William Mysterious: Bassist with punk rockers the Rezillos

Using the pseudonym William Mysterious, Alastair Donaldson played saxophone and bass guitar with the Scottish punk band the Rezillos. Combining a sci-fi, day-glo aesthetic, references to Thunderbirds and The Flintstones, and a fast, fun take on 1960s beat music, the group burst on to the Edinburgh scene in January 1977 and later that year signed to Seymour Stein's Sire Records, the home of New York punk-pioneers the Ramones and Richard Hell. Credited as Mysterious on their exuberant debut Can't Stand the Rezillos, which made the Top 20 in August 1978, Donaldson left before the band appeared on Top of the Pops to promote their paean to the very same television show but returned to contribute to their swansong release, Mission Accomplished... But the Beat Goes On, recorded live at the Glasgow Apollo on 23 December 1978.

A stalwart of the Edinburgh music scene, he also helped Mike Scott in his pre-Waterboys days, and continued performing while working for various architectural practices in the city.

The youngest of three children born to an accountant father and college lecturer mother, he excelled at music, English and art and delighted his music teacher with his prowess on the flute. He was 17 when he enrolled at Heriot-Watt University to study architecture in 1972, though by the mid-1970s he had joined the Scots folk group Silly Wizard, playing bass, organ and flute on their eponymous debut for Transatlantic's Xtra label in 1976.

Via his friendship with the drummer Angel Paterson, he gravitated towards the Rezillos (named after a variant on the Revilo's diner sign pictured on the cover of the first issue of The Shadow DC comic). At first, he guested on saxophone but soon replaced original bassist Dr DK Smythe and contributed the dynamic basslines that introduced the group's second single, the irresistible "(My Baby Does) Good Sculptures", underpinned its B-side "Flying Saucer Attack", and became a distinctive feature of their sound.

By then the Rezillos had slimmed down to a quintet comprising Donaldson and Paterson, primary songwriter and guitarist Jo Callis and the formidable vocalists Fay Fife and Eugene Reynolds. Having signed to Sire, they gave the Ramones a run for their money as their support act on the Rocket to Russia UK tour of 1977. Two months later they travelled to New York to record Can't Stand the Rezillos at the Power Station under the guidance of Tony Bongiovi (second cousin of Jon Bon Jovi) and up-and coming engineer Bob Clearmountain.

Now acknowledged as one of the best punk albums of all time, the band's debut contained a re-recording of their first single "I Can't Stand My Baby" along with "2000 AD", a Donaldson-Callis collaboration, as well as "It Gets Me", solely written by Donaldson. His saxophone was also the lead instrument on "20,000 Rezillos Under the Sea" – a reimagining of Gioachino Rossini's William Tell Overture, also known as "William Mysterious Overture" – cut during their New York sojourn; it served as the flip of the hit version of "Top of the Pops".

The Rezillos had lost momentum while the savvy Stein waited for his Sire licensing deal with Phonogram to run out before unleashing the band's album and single via a new agreement with Warners and Donaldson grew impatient and quit. Indeed, despite the success of "Top of the Pops" and their next single, the ebullient "Destination Venus", the Rezillos split at the end of 1978 after a brief tour supported by the Undertones.

Donaldson remained friendly with Fife and Reynolds and joined the Revillos, the even more cartoonish band the vocalists launched, for their "Scuba Scuba" and "Hungry For Love" singles and Rev Up album in 1980. Two years later Fife returned the favour, contributing backing vocals to "Security of Noise", Donaldson's single on his own Mezzanine label issued while living in Hull, where he had resumed his architecture studies.

"Alastair produced my first record, 'All The Boys Love Carrie', by my first band Another Pretty Face, and he played sax on it too," recalled Mike Scott. "We met him backstage at a Rezillos gig around late '78, and he was really nice to us, took us under his wing, and we became his protégés for a while, which is how he wound up producing us. He did our live sound for six months too, and was a great encourager. He was also the guy who first played me "The Calvary Cross" by Richard Thompson, with its amazing guitar intro, so his influence on us wasn't just that of a punk older brother. He was a head too, and he turned us on to stuff. We thought he was the coolest guy on the Edinburgh scene."

Alastair Gilfillan Donaldson (William Mysterious), musician: born Edinburgh 27 April 1955; married 1991 Janice (marriage dissolved; one daughter), 2004 Ksenija Horvat (one son); died Edinburgh 18 June 2013.