It's taken a long time to convince me that the mathematical appeal of architecture can be as strong as the picturesque.
That may be in part an Anglo-Saxon prejudice. The Gothic still rules in these islands - crags, castles, cathedrals, a cult of the picturesque, and particularly of the delights of buildings that have been built up over the years, accumulating accretions as they have pinnacles and parapets.
The first time that I visited Florence I was underwhelmed. It's only recently that I've come to appreciate the appeal of Brunelleschi's or Alberti's designs - the geometrical patterns that underlie the scheme, the perfect circles of the Pazzi chapel or the multiple grids of San Lorenzo. The reticence of the great palaces, of the arcaded courtyards, the simplicity and purity of the mouldings, just wasn't on my gothic wavelength. Then I came to love the baroque with its wit and theatricality - and still didn't understand the attractions of the Renaissance.
Maybe, too, the fact that every other bank in England put up between 1890 and 1930 seems to be in Florentine Renaissance pastiche style, had something to do with it. I was looking at the Renaissance from the wrong side - damning it because it looked a bit like the wretched and inadequate copies that I knew.
Now, after twenty years or so, I've been back to Florence again, and this time I tried looking at the works as if I were an English ecclesiastic of about 1500. Used to the Perpendicular style with its emphasis on almost i infinit e subdivisions of space into panelling and tracery, and looking at a style that was completely different - that tried to achieve the perfection of the basic geometrical form, that was about solids rather than planes, circles and grids rather than arches, simplicity rather than multiplication.
It worked. Brunelleschi seen through these spectacles was assertive, thinking through each geometrical element in turn - circles, grids, arches, domes (Pazzi Chapel, San Lorenzo, Santo Spirito, Duomo) ; Alberti, fluent and austere. And I began to appreciate the way that the geometrical proportions underneath the architecture create a sense of harmony and rest - very different from the aspiration of the Gothic or the drama of the Baroque.
It's a feel for the underlying mathematics, too, that distinguishes the music of JS Bach. (One of the things I found distressingly mechanical, at school, was the harmony teaching - rules, rules, rules, so that we could compose 'Palestrina' style chord progressions. It was so like doing geometry, except that geometry was more enjoyable. Whereas Handel and Vivaldi, more user-friendly contemporaries, create music of great surface appeal, Bach seems to root his music in mathematical progressions.
Sets of variations, the Art of Fugue, the whole edifice of the Well Tempered Keyboard with its 24 keys, show Bach thinking as a mathematician - carrying out processes of change which create new music from a static base.
Now music and architecture are usually kept separate. But a new venture brings them together. The Manchester International Festival has hired Zaha Hadid to create a space within Manchester Art Gallery where Bach's solo cello, violin and keyboard works will be played during July 2009. The work will attempt to echo the logic and mathematical rhythm of the music.
I'm intrigued by this concept - a building not just generally 'for music', but for a particular body of musical work. Wagner, famously, wanted to build a wooden theatre by the Rhine for the performance of his Ring cycle, to be burned down at the end of the tetralogy in a magnificent Goetterdaemmerung. And that's interesting, because this Zaha Hadid work can be seen as a collaborative Gesamtkunstwerk (total art work) - creating a whole that surpasses the boundaries of individual arts.
(In fact the thing it reminds me of most strongly is the fantastic range of musics and art forms created in Jack Vance's science fiction - attempts to embody a feeling in a perfume, a musical performance, an organ of torture victims...)