Every year, the Edinburgh Art Festival embarks on a series of temporary commissions that run in addition to the gallery shows and performances around town. This year EAF has commissioned seven artists to reimagine the idea of the city, loosely joining their endeavours together under the banner of The Improbable City, an idea based on the meditations found in Italo Calvino’s thought-provoking book, Invisible Cities.

It all adds to the rich mosaic of Edinburgh in August. The installations are not in galleries, largely, but tucked away in odd corners – a disused church apse, a darkened room at the top of an ancient spiral staircase, a railway station concourse – and rather fun to alight upon, no matter what you think of the rather variable art itself.

You could almost tick them all off in one city-centre swoop, although Julie Favreau’s film installation is the outlier, placed in the Scottish National Gallery of Modern Art some distance walk from the rest. There’s a daily guided tour (2-3pm, no booking required) until the end of the festival if you’re concerned about your navigational skills, whether geographical or arty.

I started my own tour at the top of the Royal Mile, where Hanna Tuulikki has installed her intriguing Sing Sign in a dark room under the painted timber beams of a gallery space in one of Edinburgh’s oldest houses, Gladstone's Land. Two tall screens face each other, from which Tuulikki and her male collaborator Daniel Padden literally sing the geography of Edinburgh’s closes across the ether. Each is dressed in simple white smocks, each with a paper map of the Royal Mile and its myriad closes hanging from their collars. They gesture and coo their way wordlessly through Tuulikki’s compositions, throwing the notes back and forth, created quite literally from the resonances of space calculated from a map of the Royal Mile closes.

But it’s all a little obscure on film. There’s something interesting to be said about the nature of communication here, between peoples and people and city space, but it lies a little thin. Catch Tuulikki’s forthcoming performances (August 28 and 29; free but book on EAF website) to see a live performance in the closes which may, one suspects, have rather more obvious resonance.

A quick traipse down the Royal Mile to Chalmers Close – easy to miss in the thick warren of passages giving off the High Street – brought me to Trinity Apse, a soaring empty space that was once the Brass Rubbing Centre, but now, rather sadly, lies largely disused.

Ariel Guzik’s Holoturian hangs at one end of the room, a metal deep sea submersible that looks like a cross between a metronome and a very heavy pendant containing one small cactus, a musical instrument and the climactic conditions required to keep the cactus alive under the water. Emitting cetaceous sounds that the gallery attendant tells me were recorded by the Holoturian in one of its underwater trips off Baja California, the whole, along with the semi-fantastical drawings and back-of-envelope submersible designs, has the air of a project that exists in its own fantasy.

There’s an interesting connect here, between the verticality and depth of space in the apse and the proposed depths to which Guzik’s self-designed submersible, the Holoturian, will sink. But the diverting whole doesn’t here venture much beyond an illustration of the idea of an individual’s obsession with inter-species communication and the idea of the fantastical beyond our ken, coupled with a bit of slightly pseudo-scientific research.

More imaginative worlds at the next stop, a quick hop downhill into Waverley Station for Charles Avery’s Tree No. 5 (from the Jadindagadendar). Hanging in isolation in the vast concourse at the back of Waverley, the tree is a brass and plastic weeping creation taken, so we are told, from the Jadindagadendar public park in the fictional town of Onomatopoeia, created by Avery as the main port of the imagined Island whose aesthetics, philosophy and day-to-day life have formed the backbone of the artist’s work since 2004.

The tree, here, seems like the unknown at the end of a putative journey; something recognisable but curiously alien. The context lies across the railway bridge in the Ingleby Gallery where Avery’s Island vision is writ large in drawings and sculptures of small-town tattiness, of people hanging around harbour steps, of decline and nothingness and a slightly curious economic and touristic monoculture centred around the eel. Our world, twisted but recognisable.

A dog leg, then, up to the Royal High School in which EAF has installed a nine-metre-long chalk drawing by South African artist Kemang Wa Lehulere and an expansive and nightmarish alternate reality by Marvin Gaye Chetwynd, the performance artist formerly known as Spartacus.

Chetwynd’s set – for that is what is seems, sprawling through the lecture theatre and its ante-room – is both amusing and dark, a concatenation of scrawled periodic tables and a paper-wrapped anatomy theatre in which a super-sized papier mache turtle awaits what one assumes will be its not-very-pleasant fate. It’s a promise of madness and a certain terror, but beyond that it stalls, as if awaiting more input.

And in some ways it is. The installation is almost the detritus of performance, and that for me felt a little empty, as it had elsewhere on the trail. Chetwynd’s art is centred on performance, so if you want to see the work in more context – and almost certainly more chaos, on past form – than its everyday presence, get along to the Royal High at 2pm today (free, book on EAF website) when Chetwynd will mount a performance of The King Must Die.

The Edinburgh Art Festival's Improbably City installations run until August 30, www.edinburghartfestival.org. Charles Avery is at Ingleby Gallery until October 3, www.inglebygallery.com