Its great asset is Sir Simon Rattle. He is a born teacher, with a hushed but compelling delivery and a fearless relationship with the camera. His script is aphoristic. For him The Rite of Spring “jumps, leaps, stamps”. With Debussy, “we’re talking watercolour, or some kind of painting not yet invented”, while Stravinsky’s Firebird has an “unparalleled kind of savage glitter”.

Rattle has another big advantage: he has plenty to do all the time. While Robert Hughes or Sister Wendy can do little more than look at works of art and explicate them, Simon Rattle brings them to life. He conducts with what can only be called radiance and, seated comfortably at the piano, he illustrates his words simply and effectively on the keyboard.

The main drawback, however, is time. Or rather the lack of it. Rattle wants to popularise the story of modern music. With visual art, a point can be made by a few seconds’ exposure to a painting. But music cannot be taken in at a glance, so that even with an hour to play with, fitting in more than half-a-dozen pieces runs the risk of the programme becoming, in his own words, “some purgatorial spot-the-masterpiece quiz”.

Given that limitation, he uses his time well. In the first programme “Dancing on a Volcano”, about the crumbling of tonality in Vienna in the late 19th century, he shows how Schonberg and other composers moved away from the traditional eight-note scale with its rigid loyalty to the “home” key and developed a 12-note system. Rattle talks, soloists sing, the City of Birmingham Symphony Orchestra plays relevant pieces. There are images related to the music of water, forests and clouds gliding across the moon. Then there is archive film and contemporary art. In later programmes, occasionally, a composer like Messaien or Takemitzu talks about his music. It is a familiar, even predictable mix, but it is bound together by Rattle’s restrained passion.

The most difficult problems with music programmes are poor sound on home televisions and what to look at when the band plays. The visual interpretation of the music itself is sometimes quite brilliant - watch out for the Firebird in the third programme, “Colour”, where a fleeing figure races the blood-red setting sun through a dark forest.

Rattle’s survey is - for all his reservations - a comprehensive account of new music in the 20th century which nicely balances musical analysis with an emotional response to the 30 composers featured. Rattle tackles rhythm, Eastern European composers, Americans, asks if “new” music is really possible and makes a personal choice of works which most clearly illustrate the way new music is going. This is a series to inspire and motivate not just students of music, but a general audience.

The book which accompanies this series will be reviewed in TES2 next week.