“Are there specific or correct pitches for notes on the shakuhachi?”
Most can agree that playing the basic notes in the regular head position should produce something close to the minor pentatonic scale in both octaves with minimal shift in pitch. A flute should also produce the correct notes for its length (in tune with self), though this can take time/practice as well.
Some shakuhachi, particularly antiques, may have certain notes which are supposed to be a flat or sharp (microntonal) compared to standard tuning. For example, old tuning (towari) may have notes that are 25 to 40 cents flat and the 3rd hole is often sharp by 50 cents or more. These traits can aid in the production of cross-fingered and meri notes and make for a different microtonal mood. The sharp 3rd hole is often played flattened as Chi meri anyway, making it less relevant for much of the old music. So, antiques should not be thought of as “out of tune” because the crafts-persons intended them to be that way.
“What were the pitches used in the old days/Edo period?”
We don’t really know all of the exact microtonal pitches used throughout the Edo period since we don’t have recordings but we do have access to old instruments but the vary greatly.
“What about the pitch of meri notes? Should I strive for any specific pitches in my playing?”
When it comes to the pitch of meri notes there’s less consensus. What most everyone can agree on though is that achieving flatter pitches is more difficult. It’s actually physically harder, without a doubt. So, playing flatter and deeper requires more practice. Just like how someone who can jump 10 feet has more jumping capability than someone who can jump 5 feet, someone who can flatten the pitch of any given note more has more range than someone who cannot. This is also like a painter having access to more colors to paint with. With that said, what colors an artist uses is totally up to them. What pitches one should strive for is mostly determined by their chosen teacher(s) and or school(s).
“How do you approach pitch as a teacher in your lessons with students? What is your philosophy?”
As a teacher, I make it my priority to help people with their goals. Usually, and naturally, students want to sound like their chosen teacher. So, often I’m helping people, little by little, get deeper on their meri notes because I play meri notes on the deep side. However, I consider this a long term goal and only comment on pitch when I know a student is capable of going deeper or if the student requests that I comment on their pitch.