P = Perfect, U = Unison, m = minor, M = Major, A = Augmented, D = Diminished
In the traditional system, the base tone is labeled one. The tones in the Major scale are the numbers 1-7. The tones in between are compared [paralleled] to what is in the Major. We end up with flats and/or sharps in the names of tones that aren't in the Major key. Check out Derivative & Parallel for more on this.
With Numera, we label the base tone zero. When we do this, basic math works. The root for any key center is called zero and the tones are then numbered 1-11.
There are many ways to view the structural naming following this numbering setup. We can stick with zero only for the root of the system, and other chord roots are based on their respective number, or keep moving the zero to a new root for any given chord [as we do with traditional theory naming]. We will stick with the former...the root of the key system is zero. Subsequent roots for chords or modes are based on their numerical starting point. Example: If C is zero, the ii chord, Dm, will be 2-5-9, not 0-3-7. This is one of the reasons we use this system, to avoid the renaming of every root in a system as a 1, and then paralleling it to its own Major key system. It is okay and possible to rename roots inside a key as zeros.
One other interesting idea is a fixed zero, such as the tone A. A would always be zero. And, B would always be 2 and so on. I'll continue to explore this idea.
We are all familiar with solfege [do-re-mi-fa-so-la-ti-do], and maybe even sargham [the East Indian equivalent]. These syllables do assist well with singing melodies. They are a good 'eartraining' tool, especially for children.
There isn't universal agreement on the parallel tone syllables. [In Numera]: for the 1, we can use 'ra' [rah] or 'ri' [ree]; or the 3, we can use 'may'; for the 6, we can use 'sa' [sah] or 'si' [see]; for the 8, we can use 'lay'; for the 10, we can use 'tay'.