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.
When a musical pitch is sounded, it produces a series of overtones in addition to its fundamental pitch. These overtones, also known as partials, identify what musical instrument you are hearing based on the strength or absence of these overtones. For instruments with a very pure tone like the flute, the upper overtones may be minimal or absent. The bassoon on the other hand, has a weak fundamental pitch but is rich in overtones. Each musical instrument or human voice has an additional element called a formant which also helps identify the “voice” you are hearing. The bassoon’s primary formant is close to A = 440 (high A). A sound or voice also has secondary formants which help further identify who or what you are listening to. The bassoon’s secondary formant is approximately A = 880. In the overtone series, the doubling of a frequency produces an octave in pitch or the ratio of 1 to 2 (1:2). In the example above, the octave is known as the second partial. A pure octave is a doubling of the frequency of sound and that is consistent with an octave in equal temperament. This includes partials number 4 and 8 which should also sound at equal temperament.
Partials can also be out of tune which can make the pitch or musical instrument sound “false” or out of tune. This is discussed in more detail below. The only tone possible without partials is the electronically generated sine wave. Some instruments are designed to have special out of tune partials. These include percussion instruments (cymbals, gongs, etc.) and orchestra bells and church bells. Some instruments have a predominance of odd-numbered partials or a player’s tone production can produce odd-numbered partials. The stronger the even numbered partials, the more pure the tone quality.
Pure tuning deviates from equal temperament beginning with the 2nd to 3rd partial (2:3) also known as the “open fifth” which is the practice for tuning from one string to another on a string instrument. An open fifth tuning (2:3) is two cents sharper than equal temperament and can be easily heard when the open 5th is in tune. When they are in tune, the sound produces no beats with an added depth of sound. This phenomenon is known as a resultant tone, which will be discussed below.
The pure fifth tuning of the string instruments also produces a sometimes frustrating additional element. As each string is tuned to concert A, each string (open 5th) adds two cents. For example, the cello strings from top to bottom — A/D/G/C — will be six cents below equal temperament on low C. The violin strings from top to bottom — E/A/D/G — will be two cents sharp on E and four cents flat on the low G string.
The most significant element of pure tuning as it relates to the overtone series — and the key element — are the ratios between the 3rd and 4th partial (major 3rd) and the 4th and 5th partial (minor 3rd). These ratios deviate significantly from equal temperament.
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.
The Major Scale
Unlike equal temperament which has one interval size for each half step or whole step, playing a scale in pure tuning involves 3 interval sizes which are based on the natural ratios of the overtone series. The major scale is made up of:
- The “major tone”, a slightly wide whole step Do to Re, is 204 cents (4 cents above equal temperament).
- The “minor tone”, a much narrower whole step Re to Mi, is 184 cents.
- The “semi-tone”, a significantly larger half-step, Mi to Fa, is 112 cents.
These interval sizes repeat within the scale (Fa to Sol is 204 cents, Sol to La is 184 cents, La to Ti is 112 cents).
Please note: the myth that the leading tone of a scale should be sharp in pitch is wrong! The leading tone should be 12 cents below equal temperament as it functions as the major third of the dominant V chord. The correct spacing of the intervals in pure tuning/just intonation leads the ear to recognize the tonality (key) that the music is in. If the music is in a minor key, the intervals of the 3rds and 6ths are flipped. (See minor scale below.)
Comparison of equal temperament to pure tuning in C Major:
Tuning a Major Chord
It is the responsibility of the musicians playing the accompanying chords to lower the pitch of the major third and slightly stretch the fifth of the chord. This provides a pure major third interval based on the overtone series with the physical ratio of 4:5 or 14 cents below equal temperament. (See Overtone Series.) Note: all major chords are made up of a major third (root to third) followed by a minor third (third to fifth). The minor third deviates above equal temperament by 16 cents with a ratio of 5:6.
For those playing the melody, it is their responsibility to match the third of the chords in the accompaniment. This is not always an easy thing to do if the melody is moving quickly with a passing note. However, if the melodic note is held for any duration and it is not tempered to match the correct pitch in the chord it will clash with uncomfortable consequences for those holding the notes correctly. The melody should also match the correct position in the scale for the deviation from equal temperament most notably that of the sixth and seventh scale degrees (see the major scale diagram above).
How does a person learn to place the third correctly at the right pitch? Many of the digital chromatic tuners show the correct position on the meter for the major third with a hash mark at -14 cents (see tuning meter image below). Note: there is also a hash mark for the minor third at +16 cents. The musician must be aware of what note of the chord they are playing be it the root, fifth, or third of the tonality and make the necessary adjustments be it playing an interval of the chord or the melody.
A general rule: the major third, major sixth, and major seventh of the scale are always played below equal temperament.
The most accurate tuning meter is a strobe tuner which will show the correct position for every note of the scale for the tonality for which it is set.
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.
The Minor Scale
The difference between and major and a minor scale is that the 3rd and 6th notes of the scale are flipped. In both cases they are significantly sharper than equal temperament.
Comparison of equal temperament to pure tuning in C minor:
Ensemble Tuning of Major and Minor Chords
The best way tune chords in an ensemble is to establish the root and 5th before adding the 3rd as follows:
- Tune all players on the root to match their pitch.
