@andy42 Huh? What you wrote really makes no sense to me, and I think you are confused on a couple things or getting mixed up on terminology.
Degrees can be used the describe the position of a note within a scale. For example: in the C Major scale (C, D, E, F, G, A, B, C) we have Root, 2nd, 3rd, 4th, 5th, 6th, 7th, Octave.
Degrees can also be used to describe the distance between 2 different notes chromatically (also called the Interval), ascending or descending. This is counted in half steps (each fret), NOT including the note started on.
So, a Chromatic Scale, starting on C ascending = C, C# (Db), D, D# (Eb), E (Fb), F (E#), F# (Gb), G, G# (Ab), A, A# (Bb), B (Cb), and C (B#) - see chart below.
So, lets take a C Major Scale, for example.
When describing going from Root C ascending, going from C to G is a 5th, because it is the 5th note in the scale.
When describing the Interval between C to G, we are counting # of half-steps (again, not including the starting note). To get from C to G we are ascending 7 half-steps, which is called a Fifth (see chart).
I think your confusion comes from confusing the difference between those 2 descriptions.
Lets look at it on a fret-board chart:
This first image is showing the notes played in a C major scale in relation to the position of the note in that scale.
This image is showing the Intervals between the notes in a C major scale (in relation to the Root note of the scale):
So, to answer your question. If we look at the above representation and want to know the Interval between the Octave (C) and the 5th (G) - ie., a descending Interval, we would count the number of half steps starting with the C on the G string to get to the G on the D string, which is 5 half steps. Thus, the G on the D string is the Fourth of the C on the G string because there are 5 half steps (descending) between the starting note and ending note.
I think this would make more sense when looking at a 5 string bass. The root is in red, the Octaves are in orange. Ascending from Root in half-steps is shown in positive numbers (also in same octave as root, except for the Octave which is one octave higher than our starting position), Descending from Root in half-steps is shown in negative numbers (lower octave).
So, for your examples in your post.
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Descending from 5th fret G string (C) to 5th fret D string (G) = Fourth (5 half steps lower), whereas ascending from 3rd fret A string (C) to 5th fret D string (G) = Fifth (7 half steps ascending), and so forth.
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Descending from 9th fret G string (E) to 9th fret D string (B) = Fourth, ascending from 7th fret A string (E) to 8th fret D string (B) = Fifth.
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Descending from 7th fret G string (D) to 7th fret D string (A) = Fourth, ascending from 5th fret A string (D) to 7th fret D string (A) = Fifth.
A bass guitar is completely symmetrical instrument. What is true in one area of the fret-board is true for another, there is no deviation.
To say this another way - when looking at the last picture:
- when going from 12 to 7 (5 half-steps descending) it is a Fourth
- when going from 7 to 12 (5 half-steps ascending) it is also a Fourth
- when going from 0 to 7 (7 half-steps ascending) it is a Fifth
- when going from 0 to -7 (7 half-steps descending) it is also a Fifth
- when going from -12 to -7 (5 half steps ascending) it is a Fourth
- when going from -12 to -5 (7 half-steps ascending) it is a Fifth
- when going from 0 to 5 (5 half-steps ascending) it is a Fourth
- when going from 5 to 0 (5 half-steps descending) it is also a Fourth
and so on.
Mind blown. What gives? why wouldn’t the 7th fret follow the same logic as the 5th and 9th fret?
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