Alternative tuning of alternative fretting.

If you wish to explore alternative tunings and alternative fretting,
both subjects for guitar are covered in the tech. downloads, at
our site:
http://www.wonderlandinorbit.com/projects/lullaby
The string tunings can be used on 12tET (by note name) as well as
for LucyTuned guitars, and include all the "slack-keys" that I
could find plus many others all arranged in consonant to
dissonant order.
Anyone who wants specific fretting positions can get them for
any nut to bridge distance by EMailing me at lucy@hour.com.

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[snip]
I have my own elaborate temperament spreadsheet that I developed while
I was working on one of my doctoral projects a few years back.
This past New Year's Eve I finally got around to converting it from its
original Quattro format over to Excel (Windows 3.1), and then over the
next few days put in some new refinements. (But no, it doesn't generate
tones.)

Features: this spreadsheet is designed to be both objective and subjective
in temperament analysis. The objective part: it makes complete beat rate
charts for all thirds, fourth, fifths, sixths, and sevenths (including 7/6
minor thirds and several types of minor sevenths) showing how far sharp or
flat of pure (simple integer ratio) the interval is in the programmed
temperament. It also converts everything to both cents and Hz, and
arranges its analyses both chromatically and in a circle of fifths. Then,
getting to the subjective part, I've tried to come up with formulas of
subjective tolerability of the minor and major thirds and sevenths, and
the fourths and fifths. The triads and seventh-chords on all scale
degrees get analyzed for usability, tension, etc., and displayed in
tables. These subjective formulas are based on my own tuning experience
with many temperaments over the years, and reading historical and modern
sources about what the ear finds tolerable (so it's not *completely*
arbitrary!). The formulas automatically choose the nearest simple ratio
(for instance, choosing between the 9/5 and 7/4 minor sevenths, or the 6/5
and 7/6 minor thirds), then look at the beat rates.

The upshot of all this is that simply entering a temperament recipe in one
place yields beat charts for actually setting it (from either a C or an A
fork of any specified frequency), and charts that show which keys are the
best/worst to play in, and how the ear might take it on all scale degrees
of those keys. For example, in a well temperament, it's easy to see how
modulation around the circle of fifths increases/decreases tension in the
triads and sevenths. And in 1/4 comma meantone, the Bb-D-F-G# chord shows
up sounding like an almost pure dominant seventh (that low pseudo-Ab and
all). The spreadsheet makes these features obvious without requiring one
to go set the temperament first on an instrument...it could also help in
planning an effective overall temperament for a recital, given the keys
and modulatory depth of the pieces to be played.

Temperaments are specified with superscript comma adjustments plus or
minus, the familiar way the old Barbour book did it. My old Quattro
version had about 70 temperaments in it, including (I think) all the
Barbour ones, some of Jorgensen's, plus others I made up as "what-if"
scenarios. I don't remember how many I've converted to the new Excel
version, but in any case it's easy to enter new ones...takes only about a
minute or two once ye get the hang of it. Twelve notes per octave, and it
determines automatically what the enharmonic name of a note is based on
the superscript value.

The parameters are: start from either an A or C fork; frequency of that
fork; temperament name; tuning recipe in fractions of commas; which
comma is used; which temperament in the recipe library to display (index
number). Everything else is derived. It's also easy to change the
subjective formulas that analyze triads and seventh chords.

V1.1 has several more temperaments in its library, and displays four
more beat-rate intervals (such as the 7/4 minor seventh that a
meantone Bb-G# almost is).

http://www-personal.umich.edu/~bpl/temper.html

-----------------------------------------------------------------------
Bradley Lehman, bpl@umich.edu http://www-personal.umich.edu/~bpl/

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