Playing in Tune
What is Playing in Tune?
(Note: This article is still a work in progress…)
How is tuning measured? Equal temperament… strobe tuners and overtones. 1200 cents, each half step = 100 cents…
Playing in tune is both a science and an art. It also requires some knowledge of music theory. It begins by developing the ability to play every note comfortably in tune at equal temperament from note to note and register to register. Equal temperament divides the octave into 1200 parts. Each half-step interval of the 12 notes of the chromatic scale gets 100 units which we call “cents” and each whole step is 200 cents. If we add up all the half steps in an octave we might say that we have 12 “dollars”! As a way to remember, think of each half step as a dollar and any tuning deviation above and/or below is measured in “pennies”.
Equal temperament is easily checked with an automatic chromatic tuner, but is not always easily achieved. It requires the resonant core of every note to be centered chromatically at equal temperament using standard fingerings, but not so rigid that the pitch cannot be moved higher or lower without suffering in tone quality. Achieving this requires:
- A well-maintained instrument with proper pad heights and correct tone hole sizes,
- A reed that is adjusted for proper tuning, note to note and register to register,
- A reed style and strength that is compatible with the instrument, mouthpiece, and player,
- A mouthpiece/bocal that has a good “scale”, one that is even in pitch throughout the registers,
- Understanding proper tone production for each note and register (embouchure, air speed, and vowel shape).
Is Playing at Equal Temperament Playing in Tune?
Yes, and mostly NO! There are a growing numbers of young musicians who believe that if they are playing at equal temperament they are in tune, period! They’ve practiced hard to be able to “nail” any note at equal temperament. Good start though. While this may work to some degree playing with a piano, which itself is not totally tuned to equal temperament (more on this phenomenon later), several generations of musicians have had automatic chromatic tuners at their disposal and have learned this is playing in tune. There can be an attitude among some players that I’m right and everyone else is wrong, so I’ll play it here where I know it is correct. Is this person a “team player”? But if you are playing with a “fixed-pitch” instrument that is at equal temperament you absolutely must take their pitch into consideration. You can take it all this way or mix it up with your tuning of intervals with the piano or fixed-pitch instrument. Judicious use of vibrato has always been a way around some pitch problems too.
You’ll Know It When You Hear It!
Professional musicians play using a tuning system based on the overtone series called “Pure Tuning” or “Just Intonation”. In this tuning system, intervals are based on the natural physical ratios of the overtone series. All top orchestra musicians, soloists, vocalists use this method because it is more pleasing to the ear for reasons which will be explained below.
Pure tuning is based on playing in a key (i.e., C Major, A minor, etc.). When intervals are sounded together using just intonation, beats are NOT produced when using the correct ratios. The simplest explanation of the difference is the pitch adjustment when playing on the 3rd, 6th, and 7th degree of a scale. The 2nd, 4th, and 5th degrees of the scale also deviate from equal temperament but to a lesser degree. Another way to look at this is that the note “C” in the tonality of C Major or minor is centered at equal temperament, yet C in A minor is above equal temperament and C in Ab Major is below equal temperament.
Unlike equal temperament which has one interval size, playing a scale in pure tuning involves 3 interval sizes which are based on the natural ratios of the overtone series. The major scale starts out this way: the major tone, Do to Re, (whole step #1) is 204 cents. The minor tone, Re to Mi (whole step #2) is 184 cents, and the half-step, Mi to Fa, which is referred to as the semi-tone is 112 cents. These intervals sizes repeat within the scale.
The major primary chords (I, IV, and V) are all identical in the spacing of the major third using the same mathematical ratios: the 3rd of the each primary chord is 14 cents below equal temperament. The root of IV is 2 cents below equal temperament and the root of the dominant (V) is 2 cents above equal temperament. Doing the math may be confusing but the outcome is the same.
Some of the notes on every bassoon have their own acoustical pitch tendencies sharp or flat that can change with dynamics making matters worse. For example, half-hole G (top space) has a tendency to play sharp when played loudly. To compensate, we add the low Eb key (resonance key) but when G is played extremely softly the pitch is better in tune without the key added.
Strangely enough, a great playing reed may sound in tune to you, but to others listening it can sound out of tune and “false” in pitch.
To play at a professional level, every bassoon needs additional “tuning and voicing” work on the instrument to match up with a player’s bocal, reed style and tone production. There is no tuning slide or reed ligature to be quickly adjusted like single reeds. Pulling out a bocal to lower its pitch is not effective and creates other problems, just as pulling out the joints of the bassoon also causes problems. All these things create challenges that must be overcome for the professional player. The main difference between a talented amateur and a professional bassoonist is the amount of effort made to play in tune at all times.