- While the players are holding the root in tune, add the players with the 5th.
- Once the root and fifth tuning is stable, have the players on the 3rd of the chord enter one at a time, checking for correct tuning before adding another player.
General rule #1: the major third of the chord is always played below equal temperament.
General rule #2: the minor third of the chord is always played above equal temperament.
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. As you can see in the graph below, the lowest notes on the piano are almost 40 cents flat. On this graph, the bassoon’s low Bb is 10 cents flat. The notes below Low F are typically tuned sharp on the short bore bassoon. Playing below the pitch in this register requires special attention to reed tuning and tone production.
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 V7 Chord and Diminished Chords
Tricks of the Trade
What if the Music is Atonal?
When to Play Equal Temperament
The Secret Vibrato
There are times when you are playing a part or a unison with another player and you realize that you are out of tune with that player. What can you do, especially if you know the other player is the one having the problem? First of all, never assume that it is the other player that is out of tune because it may be that your pitch is false. However, if the other player is not tempering the melody to pure tuning then how do you fix it in performance? Note: a discussion or a tuning method technique may need to be discussed with the other player at the appropriate time if they are open to the idea that they may be out of tune. This is not always a comfortable discussion when a big ego is involved.
In the case of the person who is not listening, not making adjustments to just tuning or not matching your pitch, you may think to yourself “this is not working; what can I do?” The answer is the “equalizer” vibrato. Use this technique to cover the distance between your pitch and the pitch perpetrator. Vibrato is made up of two components: pitch and volume modulation. The “equalizer” vibrato eliminates volume modulation and is strictly a pitch change that fluctuates both sharp and flat, masking the problem. This is accomplished by quickly moving the reed in and out of your mouth. I like to call this “the mix master” where I am stirring up the pitch.
Technique: move the bassoon away from you, followed by pulling the bassoon back to you while maintaining your standard embouchure. The reed will be moving in and out of your mouth with a pitch change above and below what would be the normal pitch. In some cases, the recipient who’s pitch you are supposedly matching will get a clue that something is off but you will not be stuck sounding out of tune while you mix it up. It will just sound like a gutless vibrato.
Use of Vibrato When Playing Chords
It is not possible to effectively tune chords in just tuning or any tuning if all the players are using vibrato on a held chord. As in the example above this vibrato masks the correct position and pitch temperament for the notes in the chord. Therefore, it is not wise to use vibrato when holding notes of the chord especially if the vibrato speed is not matched throughout the players holding the chord. The best practice if vibrato is used with a held chord is to have the top voice be the only vibrato sounding.
If players can match the same vibrato then this can be a wonderful musical effect (as in a big band saxophone section) but may not necessarily be the desired effect nor commonly done in orchestra woodwind sections. What often happens, though, is a mishmash of different vibratos sounding at the same time, a hallmark of amateur woodwind sections. However it is not common to match vibratos when the whole woodwind section is involved in a held chord. When you are in the lead you cannot always expect another player to match your vibrato, but you can develop the skill of matching other’s vibrato. For instance, two bassoons or players should be able to match the lead player’s vibrato. It is standard operating procedure that the second chair player matches the principal’s vibrato.
If you are matching with an instrument that sounds above you as in octaves with a clarinet, an instrument that does not use vibrato, it is best to ditch the vibrato and play with a straight tone. The same can be said for the French horn, which also does not use vibrato in most cases.
Pitch is a Moving Target
“Pitch and rhythm are like a moving train: it’s not going to stop to let you get on.” — James DePriest
Solos in a Major Key
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.
Solos in a Minor Key
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! If the reed is failing, it is always possible to use a Long D and Long C# to raise the pitch. However, the C# should actually be lower and the short fingering would be preferred. It’s tendency is to be on the low side.
Tchaikovsky, Symphony No. 5, Movement 1
This solo is in the key of E minor. In this case, the G (minor 3rd) should sound 16 cents above equal temperament on a note that we commonly add the Eb “resonance key” to lower the pitch. With proper reed tuning, the G can be resonant without the resonance key and it’s natural tendency toward sharpness fits the requirement for the raised pitch. Of course it is possible to push the G up with the resonance key on, too.
At letter B, the harmony is a V7 in the key of E minor, a B7 chord where again the G natural should be played high without the resonance key.
Example of Pure V7
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.
Example of Intervallic 6ths
Tchaikovsky, Symphony No. 5, Movement 3
The first two notes of the solo are a minor third followed by an additional minor third. These intervals should be wider than equal temperament followed by a sequence of 6ths. While you might be inclined to play the upward 6th intervals at equal temperament, it will sound better if these are tuned to pure major and minor 6ths. For example, the major 6th interval from B to G#, A to F#, G to E sound in tune when the upward note is lower by 14 cents. The minor 6th interval from F# to D, F (E#) to C# sounds in tune when the bottom note is lower by 14 cents.
Stravinsky, Firebird, Berceuse
This an example of a mix of minor and major thirds in the melodic line. The choice of fingerings can make this sound horribly wrong. The Bb to Db should be fingered with the Long C#/Db to push the minor third up while the Bb to D fingering in the next bar should be the standard two-finger D to help pull the pitch down for the major third.