Three months ago, Japanese developer IHARA designed an app for iPhones et cetera which seems to be a perfect translation of Stockhausen´s conception regarding a metronome with the chromatic tempo scale. The famous "impossible" tempi of a "German professor" like 37.75 or 47.5 become what Stockhausen always spoke of: very natural, fluently moving on from one to another. Large musical sections of a score can be programmed with respect to tempo; this can help enormously while practicing.
Please see the film on the developers Website: http://ihara-product.com/products/sm.html
Does anybody have experience with the metronome?

Wow, thanks for sharing the link to the video. I'd heard of this but did not know it had programmable sequencing as well. I'm not a performer (these days anyways) but I can see this being really handy.

Which brings me to a question: is it theoretically OK to proportionately increase or decrease the written tempi in a Stockhausen piece? I understand that KS's tempi are based on a 12 step chromatic scale from 60 - 120, but what if one were to conduct it at a proportionately faster/slower speed (with all the tempi changes altered accordingly)? One of the great things about Beethoven is that you can have both Toscanini and you can have Klemperor, and they reveal different things. As far as I know there's no special significance to 60 or 120, they were just the low and high ranges KS picked.

My inclination would be to say no, the tempi shouldn't be transposed up or down what has been written in the score. I think Stockhausen very much saw the tempi as being just as crucial in the overall scheme of his works as any of the other elements - pitch, dynamics, attack - and so to change the tempi, even in precise proportions, would be like transposing the pitch, or the dynamics. That's not to say that it would no longer be a good piece or an interesting piece, but just that it would no longer be the piece that Stockhausen wrote - whereas, in the case of Beethoven, my understanding is that variability around tempi were much more commonplace in Beethoven's day, and much more expected by the composer. Nonetheless, it's interesting that Beethoven was one of the first composers to use metronome markings in his score - and yet very few performers (possibly even Beethoven himself, for all I know) observe them. But somehow that sort of latitude seems much more out of place in a Stockhausen score than in a Beethoven score.

Ah that's pretty good reasoning, I see your point! I have to admit, I personally am pretty fast and loose with tempo and key for almost any work, especially as a guitarist. It's pretty common practice of course in pop/rock to transpose songs to fit the range of whatever vocalist you are playing for (and guitar is probably the easiest transposing instrument that I know!). I don't play any KS pieces so they're safe :)

Beethoven no longer performed in public by the time he started using the metronome to mark his tempi. I have a feeling he considered those as guidelines. One great regret is not having a recording of Beethoven improvising, considering he was the best improvisor of his day.

Although transposing tempos is generally as unsuitable or even impossible as transposing pieces up or down in pitch (I'm thinking especially of "Das grosse Geweine" from Montag, where synthesizer III plays a Lucifer chord that covers the entire range of the keyboard, from the low A to the high C), there are some exceptions, especially Tierkreis, which exists in versions transposed by Stockhausen both in pitch and tempo (with some interesting anomalies). There are also the variable durations of sections in Mixtur and Adieu, where a counting unit from 40 to 60 beats per minute can be chosen for a performance, but this does not involve tempo since there is no regular pulse in either of these pieces. Aloys Kontarsky wrote an article for the Darmstädter Beiträge back in the mid-1960s about notation of new music (it was later translated into English for PNM), in which amongst other things he said that a sense of "absolute tempo" is important to develop, and should be taught in conservatories in the same way that absolute pitch is taught. I have seen Stockhausen in rehearsals correcting tempos without reference to a metronome, which can be a little scary. I am thinking in particular of the rehearsals for Luzifers Tanz, in the introduction where the conductor must lead the wind band through all of the changing tempos that will occur in the piece, pulsing on a single chord. At one point, H. Robert Reynolds was sure he was right and Stockhausen was wrong, and got out his pocket metronome to settle the matter. Guess what? Stockhausen was right. It didn't always work out that way. There are anecdotes testifying otherwise but, in general, he knew just what tempo he wanted. Why should anyone think they know better than he did?

