TrumpetI started playing the trumpet in my middle school concert band. There was a whole section of

ten or so trumpet players. Non of us sounded good at first. In fact it was a struggle just to be able to play a single note. Learning to play the trumpet, you start on the mouthpiece. The band director had us all try to make a buzzing sound together. Everyone jokes that the buzzing sounds like a duck call. The lips vibrate in the cup of the mouthpiece. It feels funny until you get used to it, like when we used to make farting noises to annoy teachers in elementary school. The lips vibrate hundreds of times a second, so it is no surprise that trumpet playing can tire your lips.

Mouthpiece

The cup contains the vibrations of yourlips and amplifies them. Some of the vibrationsleave through the stem and on to the trumpet.

After learning to buzz a few notes weinserted the mouthpiece into the actual trumpet. The trumpet is one long tube which curls around to give it more length. The buzz that we created in the mouthpiece fills up the whole instrument. The sound travels along the air in the trumpet, guided by the metal walls. The trumpet snaps to the closest resonance to what note you are buzzing. So if you buzz the wrong pitch but with the right fingering, it’seasy to play the wrong note, or chip a note, which makes a noisy, non-resonant sound.

The mouthpiece is precious to a trumpet player. One time in high school band a fellow band member (I hesitate to call him a friend) got a hold of my mouthpiece somehow. He was tossing it up and down like a fool, and he dropped it on the floor of the band hall. I got so angry, because it was going to cause a dent, I punched him in the chest. I am usually not a violent person but a musician feelspain in their own self when their instrument is damaged. Metal can only be reformed so many times before the metal fatigues and it becomes brittle. Maybe you should take this as a life lesson: take care of yourself, or else you will fatigue and become brittle.

Partials

The trumpet plays different notes with the same fingering based on how many oscillations of airpressure fit in the space between the mouthpiece and the bell.

With open fingering (novalves down) you can play manydifferent notes, but not nearly all ofthem. The notes you can play are

Low C, G, Middle C, E, G, Bb (this note out of tune – more flat than it should be), High C, D, E, F …

As a beginner it’s pretty good if you can play the bottom three partials. With more years of experience you can get up to G, and if you practice daily for a few hours (something I didn’t always do) you can play high C. You are hardly ever asked to play higher. After high C, the partials start to blend together and they are only a whole step apart or closer. If you take a break for too long on trumpet you can’t play the high notes anymore. It takes a lot of lip control which you lose quickly. So remember to practice…

A good practice on trumpet is to play lip slurs – using your embouchure to slur through the different partials without changing the fingering. It isolates the lip action from the other actions of playing trumpet – the valves and the tonguing. Another use of partials is bugle calls. All of the bugle calls are played on the same fingering, since the bugle is a trumpet without valves. In fact… I was the bugler in my Boy Scout troop. Troop 952 – I was the first, and the last bugler. I played reveille in the morning and taps at night. There are a host of other bugle calls, such as “swimming,” which tells the Scouts it is time to go swimming. Ah, the simple life of the Scout.

Valves

The valves are there to let you play the notes in between the partials. The valves redirect the airflow through three additional tubes. One of the constants of music (and the wider, scary world of physics) is that a longer tube/ larger resonant cavity means a lower frequency.

The three valves increase the length of the resonant cavity by different amounts.

The first valves takes the pitch down 1 whole step (2 halfsteps).The second valve takes the pitch down 1 half step.The third valve takes the pitch down 3 half steps – but onsome notes you need to bring it down even more, eitherwith the valve slide, or with your mouth.

You might notice a few notes have multiplefingerings that work. There is a standard fingering for allnotes, but in some situations you might want to try analternate fingering to get the tuning and tone right.

Valves are the most critical moving part of atrumpet, so they need to be oiled. Paradoxically, sometimes they stick right after being oiled. For example, inmiddle school in 7th grade, my second year of playingtrumpet, I had a solo. It was only 10 notes. All the notesinvolved either the first or second valve. I had just oiledthe valves, so everything was good to go, right? Well, thesecond valve stuck on the first note, so my solo sounded abit like“Dah, blararahraa blah bleh dat dat dahhh.”

I still remember the exact notes I screwed up, though nothing else about that piece of music. In a way, I suppose it enhanced the experience for me. I was extremely embarrassed for a few weeks. As time goes by, I realize that people make mistakes in solos all the time, and no one could judge a player in his second year for a mistake like that. But as a middle schooler I was extremely prone to stage anxiety.

