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I'd like to know if it's possible to modify the tuning of every single note with a given frequency on a keyboard and store it in a specific "scale set". Is that possible? The idea would be to play temperaments in a live execution without too much effort (ideally press a button and you switch temperament).

Dac0
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  • Multiply all the temperaments by 12, to find number of combinations, and 'press a button' starts to get very expensive - especially regarding the very limited market for such an instrument. That apart - recommending products isn't part of this site's remit. Vtc. – Tim Aug 14 '21 at 08:00
  • @Tim could just be something that stores 10 "scale sets" and press a button to switch in between one of them, I don't nee to have stored all possible combinations... – Dac0 Aug 14 '21 at 08:05
  • @Tim why multiply all the temperaments by 12? That's not how temperaments were used in the days before equal temperament. – phoog Aug 14 '21 at 13:43
  • @phoog - each key would need slightly different tuning for its notes - that's 12 different tunings for one key, or 7 minimum for diatonics. I felt OP wanted to cover loads of different temperaments, so would need loads of different tunings - one for each key at least. – Tim Aug 14 '21 at 13:53
  • @Tim that's not how temperaments work. The point of unequal temperaments is that different keys sound different. If you base your temperament on the key you're playing in then you lose that. – phoog Aug 14 '21 at 14:00
  • @phoog - not quite with you. Tune for, say, just intonation, in key C, and it'll sound fine. Leave all notes tuned thus, but play in key Eb, it won't. So, I think it'll then need re-tuning for ji in key Eb. Then it won't sound quite right for another key. Am I wrong? – Tim Aug 14 '21 at 14:07
  • @Tim just intonation isn't a temperament. You can't reasonably use it to tune a keyboard unless you're willing to accept some serious limitations. If you tune just intonation in C, then D, Dm, D7, Dm7, and Asus4 (among others) will actually sound horrible, so it will only "sound fine" if you avoid those chords. The point of a temperament is to make a keyboard actually playable, and historical temperaments were devised to make them playable in all of the commonly used keys (which means that later temperaments enable more keys), though each key sounds a bit different. – phoog Aug 14 '21 at 14:38
  • @Tim (correction of an earlier comment): So the idea is that if you want your piece to sound peaceful and calm, you use a key that has low major thirds that are closer to just, which would typically be the keys with fewer signs in the key signature, such as C. If you want it to have more tension, you play in a key with more signs in the signature, such as E or A flat or B, where the thirds will be wider, closer to Pythagorean. In your example, the fact that the E-flat piece sounds different from its transposition to C is a feature, not a bug. – phoog Aug 14 '21 at 15:15
  • @Tim to make it a bit more concrete, here's the interval between D and A in just intonation for C, although this is actually A and E. In other words, if you tune your keyboard in G using the usual prescription for just intonation, in which the second degree is 9:8 times the root and the sixth is 5:3 times the root, you get this fifth with a ratio of 40:27 between A and E: https://en.xen.wiki/w/40/27. Tuning JI in C, you get this fourth between A and D: https://en.xen.wiki/w/27/20 – phoog Aug 14 '21 at 15:38
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    Logic Pro has such a feature, comes bundled with loads of historical tuning methods and allows the user to design their own, too. – OwenM Aug 16 '21 at 11:36

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It sounds like you want Scala:

Scala is a freeware software application with versions supporting Windows, OS X, and Linux. It allows users to create and archive musical scales, analyze and transform them with built-in theoretical tools, play them with an on-screen keyboard or from an external MIDI keyboard, and export them to hardware and software synthesizers. (Wikipedia)

Scala is a powerful software tool for experimentation with musical tunings, such as just intonation scales, equal and historical temperaments, microtonal and macrotonal scales, and non-Western scales. It supports scale creation, editing, comparison, analysis, storage, tuning of electronic instruments, and MIDI file generation and tuning conversion. All this is integrated into a single application with a wide variety of mathematical routines and scale creation methods. Scala is ideal for the exploration of tunings and becoming familiar with the concepts involved. In addition, a very large library of scales is freely available for Scala and can be used for analysis or music creation. (Scala Homepage)

You might also find useful information in the following posts on this site:

And a bit indirectly...

Aaron
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  • And there certainly are keyboard models that switch temperaments "at the touch of a button," though I don't know that the Roland C-30 lets you save custom ones... https://www.roland.com/us/products/c-30/features/ – Andy Bonner Aug 16 '21 at 14:33