Brass Instrument Intonation/Tuning Guide Background There are a number of things to consider about how sound works that will aid you in being able to play with better intonation. The purpose of this guide is give you the information necessary to understand intonation so you can truly play “in tune.” First, we’ll cover the difference between Equal Tempered and Just Intonation, then cover the natural tendencies of the instrument. After that, we will talk about the adjustments needed for chord tones in order to play them in tune. Finally, we’ll put it all together and look at how you, as a player, need to adjust to be a part of an ensemble. This guide contains quite a bit of the technical and very detailed information. That is to give you a better understanding of how everything functions - but what you need to take away from this is an understanding of the general adjustments you’ll need to make while playing. You’ll find that you are probably doing a lot of this stuff already as an experienced musician - but now you’ll get why you need to do it!
Equal-Tempered vs. Just Intonation The first thing to know is that nearly all tuners are built around “Equal Tempered Tuning.” Equal Tempered Tuning was invented so that pianos and other keyboard instruments would sound reasonably in-tune regardless of what key was being used. The octaves are set in tune, then the 11 notes between the octaves are evenly spaced with an arbitrary “100 cents” between each. This conflicts with natural acoustics, also known as “Just Intonation” or “Pure Intonation.” In Just Intonation, there are only 386 cents between C and E, rather than the 400 cents between the C and E keys on a piano (see example below). If you play wind instruments tuned to Equal Tempered Tuning, you will actually be out of tune and hear the “beats” in the sound. Those beats are a byproduct of sound waves that are not moving at the same frequency and are thus air molecules vibrating at conflicting rates. Throughout this guide, when you see adjustments to intonation, they are in reference to a standard tuner’s Equal Tempered calibration.
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Natural Acoustic Tendencies The next thing to discuss is the natural intonation tendencies of your instrument. Assuming that you are playing with a good embouchure and proper air support, the open notes (also known as the overtone series, or the partials) on your instrument will have some variance from 0.0 cents on the tuner - those variations are show in Table 1 to the left. Table 1: Natural pitch tendencies of the overtone series Tuba/Bari
Trumpet/Mello
Natural Tendency
High Bb
High C
In Tune (sometimes drifts flat due to air)
High Ab
High Bb
31 cents flat
High F
High G
2 cents sharp
High D
High E
14 cents flat
Middle Bb
Middle C
Tuning Note
Middle F
Middle G
2 cents sharp
Low Bb
Low C
Fundamental: In Tune
Pedal Bb
Pedal C
(Drifts sharp)
Each variance that you see is the natural, acoustic tendency of those pitches in relation to the fundamental pitch of your instrument. If you play with a comfortable, well-formed embouchure, not every tone will sound at 0 cents/“in tune.” This is actually correct! As an example, take the “middle F” for the baritone (show in the example to the right). This note will naturally drift two cents sharp. In order to play this note “in tune,” you must “lip” it down slightly. You can assume that any valve combination that comes from each of those open notes will have a similar intonation tendency.
These references and adjustments apply only to cases where these pitches are the root of the chords being played at the time. We will get to that part momentarily.
Brass Instrument Overtone Series
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Tuning Your Instrument with Itself Now that you understand how your instrument’s acoustic tendencies work, we’ll next go over how to adjust the slides on your valves. It is important that not only is your main tuning slide easily moveable, but the slides on each of the valves, as well. The slides on the instruments are naturally built such that, if they are all the way in, they will be sharp in comparison to the fundamental of the instrument. Your job as a musician is to first start with an instrument that is in tune with itself. 1. Tune your tuning note - Middle Bb on baritone/tuba or C on trumpet/ mellophone. - to 0 cents on a tuner. This will get you into the ballpark to start. 2. While sustaining your tuning note, depress valves 2 and 3. Adjust your third valve slide (It will need to come out) until your tuning note (Bb or C) has the same intonation whether it is open or played with the valves. 3. Now move to Middle F (baritone/tuba)/Middle G (trumpet/mellophone). Ensure you are playing in tune (0 cents) by adjusting your embouchure (not the tuning slide - remember, the fifth of the instrument is naturally sharp to begin with). Continue sustaining that pitch while depressing valves 1 and 3. You will need to now pull out your first valve slide to bring that pitch down to match. Check that your intonation matches, whether the valves are open or closed. 4. Finally, check to see that smaller intervals sound correct. Playing your tuning Bb, then pressing first valve (to go down to Ab) should sound like “re-do” of a major scale. F to Eb should sound the same way. Continuing down, Ab-G-Ab (1-12-1) should sound like “do-ti-do” of a major scale. Playing an F, then up to Gb (valves 2 and 3) should be a half step up, also as in “ti-do” in a major scale. Lastly, check your low Bb (open) to B natural above is (1-2-3). This should also sound a half-step up. If all of your slides are adjusted appropriately, you should feel a minimal tendency to need to “lip” any notes up or down. Once your instrument is in tune with itself, the next step is knowing the necessary adjustments in order to play chords in tune.