Jerry's right that there are certainly pieces where Stockhausen builds in flexibility for the performer, like the tempo ranges in Mantra. Such instances are rare in Licht, however. In my first lesson with Markus, I asked the most basic question possible. "How do you practice a tempo like 75.5?" Markus smiled and dialed "76" on his metronome. End of discussion. (Of course, that was pre-smart phones, which make micro-tempi easy.)

There is leeway, obviously. The metronomes come out when things are audibly incorrect. No one, not even Stockhausen, would catch the .5 bpm difference between 75.5 and 76 in, say, Michael's formula. But, what is obvious is if the relationship is not correct with the surrounding tempi. That's when it's time to check the metronomes, and as Jerry says, you're not usually going to win that argument.

One of the things we do quite often as a game is quiz each other with metronomes. Some guys run hot, others cold. One of the secrets of learning Stockhausen's music is that the correct tempo often is a big help. This is a general precept altogether, which my main trumpet teacher called "playing the ink". In other words, stick to what's on the page, nothing more. It makes things so much easier!

And then, of course, often the metronome markings themselves are approximations, as they are in LICHT, where everything is rounded up or down to the nearest 0.5 bpm from the 12-step logarithmic scale.

On the other hand, the fact that no one (not even Stockhausen) might notice a 0.5 speeding up or slowing down of the tempo is not, I think, the issue. You could possibly get away with playing some wrong notes in places too, maybe even with transposing everything up or down a quartertone. The point is that they would still be wrong. Unless of course there is the flexibility for performer choice, as you mention.

My main question at this point would be why KS chose that particular range to base his LICHT tempo scale on. I'm always curious as to his reasons for the musical decisions he makes. Sometimes they are just based on taste, most times they are based on a design concept (all-interval series, Fibonacci, formula, etc...what his son's favorite instrument is ;)). I think I recall KS saying that leading up to a GRUPPEN performance he drilled himself for 3 months on blind tempo tests, so that he would not be the "weak link" conductor (of course the other 2 guys were all over the place, Boulez one of em). I'm guessing that's where he started regarding tempo as audible as pitch. I suppose if I obtained the ability to see ultraviolet rays, I'd start painting works with those colors as well...

Tempo is such a controversial topic in classical music. I love it when critics say a particular performance was "dragging" or "fiery". If the tempo is slow or fast then that's what it is. Freidrich Gulda's Beethoven piano sonata is blazing fast, that's just a fact. One person can call it "barnstorming" and another can call it "overly-facile". Claudio Arrau's cycle could be called "sonambulant" or "meditative". With Stockhausen it really becomes kind of a moot point (if played to score indications).

Anyways, aside that that aside, I am now convinced that Stockhausen's tempi are there for a reason and should be adhered to, but part of me does fear that that will lead to less diversity in performances. There are well over 500 recordings of Beethoven's 9th Symphony (of which I have probably 25). Tempo is probably the first factor that strikes a listener when hearing a new recording (present company excepted, of course).

The stray wrong note is one thing, an entire passage transposed to the wrong quarter tone is another issue entirely though. Everyone will make mistakes. It's just life as a performer. The discipline with Stockhausen's music is to make sure you are not ignoring any of the things that he took the time to spell out.

I agree with Ed that it's funny to watch people who don't have a lot to offer cite a performance tempo as a kind of holistic indicator of a performance's net worth. It usually isn't. So too with Stockhausen's music. Yes, the tempi are generally fixed, but that doesn't preclude wildly different performance styles. As I mentioned in my recent talk about humor, a performer has a great deal of freedom within the confines of Stockhausen's musical prerequisites to still play up certain aspects. You see that all the time when different performers tackle the same work.

The challenge to diversity in performances is really that so few people are willing to tackle Stockhausen's music. If they really master it, they will find a great deal of latitude for different interpretations. In this way, his work is no different than other highly elaborate performance traditions.

Just to clarify - I'm not for a moment suggesting that an accidental wrong note is the same as a conscious decision to transpose the pitch or tempo of an entire passage: just that either might not be noticed, and yet both would be incorrect.