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A beautiful new app for the iPad, called Rotor, lets you make music on your screen, and record it and alter it, by moving shapes around with your fingers. There are several such virtual controllers on the market; this one's shapes are particularly ingenious. Rotor lets you lay down loops and samples; each one of these looks like a little circle. You drag and drop them from a sidebar onto the centre of the screen. You can alter the tempo and the volume of each throbbing circle by rotating its edges. To make them play together, you draw a line between them. The computer will synchronize their beats, and even their keys, if you like. You can put as many synchronous sounds on the screen as you like, and move them around and cut them in and out, just using your fingertips. It's like conducting an orchestra.

The company that makes Rotor – Reactable – is also about to release a pair of hand-held controllers that go with the program: They appear to be like two stubby styluses you move over the screen to give you greater control over your burbling soundscape.

Once you have a bunch of these sounds interacting together on the screen, with the lines between them vibrating or shuddering exquisitely with every beat, the resulting visual pattern is beautiful in itself, like a dancing diagram. Most of these synth/controller programs – even down to the simplest one of all, which is the game Guitar Hero – rely on visual appeal as much as nice sound for their fun. These are games of sound and colour.

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And, amazingly, you could play a DJ set or an entirely improvised set in a giant club this way and no one would know your whole set-up was the size of a paperback book.

When Kraftwerk purchased its first synthesizer and brought it to its industrial sound studio in Dusseldorf, Germany, in around 1973, it was an operation like installing a cathedral's organ. The thing was the size of a room, as expensive as an entire new studio would be today, and had no screen as an interface. You plugged cables into sockets, like early telephone operators, to create sounds, and there were no lights or drop-down menus to guide you. The visual revolution of this was important, too: The banks of sockets were a new way of arranging musical notes, radically different from the black and white keys of a piano or the parallel strings of a guitar. Those pioneers were also experimenting with new ways of seeing music.

Computers revolutionized composition again, with the advent of sequencing programs that allowed you to drag and drop bars of music like glowing lozenges of candy. But for years, computers had to be paired with bulky physical controllers, keyboards and mixing boards, complicated set-ups that required techies with degrees in computing to prepare for each concert.

Touch screens have propelled the process into new territory again: Now, one can compose, record and alter music on the fly, using an almost limitless orchestra of virtual instruments, using one screen and one screen only.

There are a couple of repercussions from this development. First, it opens the game to amateurs and to those without an intuitive understanding of electronic machinery and its perennially frustrating problem of compatibility. People with deep musical talent are not necessarily also good at increasing their output buffer sizing for RAM optimization. Friendly screens mean more non-nerds will get involved in this kind of music.

Second, in dance-club culture, the new software and hardware promotes the idea of DJs and bands playing "live," that is without prerecorded songs. This movement is already powerful. Tech-loving techno DJs such as Richie Hawtin use loops and drum machines to create original work for most of their sets. Music snobs seek this talent out as a marker distinguishing "real" DJs from the stadium-filling, playlist-following, fist-pumping megastars of the EDM scene, who spend more time dancing than they do playing.

DJ software is reacting to this creativity by allowing users to use "stems" (isolated drum, bass and vocal tracks) of their favourite pieces, and the online purveyors of dance music are now selling stems – effectively selling music like Lego kits that can be disassembled and reassembled at the user's whim. Experimental electronic musicians, such as San Francisco's Holly Herndon, make a big deal of promising their audiences that, although we can't see exactly what she is doing on all her screens and consoles, she is not playing premade tracks. (In a recent concert in Los Angeles she flashed a sign on a screen behind her pronouncing, "EVERYTHING TONIGHT IS LIVE. THIS IS IMPORTANT … WE KEEP THIS LIVE OR THE END RESULT IS DEAD.")

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More nebulously, this pretty technology can be seen as part of a larger tendency in our lives towards the graphic representation of everything. Very little is abstract any more. Sounds and words and numbers are all spinning and glowing, colourful three-dimensional objects in our minds, because that's what they look like on our screens. When we check the weather forecast on our phones we see an image of a stormy sky or a sun. That hits us before the actual temperature does.

When we use screenplay-writing software we become used to moving scenes around physically, as if stacking neat plastic boxes. Similarly our music – once represented only as cryptic black scratches on white paper – is now circles and squares and starbursts. Whether this has any long-term effect on our cognition will be for the scientists to study; I wonder if our ability to conceive the invisible will change, or even shrink.

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