What is false pitch and what causes it? For some reason, as a performer you are not able to accurately hear the sound that is projected from the instrument especially its overtones. While there is a natural series of overtones for any fundamental pitch, the balance and strength of individual overtones varies for each instrument. In addition, each instrument has a formant and secondary formants at specific pitches that also help identify the sound of an instrument. The bassoon’s primary formant is around A440. Below is an example of the overtone based on the fundamental C. The notes indicated with arrows are considered “out of tune” however the use of the pure seventh overtone in tuning is stunning when used in a chord (see Mendelssohn excerpt below) and is sometimes used with brass instruments as these notes are what are naturally produced by a bugle.
The overtones on a bassoon based on Low Bb are shown below (courtesy of James Kopp):
While it is possible for a note to be perfectly in tune with an electronic tuner, to the musician’s ear the perception can change when the ear is plugged if the note is false. This test is only possible if you are playing a note or a wind instrument that requires only the left hand. The difference is the acoustic input of the open ear and the sound heard through bone conduction (inner ear) with the ear plugged are at odds with each other. This is likely due to the inability to hear the offending (false pitched) overtones with the open ear. The plugged ear is a more accurate measure of true projected pitch. What causes false pitch can be any of the following: incomplete reed tuning, tone production issues including under or over blowing the instrument forcing or constricting the tone, improper vowel shaping within the oral cavity, and improper placement of the lips in forming the embouchure.
False pitch is not unique to the bassoon. For example, on a string instrument an individual string after being stretched out and re-tuned over and over will also become false in pitch. To hear the true pitch, the player can place the tuning peg against the head or closed ear to hear the true pitch. It is expected that at some point this will happen on every string instrument. For brass instruments, it is common when played loudly to over blow the instrument creating a perception to listeners that they are playing sharp in pitch. Under blowing a woodwind instrument can create the perception that they are playing flat. But the reverse is also true depending on the reed and tone production. On a woodwind instrument, a worn out reed will become false in pitch just as a reed which is not properly tuned or played correctly will be false in pitch.
The word inharmonicity is commonly used (especially by piano tuners and players) in reference to overtones that are not in tune with the fundamental frequency of the note being played. Wikipedia defines it as follows:
In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency (harmonic series).
One of the best ways to check for false pitch is to listen to a recording of yourself or your group’s performance to see how your pitch sounds when projected. What you will find is that some notes will sound out of tune yet notes next to them sound in tune. On the other hand, a note can sound out of tune because care has not been taken to place the note in its proper tuning location be it equal temperament, just temperament (pure tuning), or another historic tuning temperament.
An automatic chromatic tuner is essential to check pitch to direct attention to any problem notes when tuning your reeds. And reed tuning can do only so much if the bassoon is out of whack or leaking (80% or more bassoons leak to a significant degree). Again, achieving an equal tempered chromatic scale is the starting point to playing in tune. Playing in tune in an ensemble also requires significant pitch flexibility as much as 30% above and below the equal tempered pitch. Flexibility is required to match rising or falling pitch of the group or matching another player. Pitch fluctuation is common and to be expected for several reasons which include: 1) other instrument’s pitch tendencies related to dynamics (strings go flat playing soft on low strings, brass sound sharp playing loudly) 2) the effects of stage or practice room temperature (strings go sharp in cold temps and woodwinds go flat), 3) certain key signatures are better for playing in tune. Pitch in the strings is better/easier in keys with sharps and the opposite for winds (in keys with flats), and 4) have you or the musicians you play with ever considered pure tuning rather than equal temperament tuning? What is “in tune” is best left to a question: What is the most pleasing to your ear?
For those professionals who know the answer, hearing someone playing at equal temperament or wildly fluctuating for no good reason can make you cringe or angry. It is especially frustrating if you are stuck playing with someone who doesn’t get it, or if you are playing with someone who is inconsistent in pitch placement. In listening to auditions for symphony orchestras, college scholarships or solo competitions a pro can hear within a few notes what approach, if any, is being taken. The intervallic tuning between notes make all the difference in the approach. Hearing a wind or string soloist playing strictly at equal temperament from note to note is a sensation of “dullness” or discomfort. Great performing artists can only hear it another way: tuning of intervals that are based on the natural ratios of the overtone series within a tonality. Each note of the melody or chord is adjusted according to its position within the scale of that tonality.
What Is the Problem with Equal Temperament?
