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RE: [tuning] Representing Meantone Tunings with "NNN"

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

5/17/2000 12:06:04 PM

Hey Mark -- nice work. My only comment is on this:

>5LJI (5-Limit Just Intonation):
>The Comma digits used here show the values that the subsequent Meantone
Temperament >attempts to approximate.

There is no single 5-limit JI system that meantone attempts to approximate
-- rather, it approximates a larger set of JI relationships than any single
JI system could achieve. A reasonable simplification would be that meantone
simultaneously approximates several JI systems. "Approximation" in this
sense should be evaluted not on a pitch-by-pitch, but on a consonant
interval-by-consonant interval basis.

Also, I noticed that the 5-limit system you do propose is not one of the
"famous" ones, though any of the latter would suffer the same problem. Out
of curiousity, where does your 5-limit system come from?