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To all the people with good ears:
when you're figuring out a melody by ear, are you listening to the sequence of notes and figuring out where each note sits relative to the root of the key?
Or are you figuring out what the next note is by the interval from the last note?
when you're figuring out a melody by ear, are you listening to the sequence of notes and figuring out where each note sits relative to the root of the key? Or are you figuring out what the next note is by the interval from the last note?
All of those, and none of them.
The thing is, I don't "figure it out", and it's not a matter of reasoning or logical thinking. It happens, I see the incoming melody notes, chords and bass notes in my mind on a piano keyboard or guitar fretboard. If the melody line is too fast and unfamiliar, I don't see it, or if the harmony is completely strange i.e. something I've never played, I might only see rough guesses and movements. And even if I see the notes completely clearly, it might be wrong! I have to play it to verify my guesses.
The learning process is an action-reaction feedback loop and it goes like this:
Monkey see, monkey do. Monkey don't figure out.
The important thing to realize about the process is, the guesses might be right or wrong, and the accuracy of the guesses improves over time, through practice. But it's not about logical and intellectual reasoning, it's about training and doing, practical exercises. The ability to see the notes without actually playing has come through lots of playing by ear in practice, and when I don't actually play, it's some kind of a mental simulation of playing.
If I interpret your question about tonic (which you meant by "root"?) vs. relative steps to fit this process: I "see" all aspects that I've trained myself to produce.
The "next note" / "previous note" thing is an aspect as well - even if my guess is wrong about the melody's relation to the chords and tonic, the melody notes move in steps up/down the scale. Sometimes it happens, particularly if I'm "looking" at a song on the guitar (instead of piano keyboard which is the stronger instrument for me), the melody I see (=guess) on the (imaginary) fretboard is a fifth or fourth off, particularly with some fast jazzy/bluesy lines, I might confuse notes that form extended chords, for example if the melody goes G-E over an Am9 chord, I might see it as C-A. Because the Am9 is kind of Am and Em played at the same time, I imagine the wrong minor third. But if I switch my imagined instrument to piano, I might see the notes differently.
I suppose people who are good at sight reading and composing by writing music, the music staff is like an instrument they play, so they can "see" things they hear on music staves. But that's not the case for me, I need to imagine playing piano or guitar.
You have to learn motifs and intervals. (Make your self a list of the most usual like: so-mi, so-la-so-mi, do-re-mi-do, do-re-mi-fa-so, so-do, so-do-mi, so-la-ti-do, do-do-ti-do, do-ti-la-ti-do etc. etc. and then you'll recognize them in a melody. There are lots of identical turns and formulas in folk or pop songs.
You can make (also when listening by ear) a harmonic analysis like a piano chord reduction, filtering out the triad (arpeggios) and add the other tones as change notes, passing tones and approach notes.
And you won't ask which method we prefer. Everyone uses both and not only these two. You can listen to the base line, the melody, the cadences and sequences and the transposed motifs. All are playing a role, all of them are helpful.
So start training scales, intervals, triads and 7th chords with their resolution like: so-ti-re-fa ->mi-do, by singing, writing, playing, listening.
do-re-do-mi-do-fa ... or do-mi-re-fa-mi-so (all combinations of intervals and sequences. That's what solfege is. Search for solfeggios and warming ups, also for piano etudes for beginners.
Many good answers here already, but I'd like to keep it simple:
Use all the clues that you can get, starting from the easiest.
If the interval from the previous note is obvious, use that.
If the interval to the root is what stands out, use that.
If you're not sure and you have an instrument with you, use that -- figure out how to play the phrase on your instrument, and then write what you play.
As someone with absolute pitch, when I sit down and transcribe a piece or melody by ear, I determine each note individually by ear regardless of whether the piece is atonal or not or what the note intervals are.
Whoops.
For particularly hard-to-hear notes, though, I do fall back to intervals.
