Hi all
I am trying to figure out if the attached is correct, so that when I transpose the line, I can refer to the numbers as a guide (understanding that the ear is king).
The concept of 1 3 5 7 #9 etc. is clear to me when it comes to chords, and some patterns are easy to assign numbers to, however I am unsure if what I have done is a) correct and b) the best way to do it (eg it is appropriate, pragmatic or applicable to do).
N7 stands for natural 7th in this example. The G7 bar I can transpose and understand better than the Dm7.
Thanks!
View attachment 7389867
Why start with 13. IMHO in terms of chord intervals, the A in the first bar is a 5th. The F in the first bar is mislabeled; it's a 10th or 3rd.
There are various ways to think of this and all of them get messy.
The rest of this may or may not be helpful

.
Accidentals are used in chord notation. This is necessary/useful shorthand, but it causes confusion on various levels when you start discussing intervals. For example let's consider the Dom7b9 chord shape. The 9 in this chord shape is minor. In the case of G7b9 the minor 9 is an Ab; so b9 makes perfect sense. However in the case of F#7b9, the same chord shape, the minor 9 is G natural, rather than Gb.
One way to avoid this potential discontinuity:
When discussing intervals, there is no such thing as a natural 7. 7 is major, minor, augmented, or diminished. The tone you marked as N7 is a minor 7. The interval translates to minor 7 in all keys, but it's won't be a natural 7 in all keys.
The tone you marked as #7 is a major 7.
If the point is to transpose this line across keys, I think you would probably relate the intervals to the prevailing key center rather than the chords. The full scale: 1, 4, and 5 are either perfect, augmented, or diminished. If these intervals are not identified as augmented or diminished, they are assumed to be perfect. 2,3,6, and 7 are major, minor, augmented, or diminished.
I would say this is clearly in C major. So the first four notes (A,F,E,D) are 6,4,3,2---then we get to the dilemma of how to treat the C# and C natural so that it translates to all keys without causing confusion. If you are writing out the numbers perhaps ^1,6,1,6. Use the ^ for the altered (raised) tone. Since the second 1 is diatonic, perhaps you don't need to write anything. This is not consistent with the rules or standard notation, but with notation the accidentals don't translate across keys.