Thank you, Kees, its good to be back
Fall was crazy, I felt like a hamster thrown into a wheel. Better now, anyways.
Not being used to thinking in terms of tests would you mind correcting my homework, which is to interpret the meaning of these tests? Here's my work:
C#4/F4 (M3) < C#4/F5 means F4F5 4:2 is wide
C#4/F5 (M10) < C#4/F6 means F5F6 2:1 is wide
C#4/F4 (M3) < C#4/F6 means F4F6 4:1 is wide
C#4/F6 (M17) < C#4/A#4 means A#4F6 3:1 is narrow
C#4/F5 (M10) < C#4/A#4 means A#4F5 3:2 is narrow
C#4/F4 (M3) < C#4/A#4 means F4A#4 4:3 is wide
F3/C#4 = C#4F6 means F3F6 8:1 is pure
Yes, absolutely. But I would assume that Mark doesn´t check the 2:1, 3:2 and 4:3 per se (neither do I). The idea would be to step through it like this:
1) check C#4-F4 (listen for beat speed)
2) check C#4-F5, this should be faster than the previous one,
3) check C#4-F6, this should be faster than the previous one,
4) check C#4-A#4, this should be faster than the previous one.
This would give you a wide 4:1 and a narrow 3:1 with F6 as the upper note. Which is, just as you mentioned earlier, what Bill's mindless octaves and CHAS aim at.
Now, one could argue that Mark's method doesn't place the 4:1 and 3:1 equally beating, but the difference is small if not even negligible. Fact is, I end up closer to equal-beating 4:1/3:1's using these RBI's than if I listen to the SBI's. That might be just me, but if there is a difference between the "direct interval" method and "Mark's window", it is indeed very small.
I use pretty much the same method, only that I skip the 4:2 test (second step) and just check the 4:1 and 3:1. That is, I play C#4/F4, C#4/F6 and C#4/A#4. The checks should speed up progressively, then I get the stretch I desire.
But what about F3F4 4:2 and 6:3? Are these presumed to be tuned equal beating?
I would assume (from reading Mark's writings) that he aims for a 4:2+ octave (again, not maybe exactly "in between" 4:2 and 6:3, but close enough for all practical purposes.) This he does when he sets the temperament initially, and thus the F4, from that point on, is a set note of reference, not something that are to be moved to "fit the window frame", so to speak
And what about F5F6 4:2? It could come out wide or narrow, or not
From my experience using this system, the 4:2 come out just or wide. At least that is what the checks tell me when I move up through the treble. Now, I have to admit that I do practically all my aurally based tuning on good instruments, and almost always attack the scale-challenged high IH pianos with an ETD, so I am not sure how IH affects the "window". If I go aurally on the latter kind of instruments, I accept equal instead of speeding up, that is:
C#4/F6, not slower than the previous one,
C#4/A#6, not slower than the previous one.
->Mark: If I give misleading information as to how you go about this, please forgive me and correct me. My assumptions are from my own experience of using a very similar method, and there might be deviations.