It’s not the notes he did write, it’s the notes he DIDN’T write.
If you think about it, writing (musical or text) is just the older way to record sound. To preserve an image through eternity, you paint a picture. To preserve a sound for eternity, you have to use a code which tells you how to recreate the sound in the present – whether that code is phonetics, hieroglyphs, or notes on a staff. If a human isn’t recreating the sound (out loud or in the mind), the writing is just visual patterns.
As history progressed, music notation became more and more complex, giving composers complete control over the music they wanted to preserve or create. More and more musical terms and symbols made their way into scores from the 18th to the 19th centuries. By the 20th century, scores were expected to be precise down to the most miniscule subtlety. If it wasn’t written down, the performer didn’t do it. There also opened up fields of musical scholarship that studied the older scores and tried to detoxify them of modern performance practices. For example – if Bach wrote a little squiggly line above a note (called an ornament), what exactly did that mean? play an extra note below the printed pitch? two? or above? above and below? fast or slow? etc. etc. etc.
This is similar to a lead sheet – sheet music regularly used by jazz, pop, and rock musicians. It displays the melody of the piece with chords labeled above the melody. It allows the performers a good deal of freedom – they can choose which instruments to use, what sort of beat to play, and how the accompaniment will work. Take “Somewhere Over the Rainbow”, which is famous in two versions – the original and the ukulele. So, if you have a lead sheet to “Bad Romance“, you could perform it as a polka if you really wanted to (why has nobody done that yet?)
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