Today, I was in English class, and I learned about language families and then
writing systems. Of course, there is kanji, and ideographic system, but
hiragana and katakana are both syllabary systems.

How did this idea to make a syllabary writing system come about in
Japanese/Chinese history? Why did someone want to do it? Was the idea taken
over from people who had already done it?

Also, where to the syllabary sounds come from? For example, why is "yo" a
syllable in the system but "ye" or "yi" isn't?
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history linguistics
How were hiragana/katakana influenced by syllabary writing systems?
You've got two distinct questions here, I'll answer them in turn.

Japanese wasn't really 'influenced' by any other syllabic phonetic writing
systems; instead, it turns out a syllabary is the most natural kind of
phonetic writing system to create out of nothing (or out of a semantically-
based system like Chinese). Of the various examples we have of people creating
a phonetic writing system without already knowing one, exactly one instance is
anything other than a syllabary, and that's Egyptian (or 'hieroglyphics').
(I'm discounting the semantic parts of Egyptian, since you could write 100%
phonetically in Egyptian; it just had too much ambiguity to be practical.)
Egyptian was a somewhat unique case, since the structure of spoken Egyptian
encouraged the script's inventors to write only consonants and totally
disregard vowels. The Phoenicians stripped out all of the semantic parts of
Egyptian but still didn't add vowels, since they didn't need them any more
than the Egyptians. Later, the Greeks borrowed Phoenician and the Indians
borrowed a descendent of Phoenician (Aramaic), and the structure of Greek and
Sanskrit forced them to come up with ways to mark vowels. The Greeks invented
the alphabet, and the Indians invented the abugida.

All the other cases have been syllabaries. Japanese is a good example. Mayan
is another - it's totally a syllabary, and has some interesting conventions
regarding how to write syllable-final consonants. The Sumerians, Hittites and
Persians all adapted Sumerian cuneiform into syllabaries (though the Persian
version has some alphabetic traits). There are some other cases as well of
people being exposed to the _idea_ of writing without learning a particular
system, and they made syllabaries too - Cherokee is a good example. Of the
cases where people have invented straight-up alphabets (or abugidas, like
Canadian Aboriginal Syllabics), the inventors have either learned or learned a
fair amount about a system that already worked the way theirs would. (Hangeul
is probably an example of this - there's good reason to believe that it was
inspired a good deal by 'Phags-pa, which is ultimately descended from
Phoenician/Egyptian.)

So it's not surprising that the Japanese created a syllabary rather than an
alphabet, as an alphabet is a bit less obvious of an option. Further impetus
comes from the fact that Chinese characters each represent a single syllable
(so you could, if you wanted to, treat Chinese like a syllabary with a huge
amount of semantically-conditioned variation) - though this is more due to the
structure of the language than any conscious attempt to create a one-
letter/one-syllable correspondence. When the Japanese first started writing
Japanese, they used Chinese characters that sounded like whole Japanese
syllables, since there wasn't anything smaller they could use. Kana are
ultmately just a graphical simplification of those Chinese characters,
although they've since been totally dissociated from their original forms.

As for why the system is missing certain combinations, it's mostly due to what
combinations spoken Japanese allows. /ji/, for example, is missing because
spoken Japanese doesn't allow /j/ and /i/ to combine like that - /ji/ is not a
valid Japanese syllable. The language used to allow /wi/ and /we/, and so
there were kana for those syllables (ゐ and ゑ, respectively); but it no longer
does, and so those kana have been removed as there is no more need for them.
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In about 2000 years ago, people in Japan were still using clay vessels and had
no characters at all, while China had developed a large civilization and their
own writing system, kanji. In those days, Japanese and Chinese used completely
different languages, with completely different vocabulary, syllables, and
grammar.

In around the 1st to 4th century, kanji were gradually imported to Japan. At
first, kanji were only used as a part of Chinese language, by selected
Japanese people who want to study Chinese culture and religion (Buddhism).
There was still no way to write Japanese, spoken by Japanese people. Again,
Japanese is different from Chinese.

In around the 6th to 7th century, Japanese people developed "manyo-gana"
(万葉仮名). In this system, people used kanji as syllabary characters, totally
ignoring their meanings. For example, they used kanji 以 to represent the
Japanese vowel "i" (い). At last, Japanese people learned how to write Japanese
as it is pronounced. But unfortunately, manyo-gana were too complicated to
serve as syllabary characters, so they needed something better.