Tone

Tone is one of the most important parts of being a good trumpet player. It was something I struggled with, and I believe it is the main reason why some trumpet players become great and some do not. Toneis the voice of your sound, it could be bright, scratchy, dark, nasal, blasting, or a variety of other characteristics. These depend on how your lips are vibrating. A freely vibrating lip will give a rich tone,while a constrained lip will give a nasal tones. Practicing tone involves paying attention to how your lips are set, the air you are blowing, and your posture.

Tone of sound is carried by overtones, which are additional, higher frequencies which travel with the frequency of the note you are playing. The overtone series is how you tell different tones apart and alsohow you distinguish different instrument types. If your high overtones are too loud you will sound buzzy or air.

There is no simple way to improve tone – it depends on your individual body – lips, teeth, lungs and mouth. There is only one answer – perseverance.

You may be able to guess that tone was myweakness in high school. I practicedtechnique (tonguing, scales, and lip slurs)too much and didn’t spend enough time onlong tones. I also played too loudly inmarching band, and didn’t warm upenough. Basically my lips were constantlyfatigued in high school, so I had to usetricks such as pressing the trumpet againstmy lips to squeeze out notes. In addition, Iwas nervous about playing well, and life ingeneral, so I held a lot of tension in myshoulders and throat. The final result wasthat my tone was pinched and raspy. Not always, I had some good days. But I was not consistent enough.

Anyway I took a break for about 5 years, and started again. Now that I do not stress or push myself too hard, I believe my playing has the potential to be much better than when I was a foolish high school student. I don’t practice as much as I used to, because life sometimes gets in the way. So it goes.

Percussion

Percussion is one of the most popular choices of instrument for a starting musician. For that reason in middle school and high school bands they limit who can start on percussion to those who have already learned to play the piano. Piano skills aren't really required to learn percussion, but it wouldn't be school if it weren't for pointless rules, now would it?

My friends and I formed a rock/ska band in high school. After every bad performance we changed our name, but one of our best names was The Great Skatsby. The band was me on trumpet or keyboard, Evan on bass, Nick on guitar, and Thanushka on drums. The percussion of a rock back is pretty different from the percussion in a concert band or orchestra. In a rock band you have a snare drum (which is a drum with some metal strings that add a scratchy vibration to the sound), toms (just drums of different pitches), cymbals (metal plates that sound like a gong) and the bass drum, which is played using a foot-pedal that makes a loud thump that keeps the band in rhythm - theoretically, thoughNick could never stay on the off-beats (It’s a ska thing). For a while we were trying out a hardcore stylewhich involved a double bass pedal. The bass drum had two pedals, one with each foot, so the drummer can let loose a barrage of bass beats. For a few weeks I became the singer, singing in a Screamo style. Pretty rough on the vocal chords, and a great way to annoy the neighbors. Back then people were more relaxed though.

Percussion instruments come in two varieties:tonal and non-tonal instruments. Tonal instruments arelike xylophone, marimba, and bells. They can playnotes on the scale and are often laid out like a pianokeys, so it is easier to tell which note is which. Oneexception is the steel drum, which has a Caribbeansound. The steel drum has different shaped panels ona steel shell. Each panel provides produces a certainpitch.

Non-tonal percussion instruments make a non-harmonic sound that doesn’t sound like a specificnote. There are an infinite variety of objects that make

Illustration 1: Structure of Scientific Knowledge

noise when you hit, shake, swing, kick, or do a variety of other actions to them. The possibilities are endless. If you look around right now and started banging on things you will uncover the crazy variety of noises that everyday objects can create. If you do it for too long you might annoy your neighbors, but just tell them it's for SCIENCE; they will understand.

Drums are a common and ancientinstrument. They usually have a tight skin across acylindrical tube. You strike the drum on top of theskin and the skin vibrates, resonating in the tube.Easy? Like most things in science, the answer is“Yes, but...”

Depending on where and how you hit it,and whether you used a mallet or drumstick or yourhand, the drum makes a different tone. Thisdepends on which patterns of vibration are presenton the drum head. Some of the common ones areshown below. Generally the ones with moreoscillations on the drum head or higher pitched. The pictures are different from a harmonic series (created from plucking a string and a variety of other toned instruments) - they are closer together so instead of sounding like a clear thing like a bell instead the sound is a like a thump.

You can control which resonances are present in thesound by placing your hand on the drum head in differentplaces, striking the drum in different places or withdifferent mallets. Again the possibilities are endless.

