Anonymous 4 tuning analysis available!

In TD211.18 Bill Alves wrote:

> Thanks to David J. Finnamore and those others who have done empirical
> testing of a capella tuning. While I am anxious to find out more through
> such testing, my own experience with choirs leads me to believe that,
> unless you are talking about the Hilliard Ensemble or Anonymous 4 or some
> other professional specialists in early choral chamber music, it is for
> practical purposes meaningless to speak of tuning systems in choral music
> with the same precision that we do with keyboards.

Anonymous 4 comin' atcha! So happens I'm a big fan of
theirs and have a few CDs. :-)

Well, ladies and gents, the pendulum has swung the other
direction. Unlike the Spanish monks, Anonymous 4 do not
seem to use 5-limit JI, at least not on the one piece I've
looked at so far. It's a real "English" sounding melody to
me, with ample reason to tune in 5-lim. For a note-by-note
look at the entire monophonic chant, and a preliminary
attempt at an analysis of the tuning, see:

http://www.tcinternet.net/users/jfinnamore/df/a4ll_1chart1.html

Included is a table of the center frequency of each note,
the interval in cents between each adjacent note, and an
attempt to analyze it as far as possible (not very) in
5-limit JI. On an accompanying page is the spectrograph of
the first verse.

To come:
1) A chart of "stats" such as how many intervals appear to
be 3-limit, 5-limit, and "other," and how they compare
statistically to the expected intervals of a theoretical
5-limit tuning.
2) MIDI files of the melody in 12t-ET, Pythag, and 5-lim.
3) Possibly a version of the spectrograph with frequency
marks and lines showing how the overtones miss the Just mark
most of the time.

Don't wait, there's lots to digest as it is!

David