Advances in electronics and the miniaturization of the gadgets that musicians use in performance and practice have contributed to a flood of new devices designed to help performers play in tune, but do they actually lead to better ensemble intonation? What does playing “in tune” really mean? What skills come into play to help students learn to perform in tune? And what resources are available to help our students learn to play with better intonation?
What does playing in tune really mean?
When we consider accurate ensemble intonation, we really are talking about two different skills. First of all we need to be able to match the notes that we play with the notes that others are producing. Technically speaking, when two notes of the same pitch are played together, their frequencies need to match acoustically. In addition to matching unison notes within the ensemble, we need to consider how the notes we play fit into the chords being played by the group.
Don’t make waves: Beat-less tuning
Let’s consider first the skill of matching the pitch of two or more unison notes. Technically, playing in tune means producing a pitch that matches the frequency, measured in vibrations per second, of another pitch. For instance, if I play a second-space A in the treble clef on my flute, and the sound from my instrument vibrates the air molecules surrounding my instrument at exactly 440 vibrations per second, I will be “in tune” with my desktop tuner (as long as it is calibrated to the standard orchestral pitch of A = 440 vibrations per second). However if I play my excruciatingly calibrated A with my fellow flutists in an ensemble sitting under hot stage lights, and they are playing an A which vibrates at 443 beats per second, I might sound very flat (all things being equal, warmer temperatures tend to make wind instruments go sharp while string and percussion instruments go flat). Clearly in this case, even though I have stopped the needle on my tuner, I am not in tune with my section, and I will most likely feel the wrath of my conductor or section leader.
A more practical definition of playing in tune involves the concept of “beat-less tuning.” Beat-less tuning involves the elimination of acoustic waves produced when the frequencies of two pitches do not align. Figure 1 illustrates two simplified sound waves played together (note: sound waves don’t really look like this, but this is an accurate model of how frequency – pitch, represented on the x axis – interacts with amplitude – volume, represented on the y axis). Player One plays a third-space C in the treble clef while Player Two plays the same note. The sound waves of both players are added together resulting in a noticeably louder composite sound made up of both players’ individual sounds.
Consider next an example of players whose notes do not match (illustrated in Figure 2). In this example, Player Two plays a note whose frequency is slightly higher in pitch (faster frequency). The two waves are added together again, but since the waves do not align, some of the sound waves reinforce each other while others actually cancel out the sound of the other wave. The resulting sound is not uniformly louder as it is when both players match frequencies exactly. In this case, the listener perceives the fluctuations in the loudness of the sound as “beats.” The faster the beats, the further apart the two players are pitch-wise. Slower beats indicate two players who are more “in tune” with each other. Our goal then is to match frequencies by eliminating beats in the sound.
Chord tuning
Ensemble intonation also involves the skill of fitting individual notes into chords. In order to do this, the performers must consider the pitch tendencies of the harmonic series. Musicians in the Western world have been struggling for centuries to develop a system where notes sound in tune across a wide variety of key signatures. In the 18th century musicians settled on a system of tempered intonation called Equal Temperament, in which certain notes are purposefully detuned to make playing in every key possible. This remains the standard pitch reference, and modern pianos, organs, keyboard percussion instruments, and most electronic tuners are calibrated using this system.
Performers on wind instruments have the flexibility to consider another option: adjust individual pitches to fit within a particular key so that no beats occur. Using this system, known as Just or Pure Intonation, performers adjust the frequencies of individual pitches to match notes in the harmonic series of the key in which they are playing. The harmonic series is the series of overtones that are produced whenever any pitched instrument plays a note. For example, imagine that I play G on the first line of the bass clef. When that pitch sounds, it produces the overtones shown in Figure 3. The relative loudness and softness of the overtones above the fundamental pitch contributes to what listeners perceive as the timbre of the sound.
These overtones have a strict mathematical relationship to each other that was first described by Pythagoras in the fifth-century BC, and do not match our modern system of equal temperament. The third and sixth partials sound slightly sharp when compared to a piano or tuner. The fifth partial sounds very flat when compared to a pitch generated by a tuner. This presents a problem when we try to play chords in an ensemble because each note we play needs to match the overtones of the other instruments. If we play the notes exactly “in tune” with the tuner, they will produce beats if they do not match the overtones produced by the other performers.