Any reasonably solid object will have differentspectrum of frequencies when it is struck. For example, theaptly-named triangle. It produces a disconnected series offrequencies so you can't decide what note it is. Instead it'sjust a high ding.Consider the cowbell which creates apartially pitched partially dull clunk. Always remember,more cowbell. Unless you are a cow. Recent research suggests that many cows suffer hearing loss because they have to listen to cowbells all their life. Better than being a whale though, subjected to constant 24/7 sonar pings. Imagine you are going about your day and every few seconds you hear PINGGGGGGGGGG. How would that make you feel? It wouldprobably make you PINGGGGGGGGGG. Oh hi, Mr.Submarine, how are you PINGGGGGGGGGG.

Woodwind instruments

My first encounter with woodwind instruments wasblowing across the top of soda bottles. This is another good wayto annoy your friends, teachers, and neighbors, but for science no

Illustration 3: Some resonance patterns of a circular drum head

Illustration 2: Blocks of a xylophone. The frequency increases with decreasing length, in fact proportional to the square root of length.

Illustration 4: A triangle. The triangle has a triangular shape.

price is too high. The air cutting across the edge of the bottle creates eddies which excite the resonance of the bottle. A secret – if you blow very hard you can probably excite the second harmonic of the soda bottle which will really annoy everyone around you. It is a very loud and high-pitched noise. It's pretty hard to get the third harmonic, though it is theoretically possible if you blow very hard.

My parents bought me a flute at some point in high school. I used topractice it. One of my goals was to learn to play in the key of E since I learntrumpet in the key of B-flat and it is the farthest key from B-flat so I would beable to play naturally in a wide variety of keys. That was the goal – hard tosay if I succeeded, though I am pretty good at transposing (playing a song in adifferent key from what it’s written in.)

Like a bottle the flute makes a noise by blowing across a mouthpiece.The holes of the flute control the length of the resonant cavity. Closing holeslengthens the cavity which decreases the pitch. Then, if you blow harder theflute skips up an octave as it fits another oscillation in the resonant cavity,doubling the frequency. Then you start over the fingering pattern in the newoctave. If you blow even harder the flute jumps up a fifth, as it fits the thirdresonance into the flute’s resonant cavity. So, by combining the fingerings andblowing strength you can play in all of the octaves of the flute.

In high school we used to wad up paper and blow it through our mouthpiecesat the flute section. It was not very nice… but they probably deserved it.Always playing high notes.

Other Woodwinds have 1 Reed: clarinet, saxophone2 Reed: bassoon, oboe

The clarinet sounds smooth, like what a snakecharmer would play. The oboe sounds exotic. Thebassoon sounds woody, like something a tree elfmight play. The saxophone sounds soulful, likeunder a streetlight deep into the night. Theseinstruments are similar to a flute, but they use areed or two reeds to produce sound instead ofblowing across the hole. They create differentovertones so the tone sounds different.

Illustration 5: Blowing across a soda bottle excites the first resonant mode.

Illustration 6: Blowing with increasing ferocity across asoda bottle excites higher modes which have a higher pitch and are louder.

My friend in graduate school was a clarinetperformance major. Those were the darkdays when I still thought being a scientistwas a reasonable career choice. He and hisfrench horn playing friend invited me toplay with them in a performance of TerryRiley’s In C. It’s like nothing you’ve everheard. It is from an older time when peoplehad original thoughts. All musicians playfrom the same part. Each person repeatseach measure until they deem it appropriateto move to the next measure. The entireband runs through the 70 or so measurepiece at their own pace. Then, aftereveryone has had enough of the lastmeasure, the piece is over. Quite anexperience. It was the first performance I had done in a few years. It just goes to show that even in yourdarkest hour (i.e. graduate school), music will be there for you.

Music Theory

Music tugs at the heartstrings. It lifts the soul. You can tell a story, evoke an emotion, or ease our pain. But I am a curious man and I can't help but ask why? Why, why, why? Unfortunately there is no comprehensive theory as to why music affects people the way it does, not yet. Aside from a few basic observations: “Minor scale sounds sad,” “Major scales sound happy,” “Screeching violins sounds scary,” there isn't a whole lot known in a general sense about emotion in music.

