It is a lengthy discussion, and difficult to capture while standing on one foot. There is a lot of background, so what I write may not be intelligible without a course in Biblical Hebrew. But to break it down, the dagesh is a dot in the middle of the letter, and often (for what is called dagesh chazak) serves to geminate the letter, that is, double it, in terms of pronunciation. Several factors cause this gemination. Syllables with short letters need to be closed (consonant vowel consonant), and so a geminated consonant serves as both a close of the preceding syllable and beginning the next syllable. It can also come from a doubled root letter.
If you look at this Jastrow entry for the arm meaning:
you will see that the root is אממ. That would prompt gemination. So too, the full patach (rather than chataf patach) is a short vowel, so we need to close the "am" and begin the "ma".
Scroll down in Jastrow to the entry for maidservant, and you will see that the root does not have two mems. Thus no gemination. And the chataf patach is a sheva, which doesn't get closed, so no phonological cause either.
A similar process occurs for chataim / chataim, phonologically speaking, in terms of the sin vs. sinner. Different noun forms from the same root have different patterns of vowels, which carry along dagesh or no dagesh. Look at the Jastrow entries for sin / sinner (though he does have gemination as an option for one):
I'm not clear on this whole "Dagesh" thing. Can you explain why if it means arm then there would need to be a dagesh in the mem? likewise for חַטָּאִים
It is a lengthy discussion, and difficult to capture while standing on one foot. There is a lot of background, so what I write may not be intelligible without a course in Biblical Hebrew. But to break it down, the dagesh is a dot in the middle of the letter, and often (for what is called dagesh chazak) serves to geminate the letter, that is, double it, in terms of pronunciation. Several factors cause this gemination. Syllables with short letters need to be closed (consonant vowel consonant), and so a geminated consonant serves as both a close of the preceding syllable and beginning the next syllable. It can also come from a doubled root letter.
If you look at this Jastrow entry for the arm meaning:
https://www.sefaria.org/Jastrow%2C_%D7%90%D6%B7%D7%9E%D6%B8%D6%BC%D7%94.1?lang=he
you will see that the root is אממ. That would prompt gemination. So too, the full patach (rather than chataf patach) is a short vowel, so we need to close the "am" and begin the "ma".
Scroll down in Jastrow to the entry for maidservant, and you will see that the root does not have two mems. Thus no gemination. And the chataf patach is a sheva, which doesn't get closed, so no phonological cause either.
A similar process occurs for chataim / chataim, phonologically speaking, in terms of the sin vs. sinner. Different noun forms from the same root have different patterns of vowels, which carry along dagesh or no dagesh. Look at the Jastrow entries for sin / sinner (though he does have gemination as an option for one):
https://www.sefaria.org/Jastrow%2C_%D7%97%D6%B2%D7%98%D6%B8%D7%90%D6%B8%D7%94.1?lang=he&with=all&lang2=he
I'm not clear on this whole "Dagesh" thing. Can you explain why if it means arm then there would need to be a dagesh in the mem? likewise for חַטָּאִים