However, it appears the eccentric pensioner's stint on the sands is about to come to an end - after the council said his campsite was against the rules.
The 66-year-old, who hired professional movers to transport his 550lb piano to his new seafront home last week after he was kicked out by his wife, said he would be agreeable to finding a nearby flat and was keen not to outstay his welcome.
But the piano tuner, who said he was hoping to capitalise on the widespread publicity his stunt had generated to boost his business, said that his heavy-duty tent and piano would be staying at the beach, after the unorthodox attraction proved popular with locals.
"All they have to do to move me is ask politely, it'll be instantaneous," he said. "When I'm asked to leave somewhere I usually go - but the tent stays. The piano needs shelter and a lot of attention. It's extremely heavy. I don't think they'll ever be able to move it, I can't wait to watch them try.
"Everyone knows about it now, the kids would surround it if they try to move it. I plan to keep things exactly the way they are and hopefully find an affordable flat in the neighbourhood.
"I've met about 30 women I wouldn't have met otherwise because of this.
"The police and the council have both been round to say hello, the council just asked if the wind was getting the better of me."
Edinburgh City Council had initially said it wanted to "reach out" to Mr Treuhaft to offer him safety advice and ask him about his long-term plans.
However, the authority appeared to take a tougher line yesterday, saying his new home went against its rules and that he would not be staying at the beach indefinitely.
Mr Treuhaft, who previously lived in the affluent Morningside area of the capital, said he was aware of the statement and was expecting a formal letter.
A spokeswoman said: "We are liaising closely with Police Scotland in relation to Mr Treuhaft's personal safety, but it is clear that his campsite is in breach of the council's parks management rules, which prohibit camping on Portobello Beach. As such we will need to, in the long-term, take the necessary action to help him relocate."
Police Scotland said that while it had offered safety advice to Mr Treuhaft, his presence on the beach was largely an issue for the council.
Mr Treuhaft, who has been using the bathroom at a local swimming centre and eats at a local cafe, said he did not know what the future held for him and his wife, a renowned academic, who has previously called his behaviour ridiculous.
But the piano expert, who was born in New York and honed his tuning skills in piano factories in the American midwest and east coast and has worked for world famous pianists Vladimir Horowitz and Glenn Gould, is keen to remain in Scotland's capital.
His business, called the Underwater Piano Shop, was set in Berkeley, California, before travelling with Mr Treuhaft to Edinburgh via stints in Tokyo and New York. The father-of-two is the son of Jessica Mitford, who rebelled against her fascist upbringing, ran away to Spain and married a Communist nephew of Winston Churchill.
Edinburgh City Council deputy leader Steve Cardownie said that while he wanted Mr Treuhaft to be dealt with sympathetically, he hoped his actions would not set a precedent. "I've heard of people moving into friends' houses and sleeping in cars," he said. "But if every guy in Edinburgh who got kicked out set up camp on Portobello Beach, it would be like T in the Park."