I'm definitely not looking to replace traditional music theory. My naming system augments existing conventions where they fail or are less than optimal. For example, the "whw" naming mechanism breaks down with intervals larger than a whole step, and even where it does work, it is unwieldy as a way of referring to a specific scale in conversation. It makes no sense to refer to the C Major scale as Cwwhwwwh or Cwwh Gwwh. C Major in my system is C-AD5.
Tetrachords are useful for diatonic 7-note scales, and to some degree the modes of the Harmonic and Melodic Minors. They are useless for non-heptatonic scales. They are also somewhat unwieldy as naming conventions, where C Lydian Dominant becomes C Mix/Lyd, for example, vs. C-AB6 in my system.
Most of the scales covered nicely by tetrachord conventions already have more conventional names by necessity. Tetrachords also require some degree of memorization, as you have to know what the intervals of the harmonic minor and minor lydian tetrachords are before being able to derive the notes of the Gypsy Minor scale from Har.Min/Min.Lyd. Gypsy Minor in my system is B39, which is not only easier to say and remember, but you can derive the notes directly from the name. This aspect is especially valuable when you get into scales that don't have names at all.
The numeric system is more robust, but still doesn't really provide a good "handle" for general conversation or visual shorthand. Unlike the tetrachord method, you can't abbreviate numbers, so a 7-note scale with a specified tonic will always be 8 digits, ala C2212221 for C Major.
The brief nature of xenomes offers a lot of benefits not only conversationally, as mentioned, but also as visual shorthand like my Magellan example:
Some of the problems with common scale names beyond the modes of the major scale are that they can be long, most musicians won't know Enigmatic Minor from Neapolian Major without research, and some scales just simply don't have common names. I'm definitely not suggesting anyone forego common scale names altogether, because they are just as useful, and in the case of the most common ones, much more useful than my scale codes. They just don't cover all of the bases, and without prior knowledge of a given scale, the name is purely arbitrary, providing no usable information.
If I asked readers to list the notes of the C# Hungarian Major scale without removing their eyes from the screen, I'd be surprised if anyone could do it. However, just based on the info in this thread, I think an acceptable number of readers could list the notes of C#-9B6 without looking away. Or even a totally arbitrary scale like G-DF4, a no-name octatonic scale.
Combined with the ability to derive all of the harmonic information from the scale name, the ability to name any combination of notes consistently in a form that can be communicated to other musicians opens up a lot of possibilities for exploring beyond common traditional harmonic theory.
As for fractional steps, microtonality and xenharmonics, the current western naming conventions don't cover them very well, or at all, and traditional notation has to be bent quite a bit to accomodate them. My system could easily be extended to cover 19 or 51 notes per octave by increasing the number of digits, but I think that would reduce the value of the system for the 99% of musicians who will find 2048 unique note combinations in 12 different keys more than enough territory to explore, especially since the majority of music produced in our lifetime has come from a much smaller subset of scales.
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