Music seems to progress organically with each composer taking ideas from those before him or her. Movie soundtracks often take bits of melodies and chords from classical music, which in turn borrowed them from earlier, more traditional forms. In many ways music evolves like a language or like the techniques of painting, depending on history, contact with other cultures, and the personalities of people of the time. Do you think your favorite band is the most revolutionary thing out there? we'll let me tell you, 95% of what they are doing has been done before in some form. Like the old saying goes, “There is nothing new under the Sun,” or more accurately, “There is not a whole lot new under the Sun.”

Still there always be new things to do the music, mathematically. The human race (or any type of an alien, or artificial intelligence, or dolphins, or whales, or some other intelligent species, maybe capybaras) could never write all the songs that could ever be written. So, there will always be room for originality.

I was always messing around with music theory. In band class I would figure out the other notesof chords and play them instead of the one I was supposed to. One benefit of high school band – there are usually bigger things for the director to worry about than one trumpet player playing the wrong (butin the chord) note. I took a music theory class my first year of college, unfortunately the music theory

Illustration 7: Some of the flute fingerings, with the resonant modes shaded in.

education system has gotten an unhealthy obsession with four part chorales. This is a chorale sung for four voices, like those in church hymnals. Every day it was chorale this, chorale that. In retrospect it isn’t particularly surprising – while chorales may be woefully old-fashioned, at least the assignments are easy to grade. So it goes.

Theory of Western Music

Western music is what we in the West to listen to (and what everyone else with an internet connections to listen to also). This is in contrast with traditional forms from other cultures such as Native American, Indian, Chinese, Balkan, African, etc... which use different scales and rhythms.

A scale is a certain number of notes which span an octave, and determines which notes should be played in a piece of music. The oldest most traditional scales are pentatonic scales – 5 note scales – Learn these and you can noodle for hours on guitar, annoying your more snobby guitarist friends. Thesescales are also the backbone of the blues scale, which is a pentatonic scale plus some bent notes. The pentatonic scale can extend infinitely upward or downward always giving notes to play in any octave.

Illustration 8: C major pentatonic scale in 4 octaves. This scale contains the sequence of notes: C, D,E,G,A

The starting phrase of the Fanfare for the Common Man by Aaron Copland is in a pentatonic major scale. Here it is transposed to C. Aaron Copland was right to use the pentatonic scale in the Fanfare for the Common Man, since the pentatonic scale is one commonality that is widespread in many cultures musical traditions.

Full major and minor scalescan be constructed by adding twonotes to the pentatonic scale.

C D E F G A B C - C majorscale, adding F and B to the Cmajor pentatonic scale

D E F G A Bb C D - D minorscale, adding E and Bb to the Dminor pentatonic scale

In elementary school music class they unleashed us on their collection of tonal instruments – xylophones and marimbas mostly. The rule was to remove the Burgers and Fries – Bs and Fs. Little did

Illustration 10: First three measures of Aaron Copland's Fanfare for the Common Man, transposed to the key of C.

Illustration 9: D minor pentatonic scale in two octaves. This scale contains the sequence of notes: D, F,G,A,C

we know, we were being confined to the C major pentatonic scale. Since all notes on the pentatonic scale sounds good with every other note, we could only play consonant music. Kind of a shame really. If we had discovered how bad B and F sound together we could have caused some real trouble. This interval, B to F, is called a tritone – also known as the devil’s chord. It is simultaneously the most offensive and the most dynamic chord in Western music. So how about that?

If we split the major and minor scales further we get the chromatic scale which contains all notes (that Western instruments are designed to play). The notes in the cracks are written either with a sharp up from a lower note or a flat down from a higher note. Each note can be written in multiple ways.

If you want to get technical there is also double sharp and double flat. So, you could write a scale in thekey of E# if you wanted to use double sharps (and some composers do, just to confuse you. They would call it “correct spelling”, but they are really just showing off.) Here is Twinkle Twinkle Little Star in creative notation.

Is learning scalesimportant? I'm not sure. Allyour band director and lessonteachers are going to tell you tolearn them and you will have toplay them for auditions. Do theyhelp you play better? I'm notsure? Some of the famous rockor jazz musicians barely knewany music theory. For me musictheory is interesting in its ownright, and I'm well aware thatlearning it probably won't makeme a better player. I'm also aware that it isn't interesting to everyone. Hopefully I can share with you some of the things I enjoy about music theory, and if not, c’est la vie. That is French for “that is life,” or in the classic war novel Slaughterhouse Five, “So it goes.”

