Last month I wrote a post on how to hear yourself better. I used intonation as an aspect of playing with which I see many musicians struggle. They don’t hear themselves deeply enough. So let’s dig further into intonation since it is such a core element to your sound and musicianship.
This is the first of three pieces I’ve written on intonation. The next one is on the evils of tuning apps and the third is an exploration of pitch and intonation as a musical color.
I’m writing this for instruments that require ongoing tuning is required while they play. With a well-tuned piano, intonation is more or less fixed at that time, and drummers tune their sets but in a much broader context. I’m addressing wind players, vocalists, and string players.
Good intonation is so much more than the position of a tuning slide, woodwind mouthpiece, or tuning peg. Those mechanical positions are rough approximations. Good intonation is created with one’s ear directing the tiny nerves of the mouth and fingers.
I’ll sometimes say that as trombone players, we play a tuning slide. Even the slide position is an approximation rather than an absolute since the fine adjustments to pitch occur within the mouth. With the slide held firmly in first position, a skilled player can lip up or down by a semitone or more. Plus, the correct intonation for C is different within C major than it is from within Ab major. Same note, but a slightly different pitch is called for, especially for groups not playing with a fixed pitch instrument like piano. For now, let’s not get into the difference between just intonation and equal temperament.
So how can you play with better intonation? From hearing it.
I know that sounds simplistic, but your ear guides your fine tuning, not your tuning slide or mouthpiece position. Those gross movements simply make it easier for your mouth to more easily dial in the correct pitch for the harmonic context. And it is your ear that guides your mouth (or minute finger positions for a stringed instrument) to find the proper pitch sounding good for every particular harmonic context. There’s a lot going on in order to play in tune.
The obligatory tuning at the beginning of a playing session does not guarantee good intonation even for the players who nail the tuning pitch of A or Bb given to them by the piano or other instrument. That tuning directs the tuning slide or mouthpiece to its optimal position but guarantees nothing once the group begins to play.
Hearing your intonation
If you are playing out of tune, you are not hearing your pitch well enough relative to the harmonic context around you. Let’s try to strengthen your ability to hear pitch more deeply with some simple playing and listening exercises.
Every key or note mentioned within these exercises is concert pitch.
Let’s start by getting your tuning slide, mouthpiece, or strings on A-440 Hz or A-220 Hz, or if you prefer, Bb-466 Hz or 233 Hz. Play the following sound files and listen closely to the reference pitch and to your playing. Move your tuning slide, mouthpiece, or tuning peg in order to match the reference tones.
The good news is that you are not doing this in front of a band watching and judging you getting yourself in tune. Take your time and listen.
- A-440/220 Tuning Reference
- Bb-466/233 Tuning Reference
With your tuning slide, mouthpiece, or tuning pegs in a good place, Here are some fun audio tracks over which you can exercise hearing your pitch.
But the goal of this exercise is not to simply play a note, confirm it’s in tune, and move on. Go beyond your normal mindset about your intonation. Good intonation is not as much about the mechanics of your instrument, but rather the character you shape of your sound. Your intonation is the color or personality of your sound. Taking full command of the pitch is sexy!
With that in mind, think of the following exercises as the means to put a microscope on your intonation and to hear beyond simply being flat or sharp. If it helps, think of the following as tone shaping exercises.
Listen to the following audio files. The each contain sounds that alternate between harmonies. They start with more simple piano harmonies and evolve to more sophisticated sounds containing more and more complex overtones.
The objective is to play one long note, and hear the intonation of that one note over the changing harmony. For example, this first audio file is piano alternating between basically C major and Bb major. Play C over these two key centers and listen to the color of C within these two chords.
If you are simply playing the note C over the alternating harmony without making any adjustment with your mouth or fingers, you may not be hearing the deeper subtleties I want you to hear within these audio files. Don’t play these with the same mindset you have when playing a long tone A over the tuning reference in your band. That’s too superficial.
#1 For this first exercise and every audio file that follows, you can play any one of the 12 notes. But start with the more consonant notes within the basic harmony. That is why C works so well with this first track. C is the root of C Major and it’s the 9th of Bb Major. Try also playing D, G, E, and G over the track. And for more advanced hearing, try A, F, and even F#! Are you hearing where those notes can be placed with the context of the audio. (Trombone players: it’s not about slide movement.)
