Yotsugana
If you combine 鼻 (はな: nose) and 血 (ち: blood), what do you think you get?
In most ways, the answer isn't surprising. You end up with a nosebleed:
鼻血 (はなぢ: nosebleed)
As you can see, the ち has turned into ぢ in an act of voicing. This is not at all unusual. When kanji meet up in compounds, their yomi combine, sometimes changing a little in the process. (If you're unfamiliar with this concept, see "voicing" in the "Singletons, Compounds, and Voicing" section of the glossary.) However, this seemingly simple alteration has several underlying issues. Let's take 'em one at a time.
When to Use ぢ and づ
Because ぢ and じ sound exactly alike to most of us, appearing as ji in romaji, people usually treat them as if they're interchangeable. If anything, people favor じ. My proofreader tells me that when facing a choice between ぢ and じ, "Basically you go for じ, but in some words you need to use ぢ." Here are more terms that require ぢ:
猿知恵 (さるぢえ: shallow cunning), because this yomi is さる + ちえ.
馬鹿力 (ばかぢから: enormous strength), because this yomi is ばか + ちから.
That is, when a kanji isn't at the head of a compound and when its yomi starts with ち, the voiced yomi must be written as ぢ, not as じ.
The issue also applies to ず and づ, both written as zu in romaji. Generally, people represent this sound as ず. However, when the yomi of a kanji begins with つ and needs to be voiced, it becomes づ:
人妻 (ひとづま: married woman, someone's wife), which is ひと + つま.
横綱 (よこづな: grand champion of sumo wrestling), which is よこ + つな.
The matter is not limited to compounds. It also crops up with singletons when the syllables of a kun-yomi repeat:
続く (つづく: to continue)
綴る (つづる: to spell)
The second kanji is non-Joyo, but the word is very common and is indispensable for Japanese people learning English, I'm told.
鼓 (つづみ: small drum used in traditional Japanese music)
縮む (ちぢむ: to shrink)
My proofreader explains that in these cases, "The second syllable is considered to have come from a repetition of the first one, so it's correct to use づ/ぢ."
Errors Abound, Even in Dictionaries
As long as we're speaking of what's correct, he notes another unexpected aspect: "Even native speakers sometimes do it wrong. One would write 猿知恵 as さるじえ if one weren't aware enough of where it comes from. Japanese kids often write 鼻血 as はなじ and get corrected by teachers."
Believe it or not, even dictionaries can make this type of error! One electronic dictionary lists the yomi of 猿知恵 as either さるじえ or さるぢえ—in that order—and it also has the same mistakes with other -知恵 words.
I consulted the dictionary maker, who acknowledged that it was an error, one with technical origins. He said that he had tried to catch them all but that some slipped through anyway. He added quite charmingly, "You are welcome to mention that I had them in the wrong order. Homer nods all over the place here." Well, at least it sounded charming, but I wasn't entirely sure what he meant. Was Homer nodding off to sleep or nodding in agreement? I asked him (the dictionary maker, not Homer), and he said, "It really refers to the occasional internal contradiction in the Iliad and Odyssey." Ah. I suppose Homer was nodding in acknowledgment of his fallibility ... but I could be wrong.
Suddenly, we're very far from the world of kanji!
Exceptions to the Rules
Now that you've gotten it into your head that you need to make these two orthographic changes, it's time to consider some exceptions. You're undoubtedly familiar with this word:
世界中 (せかいじゅう: all over the world), which is せかい + ちゅう.
If we apply the rule introduced above, the yomi ought to be せかいぢゅう. That spelling is an acceptable alternative, though not a common one. The mainstream yomi is せかいじゅう. This has come about because another rule has overridden the one above. With せかいじゅう, the salient rule is that people use じゅう instead of ちゅう when the suffix -中 means "throughout (time or space)."
Here are three more exceptions:
差し詰め (さしずめ: for the moment, eventually), which is さし + つめ.
融通 (ゆうずう: lending (money or belongings)), which is ユウ + ツウ.
稲妻 (いなずま: lightning), which is いね/いな + つま.
In all cases, ず prevails over づ. However, in the last word, いなづま works, too.
Yotsugana and Regional Variations
Collectively, the four kana じ, ぢ, ず, and づ fall into a category known as 四つ仮名 (よつがな), which literally means "four kana." One might think that they would form their own linguistic category because of their connection to these voicing oddities, but the issue is larger than that. It's actually as big as Japan. Look at this map from Wikipedia:
Made by Enirac Sum
In Region 1 (marked in green), people pronounce the four kana identically! Region 1 is substantial, including the big cities of Sapporo and Sendai, as well as Okinawa.
Region 2 (in yellow) is the largest, and it reflects the Standard Japanese usage that strikes students of Japanese as "normal." That is, in those parts (including Tokyo, Kyoto, and Nagoya), じ sounds just like ぢ, ず sounds exactly like づ, and these two sets of sounds are very different from each other.
Region 3 is tiny, filling only part of Oita Prefecture. In that small area, じ and ぢ are identical sounds, but ず and づ are not.
Finally, in Region 4 (which is by no means small), people pronounce all four kana differently.
Typing ぢ and づ
One last issue—you may be wondering how to type ぢ and づ. When your computer is in hiragana mode, input di and du respectively, and everything should work out well for you.