Tuning Chords
When playing a chord, the goal is to combine tones that sound harmonious together for a combined sonorous effect. Sometimes the harmonies are consonant, sometimes they are dissonant. In either case, as long as the tones are all properly in tune (with Just Intonation), those chords will still retain the harmonious effect. If each tone is played at 0.0 cents to Equal Tempered Tuning, the chord will not sound in tune; that is, you will hear beats in the sound.
Brass Intonation Guide
Using Table 2 to the left as a guide, you can see what adjustments are needed to intervals above the root of the chord in order to play that part of the chord properly in-tune.
Table 2: Pitch adjustments for intervals above the root of a chord Interval
Adjustment
Octave
0
Major 7th
-12
minor 7th *
+18.0
Major 6th
-16.0
minor 6th
+14.0
Perfect 5th
+2.0
Tritone
-10.0
Perfect 4th
-2.0
Major 3rd
-14.0
minor 3rd
+16.0
Major 2nd
-18.0
minor 2nd
+12.0
Use a Bb Major chord as an example. The three tones in that chord are Bb, D and F. Bb is the root (the name of the chord), D is a major third above the root, and the F is a perfect fifth above the root. Regardless of what instrument you play, if you are playing the root of the chord (Bb on Tuba or Baritone, F on Mellophone and C on Trumpet), you want to adjust your pitch so the Bb is 0.0 cents on an Equal-Tempered tuner. If you are playing the fifth of the chord (F on Tuba/Baritone, C on Mellophone, G on Trumpet), you will need to raise the pitch slightly, to 2 cents sharp. If you are on the third of the chord (D on Tuba/Baritone, A on Mellophone, E on Trumpet), you will need to lower the pitch by 14 cents in order to play in tune.
If you are using a standard tuner that gives you a spectrum of cents sharp to flat, with an indicator for “in tune” at zero cents in the center, you have probably noticed small tick marks to either side of the 0 cents mark. Those t i ck m a r k s correspond to the interval adjustments above and below 0 for the Major and minor thirds and sixths. (See Table 2)
* Note on the above chart:
There is discrepancy on the frequency of a proper minor 7th which comes from different mathematical formulas used. The two most common results are either 18 cents up or 29 cents down. As the 29 cents down is an extremely large adjustment, it is accepted to raise this tone according the 18 cent adjustment.
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Next is the part of putting it all together - where all of the above processes need to be considered. Use the following two examples to see how it works.
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How to Adjust Members of a Chord In this first example, we see a typical chord in the key of Bb. Let’s start from the bottom and work our way up. In this example, the tuba has the root of the chord, and this corresponds to the tuba’s tuning note, so it will be in tune: no adjustment is needed.
Example 1: Bb Major Chord
The baritone has three pitches: the lowest, F, is the fifth of the chord. This will naturally be in tune, as the 4th line F, on baritone, naturally sounds 2 cents sharp. No adjustment is needed. The middle note for the baritone is also the tuning note and the root of the chord. Again, no adjustment needed. The top pitch for the baritone, the D, is the third of the chord and will naturally fall 14 cents flat. This is correct for a major chord (compare Table 1, natural tendencies, with Table 2, necessary adjustments). No adjustment is needed!
In the mellophone, there are two notes. Due to the mellophone’s transposition, we actually find that the bottom note for the mellophone is the root of the chord. Because it is the root, it needs to be at 0 cents to Equal Tempered Tuning. However, this note comes from the Middle G partial, which is naturally 2 cents sharp. The mellophones will need to slightly lower this pitch, either with a slight embouchure adjustment, or by slightly kicking out the 1st valve slide with the thumb trigger. The mellophone’s upper note is the third of this chord. The third needs to be lowered 14 cents to be truly in tune. As the A is played as a derivative from the tuning note (middle C, naturally at 0 cents), the total adjustment is simply 14 cents lower. For the trumpets, we find the bottom note is the third of the chord, and this E comes from the middle G (the fifth of the horn). Since the G is naturally 2 cents sharp, and we need the E to be 14 cents flat, you will need to adjust this E a total of 16 cents from where it will naturally occur. The middle note for the trumpets is G. This is also the fifth of the chord. Its natural tendency to play 2 cents sharp puts it in tune already. Likewise, the trumpet’s top C is the root of this chord as well as the fundamental of the instrument. It will naturally play in tune.
