I'm two months in the stage of a long overhaul to train my ear and "master the language of music." Practically speaking, I'm transcribing a group of albums that have the concept/sound I'm looking for in particular to write my next album.

My question is: What's the correct way to transcribe music to reap the most benefit? Is it correctly done fully by the ear/singing solfegge and absolutely nothing else? I akin this to being able to write music away from the instrument.

Or is it okay to write with an instrument in hands and fiddle around with the notes til you hit the write notes? I akin this to writing music by fiddling around with notes til you hit what sounds good.

I've been doing a combination of both but each are just as frustrating. What is your method or what tips do you have?

TLDR: Correct way to transcribe music for the most benefit?
We're all alright!
I do both. They have different benefits in my opinion.

Writing away from your instrument improves your ability to go from an musical idea to having it down on paper fast. I often do this when i am out working and i want someone i am playing with add a line on their part. I then sit down, sing the line for myself and then write it down and give it to them. It's therefor good to practice transcribing and notating it.

It is also good to transcribe with your instrument in your hands. Cause you want to make the connection between the sound you want to hear and where to put your fingers as strong as possible. That being said, i always sing what i play, even if i am playing it on my instrument at the same time.

So i recommend both.
Fusion and jazz musician, a fan of most music.

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You will get more benefit from doing it away from your instrument.

It's a lot harder, though.
For ear training, I like to try replicating good melodies/ simple solos. For example, I listen to a lester young line and try to sing it without making mistakes

In a more technical aspect, if Im transcribing a guitar solo, I like to have a guitar in my hands. By listening closely to the different inflections (hammer-ons, pull-offs, and slides) used in the solo, you will find the most efficient way of playing the notes and avoid some awkward left hand positions that will make it impossible for you to play the solo along the recording