In around the 7th to 8th century, Japanese Buddhist monks started to simplify
manyo-gana, and developed purely phonetic characters, katakana. At first,
katakana were symbols rather than characters, used to instruct how to read
difficult scriptures from China. But they turned out to be useful to write
ordinary Japanese, so katakana were adopted everywhere. This was when people
started to mix kanji and katakana.

Almost at the same time, noble people developed hiragana, which is another
simplification of manyo-gana.

In summary, Japanese needed to develop syllabary characters (hiragana and
katakana) because kanji were only borrowed from Chinese, and only using kanji
was not enough to express Japanese language well. Chinese people did not need
such things because kanji were their native characters, optimized for writing
their own language.

I think Japanese people could have stopped using kanji altogether somewhere in
the history, but that never happened. Kanji have thier own strength as
ideographic characters. On the other hand, Korea used Chinese kanji until
several hundred years ago, and then stopped using them, in favor of their own
syllabary characters called _Hangul_.

I'm sorry I don't know where Japanese "sounds" come from.
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Please note that kana is not a true syllabic script anymore. The reason for
this is due to /n/. For example, take the word /sinbun/ "newspaper". If you
break it into its syllables, it is sin.bun. While accents are determined by
syllables in some dialects, kana--as well as Japanese speakers--segment this
as si.n.bu.n. The appropriate term for this mora.

> How did this idea to make a syllabary writing system come about in
> Japanese/Chinese history?

Kana are simplified forms of Chinese characters. Before the development of
kana, Japan borrowed Chinese characters to phonetically write Japanese words.
This is known as man'yoogana. Chinese of course is a different language with a
different phonology, so there was considerable differences in pronunciation of
the same characters. After doing this long enough, a short hand form of the
same characters developed into the two forms of kana: hiragana and katakana.

> Why did someone want to do it?

Until man'yoogana came around, Japan did not have a way to write their
language. Hopefully we can agree that being able to write and record words is
a useful thing.

> Was the idea taken over from people who had already done it?

Quite likely. Records indicate that it was the Koreans who initially taught
Japan about Chinese characters. Recent research has also indicated that
katakana has its origins in the Korean peninsula (more precisely Silla). If
you're interested in knowing more, search for the work done by 小林芳規, in
particular regarding the text 大法広仏華厳経.

> Also, where to the syllabary sounds come from?

The phonology of the language. Initially, the sounds were of the form ((C)V)+,
so quite simply characters were applied to each of these fully formed sounds.
A little later long vowels, palatalized consonants, and /n/ developed
resulting in several innovations: doubling of vowels, small kana, and a new
/n/. As the language continued to develop, several sounds naturally fell out
of use and are no longer used.

> For example, why is "yo" a syllable in the system but "ye" or "yi" isn't?

It may help to brush up on phonetics, particularly
[glides](http://en.wikipedia.org/wiki/Semivowel). Glides form a pair with
vowels: the glide is non-syllabic while the vowel is syllabic. These sounds
are phonetically quite similar and the lack of distinguishing is not an odd
thing in human speech. You could try the linguistics forum for more details.

That said, /ye/ existed and was distinguished from /e/ in man'yoogana, the
pre-cursor to kana. The distinction was lost by the time that the kana scripts
developed, so no need for a character.

There is morphological evidence of /yi/ and /wu/. For example, /yi/ can be
seen in the conjugation of the following verbs:

  * kuy- (悔ゆ to regret): ku **y-i** , ku **y-i** , kuy-u, kuy-uru, kuy-ure, ku **y-i**
  * mukuy- (報ゆ to repay): muku **y-i** , muku **y-i** , mukuy-u, mukuy-uru, mukuy-ure, muku **y-i**
  * oy- (老ゆ to age): o **y-i** , o **y-i** , oy-u, oy-uru, oy-ure, o **y-i**

And /wu/ can be seen in the following verbs:

  * suw- (据う plant): suw-e, suw-e, su **w-u** , su **w-u** ru, su **w-u** re, suw-e(yo)
  * uw- (植う plant): uw-e, uw-e, u **w-u** , u **w-u** ru, u **w-u** re, uw-e(yo)
  * uw- (飢う starve): uw-e, uw-e, u **w-u** , u **w-u** ru, u **w-u** re, uw-e(yo)

While they are apparent in the morphology, there is no evidence that they ever
existed phonologically. You can handle this as a natural result of phonetics,
or you could posit phonological rules such as /y/ --> ∅ / _ [i] and /w/ --> ∅
/ _ [ɯ].
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