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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?
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?