The reason that the two musical cultures drifted so far apart, before 1971, has, I think, to do with the commercial success of a popular culture that does not require its participants to have learned to read. In contrast, we students of "serious" music belonged to a print-culture. So we failed to understand McLuhan — and ignored him.

Pure oral traditions are beautiful and important, but human short-term memory has its limits.
For me, writing is still very important. It has always been the prerequisite for the development of higher cultures. It enables writers to think about and (re)consider their ideas while writing, before the ideas are finally made public. Also, its impossible to tell stories without using symbols. A Brückner symphony is unthinkable without writing.

At this point, I´d like to say something about Walter Benjamin´s 1935 Essay “The Work of Art in the Age of Mechanical Reproduction”. This famous text stands at the beginning of modern media-theory.
My impression now, 89 years later, is that Benjamin and his contemporaries underestimated the importance of the commercial interests of the printing industry in the 19th century. Scores and sheet-music were goods which were sold.
The 19th century (music) printing industry played a major role in supporting a star-cult: Big names sell books and scores. But it was also in the publishers´ interest that there should be a wide public that could read and play the scores. Great heroes, like Beethoven or Brahms, sold printed scores that had to be played live by the customers because there were no recording devices. The publishers therefore promoted musical literacy.
Benjamin´s contemporaries read not only music, but also ordinary printed text (novels, history, other non-fiction etc.). Printing and reading were simply taken for granted.
Of course, Benjamin was writing under the overwhelming impression made by the new medium film. Possibly he was afraid that print-media, live Performing Arts (whose roots are in print-media) and the educated middle-class would even become superfluous.

This score is very important in the history of space=time and electronic music notation. It has been quoted in many articles and encyclopaedias since it was written in 1954.
The notation describes how to create a tape, it is not for real-time interpretation by humans.
I made a new edition of the score, while still with Stockhausen in 2000, because the original plates had deteriorated so much by being repeatedly re-photographed. There were a couple of mistakes in the original score, which we corrected.
The row of small numbers in the middle of the score denote lengths of tape (in centimetres) that will be played back at 76.2cm per second, so space and time are indeed equivalent here, but note that the space on each page in the score is not necessarily proportional to the tape lengths: I sometimes had to distort the time axis on a page to make space for the numbers.
Stockhausen preferred his original version of the tape (in which the faders were adjusted by hand) to the computer-generated versions which he heard later. This shows how important fine performance details are: Equating space in the diagram to performance time does not improve the listening experience. Temporal perception depends on subtle temporal relationships, not on the way the events may have been notated.
Remember the shock when we first heard Bach played literally in the 1980s?

Stockhausen and his contemporaries thought of time as being equivalent to a dimension of space. They inherited this idea from physics and standard 19th century notation, but it does not apply where human memory is involved.
20th century neo-classic composers assumed that performers (and audiences) would be able to perceive smoothly flowing time in the form of accurate, memorizable tempi, and that they should therefore be able to divide time arbitrarily in the way that space can be divided. This is, however, incorrect.
Usefully accurate tempi only exist when the durations of the individual beats are shorter than the durations that can be accurately estimated by short term memory (without “subdividing”) — i.e. ca. 2 seconds per beat (30 beats per minute). Tuplets whose outer duration is greater than ca. 2 seconds are therefore meaningless.

Stockhausen´s final thoughts on Klavierstück I´s nested tuplets were that the outer tuplets should be replaced by tempo changes, and that performers should be able to play tempi accurately. This means learning to play accurate tempi from regular click tracks (or metronomes).
As described above, “accuracy” with respect to a diagram does not result in the best performance, so I would prefer to replace all the tuplets, and create a synthetic (machine) performance of the score using the exact notated durations (to the nearest millisecond), and learn those, rather than an abstract tempo that nobody can experience. A performance then becomes a communication between the memories of the player and audience.
This approach was not available in the 19th century because there were no recording devices that could store arbitrary durations. All they had were metronomes. This is the obstacle that the SVG-MIDI score format is designed to overcome. (See above)

In practice, scores for more than one player, such as  Zeitmaße (1956) or Gruppen (1955/57), are coordinated using visual cues and/or memories of previous performances (performance practice).

Conductors are, in this respect, simply silent performers who take responsibility for the major durations and relative dynamics.
Performers relate longer duration symbols to counting rather than to absolute time. This is especially true when they are being conducted: in this case they synchronize by counting the conductor´s gestures, and do fine coordination using memory and more precise visual cues.

Music notation doesn´t just contain duration symbols: Barlines, for example, are useful for orientation during rehearsals. They can also improve legibility by breaking the score into smaller chunks. Clefs, staves, systems and pages have similar functions. (Its well known, that chunking is important when reading: words and standard chord-symbols are read as chunks, not character by character.)

This is a companion piece to The Probability of Harmony — see , and Compositions preceding Act Two.
Its interesting that, without looking at the score, a British national newspaper critic thought that Possible Developments was an epigonal rewrite of Stockhausen´s Zeitmaße that he had heard in the same concert. He can´t be blamed for having been unable to hear the difference between what we wrote.