Katajanmarja said:
The youon hiragana series represent syllables combining a palatal consonant and a vowel.
Going by a phonemic rather than a phonetic analysis, Japanese doesn't have palatal consonants. Rather, one stipulates a phonological process that palatalizes alveolar consonants preceding a close front vowel (/i/, i). Thus /si/ is realized as [ɕi], /zi/ is realized as [ʑi] (or [d͡ʑi] because of allophony between [z] and [d͡ʑ]).
This analysis is very natural (and is also the one found on wikipedia) because it perfectly accounts for the complementary distributions of [s] and [ɕ], [z] and [ʑ], [t] and [t͡s], and [d] and [d͡z] -- the former are never found before [i] or [j], and the latter always found before [i] or [j]. (Note that postconsonantal [j], as in 拗音, is usually analyzed as palatalization of the consonant, and [z] and [d͡z] are generally considered allophonic in most situations.)
A 拗音 construction is a "standard" mora (i.e. one represented by a single 仮名) with the consonant palatalized. For understandable phonotactic reasons, this is generally only allowed when the moraic vowel is not too close or front, i.e. is /o/, /a/, or /u/. There is no restriction on the consonant, so we can have e.g. にゃ, ぎょ, じゅ, ぴょ, りゃ, みゅ, etc. etc.
Since 拗音 are plainly a construction from "simpler" morae, they are considered "complex" morae, and the orthography (仮名, that is) reflects that by representing them, conveniently, as two characters, or maybe "1.5" characters.
As you mentioned, Hepburn takes a cue from English orthography when dealing with 拗音 or any other morae. In Hepburn, 「きゃ」 becomes "kya": "きゃ" is realized phonetically as [kʲa], which is close to /kja/, and in English, "k" stands for /k/, "y" can stand for /j/, and "a" can stand for /a/. Similarly, ち becomes "chi", because in English, "ch" usually stands for /t͡ʃ/ and "i" can stand for "iː". ち is realized phonetically as [t͡ɕi], which is not that close to [t͡ʃi:], but it's the closest that the English phonemic inventory can supply.
In a more notable case, じゃ, with phonetic realization [d͡ʑʲa], becomes "j" + "a", because in English, "j" usually represents a voiced postalveolar affricate, [d͡ʒ], which is a sound close to the Japanese "palatalized" alveolo-palatal affricate, [d͡ʑʲ]; and in English, "a" can represent [a], which is also the sound in "じゃ". Because in phonetic realization, a palatalized alveolo-palatal consonant doesn't sound much different from the original alveolo-palatal consonant, no "y" is inserted into the transcription, as it would be in the case of, say, きゃ -> "kya", above.
In Nihonsiki and other similar systems, however, which are phonemically based (not phonetically), two of the transcriptions above would be different. First, ち would be "ti", because the phone [t͡ɕ] is analyzed as an allophone of the phoneme /t/ caused by palatalization conditioned by the subsequent /i/. Second, じゃ would be "zya", because the phone group [d͡ʑʲa] is analyzed as /zʲa/ through two phonological processes: one, allophony between [d͡z] and [z], and two, allophony between [ʑ] and [z] conditioned by palatalization.
Note that both systems attempt to match English (or other general Latin-based languages') pronunciation to Japanese; Hepburn tries to match phones, while Nihonsiki tries to match phonemes. As it happens, since 仮名 is phonemically rather than phonetically based, Nihonsiki-like romanizations also happen to correspond more "logically" to 仮名 spelling of Japanese.
Indeed, you mentioned that:
Katajanmarja said:
On the other hand, there seem to be systems that build heavily on the hiragana logic. They may use such non-phonological yet logical forms as tibi, tubasa, and ninzya.
Apparently, jya is a compromise between phonological ja and transliterational zya.
Emphasis mine.
Those "systems that build heavily on the hiragana logic"* are not "transliterational as opposed to phonological". Rather, they are both transliterationally and phonologically based, in that they provide ultimately simple rules for transliteration from the native orthography (仮名) to the Roman script, as well as correspond directly to the phonology of the language, as detailed above. This is possible since the native orthography itself is a shallow one. So you could term these systems, such as Nihon-siki and Kunrei-siki, as "phonemic transcriptions".
The Hepburn romanization is phonetic. It works by transcribing the pronunciation of Japanese relatively narrowly and then romanizing it using approximately English graphemes (though those are shared by many European languages).
I've only demonstrated one of the ways in which Hepburn imitates a narrow, phonetic transcription and Nihonsiki et al. imitate a broad, phonemic transcription, but there are many others (such as treatment of 王 and 追う, etc.) Wa-puro romanization is a compromise between the two approaches -- in fact, most wa-puro input systems will recognize Nihonsiki or some macron-less version of Hepburn-shiki equally well.
Sorry, that was even more off-topic, and even more of a rant, but hopefully you'll forgive me :)
*By the way, "to build heavily on" something means to extend it far beyond its original scope. Here, I think you mean that the systems are heavily based on the 仮名 logic.