- Piano/Drums Alternating Harmony
#2 In this piano sound, we’ll be listening to our one note within the musical context of three harmonies. Since you have the sound of C in your ear, let’s start by using C as the common tone held over this evolving harmony. Try also G, D, B, and E.
- Alicia's Piano
#3 Let’s play some notes over more interesting sounds. This next one is an etherial harmony that changes color throughout each phrase. Start by playing D. Again, listen to where D fits into the evolution of these sounds and overtones. Try also A, D, and E. There are lots of swirling overtones for you to reference (hear) as you produce notes on your instrument.
- Airborne Visitors
#4 Here’s another complex sound with lots of rich overtones. Let’s return to C and hear how that sounds. Try also G and D. More interesting notes include A, F, Eb, F#, and even B.
Are your ears are opening up to some deeper and more subtle aspects of the pitches you are producing in relationship to the harmonies in these tracks. This is warming up your ear. Warming up the muscles to play your instrument is one thing, warming up your ear is another crucial aspect of playing well.
- Colors of Zen
#5 Here’s one last one. In creating this sound, I was playing with the upper overtones, creating melodic movement with them. When you play with other musicians, sounds are constantly moving and changing. I’ve purposefully kept these sounds fairly static so that you can concentrate on your pitch.
The overtone movement in this one is subtle but there nonetheless. Can you hear it?
Start with our familiar C then hear the pitch of D, E, and up the C major scale. In fact, play through the C major scale slowly to lock in your pitch, this time with more movement. Work your way clockwise around the circle of fifths starting at the bottom and hear the progressively more dissonant notes of F#, C#, and so on. Give yourself the challenge of seeing how far around you can go while still hearing the relationship of your notes to the audio track harmony.
After playing through some or all of these exercises, can you sense any change in your hearing of intonation?
Assess your hearing
Let me give you something different to help you assess your hearing of pitch . The following audio file is the second, third, and fourth part of the Bach Choral called In allen meinen Thaten (In all my deeds). This exercise comes from my book Alto Trombone Savvy, where I teach alto trombone players the positions and how to play more in tune on the alto. But for this, it doesn’t matter what instrument you play.
Below the audio file is a download for the lead voice for the choral. I’ve made it available in C, Bb, Eb, and bass clef. Choose your instrument’s clef and key, then play the first part over the audio of the inner three parts.
Unlike the audio files for the above exercises recorded with perfect piano and synthesizer tuning, these three inner parts were recorded by me on trombone. Like the other musicians with whom you play, my intonation is not machine perfect, but finding your pitch amongst the humans and imperfect piano/guitar tuning is, after all, the point of strengthening your ear for intonation.
Have fun, and bookmark this post so that you can come back to it and warm up your ear so you can continue to better hear your intonation.
- Bach choral #50
I’ve called all these exercises and sound files intonation practice. And they are.
But these 1,800 words and 8 sound files are more about opening up your ears to hear deeper.
I think all of us can listen deeper than we do. I think the eternal quest is to hear the atomic detail in music and in our playing of it.
Forgive me for sending the trojan horse of intonation into your musical mind. All this will help you intonation but I hope it will also open up your ears to so much more.
#2. Read part two on my thoughts on tuning apps
#3. Read part three on the advanced topic of using intonation as a color
Stretching. Love it!
I’m going to try these exercises on my band after I try them out for myself.
Love your work.
Great. Let me know what you find.
This is very intriguing Mike, thanks for taking the time to put all this together. I am sure it took a great deal of time to do. I’ll be checking it out this week in the evenings. I really like how you tie everything to the ear, which at it’s core is brain based. I like what you said in the post, “Good intonation is not as much about the mechanics of your instrument, but rather the character you shape of your sound.” That is profound. Thank you!
Pardon my long Email in advance.
