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So I started learning music theory this January 2019, I've learned very quickly from basic to advanced because I've been playing guitar (self-taught) for 9 years...

I can now identify any interval by ear very easily... I can also sing the first pitch of any song in my head and it is mostly right (if it is wrong then it is a semitone higher or lower)... I can also think of the note C and sing it but I most of the time sing it a bit sharp (to be exact 40 cents sharper than actual C) so it is about a quarter tone sharper.

I keep listening to C for a long to fix my intonation but then if I stay hours without music and then sing it, I always sing it 40 cents higher... it is the same for other notes sometimes.

I can also sing any note without any reference just by thinking of it in my head. Do I have perfect pitch or do I just have a relative pitch with a good pitch memory?...

...Or maybe I had it and I didn't know before? So now I'm getting it back with practice?

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I would say that you definitely have perfect pitch, since you can at least identify a C within 40 cents. That means you can still "round it" to the nearest semitone. I think from general usage, if you can at least distinguish one semitone from another, you'll have perfect pitch, not relative pitch.

For this answer I did some Googling, and found a study where a person who has perfect pitch was asked whether he can notice detuning at the end of a music performance. The music started at the right pitch, but slowly detuning at the rate of 2 cents per minute, until at the end the music was detuned by 33 cents. He could NOT notice it ! https://news.uchicago.edu/story/perfect-pitch-may-not-be-absolute-after-all

You bring a good point about good pitch memory being different than perfect pitch. I don' know whether in general usage it matters. But I DO sometimes resort to pitch memory if the sound is not keyboard instrument (I'm a trained classical pianist and organist), such as vocal music. When I'm not sure, I resort to my memory of a piano piece I practiced a LOT in college: J.S. Bach Italian concerto (in F Major). By remembering the piano sound of the first few measures, I found that I can reliably produce F1 within 20 cents accuracy. With this F as my "tuning fork" I can then produce other notes.

So my suggestion for improvement is to pick a piece that you really enjoy and practice the piece a lot with a perfectly tuned guitar. Hopefully overtime the neurons in your brain can record some measures of the piece. Then try to recall the whole measures as a "hint" to get at one note you'll use as reference. Maybe that way your sharp bias can be corrected.

Cheers!

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