Tisha B’Av and Simcha generally
The gemarra says that just like in Adar we increase the simcha, so too in Av to we decrease the simcha. This decreased simcha culmitaes with - and indeed originates from - Tisha B'Av. The question is 'what exactly is simcha?' And thus what does it mean to decrase or increase the presence of simcha?
Let's start by mentioning some of the contexts in which the concept of simcha is written, and then deduce an answer from there...
Chazal (as told by the torah too) tell us that the festival of sukkos has 'simcha yeteira' ie extra simcha; as demonstrated by the ceremony of the simchas beis ha'shoeva in the beis hamikdash with was in essence a very busy 7-day festival. [In fact, the gemarra at the end of sukka tells of different things some Rabbis used to do in celebrating.] Another famous phrase regarding simcha comes from Rav Nachman of Breslov, who famously said 'mitzvah gedola lihiyos besimcha tamid' (ie it is mitzvah to be in constant simcha). The idea (as found in orchos tzaddikim - an anonymous mussar sefer) is that simcha does not mean happiness as we would define it today. We tend to equate short-term happiness and long-term
happiness under one banner of 'happiness' - a child eating an ice cream would be called 'happy' as would someone who has completed a 20-year project be called 'happy,' despite their clear differences. Simcha means the feeling of completion of a long-term process of working on something (preferably oneself) to produce a desired result. (I think I saw this idea quoted in a Rabbi Tatz book too). In short, simcha is long-term happiness from long-term work. This is why sukkos is called 'extra simcha' for it is at the end of a very intensive 45 days of work from the month of elul - now it is the chance to enjoy the fruits of one's labour in being in a chupah with HaShem - the sukkah (R Pinkus). This is what Rav Nachman means as well; he does not mean that evryone should go around smiling the whole time (smiling is also a mitzvah), but he means that one should always be b'simcha ie always be working on oneself to reach long-term goals and thus end up with long-term feelings of achievement.
Now that is all very nice, and simcha is thus a very positive thing. But why in the world should we be told in Av to reduce the simcha - should we stop working on ourselves? The answer is a definite 'no;' the point of a fast day is teshuva (gemara taanis as brought by the mishna berura 549;1). So what does 'reducing the simcha' mean? Ahh - this means moving slightly away from the long-term and focusing on short-term boosts. A reduction in simcha means a reduction in long-term working on oneself, (not no working whatsoever) and thus means that the focus should be on short-term spiritual boosts. I shall endevour to explain...There are two types of religious boost in Judaism. One is a short-term burst of emotion for example; a sudden realisation of gratitude to HaShem . The other is a longer-term boost that comes with long periods of working on a particular middah. Both are important. [In fact, Rav Kook suggests that this is why women are exempt from time-bound positive mitzvos, since all those mitzvos are aimed to kick-start a short-term connection, and women are created with that connection anyway.] Anyway, the point is that Av sees a focus on a short-term spark. Thus, the halachos of Av centre around this theme - one cannot build certain buildings, one cannot plant certain gardens because they produce 'simcha' (orach chaim 551;2). None of these things are going to be enjoyed immediately - it does not take a garden one week to grow, nor a building project 1 week to complete. The point is that these produce simcha for it marks the beginning of a long-term project which thus produces simcha even upon their commencement.
This distinction between short-term boosts and long-term projects can ultimately be described by what is called 'lev' and 'sechel' ie heart/emotion and brain/intellect (fogive me for poor translation of sechel). The heart is the focus of emotion, which is by nature a short-term fuse (the emotion of anger is never a long thought-out process - perhaps only the plan of revenge is!). Whilst the intellect has a long-term process of steps of understanding. And we put one box of tefillin by our heart and the other by our brain to signify that both are integral to religious growth. [so too do chazal learn remember amalek in your mouth and heart in referring to these two attributes.] I heard Rabbi Roberts (from London; he works for Seed and teaches in Menorah amongst other places) once ask what the mitzvah of the day of 9 av is? This means the following; sukkos has a lulav to do a mitzvah with. Pesach has matzos (both amongst others), Shavuos has the torah essentially (or maybe cheesecake!), channuka has the menorah as the mitzvah-kli. But what is the kli shel mitzvah on 9 av? The answer, he says, is the proper use of human emotion. For that was the sin of Tisha B'Av - it started officially when the Jews cried upon hearing the reports of the 10 spies. And HaShem told them 'you cried for no reason on this day, I'll give you real reasons in the future to cry on this day.' [The Spanish inquisition and 'final solution' in WW2 were both hatched on 9 Av.] This was a misuse of the human emotion. Thus, the mitzvah of Tisha B'Av (aside from teshuva like the other fasts) is the proper use of human emotion and tears for the correct reason. [As one chassidc Rebbe once put it harshly, 'if one cannot cry over the destruction of the beis hamikdash, then one should cry over their personal spiritual destruction.'] The point is that this complements the above - the focusing upon the short-term human emotion couples the definition of 'reducing simchah' above ie a focus on the short-term bursts.
One last thing, which I personally find quite nice. If decreasing simcha means focusing on the short-term boosts and increasing simcha means focusing on the long-term work, then Adar should encapsulate long-term work and intellect as opposed to emotion. This is because 'when Adar comes along, we (pump) up the simcha.' So let's spend the final part explaining this. Rashi (taanis) says that the 'increase of simcha' regards both Adar and Nissan due to Purim and Pesach. Now it is quite easy to see the focus on sechel in Pesach; we are encouraged to ask questions at the seder night to delve deeper into the story - the personal connection to the exodus forged here seems to be more of a 'sichli' one than a 'lev' one. (That does not mean that one cannot have an emotional connection to Pesach.) But Purim; surely that is nothing to do with intellect - we are supposed to get drunk so we cannot tell the difference between Hamman and Mordechai; that is hardly intellectual prowess??? But it is exactly herein that lies the point. The pasuk says 'Reishis chochmah yiras HaShem' ie chahmah starts with fear of HaShem. A prerequisite to chochmah is realising Where it came from (HaShem) and thus directing it to good use. As the pasuk in Iyov says 'HaShem can remove the wisdom from the wise.' The way to demonstrate openly that wisdom starts with HaShem is to have a moment whereby one gives up this intellect to HaShem upon his command. And that is exactly what we do in getting drunk on Purim - we give our intellect back to HaShem and thus show that He is the Source of chochmah. And this comes at the start of the period of 'increased simcha' for that is the prerequisite to sechel and chochmah.