Hi all. Thought I would write up a chart for most common use intervals in JI, showing the minute differences in intonation amongst the 39-odd limit ratios. The 20x20 diamond seems to have 317 unique pitches, so it's taking a bit of a while, but I'm getting there, and will definitely post here and on facebook when I'm finished, to show people how well Sagittal can handle almost all intervals. I haven't really heard of people using primes higher than 37 in their work (except perhaps Johnny Reinhard) but this should be a good test. One can of course, continue a chain of fifths from any note in the diamond to get >99% of the pitches ever used or conceived of in JI, uniquely identified using Olympian level symbols. One can of course leave off some diacritics to make things quicker, but then a whole bunch of pitches are conflated. Using this chart, pitches in any of Ben Johnston's string quartets or other works of similar JI complexity can be read/written/spoken/understood at a reasonable fluency, and pitch height is always close at hand, unlike many other JI notations.

I'd like to see something like this done with Sabat or Johnston to see how they cope with a similar complexity.