I'd argue interval training is more valuable than absolute pitch in improvisation. It's rare you find yourself in a scenario where key is unknown and unknowable, especially playing with other musicians. Being able to hear and distinguish a minor 3rd from major 3rd is much more valuable.

Additionally, it's the intervals that give music its emotional content. For example, a minor third sounds "sad" while a major third sounds "happy". Absolute pitches are meaningless in this regard.

Playing a single note confers no meaning. It's only when subsequent notes are played that a context emerges, and music gains its emotional qualities.

Wonder if folks with absolute pitch form emotional associations with different keys.

Collier gives his answer to that here: https://www.youtube.com/watch?v=hyXCWYqpId4&t=836s and it seems to be yes for him, without giving any details why(!)

I would say it makes sense - perfect pitch or not - every key has a different relationship to your own voice, which makes it feel different.

I am not really convinced having absolute pitch will make you a better improviser than someone who has good relative pitch.

In most jazz music you will have the lead sheet so you don't really need to know anyway. Besides that, you don't really need to calculate anything if you have relative pitch. If you practice enough it's instant. If I hear a note or chord followed by another note or chord I can tell you their relationship in real time. Anyone who has done enough ear training can. In fact, it's one of those things where you either know instantly or you haven't practiced enough. I was never really in an in between state.

I'm keeping "you either know instantly or you haven't practiced enough". Thanks!

From the musicians I've met who have it most have actually highlighted the annoying aspects of it more than the useful aspects, in that they can find it bothersome to hear music they're familiar with played in different keys or offset from standard pitch.

I've never experienced any correlation between pitch sensitivity and improvisation skill in groups of trained musicians.

I play a lot of improv and normally it takes no more than 2 notes playing along to determine the key of the piece and relative pitches are very learnable.

That one has an extra layer to it. Many people with absolute pitch will start drifting as they get older due to physical body changes. I've heard the comment of "now everything seems out of tune and annoying". I'm not sure I'd like to experience that as a trade-off.

Losing some high pitch hearing is bad enough.

> [...] but it is much harder, as you have to calculate the intervals between notes in real time [...]

Not necessarily the intervals between any two notes, but the note of interest in relation to the tonic. But still may require the relative position to be mapped (offset) to a specific note.

> but it is much harder, as you have to calculate the intervals between notes in real time

Not at all. You just hear interval.

Exactly. You have to internalize the process of "calculate" so that it's automatic, and occurs without thinking. And for other processes as well. My favorite teacher and I used to refer to it as "moving things into muscle memory". We're guitarists, but I imagine the conceit transfers to other instruments as well.

For Jazz musicians, scales can be a curse. It depends greatly on what you're training yourself to do. If you're training yourself to play notes in order, that's what you're going to be able do. A more helpful thing to aim for might be to train yourself to "hear-it -> play-it" for every degree of a scale, preferably in random order so you avoid the "consecutive notes" thing. Or, maybe better (at the risk of side-controversy that's probably not worth hashing over here), "hear-it -> play-it" for every degree of a mode.