Re: temperament in "Ad chlvichordium faciendum"

Neal Plotkin wrote:

> But here is (yet) another way to display the tuning Roland got from
> the document (this should be viewed in a fixed-width font):
> 
>                   Db
>      G#   D#   Bb    F   C   G   D
>                        A   E   B   F#  C#
> 
> using Roland's parenthetical names for the black notes, except for Db
> for the note in step 3, to distinguish it from C# in step 9.
> 
> This kind of diagram shows (pure) fifths in horizontal rows, and
> (pure)
> thirds as adjacent notes in adjacent rows:  major thirds going from
> upper left to lower right (like F-A) and minor thirds going the other
> way (like A-C).  So pure triads show up as triangles.

> Also, the string of fifths in the bottom row are all 1 syntonic comma
> lower than the string in the main row, so in Roland's follow-up
> article
> notation, they would appear as A-1, E-1, etc.  And the lone Db is
> Db+1.

Not my notation as such, at least not in the sense that I originated 
it!: I was following Margo, who was possibly following Barbour who was 
following Ellis (? or something like that).  It's worth mentioning for 
those unacquainted with this notation that the "-1" or "+1/2" or 
whatever is customarily printed as a superscript when superscript type 
is available.

> I like this kind of diagram (which is adapted from one in a couple of
> Mark Lindley's articles) because it makes *all* the pure fifths and
> pure thirds obvious, and also makes it clear that D-A is *not* a pure
> fifth.

It's a very nice way of showing a lot at once.  Lindley uses it a lot; 
I'm not entirely sure whether he invented it or borrowed/adapted it 
from someone earlier, but he certainly has made it familiar in widely 
consulted reference works as well as in his journal articles.

I like your idea of using this "honeycomb" layout to show only the pure 
intervals of tunings like these.

-- 
Roland Hutchinson              Will play viola da gamba for food.

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