Ok, all.... grab your popcorn for this one! I couldn't find any popcorn, so I'll grab some noodles.
Intonation... Other than the general sound you produce on your instrument, nothing
matters as much as your intonation does. If you ask me, intonation is part of that same sound concept - it's all part of the "circle of fundamentals" (the 4 T's: Tone, Time, Tuning, & Touch or expression) But, as we are talking about intonation here, I will keep my comments to intonation, specifically.
So, what is intonation anyways? If you look it up, it may say something like this:
the rise and fall of the voice in speaking.
as in "she spoke English with a German intonation"
synonyms: inflection, pitch, tone, timbre, cadence, lilt, rise and fall, modulation, speech pattern.
accuracy of pitch in singing or playing a musical instrument.
as in "poor woodwind intonation at the opening"
the opening phrase of a plainsong melody.
Lets take a closer look at definition No. 1, arguably the most non-musical definition presented (or is it?). If you check out the synonyms we notice many terms used in music (inflection, pitch, tone, timbre, etc.). In fact, most of the terms listed can be seen and used musically. And, they all have to do with how something "sounds". Even the definitional use of rising and falling has everything to do with intonation. Therefore, we can deduce that intonation has everything to do with sound. See where I'm going with this?
Wrap your head around this... a note that sounds good, can be in-tune, and... it can also be out of tune. (I know, head blown!). This all depends on the context of the note played and the instant this note sounds. A note, by itself, is neither innately in-tune or innately out of tune if it is without context (for our purposes. I know, all the "I have perfect pitch" people out there will disagree, but hear me out. I too have perfect pitch, and this all makes sense). It all hinges on the perspective of the listener, when there is no context in which to go by. Intonation is only given this context when the player is playing with others or the player plays a second pitch - in which the interval value we hear between these two pitches sheds context on whether or not the player is in-tune. The funny thing is you can also have a poor sounding note that can be in-tune, or out of tune. The tuner can say you are in-tune, and you may be playing the correct intonation of a chord, but if it doesn't sound good.... then, why play it?
We, as musicians of Western music, tend to think of pitch within the context of A=440 (some orchestras play at 442, some may play elsewhere, but 440 has long been a commonality). So, within this context, each note has a particular value - and this value tells us whether or not we are in tune. Yet, and this is a big one, even this may not tell us if we are in-tune. What happens when playing in a particular key?
Let's use the key of C as an example... You are playing in the key of C, your principal has a C and you have an E. How do we play this note in-tune? If you use a tuner and play this note smack in the middle, it is still out of tune. Why? Because the harmonics that are needed to line up are not lining up properly. To play that E in-tune, you would need to lower the pitch by approx. 14 cents (approx. 14 points lower on your tuner). Only then does this interval sound like it is in-tune - giving off harmonics and a ring in the sound. When we play by ourselves, it's a lot easier to get away with being out of tune like this, but when playing with others it makes a huge impact on the end result. This type of tuning is known as just intonation (a piano uses equal temperament - although even piano tuning is stretch at both ends to obtain a fuller sound). A great book to read on this subject is A Study on Musical Intonation by Chris Lueba. He explains, in great detail, why certain notes should be played a certain way to obtain maximum resonance and intonation, especially when playing in a group setting. Be sure to check out how to play a minor 7th in-tune! I remember when my eyes were opened in a lesson (eons ago) as an undergraduate. My teacher, Mr. Darling (former member of the Cleveland Orchestra) demonstrated and we went back and forth playing a minor 7th in-tune. I was spellbound at the fact that I needed to lower the note a tremendous amount, approx. 29 cents!
Further, where we play any particular pitch in-tune tells us a lot about our playing - how efficient or inefficient it is. For example, if you play a low Ab, chances are that note is flat. What if I told you that this note is not inherently flat? What does this tell you about what you are doing in the lower range? From experience, most people tend to relax their embouchure too much in the lower range, "falling into the low notes", losing focus on the corners. As a result, their low range is flat - which is funny, because it actually assists the intonation with all the other notes! Yes, I'm saying all the other notes have the tendency to be sharp! (I know, mind blown again...). Just think about the fingering positions for these notes (granted that you do no "lip" things in-tune) and it tells you what their pitch tendency is going to be:
0 (open) - hopefully fairly in-tune (yes, the 5th partial will be flat, E, as it should be in a C major triad)
2 - fairly in-tune
1 - slightly sharp (slide not long enough, pull out a little)
12 - sharp (the 2 slides are not long enough, pull out)
23 - fairly in-tune (slide is very close to the correct length)
13 - sharp (the 2 slides are not long enough, pull out a little more than 12)
123 - very sharp (the 2 slides are not nearly long enough, pull out much more than 12)
The amount you adjust depends on a few factors:
