Margaret Robertson, 54, was discovered at around 1.20pm on Friday at 45 Promenade Court in the city.Detectives are trying to piece together her movements since she was last seen on Tuesday September 24.
They appealed to the public for information and said the suspect or suspects may have blood staining on their clothes.
A 27-year-old man arrested on Saturday has since been released from custody in relation to the death.
Detective Inspector Gary Winter, from Police Scotland's Major Investigation Team, said: "We are continuing to investigate the circumstances surrounding Margaret's violent death.
"I am particularly anxious to speak with anyone who has any knowledge of Margaret's movements between 9am on Tuesday September 24 and when she was found within her home address at 1.20pm on Friday.
"Given the nature of the attack, the person or people responsible may have blood staining on their clothing.
"If you have any information about who was responsible for attacking Margaret, please get in touch with Police Scotland as a matter of urgency."
Local Area Commander Chief Inspector David Howieson said: "Our thoughts are with the family and friends of Margaret Robertson at this tragic time.
"I understand that a violent crime of this nature may cause concern to the local community, however I would like to reassure them that extensive inquiries are being carried out by a large number of local, national and specialist officers.
"We will also have an increased visible police presence in the area for the foreseeable future."
Anyone with information should contact Police Scotland on 101, quoting incident number 1735 of September 27, or email [email protected]