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mukha;nAsikA-vacano 'nunAsikaH

मुखॱनासिकाॱवचनो ऽनुनासिकः ONPANINI 11008

What is said through mouth and nose is called /anunAsika (nasalized).

IOW, when some sUtra tells you to nasalize something, that means you should say it as usual, but letting some air out through the nose meanwhile. We might call that "noseleak", but the word "nasalization" sounds, like, more scientific.

A nasalized i is an i with noseleak. It is written as i~ इँ, with a /candrabindu over it. These are created by a few sUtras, like atrAnunAs....

You can hear a nasalized U~in ऊँइन् sUtra U~ 10>.

A nasalized d द् is a d द् with noseleak, namely a n न् sound. It is written n न्. No one writes it as d~ द्ँ. So when sUtra yaronunAsika यरोनुनासिक says "nasalize a stop", this means replace the stop with the last letter of the same /varga. So nasalized d द् is n न् and nasalized th थ् is n न् too.

Rule torli teaches the replacing of n न् with nasalized l ल्. That nasalized l~ ल्ँ is a l ल् with noseleak.

My Sanskrit textbook says that the /anusvAra dot above a letter shows that the vowel is nasalized. If so, what do we need that /candrabindu for?

That's basically a mistake in some textbooks.

As far as /pANini is concerned, the /anusvAra is a nasal sound that comes after a normal vowel. It does not show nasalization of the vowel.

Of course, in actual pronunciation most people will nasalize the vowel before a nasal, but that's entirely another story. In correct Sanskrit aMzu अंशु has a short a followed by a hum sound. It is not a nasalized short a~ अँ. You are forbidden from ending a zloka line in aMzu अंशु, because this a is heavy; the sound a~zu अँशु has light a~ अँ.

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