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Start with inclusive counting of note names. That gives the "number", eg a 3rd or a 6th. Then use the maj scale as a yardstick, compare the number of semitones (or frets up one string) of your chosen interval with what you'd get if you went the same number of steps as the maj scale. If the same, it's either a major interval (2,3,6,7) or it's "perfect" (4,5). If it's one semitone shorter than a major interval, then it's minor. If it's a semitone shorter than a perfect interval then it's diminished. If it's one semitone larger than a major or one larger than a perfect, then it's augmented. EG: C->F# is an augmented 4th, C->Gb is a diminished 5th.(count the note names inclusively).
Seriously: If you value it, take/fetch it yourself
I agree with you about using relative notation, it is my default mode when thinking about music.
When envisaging the various Keys as I ii iii IV V vi vii° and scale degrees as Tonic (1), Dominant(5), etc, I already know what mood I want to create, so I just plug-in the various chord and note values. Using this method I can compose verse/chorus/melody arrangements in around 3-5 minutes.
It all came about by being rubbish on the keyboards, so I just learned everything in the Key of C, modes, inversions, variations, etc. I then learned about transposing, so I never had to leave the white keys! The Tonic is always on the C note position and the Dominant on the G note position.
OK I'm trapped, but as a guitarist it is very effective for songwriting and recording keyboard parts in any Key, and I have also gained a comprehensive understanding of music theory. Just don't ask me to play on the black keys
When playing guitar, I mentally track the Root (Tonic or 1) & Dominant (5) positions all over the fretboard for whatever Key I am in. I'm not sure if my approach is unorthodox or not, but it works for me and I feel as though I have simplified the whole process of understanding music. BTW I am entirely self-taught
PS I just reread this and I bet nobody knows what I am talking about!
Seriously: If you value it, take/fetch it yourself
Once you are comfortable thinking about music in relative terms, I've found Hooktheory to be a great website for learning about music composition. Now I see everything as chord tones and non-chord tones, and individual notes as 1 2 3 4 5 6 7, with 1 being home, and 5 being where you want to go You have so much more control over your music when you have a little music theory under your belt, especially when you want to create tension and release, or add music to lyrics, etc.
It's quite a journey before you get to the eurika moment though, but it is definitely worth the perseverance!
This free lyric songwriting course from Berklee ties in nicely with what I have been saying, and the tutor uses the "stable" and "unstable" tags for manipulating feeling and mood.
https://www.coursera.org/learn/songwriting-lyrics