A gas turbine engine including at least one high pressure turbine rotor and at least one high pressure compressor rotor drivingly engaged to a rotatable high pressure spool, a low pressure spool rotatable independently of the high pressure spool, at least one low pressure turbine rotor drivingly engaged to the low pressure spool, and a rotatable load drivingly engaged to the low pressure spool. A fixed rotational speed ratio is defined between rotational speeds of the at high pressure turbine and compressor rotors. A fixed rotational speed ratio is defined between rotational speeds of the low pressure turbine rotor(s) and of the low pressure spool. A low pressure compressor rotor is in driving engagement with the low pressure spool through a variable transmission which defines a variable rotational speed ratio between the rotational speeds of the low pressure spool and of the low pressure compressor rotor.