FW: Re: An interesting non-just non-equal temperament

> Dave Keenan wrote,
>
> >No. I haven't seen this one before. Thanks. I love these things!
> >
> >I can however describe it as a third (and previously unsuspected) member
> of
> >a class of 12-tone 7-limit tunings for which I don't have a name. The
> other
> >two members are a 12 of 31-tET (or nearby meantone) that I found (I
> really
> >just converted an existing Just scale to 31-tET/meantone) and a tuning
> >where the 225/224 disappears due to Carl Lumma (and we later learned that
> >Fokker had described it earlier in Just terms, rather than tempered).
> >
> >So in mine we distribute the 81/80 and in Lumma's we distribute the
> >225/224. Yours is right in between with its distributed 126/125.
> Beautiful!
> >So it is also intermediate in its tradeoff between the number of
> available
> >7-limit harmonies and their accuracy.
> >[...]
> >What this class of tunings (mine, Lumma's and yours) have in common,
> apart
> >from all being proper 12-tone 7-limit scales, is that if notes are mapped
> >to the nearest 31-tET notes, they all come out as the same mode, which,
> as
> >a chain of fifths, looks like:
> >
> >Db Ab . . F C G D A E B F# . . D# A#
> >
> >So they all have the 3 wolves A#:F, F#:Db and Ab:D#. Lumma's has an
> >additional wolf D:A as the price of all the remaining 7-limit intervals
> >getting to within 2 cents of Just (which really *is* Just in my book).
> >Yours has two additional (but mild-mannered) wolves, or no wolves but 4
> bad
> >fifths, and can get the remaining 7-limit intervals within 4.6 cents (the
> >tempering you describe has a 5:7 which is 6.5 cents narrow).
>
> Thanks, Dave, for looking at this! Someone should make a web page
> describing all these varieties, starting with Fokker's. These are the
> answers to the question "How can we tune a 12-tone scale so as to get a
> significant number of 7-limit harmonies with considerably better tuning
> than 22-tone equal temperament?".