Supervisor: Karsten Riisager

The human voice is one of the most versatile and expressive musical instruments in existence. Unlike any manufactured instrument, the voice combines physics and biology to create an intricate spectrum of sounds. But what makes voices, melodies, and harmonies sound "good"? Is harmony a matter of subjective taste, or is there an objective foundation behind what we perceive as consonant and dissonant? This colloquium delves into these questions by exploring harmonics, overtones, and the fascinating world of tuning systems—with a special focus on the barbershop singing style.
The colloquium will begin with a short introduction to the concept of harmonics, discussing how they arise in nature, and why they are crucial in the discussion of sound and music. This will be followed by a very natural example where such harmonics arise: the human voice. Through the lens of physics, you will learn how vibrations in the vocal folds generate pressure waves that propagate through the air. With Fourier analysis and numerical simulations as key tools, we will discuss how the human voice creates a rich tapestry of sounds, vowels and timbres that define human speech and singing.  
Western music traditionally relies on a system called equal temperament, in which an octave is divided into twelve logarithmically spaced notes. While this system allows musicians to play in any key without retuning, it introduces slight mathematical inconsistencies that make certain intervals sound less pure. In other words, this system does not align perfectly with the natural occurring overtones in different sounds, because every musical interval, except the octave, must be tuned slightly “incorrectly”.
We will contrast this tuning system with just intonation - a tuning system based on simple frequency ratios that align with the overtone series. This raises the natural question: why do we not tune according to just intonation instead of equal temperament? Unfortunately, just intonation comes with its own flaws. Most importantly, tuning mathematically according to naturally occurring overtones must happen in reference to some fundamental tone or pitch. This means that it is also impossible to have a static tuning system that works for more than one fundamental tone.  
However, when we are talking about tuning between equal temperament and just intonation, we are often only tuning a very, very small amount (sometimes only a couple of hundredths of a semitone), which can be difficult to hear for even a trained ear. In order to quantify how much the discrepancy between these systems is actually important or relevant, numerical simulations will be demonstrated live, where participants will be able to hear the difference between these tuning systems, most starkly by the presence or absence of beat frequencies.  
But what now? It seems that tuning with just-intonation is unrealistic, since we want music to be able to express melodies and accompanying chords with different fundamental tones. But it also seems unfortunate if we have to rely on a system where almost all intervals are slightly mathematically incorrect.