I recently started playing the trumpet my first brass instrument and I got a tuner to help with practice. I got istrobesoft by Peterson on android, it got a display of its real time spectrum analysis but I don’t quite understand how to read it. That is to say what is the desired result for a good tone. It doesn’t have to be specific to istrobesoft. I want to know in general how do you use a spectrum analyzer for practice, what to look for and what it means.
There's tone, then there's tone!
The pitch of a note is often called its tone, meaning is it in tune or not.
The timbre of that note is called its tone, and will vary from player to player, instrument to instrument.
While a tuner will be capable of checking the former, it certainly will not be able to check the latter.
However, one's ears should be able to do both! And certainly should be the articles used when playing any instrument. Relying on a needle or flashing lights may help if one is 'tone deaf', but that's a rare condition. Get used to listening (a muso's best skill) and adjust accordingly. Recording is a good secondary check: most beginners find it difficult to multitask, as in play and listen simultaneously. That comes with experience and lots of critical practice.
So, use the tuner sparingly, and use those ears a lot!
That apart, there are many other aspects of trumpet playing to concentrate on - reading, tonguing, embouchure, to name only three! And no super-fabulous tuner is going to be of much help there, either.
Maybe that's nitpicky: but a tuner and a spectrum analyzer are fairly different things. A tuner will measure the frequency of the fundamental with very high precision. That will tell you if you are in tune.
A spectrum analyzer will give you a real time view of the fundamentals and the harmonics (or over tones). That's more related to tonal balance and timbre and not to precise pitch. This is actually a very interesting method to observe how different ways of playing affect your tone. For example if you play a note on the bass you can plucking with a finger, with a pick or slap with your thumb. Either one will give you the same pitch on the tuner but will look quite different on a spectrum analyzer.
I want to know in general how do you use a spectrum analyzer for practice, what to look for and what it means.
I will answer that in two parts: the first part is what a spectrum analyzer does, the second part will be why you can't use it for your purpose.
What does a spectrum analyzer do?
There is a mathematical proof that every - really every - curve (said in a very un-mathematicalway: every line you can draw on a piece of paper) can be constructed by adding (a countable number of) sine waves. This was actually found in the 18th century by french mathematician Charles Fourier. This is called the "Fourier-transformation".
Since one can construct any curve by adding sine waves one can also do the reverse process and dissect any curve into the sine waves which - when added - would create this curve. This is called Fourier analysis and comes in two forms: continuous and discrete. Basically, the continuous form is for regularly recurring curves, which repeat a certain pattern over and over. The discrete form takes a certain part of the curve, pretends that this one pattern, does a Fourier-transform, then takes the next part and repeats the process. This is for curves which change over time. Read more about it in Wikipedia. Since tones are basically sine waves (see below) it is easy to see how that relates to music.
A spectrum analyzer now is a device which does such a (usually discrete) Fourier transform of an input signal and displays the results. The input signal is most times an electrical signal, but any other signal (including acoustic signals) can be used too.
What is a tone?
Tones are - in theory - sine waves. The frequency is responsible for the pitch, the amplitude is responsible for the volume. Still, if this would be the case, how comes we can distinguish different instruments? How comes we can tell if the same tone is played by a guitar, a trumpet or a violin?
There are three things which make all the difference: overtones, noise and ADSR.
ADSR (short for attack - decay - sustain - release) or "envelope curve" is the change of a tone over time: you pluck a string on a guitar and the tone develops (attack), stabilizes (decay), sounds out for some time (sustain) then starts to fade (release). It is easy to see that this characteristic looks different for instruments like e.g. guitar (the string is excited once) and violin (the string is excited constantly).
noise is also a part of musical events. For instance, if a bass guitar is not plucked with the fingers but "slapped" with the thumb part of the sound is the produced tone and another part is the noise of the string hitting the fretboard, which, in sum, produces the characteristic sound of "slap bass".
overtones: and lastly we come to the meat of it. A tone in theory might be a sine wave, but a practical tone produced by a real instrument is a base tone (so-called "fundamental") and a whole bunch of overtones, so-called partial harmonics. See also Wikipedia for more.
How an instrument "sounds" depends (aside from the noise and the ADSR) on what overtones are stronger and less strongly emphasized. How much of each overtone gets into the produced mix. This is also called the "colour" of the tone. Noticeable differences are not only between different instruments but also between individual instruments of the same sort and even different players, which is why experts are able to distinguish e.g. a Guarneri violin from a Stradivari or how they can hear if, say, Chet Baker or Miles Davis plays the trumpet.
Why you should concentrate on other things
Above I said that spectrum analyzers dissect a sound signal into sine waves - "pure" tones, as we learned - and display these results. Why shouldn't that help you: first, because what we hear (and what we feel hearing it) is much too complex to express it in mathematical terms. Yes, it is possible, but ten pages of some Riemann sums and other really difficult mathematical expressions will only partially convey what "this is a warm tone" says. Guess, which one is easier to comprehend.
Therefore the display of a spectrum analyzer will be about as helpful for you as a mass spectrometer output will be for a cook. Look at this and tell me if more salt needs to be added. If you want to know where a thrown ball is going to land you can start to calculate parabolic curves - but little children have been known to register on the target even without knowing what a "function" is.
Your brain (with the ears connected to it) is a fantastic device for integrating information. It might paint over many of the details a spectrum analyzer will provide, but it will tell you "good" or "vibrant" or "shaky" or "bad" where the former will give you hundreds of details leading up to that judgement but withhold exactly this. Lastly, though, you aren't interested in knowing if there is more or less volume in the 800Hz-1.2kHz band - you want to know if your tone is "bright" or not. The spectrum analyzer will tell you the former, your ears will give you the latter. Trust your ears.
PS: If you happen to be a sound engineer and need to tweak audio recordings then this (a "Fast Fourier Transform" system) is exactly what you need. These guys need the underlying details, not only the integrated judgement the brain provides. But you, being a musician? Not so much ....