BEATS! What sounds best to the ear are scales and especially intervals that do not produce the flutter of beats when sounded together, but produce a pure combination of tones without beats. If intervals are “acoustically correct” based on the natural physical ratios of the overtone series, there are no beats, no flutter. Pure intervals have a distinct positive side effect. In some cases this can be easily perceived. Two or more notes sounding together can “produce” what are called resultant tones (phantom tones sounding lower) or summation tones (sounding higher). Other terms used are subjective tones or more commonly difference tones. Those who have played duets with recorders or flute or clarinet duets in the high registers can hear a third phantom tone. These are perceived as a buzzing in the ear. In fact, some composers have written duets called “trios for two instruments” where the third tone is designed to be an audible component of the trio. In ensemble playing, like instruments playing acoustically pure intervals together sound BIGGER whether the phantom tone is audible or not, than if the interval played is not pure. Beats cannot always be heard clearly as their intensities change with the note combinations sounding in the register(s) played. But for the second bassoonist at the bottom of a chord it can be impossible to find the right pitch when the intervals in the upper winds (major 3rds, etc.) are not pure intervals. If the upper notes are outside of pure tuning, there is no place to put the second bassoonist’s note that will sound or feel correct to the player at the bottom of the chord!
Resultant tones are based on simple math. If you subtract two note’s frequencies from each other the result should be an in tune note below (heard or sensed) at the frequency of the remainder. Here’s a hypothetical example: two high notes are sounding together, one at 500 cycles per second (cps) and another at 400 cps. The resultant tone (phantom tone) will sound at 100 cps. If one of the upper notes is off (i.e., 505-400=105), the sounding/sensed resultant is in conflict with the correct 100 cps frequency. This is the second bassoonist’s dilemma.
Why Do I Have So Much Trouble Matching Low Notes With the Piano?
In piano tuning, getting the beats out of a single note’s three strings must be done and then getting the correct number of beats between intervals must be balanced. Piano tuning is built on beats. And pianos do not have a perfect equal tempered scale either. The highest and lowest notes are “stretched” away from equal temperament on purpose! So when the bassoonist plays a matching low note below the staff with a piano accompanist, why do you feel so sharp on your low note? The low strings of the piano have been stretched/lowered in pitch which is a standard tuning technique for all pianos, and stretched upward on the highest piano notes.
Keyboard Tuning Problems
Prior to equal temperament, keyboard instruments and even woodwind instruments were tuned to a tonality of the composition’s key signature. The primary chords and scale produced what would be considered pure intervals as it relates to the overtone series. The difficulty with this type of tuning was any chords that strayed too far away from the key center clashed when these intervals sounded. The intervals in a tonality if measured, all equal simple ratios. For instance, an octave is a doubling of vibration with a ratio of 1:2, a fifth a ratio of 2:3, a fourth a ratio of 3:4, a major third a ratio of 4:5, and a minor third a ratio of 5:6. During the Baroque period, keyboard instruments were sometimes tuned in such a way that they could accommodate key signatures closely related to a central tonality. These “historic” tunings that went by different names such as Werckmeister and others which also became known as the well-tempered klavier.
The advent of equal temperament tuning allowed the keyboard instruments to modulate to any tonality without clashing intervals. However, equal tempered intervals produced “beats” of secondary vibration not heard in the pure tuning. Our ears have become accustom to the sound of equal temperament but the traditional pure tuning is related to the overtone series that is called “just tuning.”
The Pure Scale Showing Deviation From Equal Temperament
Beethoven, Violin Concerto
This solo entrance is scary! If the reed is not tuned properly, the D can be false in pitch and the F# (an acoustically sharp note on all bassoons) is a problem in this register, especially when playing very soft. The F# should be played 14 cents below equal temperament and the B and C# should also be below equal temperament while the E should be slightly above equal temperament. Making matters worse, the upper D is often played flat by a majority of bassoonists. This is a very good example of why it is important to use harmonic tuning in the middle register to correct the acoustical tendency of several notes. Furthermore, the D (the nexus note) should be carefully checked that it is not false in pitch using the ear plug test.
This solo is in the key of B minor. In this case the D natural (minor 3rd) should sound 16 cents above equal temperament on a note that is commonly played flat by most bassoonists. The effect of a flat D in B minor is excruciating!
Mendelssohn, Symphony No. 4, Movement 3, “Trio” Section
Solo quartet of two bassoons and two horns in E. A good example of the natural 7th (A natural) in the second bassoon sounds wonderful! The natural 7th of the B7 chord is played 29 cents below equal temperament and resolves “upward” to the major third (G#) of an E Major chord which is 14 cents below equal temperament.
Tchaikovsky, Symphony No. 5, Movement 3
Stravinsky, Firebird, Berceuse