S4S: Songs for... Sunday?

[mdlbear]

Since I got confused and ran this week's "Done Since..." post yesterday, I think I'll overcompensate and post an "s4s" post as "Songs for Sunday". (It wouldn't be the first time for either of those, although it may well be the first time I've done both in the same week.) And besides, this isn't really about songs.

Anyway, this week's rabbit hole started with an article on Aeon.co called either "The pharaoh’s trumpet", or "What King Tut's treasures reveal about daily life in ancient Egypt", depending on whether you look at the page's H1 tag or its title. In any case, last Sunday was the 100th anniversary of the discovery of Tutankhamun's tomb. Among the lesser treasures there were a pair of trumpets, one made of gilded bronze, and one of silver. The article embeds a video, Tutankhamun's Trumpets played after 3000+ Years. I'll wait while you go and listen.

Which led me to Wikipedia, to find out why they were called "trumpets rather than bugles. There, I learned that "bugle" typically refers to the military signaling device, which is limited to the five notes of the "bugle scale", corresponding to the second, third, fourth, fifth, and sixth harmonics of the horn's fundamental. In the key of C these would be C, G, C, E, and G. You'll note that the 2nd and 4th harmonics are an octave apart, as are the 3rd and 6th.

That led me to the Natural trumpet, on which by going up to the 16th harmonic a skilled player can play an entire chromatic scale by bending, or "lipping", the 7th, 11th, 13th, and 14th harmonics to bring them into tune. Modern trumpets and other brass instruments use valves, of course, which side-tracked me for a while into looking up the difference between piston and rotary valves.

From there I started getting into the difference between "just intonation", which uses pure whole-number ratios, Pythagorean tuning, and the modern equal temperament system, which divides the octave into 12 equal semitones with a ratio of 2^-12 (the 12^th root of 2) between them. Just temperament is used primarily by a capella groups and string quartets.

After that I started getting into modes, diatonic (and other) scales, and some of the more arcane places music theory has gone in the last hundred years or so. I think things beyond that point are mostly of interest to academic music theorists -- mathematicians and physicists got off this bus around the harmonic series.