These instructions will work with instruments like bowed psalteries, autoharps, banduras, and panpipes, where you tune every note separately. They can be applied to fretless stringed intruments, trombones, and slide whistles, where you control the pitch of notes as you play them. If you want to play the guitar in these tunings, you're going to have to do some fancy bending.
The note names are in the key of C. Tuning in other keys is done exactly the same way, except that different notes are altered. For example, in C Pythagorean, C is tuned four cents flat. C is the first note of the C scale, so to tune to Pythagorean in some other key, you would tune the first note of the new scale 4 cents flat.
The following table shows how many cents sharp or flat you should tune each note, starting with 12-note equal-tempered tuning. (12-equal is what your electronic tuner shows as "in tune", unless you have a very sophisticated tuner that knows about fancy tunings.) Corrections are to the nearest half cent, but if you tune to the nearest cent you're plenty close enough.
Scale Position 1 2 4 4 5 6 7 Note C D E F G A B --------------------------------------------------------------------------------- Strident -6 0 +6 -9 -3 +3 +9 Pythagorean -4 0 +4 -6 -2 +2 +6 12-Equal 0 0 0 0 0 0 0 Eighth-Comma +1.5 0 -1.5 +2 +0.5 -0.5 -2 Sixth-Comma +3 0 -3 +5 +1.5 -1.5 -5 Two-Cent +4 0 -4 +6 +2 -2 -6 31-Equal +6.5 0 -6.5 +9.5 +3 -3 -9.5 Quarter-Comma +7 0 -7 +10.5 +3.5 -3.5 -10.5 Lucytuning +7.5 0 -7.5 +11 +4 -4 -11 19-Equal +10 0 -10 +15 +5 -5 -15 Perfect +5 +9 -8 +3 +7 -10 -6.5I've chosen corrections so you tune some notes up and others down, so the total tension of the harp doesn't change. You'll notice that to play in any meantone tuning in C, you tune G up a bit, C up more, and F up still more, leave D alone, and tune A down a bit, E down more, and B down most.
I've added two tunings that I didn't discuss in the theoretical page. Two-Cent is pretty close to sixth-comma and has the advantage of being easy to tune to with an electronic tuner. Strident is what happens when you go from soothing quarter-comma to harsh Pythagorean and keep going in the same direction. You could use this scale to emphasize the different sound of a medieval piece.
But in the new key, we need F# to be 3.5 cents flatter than B, which is already 10.5 cents flat. F# must end up 14 cents flat instead of 10.5 cents sharp. So to stay in quarter-comma, you'd have to adjust the lever to sharpen the note by 24.5 cents less that 100, or 75.5 cents.
In general, whatever the amount by which our fifth differs from 700 cents, we'd have to set the levers to have seven times that much correction from 100 cents. Otherwise, we get a variety of different tunings, returning to our original tuning 100 cents higher when all of the strings are sharped for the key of C#.
Alternatively, we could tune the harp in 12-equal, then adjust the F levers 10.5 cents sharp, the C levers 7 cents sharp, and so on down to the B levers 10.5 cents flat. Now we have a harp that is in 12-equal in the key of C and quarter-comma in the key of C#.
I don't seriously suggest that anyone should start moving his/her levers around, at least not until he/she is completely in love with one of the alternate tunings. Harps are too difficult to adjust. Now, if you have a pedal steel to play with, THAT would be feasible. Let me know how it works out - Zeke Hoskin.