A B Sinusoid D E F G 🎶 (part 2)

A B Sinusoid D E F G 🎶 (part 2)

In the previous post [1] we established how sounds and notes works. We also explained the functioning of some of the most famous instruments: guitars and pianos. These two are part of string instruments, one of three instrument families. The other two families are going to be describe in this post: wind instruments and percussion instruments. There is still one other question remaining that we will answer: why instruments making the same note sound so different?

Hit music, literally

Percussion instruments produce music when being beaten or scraped. Depending on the method, we can differentiate several kinds of instruments.

Membranophones are instruments where an acoustic membrane is beaten. Drums, djembes and kazoos are membranophones. The frequency of the sound depends on the tension of the membrane. Membrane vibration is the 2D equivalent of the string vibration we have seen last month [1]. Fun fact: an acoustic membrane is also used in microphones to capture sounds and in speakers to redistribute sound.

Example of 2D membrane vibration of a circular drum head, Oleg Alexandrov

With idiophones, it is the instrument itself that vibrates producing music. They make sound either when you hit them directly with the hand or a stick (triangle, chimes, xylophone) or when you shake them (bell, maraca).

Some percussions are also categorised as string instruments (piano) or wind instruments (sifflet).

Wind makes music

For wind instruments, the note is determined by the air vibration frequency inside a pipe. It depends on the air pressure inside the pipe and the pipe’s length. We distinguish two kinds: brass instruments and woodwind instruments. Don’t be confused by their name, they are not necessarily made from the said materials but designs how they make sounds.

In brass instruments, the lips of the player vibrates causing the air to do the same with a sympathetic resonance. The length of the signal, the frequency, is changed thanks to keys, slides, piston valves or crooks.

In woodwind instruments, we also have different categories depending on how the sound is made. With flutes you blow air into a cylindrical tube which will split and then vibrate with the closed cylinder (organ pipes, ocarina) or with a hole at the end of the cylinder (panpipes). With reed instruments you blow in a mouthpiece that makes the reed vibrates. You can have a single reed (saxophone), a double reed (oboe) or a combination of both (bagpipes).

The voice, a forgotten instrument

Voice is also an instrument, the first one there was, even if it is often not considered of one. It is classified as a wind instrument but also uses membrane vibration.

Air is sent from the lungs through two vocal cords (or vocal folds, more suited term due to their membranish form) vibrating and is amplified by resonating with the rib cage, the pharynx, the mouth and the nasal cavity which increase the intensity of the sound. The frequency however depends on the contraction of muscles in the larynx which changes the tension and the deformation of the vocal cords.

Four different mechanisms exist depending on how you use your larynx [2]. Laryngeal mechanism 0 corresponds to “vocal fry”, “pulse” or “strohbass” register and produces lowest tones thanks to short, thick and slack vocal cords. Men use it for speech. Laryngeal mechanism I corresponds to “chest” or “modal” register for both men and women and “head” register for men. Mechanism II however is the “head” register for women and “falsetto” or “loft” register for men. Speech and singing both use mechanism I and II. Mechanism III is “whistle”, “flageolet” or “flute” register and produces the highest tones. Here, the vocal cords are thin and very tensed.

Thanks to this variety of mechanisms, the human voice can go from 60 Hz to 1500 Hz. A glissando (a progressive transition from one frequency to another) can show more clearly this mechanisms.

Glissando showing the different mechanisms of the voice
Illustration of the four laryngeal mechanisms on an ascending glissando sung by a soprano [2]

Sonority is a matter of complexity

The same note played with different instruments has different sounds. It is because reality is not as simple as theory.

The first clue comes from guitars and pianos which plays several notes at same time, called chords. We have a combination of notes and frequencies with a dominant one that gives the general frequency. We call that a complex sound, in opposition to pure sounds which is a single note.

But what about instruments that can only play one note at a time? And even with guitars and pianos, the same note between the two still sounds different.

Well, it is still linked to complex sounds, but with a different origin. An instrument creates a vibration in the air going from one medium to another, going through the different parts of the instrument. This will slightly change the shape of the sound pattern [3]. The sinusoid gains fluctuations, looses smoothness, creates a more complex sound, while still keeping the same frequency corresponding to the wanted note (see the following figures).

C3 (260Hz) played by an organ pipe
Organ pipe playing a C3 (260 Hz) [3]
C3 (260Hz) played by a violin
Violin playing a C3 (260 Hz) [3]

Next time you hear someone play an instrument or your favorite song at the radio, try to keep in mind the complexity that comes from basic acoustic science through instrument engineering to the music in your ears. Remember that this beauty came from science.


[1] All You Need Is Science, A B Sinusoid D E F G (part 1)

[2] Henrich N.; Roubeau B.; Castellengo M. (2003), “On the use of electroglottography for characterisation of the laryngeal mechanisms”, Proceedings of the Stockholm Music Acoustics Conference, August 6-9, 2003 (SMAC 03), Stockholm, Sweden, doi:

[3] Ministère de l’Éducation nationale, de l’Enseignement supérieur et de la Recherche – Juin 2016, Enregistrer et analyser des sons avec des outils numériques, https://cache.media.eduscol.education.fr/file/Signal/70/5/RA16_C4_PHCH_enregistrer_sons_signal2_619705.pdf

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  1. […] digest the equations and informations in this post and we will answer all this next month in the part 2. Meanwhile, try to hear the sinusoids when you play or hear string […]

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