Is there an easy way to set up an unequal temperament in Dorico?

Dorico
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By unequal I specifically mean anything from Pythagorean to Kirnberger III, but still with 12 tones to the octave. (It has to be playable on an ordinary harpsichord.) The Tonality System menu seems more geared towards equal microtonal temperaments.

I guess I could use 1200 (or 12000) ET and then set an unequal number of steps between all the white-key notes, according to the cent amounts. Correct? But that would still leave all the black-key notes unaccounted for. Is there an easy way to set those as well?

Many thanks in advance!

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Honestly, I think the easiest way to achieve this is to just use a VST that allows these tunings, rather than forcing Dorico to try and manipulate midi data to make other programs do it. Hauptwerk (organ software) for instance, allows you to change tunings on the fly. So, you just write in the normal notes and then choose whichever temperament you want to hear it play back in. I’m not sure about other VSTs and how they handle this, but I’d have to imagine that some others support such features as well.

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Yes, PianoTeq allows the user to change both the reference (440, 415, etc.) and the temperament, no matter what your software does. Of course, it’s vst3 so it also understands the microtonal features from Dorico…

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Yes, I concur. There are things called Scala files, which specify temperaments and tunings. Logic uses them, as does ARIA Player and Pianoteq. Kontakt doesn’t use them directly, but they can be converted into files that will change its tuning.

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Did you check How to Set Up Microtonal Tunings | Discover Dorico - YouTube ?
One does not need to define all pitches in an (for example) 12000 ET in Dorico.

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Dorico’s microtonal approach is based on sizes of intervals defined between the white notes and for each accidental. This can be appropriate for regular temperaments of the 12 tones such as Pythagorean and meantone – in which ♯ and ♭ always alter the pitch by the same amount.

But beware that this will not work properly for circulating temperaments such as Werkmeister and Kirnberger, as they are designed with different sizes of interval at each different pitch. For this you need to scale-tune the VST itself, as per posts #2–4 above.

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Thanks! Meantone (1/4 comma) is acceptable to me.

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I tried out some ¼-comma meantone today, and found the usual mathematical peculiarities:

  • The whole step ≈ 193.157 cents and the diatonic semitone ≈ 117.108 cents. When we round those to 12000 EDO, 5 × 1932 + 2 × 1171 = 12002. So I cheated slightly and reduced the two semitones to 1170 in order to make it add up to exactly 12000. (These errors are much too small to hear. There are similar rounding errors even if you use more divisions, such as 32768.)
  • The chromatic semitone (for ♯ and ♭) is 76.05 cents, so 760/12000. Double sharps and flats (if you get that far) round to 1521/12000.
  • With this you can write freely in extended meantone, with up to 21 different pitches per octave! With double accidentals, 35 different pitches.

However, there are big drawbacks:

  • Using custom defined accidentals means you can’t use the normal keyboard commands for ♯ and ♭. 0 still works for ♮.
  • Music entered in the 12-EDO Tonality System does not paste into a different system with the accidentals intact. Every one has to be reassigned.
  • You also have to manually define every key signature you want to use, with the custom accis.

So overall for unequal temperaments with 12 tones it’s still better to scale-tune the VST.

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