I keep hearing that naming chord note a 4th or 6th is wrong. To me, it is just number for note from given ascending collection, but some musicians insist it should be counted using triads, and effectively an odd number like in augmented 11th.
Is there any reason for this other than preference or tradition? Does it make any difference if 11th is 4 notes above octave of bass note?
My reply is based on jazz/contemporary knowledge, it may differ from the classical usage.
Whether a 6 or 13 (or 4 or 11) is used depends on the context.
When used in chords:
C6 = C E G A = R 3 5 6, a major triad and a 6th
C13 = C E G Bb D F A = R 3 5 b7 9 11 13, a dominant chord with all extensions up to the 13 (though any chord that has a combination of R 3 b7 and 13 is often referred to as a 13 chord)
Csus4 = C F G = 1 4 5
Csus11 = C G Bb D F = 1 5 b7 9 11, a regular 11 chord (a dom chord with all extensions up to 11) with the third omitted.
When used to name intervals they are often interchanged and it is reasonably common to see either used or even both eg you may see scales written like so: R 2/9 b3 4/11 5 6/13 7 (melodic minor)
I'm a professional jazz, classical pianist and author in NY scene.
If you want to name like A4 or Apinkpinkboo23^555 etc. That's all right. Your music your brain. There is nothing to say.
If you want other musicians to understand what you mean, you must use the same mind set with them. For it, study chord names and a bit functional harmony.
P.S.
4 is 4 and 11 is 11. That's why the names are different. 11 includes other degress until itself. 4 which is sus4 only has himself, root and 5th.
Good luck
Let's look at the notes G, C, and E. What chord would this be? If we take the G to be the root of the chord then we have a root a P4 and a M6. Now let's rearrange the notes to E, G, and C. Now let's take E to be the root of the chord and now we have a a root, a m3 and a m6. Now let's rearrange the notes to C, E, and G. Now let's take C to be the root of the chord and now we have a a root, a M3, and a P5. They all contain the same notes so doesn't it make sense that they should be named the same even though there are different intervals making up the chord in each spelling? Of course they are all C major in different inversions.
The reason chords are stacked in 3rds is because 3rds are very stable (consonant) and have a major/minor quality to them. 6ths(the inverse interval of a 3rd) also have the same property, but it is a lot easier to stack 3rds on top of each other than 6ths.
There are many times when you examine the notes of a chord that they may be inverted and can in some way, shape, or form be stacked in thirds to form a complete chord. If we took each spelling above to have an independent name we would have three different names for a C major chord! This would get very confusing. There are certain chords, like sus chords, that are usually named independent of this idea because they are missing a lot of the notes that would need to be included for it to be stacked in 3rds.
Specifically to your question most 11th chords can be stack as a root, a 3rd, a 5th, a 7th, a 9th(2nd), and an 11th(4th). Because it is an 11th chord we know it also has the other notes in it and they don't have to be notated individually unless they differ from the standards. That is a big advantage to writing each interval out or naming it differently based on the inversion.
It is idea to have one name for a chord rather than many so it is easier to communicate to others.
