INTONATION, ACOUSTICS, ETC.
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 (we don't do that much), melodic intonation can be very expressive.
Just as obviously, you can't use a slide rule (Google it) or a spreadsheet in the heat of performance. 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, (available here and as an ebook on iTunes and Kindle) 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)
Also, David Vining's Long Tone Duets for Trombone: Ralph Sauer Edition (hard-copy or downloadable pdf/mp3) 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
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 (we don't do that much), melodic intonation can be very expressive.
Just as obviously, you can't use a slide rule (Google it) or a spreadsheet in the heat of performance. 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, (available here and as an ebook on iTunes and Kindle) 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)
Also, David Vining's Long Tone Duets for Trombone: Ralph Sauer Edition (hard-copy or downloadable pdf/mp3) 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 (a great book)