In addition, Jim Dowling has been appointed managing director for the UK arm of the Havas-owned Cake.
In a statement, Cake said Mathieson, the former head of PR at Virgin Records, has been developing his new venture for the past few months. He will be joined by Macky Drese, former VP of the Brand Partnerships division at MTV/Viacom International Media Networks.
"Harmonic will launch with a number of artist clients in place and key developments to be announced in the coming weeks," the statement said.
Mathieson, who is to leave Cake at the end of 2014, said: "The next iteration of the music industry is going to rely heavily on income beyond tickets, merchandise and sales and that is going to require brand and agency-based thinking, particularly around data and IP. Artists are fast becoming their own sizeable media distributors and marrying this with data and insight to create harmony between brands, bands and their fans is going to be key."
Pettett, who co-founded Cake with Mathieson and Mark Whelan in 1999, said: " Whist I am extremely keen to capitalise on the energy we have at Cake, there is no doubt, we will all miss Mike greatly, both for his drive and vision over the past 15 years as well as his infectious enthusiasm for the business.
"I know all the teams within Havas join us in supporting him in his new venture with his first love - music. For us at Cake it is a real opportunity to build on the momentum we have generated over the past year with a string of high profile new clients and awards. These are exciting times at Havas as it continues to invest in data and content, the opportunities for Cake to play a front and centre role in a truly joined up network are greater than ever."
Mathieson added: "We co-founded Cake on four basic principles: to be creative, have fun, make some money and that’s it. Fifteen years on, I think I have finally achieved all four of those principles and I’m excited to be making a return to the music industry. Of course I am sad to leave the business that I founded, but I leave it in the safe hands of my long-time partners and the Havas Group."
Pettett and Dowling start their new roles on 1 December.
Recent high profile account wins from Cake include Shop Direct, Sainsbury’s and Google-owned Nest.Cake's roster includes names such as Sony, River Island, Microsoft, Virgin Atlantic, One Direction, Carling, EE, Weetabix and Alton Towers. In the US, where Cake has an office in New York, clients include Pernod Ricard, Keurig, Havaianas, and LVMH.