and watching a tuner to achieve that zero cents perfection.

Recently I hooked up with a teacher who wants me to work on intonation by playing duets. Huge difference between what sounds in tune in a duet versus what a tuner says. It dawned on me that what I've been doing in my practice with a reference tone, intervals and the tuner is teaching my ear and brain and body to accept out-of-tuneness / equal temperament as correct interval intonation. Definitely a wrong way to use a tuner.

Now instead I've started working on intonation by playing duets with harmony, and playing in unison with good recorded performances. I do also still work with a reference tone and intervals and tuner, but now I use the tuner to verify that the intervals I hear are correct in just intonation - for example, I want my major third against a reference tone to be 14 cents low on the tuner. I understand now that tuners are tools that can be used or misused.

Thanks to all for your feedback, it all helps. I agree "just listen" is exactly correct but what I've been wondering is "listen for what?" I'm hoping in this thread for insight into how best to adjust intonation in the contexts of ensembles with and without equal temperament instruments (pianos, organs, mallet percussion), and with regard to harmony and melody. Response #5 from jbtsax was right on target.
 

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This topic has come up before, of course. I think using a tuner as a quick general reference is fine, just to make sure you're in the ball park, or when testing out a new mpc, horn or whatever. But practicing or playing while watching a tuner is not very useful, for the reasons you mention, jaspire. It also takes the focus away from listening and puts it into a visual reference, which does you little good in a real playing situation.

Have you checked out the tuning cd? This is a great way to work on matching tones, and various intervals to an audio reference (a drone):

http://www.thetuningcd.com/
 

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I think you need to find some good sax music in the genera you like and play along with the sax. Like many have said tuning comes from your ears not your eyes. If you can match your pitch to good players on good recordings then you should be fine. If you over think it all this stuff you will go crazy. Get your brain out of the picture and use your ears.
 
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