INTONATION, ACOUSTICS, PHYSICS, ETC.
It seems to me there are two fundamental skills intonation-wise: playing in tune with others, and playing in tune with oneself. These do not always coincide. Some folks play in tune primarily with themselves. I was better at playing in tune with others. It has served me well as a freelance player (less so at auditions). It is arguable intonation implies two sounds. In any event, those who win auditions – and keep jobs – tend to excel at both skills. Intonation with others is the focus here.
There has been considerable discourse here and there regarding intonation; some of it nonsensical. Some of my colleagues say, "Keep it simple, just play it where it sounds good." While it is possible to over-think it, a thoughtful approach can be productive. What we do is both art and craft – impacted by science.
Obviously, the point is to "play it where it sounds good." This can vary with circumstance. Sometimes, tempered intonation is best, sometimes just intonation, and sometimes melodic or expressive intonation. Playing with a fixed (tempered) pitch instrument – that does not decay – (synthesizers come to mind) – tempered tuning is necessary. Playing in a trombone section in the back row of an orchestra, or in a brass quintet, just intonation is generally best. Playing a solo in front of an orchestra (low brass players don't do that much), melodic intonation can be very expressive.
Just as obviously, we can't use a slide rule (or a spreadsheet) in the heat of performance. (And do not take your tuner to work.) What we can do is practice intonation. Regarding "just" intonation, practice to learn what just/pure intervals sound and feel (see below) like. That involves work away from performance.
A pure, justly tuned, perfect fifth is two cents wider than a tempered fifth. The human ear cannot discriminate a two-cent discrepancy; however, it can hear when the "beats" stop. A pure interval is a sonority that can be heard – frankly, it can be felt. Since the bell of a brass instrument works in both directions, sound waves in the air can enter it and can affect lip vibration. There is almost a sense of gravity subtly pulling towards maximum resonance – you can feel when the beats settle down. Drone practice (see the buttons below), for one, facilitates learning these sonorities.
David Blum wrote in Casals and the Art of Interpretation, “Casals was of the opinion that, when a stringed and keyboard instrument play together, the discrepancy between expressive and equal-tempered intonation is easily tolerable. Except in unison passages, he believed it unnecessary and devitalizing for the string player to adjust to equal-tempered pitch.”* I would extend this to brasses and to the discrepancy between just and tempered intonation. Opinion varies on this.
Christopher Leuba's book, A Study of Musical Intonation is exemplary; it should be required reading. Read it over, and over, and over, and . . . It is worth mentioning “. . . the typical brass instrument will have several resonant frequencies that fall approximately along a harmonic series.”** – (italics added)
Leuba mentions Casals' ideas and discusses "Solo vs Ensemble Intonation" writing: In a truly solo role, the soloist must never sound "flat." . . . If the nature of the players role is primarily "solo", i.e., the intention is to ‘stand out’ in contrast to the accompanying environment, adjustments (i.e., "going sharp") might be made. But, this is not "playing in tune" in the true sense of the words.
Music and Engineering: Just and Equal Temperament, by Tim Hoerning is a good resource as well – and shorter than the Leuba. (Note: the link in the pdf to Bobby McFerrin Hacks Your Brain With Music is dead.)
Also, don't go crazy trying to tune minor triads. Leuba wrote, “The placing of intervals in minor triads presents problems which seem to the writer to be impossible to resolve completely. . . . It is this writer’s hypothesis that the preceding phenomenon is the basis of the origin of the 'Picardy third' resolution, to eliminate these undesirable resonances in the environments of large cathedrals.”
Also, David Vining's Long Tone Duets for Trombone: Ralph Sauer Edition is pretty special. It is a GREAT just intonation tutor and it can be "a lesson with Ralph" every day! As Vining says, "This edition not only captures Mr. Sauer's sound on an included CD, but also reflects some of his teaching ideas embedded in the duets. By playing along with the CD, you can match Mr. Sauer's clear tone, exquisite intonation, and superb articulation." I suggest playing duet number one every day, and working your way through the rest, one duet per week. When you get to the end, start over. (Play it with your pals, too.)
NOTE: when playing with drones or any play-along track, it best to play the tracks through speakers rather than headphones or earbuds. It's easier to hear pitch, beats, and sonority, in the air around you than it is inside your head. Again . . . you can feel intonation in the instrument in addition to hearing – but only if the air around you is activated.
This LECTURE is great!
This BOOK on the history of temperament is fascinating.
This VIDEO is illustrative.. (It should be cued up to 4:45.)
ALSO: slide positions are just a guide; play pitches, not positions!