We talked about major minor and pentatonic scales but there are a lot of scales. Each different scale has a different feel. Here is a list of the scales whose names start with A-E taken from the wikipedia page: Acoustic scale, Algerian scale, Altered scale, Augmented scale, Bebop dominant scale, Blues scale, Chromatic scale, Dorian mode, Double harmonic scale, Enigmatic scale...

Illustration 12: Twinkle Twinkle Little Star, written in maximally confusing notation.

Illustration 11: Chromatic scale. Notes written aboveand below represent the same pitch, using a differentnotation. Each note can be written in multiple ways.

Representing Sound on Paper

There are at least four ways to represent sound which are used for different purposes. The familiar one is musical notation. Notes are graphed on a staff, usually five lines, but sometimes a different number. Lines and spaces each mean a different note. Going up on the staff means higher pitch.

The length of a note depends on the head – filled in or open – and the number of crosses on the stem. The notes are divided into sections of 2.

Another way to write is in the piano roll notation – which is a frequency vs. time graph. Distance horizontally means the note duration and vertical position is the pitch.

Illustration 13: The length of notes and rests is indicated by the shape – the note head and how many crosses are on the stem. Rhythm of Safety Dance by the Men Without Hats is indicated.

.

Waveforms are time versus amplitude graphs. This is a graph of air pressure over time, which is the format sent to speakers while playing music.

Frequency versus amplitude graphs show which pitches are in a sound including overtones.

Time versus amplitude and frequency versus amplitude graphs are mathematically related by the Fourier transform. It converts time-amplitude information to frequency-amplitude information. Time – amplitude graphs are good for seeing impulses, entrances and ending of notes, and the overall loudness of a sound. Frequency-Amplitude graphs are good for seeing what notes are in a chord and overtones

Time – frequency graphs show both at the same time. Therefore they are very useful for visualizing dynamic sound files and pieces of music.

Graphs are your friend. If you can learn to use them for your own purposes, you will gain great power.

Resonant cavities

At some point in my life I made the foolish decision to try to become a scientist. I thought that my work would have a meaningful impact in this troubled world. I like music but I felt being a professional musician was a frivolity in our chaotic civilization. Music will save us? How? On the face of it, music is a form of entertainment. Science has the concrete power to transform civilization.

But I became aware over the years that the life of a scientist as one of relentless, intense work, high stress, and low appreciation. Not for me. Possibly the situation will improve in the future, but possibly not. The year I left graduate school, 11 other students in my class also left. In fact over 50% ofall STEM students (Science, Technology, Engineering, and Mathematics) leave the field so I am actually in the majority.

Anyway, before I realized this I found myself living in the forested mountains of Los Alamos, reading The Hunger Games series by Suzanne Collins while performing measurements on a resonant cavities. The resonant cavity was an enclosed box lined with copper that reflected electromagnetic waves (microwaves) and its insides. I learned of the different modes of oscillation that can fit inside a resonant box.

Illustration 14: Some uses of pie charts and bar graphs

You might see a pattern fromthese images – a rectangular cavitycontains oscillations in thehorizontal and vertical dimensions.These modes of the same modes thatone would find on a squaredrumhead. Too bad I've never seenthe square drum.

So there I was sitting in a labin the middle of the mountains inNew Mexico. I realize now how areunique an experience that was andhow few people have seen what Ihave seen. Most of the day I was notbothered in so between readings Iexplored the warehouse I worked in.It was full of discontinuedexperiments. Extremely technicalsetups that must have takenthousands of hours of work to build.

These are the relics leftbehind by the scientific method. Experiments that never led to a definitive result and languish encounters warehouses. Their technicians have long ago moved on and have forgotten about them. What does it mean? We should all take a moment of silence to contemplate unfinished experiments; these tools which were precisely constructed for one specific purpose that is no longer desired.

So anyway, I finished the whole Hunger Games series while measuring resonant modes. I wrotea paper about it, too. It is currently being held up by some lawyers, so it has not yet been published. Still, it feels good that I contributed to the scientific body of knowledge. I assume it will be published in the next decade or sooner. For now I have left the life of a scientist behind. The moral of the story is that resonant cavities have different modes that can live inside them which make up their spectrum. Theother moral about the nature of scientific research and how to choose a career, I haven’t figured that one out yet.

Illustration 15: Transverse Electric Modes of a rectangular resonant cavity. The shaded regions are regions of high magnitude electric field. These modes are the same found on a square drum head, where the shading represents maximum distance of motion of the drum head skin.