This is a cool insight! Can choruses be shown to dynamically adopt "optimal" tunings for a particular song? I.e. the singers settle onto frequencies that make the song's intervals sound best?

To be clear, I'm trying to explore the idea that individual songs have optimal tunings because they only use certain intervals. So, something more fine grained even then singing for a particular key.

You can absolutely sing a perfect chord. That's most of the idea behind styles like barbershop, for example. But things start to fall apart when chords transition between each other. The first and third notes of the central chords in a key will line up on top of each other, but the middle notes of the chords and triads based on other notes don't. So just like an equitempered scale sounds a tiny bit off, harmony gets wonky too if you try to do interesting things.

So the compromise we've all settled on is that we play music in the equitempered scale, and only adjust a little bit here and there to exploit perfect tunings in limited, style-dependent ways.

Which is to say: perfect chords are interesting flavor, but at the end of the day kinda boring in isolation; "real" music needs more rules.

Awesome appreciate you explaining this. Hadn't considered the idea that transitions vs simultaneous notes "compete" on what the optimal note frequencies are. And very cool to understand that people are dealing with this pragmatically all the time.

For a demo, you can search YouTube for “Jacob collier g half-sharp”

Singers will do this via intuition - you don't think of, say, a perfect fifth as 2^(7/12) = 1.4983x over the root. You think of it as a particular pair of sounds that resonates well, much like when you picture "red" in your mind you're not thinking of exact HSV or Pantone values. At most, you'll think of a perfect fifth as exactly halfway between the octaves (1.5x over the root). As the sibling comment points out, this isn't the singers choosing a particular temperament for the entire song; it's them constantly tuning individual chords and intervals to each other and to their previous notes as the song goes on. The same note on paper can be several slightly-different frequencies in different parts of the song, and most singers won't even be able to tell you that they're doing that.

(This is also the same mechanism at work when an entire choir singing an unaccompanied piece goes flat without realizing it. Someone will not quite make an ascending interval, and everyone else will adjust to cover it.)

Thanks, that explains why singers, when they go wrong, are almost always on the flat side.

Brass instruments (not just the trombone) can have micro-adjustments in pitch through the embouchure (lip position/tension) of the musician.

Does this apply also to sax? I've listened to some (mainly old) recordings where the sax seems clearly out of tune; sometimes it's subtle but there are recordings in which it's so off that one wonders if it's done on purpose (1) and personally I really dislike it. Back in the day there weren't digital effects or they were so primitive that applying pitch correction on the fly while maintaining sound quality and spectral integrity was out of question, still tape recorders allowed to finely set their speed, so tuning the song to a sax being recorded would have been trivial.

(1) Example: "get up an get out" by Iggy Pop. https://www.youtube.com/watch?v=R1ld5jG3f-M

As far as I know it applies to both brass and woodwinds, though the degree of difficulty involved probably varies between types of instruments and also (at least on the woodwinds I'm familiar with) note to note.

A sax is really easy to control (or lose control) of the pitch. And in fact, many saxophonists will just shift various ranges around sharp or flat to suit their style (cough Phil Woods cough).

So basically, a woodwind like a sax will tune a few notes with a piano or whatever, but it's really up to the player to keep playing in tune. I would not even bother trying to autotune or use post-processing; it'll just sound weird.

This is also how you can get a room full of student musicians "tuned" but it still sounds like a disaster.

If you listen to the start of Acker Bilk's "Stranger on the Shore", you can hear him bending the notes deliberately.

retuning via tape velocity modulation would be easiest if the instrument in question was consistently out of tune with the rest of the band - like if the sax was always 15 cents flat relative to the harmonic structure.

usually that’s not the case though. typically it’s individual notes. much harder to precisely and accurately modulate tape velocity (especially by hand).

Yep. And - where musically appropriate - if you know which note of the chord you're playing, you can tweak the pitch towards the Pythagorean tuning and get the harmony to "ring" as the harmonics of each note reinforce each other.

This sort of hybrid tuning is common in barbershop quartet singing as well.

Also, the tubes for the individual valves have their own tuning slides. A trumpet will typically have a little thumb-operated lever for one of those slides, to help with some of the notes. I saw a video of a tuba solo, and the tubist was working the tuning slides almost as much as the valves.

Thumb-operated levers on trumpets are uncommon (though, IMHO ergonomically superior). More common are a ring in which you place your left ring finger. The ring is directly attached to a slide on the third valve, so you can flatten notes by extending your left ring finger.

What I've seen is a thumb lever for the 1st valve, finger ring for the 3rd valve.

Those removable slides are usually just to get the spit out of the loops. I haven't seen the lever you mention - are you sure you are not just looking at the usual [water key](https://www.youtube.com/watch?v=vMbb8-WK_VM)?

With valved brass instruments you are trying to approximate a logarithmic relationship with a linear sum of components. Trumpets have a high resonant Q, so not using the valve slides is going to produce out of tune notes. I played horn once upon a time. Horns have low resonant Q, so you just “lip it in”.

one of my favorite aspects of learning the tuba was when we covered logarithmic approximations via linear summing.