This above example is designed to be pretty close to about as perfect as it gets. Which is rarely how music actually happens. So let’s take a look at a second example that has more considerations.
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In this next example, we now have an F7 chord in the key of Bb. First, we need to identify the parts of the chord: The root of the chord is F The third is A (a major third above F) The fifth is C (a perfect fifth above F) The seventh is Eb (a minor 7th above F) Working through this again, from the bottom to top, we find the tuba has the root of the chord, which needs to be at 0 cents. Since this is the fifth of the horn, it will naturally be two cents sharp and will thus need to be slightly lowered. In the baritone voice, the lowest note, A, is the third of the chord. This needs to be lowered 14 cents. Since the A is derived from the tuning note (naturally in tune), the total adjustment is 14 Example 2: F7 Chord cents lower. The middle note for the baritone is the fifth of the chord, which needs to be raised 2 cents. The C here comes from D, which is naturally 14 cents flat, so the total adjustment will be 16 cents higher. The top note in the baritone voice is F. This is the root of the chord, which needs to be at 0 cents, but the natural tendency is 2 cents sharp. This note will need to be lowered two cents. In the mellophones, the lower note, the E, is the third of the chord. The third needs to be lowered 14 cents, but in this case, it falls on the natural third, which is already 14 cents flat. No adjustment is needed. Likewise, the mellophone’s upper note is both the fifth of the chord and the fifth of the instrument. It naturally falls 2 cents sharp, which is correct.
For the trumpets, the lowest note, D, is the fifth of the chord and comes from the E partial. The partial itself is naturally 14 cents flat, but the chord tone needs to be raised by two cents. So, in this case, the total adjust to raise the pitch 16 cents. The next note for the trumpet (second from the bottom) is the seventh of the chord. The minor 7th needs to be raised 18 cents. In this case, the partial from which the note comes is naturally 2 cents sharp, so the pitch will need to be increased 16 cents from its naturally occurring tendency. The next trumpet note, G, is the root of the chord in this case. As it falls on the fifth of the instrument (naturally 2 cents sharp), it will need to be lowered 2 cents. The last note, the top trumpet note, B, is the third of the chord. As it comes from the fundamental tone of the instrument, it will naturally be at 0 cents. Since the third needs to be 14 cents flat, this needs to be adjusted a total of 14 cents lower.
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Tuners Finally, there are many options for tuners to use out there. Some are standalone pieces of equipment, be they pocket tuners or larger, desktop strobe tuners, while others come in the form of an app for your smart phone. Without specifically endorsing any one type of tuner over another, as there are many which are useful and appropriate, a very strong recommendation goes toward the smart phone app called “Tonal Energy.” This is a paid app (approximately $3 on the iPhone App Store), and is worth the investment. This tuner app will allow you to tune chords in addition to individual notes. It “listens” to the entire harmonic texture to find the chord. It can be adjusted to Equal Tempered Tuning or Just Intonation. So, if you set it to Just Intonation and it hears you’re playing the 3rd of the chord, it will tune you to a natural third, rather than the Equal Tempered - no math needed! Additionally, Tonal Energy allows you to record your practice sessions and provides continuous, real-time feedback on your intonation.
Conclusion There is a lot of information and a lot of detail contained in this guide. While some of it may seem complex, it does provide you with a solid and thorough summary of the necessary acoustic knowledge needed to be an excellent musician. Each step along the way is important - knowing what your instrument’s tendencies are, adjusting the instrument to be in tune, and finally finding your relationship in the overall harmonic structure of the ensemble. The best way to learn this information and how to apply it easily is to learn to tune without a tuner. Use a tuner at first to get the mechanical help to be in tune, but make an effort to listen to what you are playing while hearing how the color of the sound has a pure, harmonious quality. Once your ears have adapted to what good, in-tune playing sounds like, you will naturally be able to make adjustments without having to think through the entire process.