2. Your trumpet.
3. The key you are in and the function of the note you play.
With this knowledge, you can now begin to understand what you may be doing to your lower range. Perhaps this is why the lower range does not speak as evenly, sound as vibrant or project as much as you would like. It also explains why it might be difficult to get out of the lower register with ease or once you are out of the lower register, why the other notes may sound "funny" (out of tune). You are collapsing your embouchure in order to play in lower range. I say, the embouchure should be just as firm in the lower range as it is in the upper range. The corners always stay engaged, not matter what the circumstance or register.
The point is this - the trumpet is a compensating instrument. It is not inherently in-tune, quite the opposite. The player must adjust the pitch for a variety of reasons. Sure, you could play in-tune by "lipping" things all over the place, but is this the most efficient way to play? Will you sound the best, throughout your entire range, playing in this manner? If you lip everything, what do you think this does to your endurance? Its difficult to play in the resonant part of a pitch when you have to physically move it into place. Why not just use your tuning slides? Isn't this easier? I'm always amazed by the number of people I meet that never use their tuning slides (particularly college students). Friends, we MUST use our using slides to have a better shot at playing in-tune, at playing more resonantly, at playing with greater ease, at having a better tone, better flexibility, better range.... better everything.
Use a tuner to get a picture of where you play a particular note (but don't live by it, learn to hear better!). Knowing this helps. It's knowledge and knowledge helps greater understanding. From here, try using a Shruti box (a box that produces drones with harmonics - much better than a tuner!). With this, you can further explore, not only the necessity of adjusting, but the amount of adjustments that need to be made in any particular key - just by listening to the resultant tones (the sound/s that are generated by playing well in-tune with the Shruti box. Cello drones are also a great way to experiment with this idea. If anything, it gives you greater insight into how much you need to adjust your slides.
In conclusion, slides are very necessary. The trumpet is just not long enough much of the time. On 4th spaced D, its often not short enough! We need to adjust. Using your slides allows you to adjust and maintain greater balance in your playing, improving your overall game. Perhaps those open E's and send position Eb's are not that out of tune after all.... We need to play in-tune based on the key we are are playing in and the function of the notes within that key.
Some exercises to help improve your tone and sense of pitch:
1. Bending. By bending any pitch down 1/2 step and slowly moving back to the pitch, you will begin to hear where the note sounds the most resonant. For some, it may be lower than you think it should be and for others, it may be higher. Listen for the resonance.
2. Vibrato. Not just any vibrato, but hand vibrato. Use heavy hand vibrato to give you an idea if you are on the most resonant part of the pitch. If you hear "beats" happening, this is the center of the pitch trying to get your attention. Move to the direction of the loudest "beat" and you will notice a huge change in your sound production. Rinse and repeat until you remove these beats - meaning, you are already on the centered, most resonant part of the note.
3. Shruti Box. This is a drone box and can really open your eyes as to playing in-tune with just intonation. It is REALLY easy to hear whether or not you are in-tune. Cello drones are a close second.
4. Breathing. What comes out is only going to be as good as what goes in... so, your breathing can help keep you relaxed, reducing the tension in your playing that may be hindering you reaching a centered and resonant sound, consistently. There are many breathing exercises out there. Find something that works for YOU.
5. Listening exercises. Yes, listen to recordings of great players and ensembles, etc., but also train your ear. The best way to do this is singing - you HAVE to sing. Its the only way to truly know where what you internalize is happening the way you think it is. Sing along with a drone, form chords over them. Have a friend play a drone and take turns forming chords. Get a group together and play some Back Chorales. Not only is this fun, it it is eye opening!
6. Experimentation. Use your slides and experiment how much you need to move them without having to adjust with your embouchure. With experimentation comes experience, with experience comes knowledge, with knowledge comes habit, with habit comes consistency.