In what type of scenarios (other than tuning) would it be helpful to have microtonal perfect pitch?
I have perfect pitch (I can identify the note name of a given pitch in 12-tone equal temperament like a note on a piano), but often I cannot tell how far off is a note from the quantifications in 12TET when it is not significantly (more than a quarter tone) different, especially when tuning. It seems like I can be carried away from the quantification grid of 12TET temporarily, and I think it is because the quantification grid of 12TET has wide gaps so my brain tries to adjust notes I hear and put it on the grid. However, my primary instrument is piano so my focus is not on tuning instruments, although it would be a clear benefit for this scenario.
I suppose that training my brain to recognize pitches of microtonal tuning (like 24-tone TET or something similar) will mitigate this problem, but what other scenarios can a more refined tuning system (i.e. a tuning system with more divisions between an octave) for perfect pitch (i.e. be able to hear a pitch and associate it with one of the tones in that tuning system) be helpful?
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If your primary instrument is piano, then unless you are interested in tuning the piano yourself, or assessing its tuning, then there's no advantage I can see in trying to make your perfect pitch more precise. If you want to sing, or play some instrument with variable tuning, then it might be of service to work on recognizing different tuning systems.
Microtonal perfect/absolute pitch comes in handy - if not enjoyable - when it comes to listening to open mike-quality or talent show singing. When evaluating how good that singing sounds, it helps to be able to discern between a C, a flat C, a sharp C, and the quarter tone between C and C sharp (for the matter, I can detect all 4 with my perfect/absolute pitch, although my quarter tone recognition may be 10 or more cents off). It also helps to be able to determine whether the background music and the singing are out of tune by roughly the same amount.
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