I have been transcribing music without an instrument for quite some time now, if I have my instrument in hand I am able to almost always quickly figure out what is being played but when I step away from it which I have been doing a lot lately while actively listening to music, why do I find it difficult to quickly decipher the intervals even when I know the intervals. Does internalizing the intervals take time...
As Tim correctly says, it's an entirely different thing. Here's what I would recommend (i. e. what helped me):
Practice sight-singing (i. e. singing from the score only if you are played the first note on an instrument). It's sort of an inverse problem but it helps immensely (and not only with transcribing). I bought a sight-singing book to practice with; you might do the same or just look something up on the Internet.
Transcribing takes time even if you know how to do it. Typically you will need to break the song into bits (each few seconds long) and play each of them multiple times. (It's not something you would plan beforehand. You just play the song, and pause it when you see you won't be able to transcribe more in that one go.) It also helps to slow the playback down, if you have a player that can do it.
If a particular bit is too hard to transcribe, use your singing as a proxy. You will quickly catch the problematic melody and be able to reproduce it by singing, and then you can sing it as slow and as many times as you want. I use this especially when transcribing complicated rhythms (they are often easy to reproduce but hard to write down).
Obviously it also helps to practice transcription itself. There are many apps for ear training and this is usually dubbed "Melodic Dictation". I have been using ToneSavvy, but there is gazillion more — just Google for them or look into your phone's app store and you will find several.
There are two different ways of attacking the sight-singing/transcription problem: you either track intervals between each note and its successor, or you concentrate on the tonic and track each note's relation to it. For me, the second method wins, but everybody needs to decide what works the best for them — it's entirely personal.
In short, it's just like transcribing with an instrument, but the instrument in question is your voice. However that's far more than using just another instrument, since when singing, your brain will internalize the intervals etc. much better (it's much "closer to the CPU" in a sense and not reduced to putting your fingers somewhere).
I think there's a big difference between hearing two notes (or more), and being able to play them on your instrument, and hearing those same notes and naming their intervals with no other reference.
In fact, often, on guitar in particular, (but in reality on any instrument) we can hear a couple of notes, and instinctively hit the second one once the first has been found. I think that most of us will not even consider what the note/s are called, or even what interval there is between them. After lots of playing, it often becomes 'second nature'. It's known as having relative pitch.
Once the instrument isn't there to help, it becomes more academic, and especially where two notes in the middle of a phrase are concerned, we need to stop and count. And referring to scale or root note often doesn't help.
Like most things, getting good at something does take time, and I guess you've spent a lot more time playing your guitar than trying to internalise those intervals. So keep going!
Something which will help is to visualise the two notes involved, referring to how you'd play them on guitar. Which string, which fret each would be on. Then you can come up with an answer. But - bear in mind that each interval heard or played will have a variety of names - e.g. is it an augmented 4th or a diminished 5th. For that solution, you need to determine what each note would be when written down. The plot thickens...
This may be a different perspective from other answers, but this fairly-influential study in patients with intractable epilepsy looked at the ability to distinguish note intervals in order to correlate the brain ares responsible for processing such things. They noted that with respect to timing of notes, there was a fundamental dissociation between metre and rhythm in terms of which areas might be involved. For example, the two hemispheres were involved differently during musical processing; the posterior part of the superior temporal gyrus appears to be exceptionally important during such processing. This is not to say that anything is wrong with your brain, but only to suggest that there is at least some empirical evidence to suggest that there are stereotyped pathways in the brain that are recruited during such behavior (interpreting music).
As far as the difference you experience when you have a guitar in your hand or when you do not: in motor control, the cerebral cortex is sometimes described as a "dynamical engine" that drives volitional movement. In this conception, there is a latent encoding of the state of the limb in the ongoing activity of many thousands of neurons simultaneously in the motor cortical areas, which might serve as an internal model and enable adaptive movements when the cortex is required (for example, if you are paying close attention to the way your hand moves along the guitar).
My speculation is that these things might be related in some way to your situation (please understand that it is purely speculative and not based in any empirical observation to directly validate such a claim). I think it would be interesting if the limb state information in the cerebral cortex while you have a guitar in-hand is transferred in some way to the temporal gyrus, facilitating your ability to encode or decode interval information in the music. Again, I do not have the background to imply whether such a thing actually does occur in reality.
- You probably know the trick to connect each interval with the first motif (interval) of a song: e.g. dim 5th (respectively aug. 4th) => „Maria“ and minor 7th => „Somewhere“ (West Side Story)
- Each tone of a melody has a function by its tension, or may better, a tension by its function: tonic and dominant are stable, fa and ti are leading tones, la is somehow hanging over sol, re = passing tone between do and mi etc.
- Trial and error: listen, write, play, correct.
- Composing short motifs to each interval as your own unique modules for sight reading, recognizing and working tools.
- Training systematic solfege: scale back to root: doredomidofadosodoladotidodo up and down. scale of 3rds: domi refa miso fala ... scale of 4ths etc.
- Triads and tetrads on all degrees (with resolution) e.g.: sotirefa ... mido
- Inversions and augmented 6th chords and resolution:
- Arpeggios: singing preludes by Bach with names of moveable doremi.