About changing tonal centers in jazz it´s a problem neer tried to write to paper jazz solos, but ussualy you can write them down like they where in only one tuning and then you just have to check for the acidentals, you´ll have to check for harmony and form to help you out, and discards those chords "ignored" by the jass soloist.
For slowing software I use an old version of one called Transcribe! but it isn´t free, I has in a smal interface stuff you can do with any daw (the most important is looping the frase you want to learn). If you don´t want to spend money go for a freeware daw (digital analog workstation like cubase cakewalk sequoia logic etc).
About eartraning I´m kinda untrained right now, but ten years ago I was so heavely drilled with excersices that I could transcribe a lot of stuff without the guitar, but I didn´t know why I deduced It was a II V7 I or what ever. It become kind of second nature. Now I heve very little of it couse there where 10 years of lazynes from transcribing stuff everyday.
First you must play and understand what structures you want to play (chord triad), for playing them on guitar must use some kind of visualization, but i recomend an absolute aproach. Let´s say you have absolute aproach with CAGED chords, or for example with a A chord with the Barre in V position. Now let´s look fpr a Bb chord, if you go first to the A chord and then a fret sharper you´re lossing valuable time, you must know them absolutely lika a pianist would do, if you know the notes better. For being confortable with Bb must play whole tunes and do your harmony excercises in Bb that´s the way.
Please use real music for excersices, I mean music that has a given form and a style, you like a style or a technique try using it, it doesn´t have to be a piece of art. 8thet´s the reason you see art students copying paintings at the museums).
Learning harmony will help you in recognicing funtional harmony, and color harmony, and must know that also exist chords which reason are just the justifications of diferent lines in the parts.
Transcribing is goog becouse of variety.
Style is good because you get a narrower range of dificulties and you absorb and learn what are paractice of "goog style" or cliches etc.
Good book with lot of drills for harmony is Berklee´s four volume course, for a classical aprouch you can use Walter Piston´s Harmony.
In my personala case I had at the university a year of ear training about hearing individual structures (intervals, modes, chords, rythms) and the next year you have to put them all together like a real book sheet. It was far more easier the second year aproach the structurs you have heard helps you to deduce the ones you didn´t hear so well.
What still I lack of is the abillity to memorize fast what I have to put in paper, my mind keeps inventing a new melody that isn´t what really have sound.
Another good prctice is sight-singing.
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