(As an aside, I often sing music by pitch-matching my singing to the (however flawed) recording in my head, which depends neither on keys nor intervals. Bizarrely, I am often aware of the key(s) (if any) of an excerpt I listen to for the first time before I am aware of what each individual note is.)
I don't rate my ear as good, but pretty good. (Last thing I tried to transcribe was Making Our Dreams Come True from memory. I'd say it was 85-90% right compared to the sheet music.)
I compare to the previous note. Also I make reference not to the tonic (not root) of the key, but to what I think is the surrounding chord.
That second reference to the chord is really important. In homophonic music melody is often just a series of broken chord tones with various non-chord tones added. If you can tell what the chord is and if you have a good knowledge of typical harmony changes, it can help you figure out the melody.
I think my ear improved a lot by singing along to drills on the rule of the octave (major and minor.) It got my ear tuned into the sound of fundamental diatonic harmony. Another good thing is solfege patterns like @Albrecht Hugli recommends. For me DO TI DO, DO RE MI, SOL FA MI, and DO MI SOL and the super important patterns.
Having made the point about homophonic music and diatonic harmony you should be aware that a lot of pop/rock music does not use that texture. The melody can often "contradict" the chords. When it does there is a good change the melody is following very simple scale patterns with probably the focus on the tonic or another tonally strong degree of the scale. Try testing whether the melody is using a pentatonic scale. It has a kind of natural resonance and is common.
You may find example of melody centered around stuff like DO RE MI or a pentatonic pattern while the chord progression moves through chords that "don't match the melody" for some part of the passage. In my mind it's sort of analogous to a pedal point of oblique motion. One part stays fixed on a stable point (in this case a stable portion of scale) while the other parts move through various tones/chords adding color, direction, and tension. Eventually the diverging parts will come back together. Use that knowledge to test things out when trying to transcribe.
One additional thought. When transcribing you can have passages that play note quickly. Even if the tempo is not fast notes can last only a fraction of a second. You might replay something a hundred times trying to hear one elusive, brief note! The issue isn't merely matching a pitch. If each note lasted two seconds, there probably wouldn't be a problem as long as you weren't "tone deaf." The quick change is the problem. One solution is to slow down the recording. Lots of people talk about doing that. But this is also why pattern recognition is so important. When you know common patterns you can test them and see if they match, treating a quick series of notes as single pattern unit.
If you have perfect pitch, congratulations! None of the following probably applies.
If you have good but not perfect pitch, you can probably get by...if the key and the number of voices, counterpoint, and harmony isn't that complicated. I did this in my first music theory class when we had to transcribe 2-3 moving lines, and it stunted my growth when we started getting lots of chromaticisms, secondary dominants, and hard key signatures.
For mere mortals like myself, the "correct" way according to my college professors is by training your relative pitch, or recognizing intervals between two notes. (It's been some time since I left college, so I may have forgotten some of the finer-grained details).
With good knowledge of what intervals sound like, you can do the following, given the lowest note of a chord:
This should theoretically allow you to transpose any piece of music, but it's really slow.
You can combine it with the following shortcuts to speed things up:
When playing by ear (or writing things down), I have a lot of mental scaffoldings in my head. Like a set of automatons working in parallel, each making sense of something else:
Some of those automatons are more cerebral, and some work on the finger level (even when I am not playing an instrument and just jolting down notes, I actually move my fingers).
When I play "by ear", I see a set of "green lights" in my head: the automatons all confirm each other's choices. It's like: "OK, the next sound is a minor second below... check; it's minor seventh of a minor chord resolving to major third of a dominant... check; it is the seventh tone of the current scale... check; base jumps a perfect fourth up... check; it's the same sound we heard on the beginning of the phrase... check". Sometimes it happens that one of the machines says: "bzzzt! something's wrong!", and then a frantic voting happens, I have to take things off the auto pilot and fall back to 1 (just relative intervals).
