![]() I thought back to an excellent video by YouTuber 3Blue1Brown which I’ve linked to elsewhere in this blog in my article on Frequency, Pitch, Overtones, Harmonics and Timbre (I’ll embed his video at the bottom of this post so as to not disrupt the flow). I figured my original conjecture was inadequate. It would be spurious to claim a quarter tone between C and C# is harmonic in a traditional, Euro-classical sense, but it led me to thinking about expressing notes, diatonic or chromatic, in different ways. There are other ways of dividing the octave up (more on some of these later), but 12TET is by far the most popular in Western culture and for that reason I am most familiar with it.įrom this we can infer that not only does every note, diatonic or not, appear in the harmonic series, but even the notes in between notes and everything down to the smallest scale. So from an infinite series of numbers, we extrapolate twelve discreet pitches. However, the harmonic series carries on forever, and we only measure our equally tempered scale as dividing the octave into twelve (12TET). I roughly know up to the 16th harmonic, I know that the distance between the 8th and 9th harmonic is about a tone and between the 15th and 16th harmonic is approximately a semitone. We hypothesised that an overtone is harmonic if it appears in the harmonic series, but then I thought to myself… how well do I really know the harmonic series? To cut a long story short we began discussing the language of overtones and harmonics – or rather, what qualifies an overtone being harmonic. I was walking along the canal a while back with my good pal discussing saxophone and how his work rota had allowed him more time at home during the day, meaning he can practise the (often) unwelcoming sound of overtones. ![]() I am giving the graphics and writing an update. This was originally published in December 2017.
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