How many dimensions do phonemes have?

I was wondering if there was a better or alternative ordering for the letters of the English alphabet, than the standard “a b c d e …”.

This led me to wonder by what parameters they would be ordered.

This led me to ask how many different parameters are relevant in order to specify a phoneme; that is, how many dimensions the data of a phoneme has.

I believe this question hinges on some interesting mathematical questions as well.

For example, if we decided to accept three different top-level categories like voice, location, air flow or something, each of those categories may have a different number of sub-elements, so I’m not sure how that’s expressible in terms of “dimensions” (might have something to do with an orthonormal basis in linear algebra or something).

Anyway, ultimately, what “mathematically natural” ways might there be to order the phonemes? (Even if it is a partial, not total, ordering: a set of phonemes may together come “after” some other set, but each be “parallel” with respect to one another).

• Languages are very different as for the number of phonemic oppositions which you call dimensions, e.g. Abkhaz with just 2 vowels a and ə has a one-dimension vowel system while the 8 Turkish vowels make up a complete 3D system with 3 oppositions: open vs. closed, front vs. back, and rounded vs. unrounded, and if in a language vowels can also be short vs. long and oral vs. nasal that makes up a 5D system, and then there can be more dimensions added like phonation, tenseness, or tongue root position, and there are also diphthongs and triphthongs, and all of it can be in one language. > Mar 4 at 2:10
• > And then there are consonants with their own pretty numerous oppositions. And there are languages, e.g. Chinese, which have several subsystems of phonemes, say, syllable-initial and syllable-final, which intersect just partially or don't intersect at all. And there are almost always several peripheral phonemes used in just a couple of words each like in the English interjection “hmm...” Well, what I mean is each language’s phonemes are a way different and have different oppositions, so you question cannot be answered generally, without naming a particular language. Besides, there's IPA. Mar 4 at 2:24