Profondo Rosso

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The screens opens with two shadowy figures struggling until one of them is stabbed to death while a child's scream is heard.
The film then follows jazz pianist and music teacher Marcus Daly (Hemmings) as he investigates the violent murder of psychic medium Helga Ulmann (Macha Meril). Other major characters are also introduced early including Daly's alcoholic friend Carlo (Gabriele Lavia), Carlo's scatterbrained mother Martha (Clara Calamai), Ulmann's associate Dr. Giordani (Glauco Mauri) and reporter Gianna Brezzi (Daria Nicolodi).
Before the murder, Ulmann holds a lecture in a theater where she senses that there's someone with a twisted and violent mind in the audience that she cannot clearly identify. Later that night, while Ulmann is in her apartment taking notes about the incident in the theater, someone kicks the door in and attacks her with a meat cleaver. The killer also destroys her notes. Marcus, who also lives in the same apartment building is walking home when he sees the woman being attacked through the window. He then rushes into her apartment to find the woman bleeding to death with shards of glass in her throat.
After the police arrive, Marcus realizes he had seen a certain painting among a group of portraits on the walls of the victim's apartment, which seems to have disappeared. The killing of Helga Ulmann is prefaced by a child's doggerel tune (the same music that accompanies the film's opening sequence). The music serves as the murderer's calling card. Marcus hears it in his own apartment soon after becoming involved in the case, and is able to foil the murderer by locking himself in his study. Later, he plays the tune to Giordani, a psychiatrist who theorizes that the music is important because it probably played an integral part in a traumatic event in the killer's past. Another friend of Ulmann tells him about a folktale involving a haunted house in which a singing child is heard, followed by the shrieking of someone being murdered.
Investigating the source of the music tune and the folktale, the search leads Marcus to a story from a book written by Amanda Righetti (Giuliana Calandra), titled House of the Screaming Child which describes a long-forgotten murder. Marcus tries to find Amanda Righetti to talk to her about her book, but the unseen killer arrives at Righetti's villa first and kills her by drowning her in a bathtub filled with scalding hot water. Her face soon starts to decompose as she dies. The dying Righetti manages to write a message on the wall of the steam-filled bathroom before expiring. Marcus then finds the body but afraid that the police will think he did it and leaves the place without calling anyone. Thanks to a picture from the book, Marcus locates the house where the folktale originated and learns from the caretaker that no one has lived in the house since 1963 when the previous owner disappeared. Marcus looks around the house, removing plaster from a wall that uncovers a child's drawing of a little boy holding a bloody knife next to a murdered man and a Christmas tree. Only after he leaves the room, more plaster suddenly falls off, revealing a third figure in the drawing.
Meanwhile, Giordani investigates the Righetti murder scene and, on a hunch, turns on the hot water in the bathroom and sees part of the message left on the wall by the murder victim. When Giordani returns to his office that night to investigate more. Suddenly a door opens with a laughing toy clown approaching to him as he kills it with a knife. The unseen killer then breaks in and stabs him in the neck with his own knife after bashing his teeth in on a mantelpiece. Marcus also discovers a clue that he initially overlooked in the photo of the deserted house realizing a window on one of the walls is missing. Marcus returns to the house after dark after unsuccessfully bashed in the wall where the window was (which leads to him nearly to fall off the ledge) when he enters inside. Using a pickaxe, he knocks down an end-wall in a hallway and discovers the secret room with a rotting skeleton next to a Christmas tree. The unseen figure then arrives and knocks Marcus unconscious. When he regains consciousness, he finds that the house is on fire and Gianna by his side, who arrived in the nick of time to pull him out of the house.
Marcus and Gianna go to the caretaker's house to call the police and the fire department. There, Marcus discovers the caretaker's young daughter Olga has drawn an identical drawing of the little boy with a bloody knife standing next to a murder victim. Olga tells them she copied the drawing from an old file in the archives at her junior high school. Marcus and Gianna then break into the school to search the archives for the drawing. Marcus finds the painting, which has Carlo's name on it. He looks for Gianna and finds she has been stabbed. Carlo suddenly appears before Marcus holding a gun and threatens to kill him for getting too close to the truth. Just as the police arrive, Carlo flees and climbs over a wall only to get hooked onto a rebar transported by a passing truck and is dragged down the street to a gruesome death.
The case is apparently wrapped up with Carlo being the killer. After Marcus drops off the wounded Gianna at the hospital, he heads back to the scene of the crime, he realizes that Carlo could not have murdered Helga Ulmann because they were together only for a few seconds before Marcus saw her at the window. Marcus then enters the murder victim's apartment and after looking around, finally remembers what he saw in a mirror reflection which he thought was a portrait that night is the face of the killer. When he turns back, the killer appears in front of him as the identity of the killer who's finally revealed to Carlo's insane mother Martha. In a flashback, When Carlo was still a child, he watched as she stabbed her husband when he tried to have her committed to a psychiatric hospital. Carlo, traumatized, picks up the bloody knife staring at it and entombed his body in a room of the house.
In the climax, Martha confronts Marcus and tries to kill him by wielding a meat cleaver as she chases him out of the apartment to an elevator. Marcus is then struck in the shoulder by the meat cleaver, but manages to kick Martha toward the elevator shaft. When the long necklace she's wearing gets caught in the bars of the shaft, she's decapitated when he pushes the elevator button. The film ends with Marcus staring a pool of Martha's blood.

Question: Who was the killer?
Answer: Martha