Is Rosh Chodesh Av any different than the rest of the nine days in terms of stringencies otherwise applicable during the nine days and the three weeks? For example, is there any heter to listen to music on Rosh Chodesh Av?
Orach Chaim 551:2 clearly indicates that there is no difference between Rosh Chodesh and the rest of the nine days.
I'm copying cmb's clear answer from a similar topic (good chazara):
this issue depends on whether you are sefardi or ashkenazi. although a minority opinion holds that if one always has a meaty rosh chodesh seuda then he may do so on rosh chodesh av as well, however the vast majority of poskim - including the chayei adam (133,15) and mishna brura (551, 58) rule that one may not have meat on rosh chodesh itself; they hold the nine days are just that - nine days- mishenichnas av -meaning rosh chodesh - memaatin besimcha - this means that as soon as it is rosh chodesh av the restrictions already apply.
yet, even the sefardi poskim who are machmir on the 9 days (the shulchan aruch cites 3 opinions with no ruling) hold that one may eat meat on rosh chodesh av itself - including the ben ish chai (year 1 devarim 15) and kaf hachaim (551, 125 -126). they hold lo ad bchlal, especially as sefardi poskim technically never took on 3 weeks or nine days, rather shavua shechal bo; therefore those sefardim who are machmir and start restrictions from the nine days - at least still have rosh chodosh av to be lenient with. i think the lashon in the kaf hachaim is - v'dye bazeh.
lchoirah the same would apply to the other restrictions as well