Yahoo Tuning Groups Ultimate Backup tuning Within A Fret-Width of Just (WAFWO-Just): More Acronyms

Hello, there, everyone, and here are some more acronyms on the topic
of "How just is just?" I've tried to include a bit of musical
philosophy and historical background, but mostly it's all in fun.

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1. Issues to Fret Over: WAFWO-Just
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Within A Fret-Width of Just (WAFWO-Just) might be quite descriptive
for the problems that Dave Keenan and others have discussed regarding
the tuning accuracy of such instruments. As I recall, there were
suggestions on the order of 2-3 cents for this type of
"near-justness."

Within A Fretting-Nuance of Just (WAFNO-Just) alludes to a factor
which Mark Lindley discusses in presenting Vincenzo Galilei's rule for
fretting a lute in 12-EDO: have the frets spaced by successive ratios
of 18:17 (the "18 rule" still followed by modern luthiers). Because of
fretting pressures when playing, the performer can actually come
closer to 100-cent semitones with this formula than with the "correct"
logarithmic fretting distance. Or, maybe this could also be stated:
"Within A Fingering Nuance of Just" (also WAFNO-Just).

(Aside: How about a "25 rule" for fretting in successive ratios of
25:24, which could also be described as a moderate "stretched octave"
tuning?)

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2. A Just Synthesis?: WATU-Just or WANTU-Just?
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Shifting from fretted instruments of the traditional kind to digital
synthesizers and the like, we have some more acronyms:

Within A Tuning Unit of Just (WATU-Just): This means that an interval
is within the instrument's smallest unit of measure -- for example,
within 1/768 octave on a 768-EDO instrument.

Within A Nearest Tuning Unit of Just (WANTU-Just): This is a bit more
particular, since it requires that the interval be tuned to the
_nearest_ possible equivalent, and thus within _half_ a tuning unit,
for example 1/1536 octave on a 768-EDO instrument. Note that with the
frequent need for "nanotemperament" on such instruments, in which some
intervals must be tuned to the "next-most-accurate" unit in order to
improve accuracy on others, certain intervals are likely to be
WATU-Just but not WANTU-Just.

Of course, there's also a kind of special ribbon of distinction in
this category:

Within A MIDI Unit of Just (WAMU-Just) means that an interval is
accurate within the MIDI tuning unit of 1/49152 octave.

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3. Intrinsic Units of Near-Justness: A Theorist's Delight
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Since "justness" often has an acoustical reality mediated through
instruments with "more-or-less-fixed-pitch" lending themselves to
comparisons like the above, such standards can have a certain
practical appeal. However, there's also much entertainment to be had
by going with units of measure having some connection with interval
ratios and esoteric theory, and here are some ideas:

Within A Schisma/Skhisma Of Just (WASO-Just): This may be either the
3-5 Skhisma of Helmholtz/Ellis (32805:32768, ~1.95 cents), or in a
rather free usage which many might suggest is quite lax, the 3-7
schisma (33554432:33480783, ~3.80 cents). However, my own view might
be that the 3-7 schisma is better absorbed by one fifth in a 23-fifth
chain than taken as a loose standard for "near-justness."

Within A Johnny Reinhard Unit of Just (WAJRU-Just): This means within
1/1200 octave of just, or a step of 1200-EDO, a unit of measure going
back to China in the 16th century or so according to James Murray
Barbour (if I recall the source correctly), and made famous on this
list by Johnny Reinhard as a notational unit for microtonal ensembles.

Within A Nanisma Of Just (WANO-Just): A nanisma is a unit which I
proposed here a bit more than a year ago, but Joe Monzo gave more
practical meaning in a post last year: it's the difference between the
3-7 schisma at around 3.80 cents, and the "Comma of Mercator" by which
53 pure fifths fall short of 31 pure octaves (~3.62 cents), an
interval of about 0.18 cents with the following ratio:

649037107316853453566312041152512:648966242035284859600333477874109

As our Monz observed, one could use a chain of 68 pure fourths up to
obtain a minor third only a nanisma wide of 7:6 -- and we could
similarly use 69 fifths up for a major third only a nanisma narrow of
9:7. This seems one possible theoretical standard for "just about
just."

Anyway, I hope that this article has brought people considering the
"near-just" acronyms another bit of random amusement.

Most appreciatively,

Margo Schulter
mschulter@value.net

Within A Fret-Width of Just (WAFWO-Just): More Acronyms

🔗M. Schulter <MSCHULTER@VALUE.NET>

🔗dkeenanuqnetau <d.keenan@uq.net.au>