I play guitar in a big band and inconsistency/drifts in tuning/intonation with the horn section has always bugged me (as a physicist). The guitar fret spacings comply with the Equi-Tempered chromatic scale ( i.e., frequency changes by 5.9% per fret or semitone (or 100 cents)). The piano tuning adheres to this, per consecutive key (black or white), BUT piano tuners seem to apply minor tweaks “by ear”, listening for “beats” from several pitches played simultaneously, such as 5th intervals.
Horns have “flex” tuning because of the musician’s embouchure-ear talent and mechanical sliders (trombone) or valves (trumpet). I am not sure if “holed” instruments like a saxophone have their hole placements adhering to equi-tempered or just temperament?
Another issue is drifts in pitch with temperature.
A rise in temperature causes (metal) stringed instruments to go flat (about 3 cents per degree F or about 5 cents per degree Celsius for the thickest guitar E-string, less for thinner ones). The strings expand or “sag” and the string tension drops. On the other hand, wind instruments go sharper with increased temperature (by about 1.5 cents per degree F or 3 cents per degree C) because of the increase in the sound velocity of air within the body of the instrument. So with a rise in temperature during a concert by say 3 degrees F, for example, the piano “fat strings” will be flat by over 10 cents. The guitar strings will also be flat but the guitarist can retune easily and frequently. The horns get gharper by about 5 cents for all frequencies – a spread of at least 15 cents from the piano bass notes (left hand side) which is audible. This can be offset “by ear” which is part of your “pitch” (pardon the pun) for achieving intonation on-the-fly on the horns.
Did I get this right? Has that been your experience with guitar and piano compers?
Thanks Michael !
Jerry, I can’t argue with your science, certainly not coming from a physicist!
From my experience, the biggest problem with pitch is not the physics of the piano or equal temperament, but with the ear of the player to find the correct sonic compromise (because, as you know, music performance is not perfect science).
In other words, with a skilled ear, players of any non-keyboard instrument can find the pitch and sound in tune. We could talk higher level concepts like a sax quartet playing with piano, and where those intervals should ideally be placed (like in by Bach Choral example), but I’m scratching here at something more fundamental: given the musical context in which a player finds himself, is that player hearing his place within the entire harmonic context? Is he using the fine muscles of his mouth directed almost subconsciously by his ear to place his notes in the frequency that sounds most pleasing for any particular moment?
If not, how can he strengthen that skill?
Thanks for your great comment!
The twelfth roots of 2 are all irrational numbers, yet some come conveniently “close” to 5/4. 4/3, 3/2, which is helpful in our harmony. There rational numbers create the wonderful harmonies that we seek in music. Trombone and double bass (two of the instruments in our house) are infinitely adjustable by the hands while other instruments via the mouth. Even guitar notes can be slightly “bent” and of course the voice can do just about anything. What a great topic!
The rational numbers are the way that we count things. But the irrational numbers are how we measure things. Measurements are never precise! In some sort of weird and wonderful way, harmonies really shine when we use the rational numbers (Hello Pythagoras). But we had to invent a way to play in all keys or we wouldn’t have jazz nor a whole lot of other wonderful music.
I remain convinced that there’s another way to create sound that is pleasing to the human ear based on irrational numbers like pi, e and especially phi (the golden ratio). They just keep showing up in all sorts of wonderful places. And then there’s the trigonometric functions! Holy sound wave Batman.
Michael, you have stirred the pot for big band physicists (Jerry) and small group mathematicians (me) who love to play music. Thank you for opening up this topic and helping us to discover new ways to play better. Now, I have to get to the gig. Best.
Glad to have stirred the pot. One thing I would correct is that the type of intonation accuracy I am promoting here is definitely done in the mouth for trombone. The tuning slide is a rough adjustment, the trombone slide is a finer adjustment, but the the character of the sound via the minute adjustments creating the core of the intonation, I believe is done with the mouth. Thoughts?
I absolutely agree. I was just comparing the bass (my current instrument) with the trombone (my previous instrument) in terms of being able to adjust with your hand. Based on the number of hours that my teacher spent on proper embouchure, I would have to agree that the mouth is where the real fine adjustments occur. By the way, those hours were spent over 40 years ago and are still impressed on me and still contribute to my approach to music. Pretty good teacher! I have managed to track him down and thank him for that. And he is still playing wonderfully.