SymbolismThere are three major themes related to Sayaka's character that I've noticed: music, water and the color blue. All three of these come up repeatedly in her story, her transformation sequences and magic. Because I love symbolism and thinking about why the creators chose these themes for Sayaka's character specifically, I've looked into what they could potentially represent.
MusicWhile music may not be a literary symbol, I would argue it symbolizes Sayaka's connection to Kyousuke. Bringing Kyousuke CDs and listening to music with him was the means that Sayaka was able to use in order to become closer to him. She had always been in awe of his musical talent and everything that made up the Kyousuke she had feelings for resonated with music. Even her wish, to heal his hands, stemmed from her desire to hear his violin again. Therefore, music is Kyousuke in her mind. Sayaka's magic is accented with various references to music, which likely symbolizes the desire behind her wish. Her body heals with circles of music notes and similar strings of music notes can be seen in her original transformation sequence, for example. The "c" symbol on her soul gem reminds me of the symbol for common time, a standard time to play music in. However, the music notes that accent Sayaka's magic are depicted in a similar c shape and therefore I assume it is actually supposed to be a music note. Additionally, Sayaka has a fortissimo (ƒƒ) hair clip when she transforms in the movies—a form of music notation. Fortissimo means to play very loudly, which could also represent Sayaka's tendency to be loud and dramatic!
Another possible interpretation of Sayaka's connection to music is how it may represent strong emotion, as music often evokes emotion in people and moves them. Sayaka deals with a number of strong emotions that tend to fluctuate, just like music can. While some music can be majestic, inspiring and beautiful, other music can sound destructive, hateful and be full of sorrow—even in the same song. In this way, I think music can symbolize the hope and despair that Sayaka strongly experiences.
WaterWater is another theme that is associated with Sayaka. All of her transformation sequences have water elements such as bubbles and appearing as though she is floating underwater. Oktavia, her witch form, is a mermaid and also has various elements of water in her labyrinth such as swimming fish and bubbles. As for water, it can have a variety of meanings depending on the context. I have most often seen water associated with cleansing/healing, which could potentially be linked to Sayaka's wish to heal Kyousuke's hand. It can also symbolize insight and reflection. While Sayaka is typically more impulsive than not (thus fire may make more sense as an element), she does have times where she says insightful things and reflects on what has happened. Becoming a magical girl arguably causes Sayaka to reflect on her feelings and choices, for example. Sayaka displays insight when she tells Madoka they have been living in blissful ignorance and there are other people out there who would jump at a chance to put their life on the line for a wish because they've known unbelievable suffering. Sayaka's realization of this ultimately leads her to consider making her wish for Kyousuke instead. Therefore, water could represent the insight that lead to her making a contract with Kyuubey. Water is often thought of as a symbol for the flow of life and thus transformation. Though it may be a bit of a stretch, Sayaka is arguably the representation of the transformation of a magical girl to a witch because she despairs in almost every timeline. Despair results from the unfair nature of life, and therefore water could potentially symbolize this as well. Lastly, water symbolizing the flow of life could also be connected to Sayaka's metamorphosis.
Rain is another form of water that seems to be stylistically used during emotional moments with Sayaka. It rains when Sayaka and Madoka are waiting at a bus stop after her emotionally charged fight with Elsa Maria. As the two girls talk and Sayaka becomes more emotional, the storm gets worse and the rain seems to get heavier. Further, it is also raining during Sayaka's funeral. I had two thoughts when considering both of these scenes. First, water in the form of tears and rain can symbolize despair or grief, both of which are strong feelings Sayaka experiences. Secondly, water can vary in intensity. Water can be gentle and soothing, such as a light rain shower or it can be harsh and destructive like a heavy storm that causes flooding. In this way, water could symbolize the potential for both hope and despair that punctuates Sayaka's story. As a magical girl, Sayaka is a reassuring, warm presence that offers protection. As a witch, though, Sayaka spreads despair and destruction.
The Color BlueEach magical girl has a different color focus for their design and soul gem. Obviously, Sayaka's color scheme is blue. The color blue is associated with a number of things, but I picked out the ones that make sense for Sayaka. Blue is associated with loyalty, honor and peace. I think these are traits that resonate with Sayaka's ideals of justice. She feels magical girls have a responsibility to protect others no matter what and that they exist to maintain peace in the city. Sayaka seems to be very loyal to her friends and struggles with having hard feelings toward Hitomi over Kyousuke because of it. Blue is also idealistic and inspires higher ideals. Sayaka's ideas of justice and being a magical girl are arguably more idealistic than realistic. However, she still inspires others like Kyouko to strive toward those ideals to the best of their ability. Blue can be linked with love, soothing/comfort and devotion, which I think resonates with Sayaka's relationship with Kyousuke and her wish to heal his hands. Love is the centerpiece of her story. Sayaka also spends a lot of time and energy and sacrifices her humanity for Kyousuke, which could be considered a form of devotion. Blue energy is even said to stimulate the appreciation of the arts, such as music! Music is integral to Sayaka's character as I've already described in the section on music above.
Those who like color blue are said to be frequently associated with personality traits such as appearing to be confident and self-controlled, but hiding a vulnerable side and being a rescuer who loves to be needed. I think these are both very true about Sayaka. She puts on a tough and confident front, even if she is scared and shaking. She also has a tendency to pull away from others and withdraw when feeling vulnerable, which may very well be to prevent others from knowing she is struggling with such feelings. As for the second half of that, Sayaka desperately wants to be needed by someone, as I discussed in her relationship with Kyousuke and in relation to her despair. Not being needed by someone ultimately leads to Sayaka feeling worthless. Learning to love yourself first is a lesson associated with the personality color blue. Though it isn't delved into in the series, I really think this applies to Sayaka because of how she seems to feel about herself when there's "no place left for [her]" or "no one that needs [her]." Those with a blue personality become deeply hurt when their trust is betrayed, which is evident when Sayaka processes her anger and hurt feelings toward Kyousuke in the train scene. Lastly, those with a blue personality can be incredibly rigid and stubbornly stick to their way of doing things. This immediately makes me think of Sayaka's refusal to stand down in confrontations with Kyouko even when she is clearly no match for her. NOTE: There is likely not much, if any, research behind the "blue personality," but I thought it was something fun to consider, especially because a number of the traits seemed to resonate with Sayaka's character!