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An "useless"(?) 2D tuning ... Just weird

🔗Petr Pařízek <p.parizek@...>

5/30/2009 12:48:30 PM

Hi tuners,

I don't know how important these things are but I think I simply need to say this somewhere. Recently, I've found a 5-limit 2D tuning which tempers out 273375/262144 (or about 72 cents). The generator is strikingly close to 25/18. But according to the mapping, 25/18 requires 20 generators, not 1. But the similarity is so clear that I couldn't help using it like that while experimenting with it on my keyboard. A few moments later, I realized I was unintentionally often approximating 5/3 with -9 generators rather than +10. And that all is because 19 generators are very close to 9 octaves. But if it really is like that, isn't it actually better to take the simple 19-EDO and map the approximants with just one step size instead of two? I doubt that this 2D version could have any use for actual music. To be honest, this is the first time ever that I consider a 2D tuning useless even though there is no strong mistuning there. And who knows if I'm going to say that later about something else ... Well, I'm just "pondering".

Petr