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Modern Pianos are tuned to equal temperament at A440. Are there other prominent alternate tunings used in art music or popular music? I'm accepting that historical reproductions will tune the A to 430 or something, but I'm thinking different tuning models?

UPDATE: Thanks for the answers! I guess more what I'm thinking of is anyone anywhere experimenting with different ways to tune the instrument. I saw a video of a specially made piano where EVERY key is middle C! what other experiments are going on?

  • Are you asking about what are the more popular historical intonation systems as alternatives to equal temperament that one could use, or are you asking if there are prominent players or composers using alternate intonations, or have I misunderstood the question entirely? – Todd Wilcox Dec 16 '16 at 14:02
  • Some European countries will have their pianos tuned to 444Hz=A, but not sure that's what you're asking about. – Tim Dec 16 '16 at 14:45
  • Alternatives to equal temperament! That's what I was trying to get across. A=444Hz would still be tuned to equal temperament, and I'm wondering if there is something other than equal temperament in use. Thanks! that helped me clarify that! – Caleb Dec 16 '16 at 17:03
  • @Caleb I removed the (Alternate Intonations) part of the title; my opinion is that that is not equivalent to the "alternate tunings" that you're seeking. But if you disagree, you're welcome to reinstate it! – Richard Dec 16 '16 at 20:18
  • no that's fine! I'm new, and I'm trying to ask things in the right way. cheers! – Caleb Dec 16 '16 at 20:20
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There are two recent approaches to modern temperament design that have interested me:

One is Bill Bremmer's EBVT temperament, which has undergone some revisions in recent years. It started with a compromise between temperaments of the "victorian" style and equal temperament, to suit an aesthetic that favors variation in dissonance across the circle of fifths, but is still comfortable to the modern ear in the distant keys. More recently it has focused on the contribution of temperament design to beat cancellation. That is, focusing on beat rates of interval tests in isolation does not take into account the effect of temperament on beats in chords and larger combinations of intervals.

Another is the "pure twelfths" approach exemplified by the work of Bernhard Stopper, which also focuses on the beat cancellation idea, but comes at it from a mathematical approach.

If the question is concerning experimentation in temperament design, then historical temperaments don't really apply since those such as Werkmeister or meantone have accepted definitions which are not changing. People experiment with their applicability to certain situations like spinet scales or period performance, but they are not experiments with temperament design.

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    It might be fun to play with Stopper's tuning in a physical modelling instrument like Pianoteq, where you could tweak the inharmonicity of the virtual piano to correspond "exactly" with Stopper's idea of what it ought to be for his slightly stretched tuning. More interesting than vegetating in front of the TV over Christmas... – user19146 Dec 18 '16 at 9:30
  • Stopper's tuning actually seems to go in the opposite direction though – making the 3-limit even better than it already is in 12-edo, at the further disadvantage of 5-limit intervals. – leftaroundabout Dec 18 '16 at 13:02
  • @leftaroundabout Maybe I misunderstood it (and I haven't gone back to re-read it) but ET fifths are smaller than just intonation. By my calculations, Stopper temperament tunes octaves to be 3^{12/19) = 2.00143:1 or 1.23 cents wide, which is the same order of magnitude as the stretch in the mid range of a piano (but smaller at the extremes). – user19146 Dec 19 '16 at 0:37
  • @alephzero as I was saying. Stopper temperament makes the 3:1 twelfths completely just (which I don't consider all that useful since they're already very good in 12-edo) , but most of the interesting intervals that are not so optimal in 12-edo (in particular major tenths) are already too wide in 12-edo and get even worse in Stopper temperament. – leftaroundabout Dec 19 '16 at 0:50
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Prior to the widespread adoption of equal temperament, various "well tempered" tunings, basically alterations of meantone temperament to tone down the degree of dissonance in the wolf intervals, were used. The Werkmeister tunings, are probably the most well known today.

Note: I consider historically informed performance as "modern", since it is going on now.

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La Monte Young's masterpiece The Well-Tuned Piano uses an alternate tuning that is a based on a modified 7-limit Just Intonation. One of the interesting features of the tuning is that pitches to the right on the keyboard aren't necessarily higher than the ones on the left. G is higher than G# and C is higher than C#. Apparently this has something to do with the notation or some such.

Regardless, Kyle Gann has a nice article about it here.

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