The links below are good; and take a look at: On Tuning Slides
There has been considerable discourse here and there regarding intonation; some of it nonsensical. Some of my colleagues say, "Keep it simple, just play it where it sounds good." While it is possible to over-think it, a thoughtful approach can be productive. What we do is both art and craft – impacted by science.
Obviously, the point is to "play it where it sounds good." This can vary with circumstance. Sometimes, tempered intonation is best, sometimes just intonation, and sometimes melodic or expressive intonation. Playing with a fixed (tempered) pitch instrument – that does not decay – (synthesizers come to mind) – tempered tuning is necessary. Playing in a trombone section in the back row of an orchestra, or in a brass quintet, just intonation is generally best. Playing a solo in front of an orchestra (low brass players don't do that much), melodic intonation can be very expressive.
Just as obviously, we can't use a slide rule (or a spreadsheet) in the heat of performance. (And do not take your tuner to work.) What we can do is practice intonation. Regarding "just" intonation, practice to learn what just/pure intervals sound and feel (see below) like. That involves work away from performance.
A pure, justly tuned, perfect fifth is two cents wider than a tempered fifth. The human ear cannot discriminate a two-cent discrepancy; however, it can hear when the "beats" stop. A pure interval is a sonority that can be heard – frankly, it can be felt. Since the bell of a brass instrument works in both directions, sound waves in the air can enter it and can affect lip vibration. There is almost a sense of gravity subtly pulling towards maximum resonance – you can feel when the beats settle down. Drone practice (see the buttons below), for one, facilitates learning these sonorities.
David Blum wrote in Casals and the Art of Interpretation, “Casals was of the opinion that, when a stringed and keyboard instrument play together, the discrepancy between expressive and equal-tempered intonation is easily tolerable. Except in unison passages, he believed it unnecessary and devitalizing for the string player to adjust to equal-tempered pitch.”* I would extend this to brasses and to the discrepancy between just and tempered intonation. Opinion varies on this.
Christopher Leuba's book, A Study of Musical Intonation is exemplary; it should be required reading. Read it over, and over, and over, and . . . It is worth mentioning “. . . the typical brass instrument will have several resonant frequencies that fall approximately along a harmonic series.”** – (italics added)
Leuba mentions Casals' ideas and discusses "Solo vs Ensemble Intonation" writing: In a truly solo role, the soloist must never sound "flat." . . . If the nature of the players role is primarily "solo", i.e., the intention is to ‘stand out’ in contrast to the accompanying environment, adjustments (i.e., "going sharp") might be made. But, this is not "playing in tune" in the true sense of the words.
Music and Engineering: Just and Equal Temperament, by Tim Hoerning is a good resource as well – and shorter than the Leuba. (Note: the link in the pdf to Bobby McFerrin Hacks Your Brain With Music is dead.)
Also, don't go crazy trying to tune minor triads. Leuba wrote, “The placing of intervals in minor triads presents problems which seem to the writer to be impossible to resolve completely. . . . It is this writer’s hypothesis that the preceding phenomenon is the basis of the origin of the 'Picardy third' resolution, to eliminate these undesirable resonances in the environments of large cathedrals.”
Also, David Vining's Long Tone Duets for Trombone: Ralph Sauer Edition is pretty special. It is a GREAT just intonation tutor and it can be "a lesson with Ralph" every day! As Vining says, "This edition not only captures Mr. Sauer's sound on an included CD, but also reflects some of his teaching ideas embedded in the duets. By playing along with the CD, you can match Mr. Sauer's clear tone, exquisite intonation, and superb articulation." I suggest playing duet number one every day, and working your way through the rest, one duet per week. When you get to the end, start over. (Play it with your pals, too.)
NOTE: when playing with drones or any play-along track, it best to play the tracks through speakers rather than headphones or earbuds. It's easier to hear pitch, beats, and sonority, in the air around you than it is inside your head. Again . . . you can feel intonation in the instrument in addition to hearing – but only if the air around you is activated.
This LECTURE is great!
This BOOK on the history of temperament is fascinating.
This VIDEO is illustrative.. (It should be cued up to 4:45.)
ALSO: slide positions are just a guide; play pitches, not positions!
The links below are good; and take a look at: On Tuning Slides
REPETITIO EST MATER STUDIORUM!
(Google it)
(Google it)
*Blum, David. Casals and the Art of Interpretation (p. 147). University of California Press. Kindle Edition.
**White, Harvey E.; White, Donald H.. Physics and Music: The Science of Musical Sound (Dover Books on Physics) (p. 252). Dover Publications. Kindle Edition.