Let’s use, as an example, a brass quintet playing an A-flat major chord. Figure 4 shows a typical scoring for this chord. If the tuba player plays the root, then his instrument will also produce the overtones shown in Figure 5. In order to match the natural pitch tendencies of these overtones, the horn player will need to play her (sounding pitch) E-flat slightly sharp. The first trumpet will need to play her (sounding pitch) C very flat in order to match the overtones produced by the tuba. If the horn and first-trumpet players do not make adjustments, if they play their notes “in tune” with a standard tuner, then beats will be heard as their notes fail to align with the overtones produced by the tuba player. When these players do make adjustments, their sounds blend perfectly with the overtones produced by the tuba reinforcing the volume of the overtones produced by each instrument resulting in what the audience perceives as a louder, “ringing” tone.
So why would we turn off the tuner to help our students play with better ensemble intonation? Relying on a visual pitch reference such as a tuner, or trusting the conductor to inform students of their pitch inaccuracies each fails to develop the aural skills performers need in order to play and adjust their pitch in performance. Playing in tune with others is an aural skill that involves eliminating beats by matching the frequencies of the notes and overtones others in our ensemble play. Stopping the needle on a tuner is mostly a visual skill that involves stopping a needle or lighting up a light that, as we have discovered in our chord tuning discussion earlier, may or may not actually reflect the aural reality of performing “in tune” by eliminating beats.
Rather than relying on a visual reference help performers determine whether or not they are in tune, ensemble directors should strive to give students the physical and aural skills necessary to adjust their pitch and provide reliable pitch references so that the individual players can adjust their pitch to eliminate beats. Following are some suggestions to help your students develop those skills.
- Begin by teaching your students how to adjust their embouchures to match pitch. Have your students perform a comfortable unison pitch and then, on your signal, lower the pitch using only their embouchures. On your signal, have students return to the original, centered pitch. Next have students move higher than center then return. Many times the return to the center pitch will be much more centered because students are listening more carefully. With practice, your students will be able to bend their notes further in each direction and will begin to settle into a fairly stable pitch center.
- Teach your students to eliminate beats while playing unisons and octaves. Provide your students with a reliable pitch reference and have them try to eliminate the beats as they play. This pitch reference can be an audible tuner or a reliable player in the ensemble. Remember to use an audible pitch source rather than a visual tuner. Start with small groups or in section rehearsals to keep students engaged and so that students can hear each other as they develop their ears. Keep the group active by asking non-performing students to evaluate other performers; often it is easier to hear if other people are out of tune than it is to hear yourself as you play.
- Work on chord tuning. Play a reliable pitch reference to serve as the “root” or “tonic.” Next add students playing the fifth of the chord above tonic. The fifth will be slightly sharp when compared to the tuner, but most students will automatically make this adjustment by using the beat-elimination skills they developed earlier as they matched unisons. Once performers are comfortable making adjustments in order to eliminate beats, they will easily apply this skill to chord tuning. Add the third of the chord last. This pitch will appear considerably flat on the tuner when the beats are eliminated.
- Apply these skills to musical contexts. Continue working on chord studies and chorales to help students develop their ears. Stop on long notes and select individual players and sections to help them isolate and adjust their individual sounds. Begin to wean your performers from the electronic pitch reference as they begin to adjust to each other.
Tools of the Trade – Resources for Developing Intonation Skills
There are several resources that help ensembles develop the physical and aural skills required to play in tune. The Yamaha HD-200 Harmony Director keyboard can be adjusted so that it plays notes using just intonation in any major or minor key. The keyboard will follow your input and automatically switch to the major or minor key you play on the keyboard. There are also several tuning CDs available that play pure fifths in every key. These can be invaluable aids for individuals, sections, or full ensembles as they work to develop their listening and matching skills. Simply select a CD track in the desired range and key, and have your students play scales, chords, or melodic lines with the CD tracks as they try to eliminate beats.
Visual tuners can serve as valuable aids in instruction. If directors or performers cannot hear if particular performers are sharp or flat, a quick glance at the needle or dial can help resolve the confusion. The visual reference can also serve as a helpful training aid. Having students “stop the tuner” can be a fun game as they develop their aural skills, but directors must remember that great tuning is developed by students’ work in developing skills of adjusting based on eliminating beats.
Si Millican teaches courses in Instrumental Music Education at the University of Texas at San Antonio. For 13 years prior to his university work, Dr. Millican was a public school teacher in Texas in the Arlington, Lewisville, and Belton school districts, teaching at both the high-school and middle-school levels. While at Lamar Middle School, the Symphonic Band was a Texas State Honor Band finalist twice. At Belton High School, the Marching 100 advanced to the State Marching Contest twice and finished as high as sixth place in class 4A.
Dr. Millican remains an active clinician and adjudicator across the state of Texas and is on the Active Concert Band list of the Texas Music Adjudicators Association. He remains an active arranger for concert and marching band through his company North Music, LLC – www.NorthMusicOnline.com.
