>> Tunes in A are often pipe tunes and hence might be expected to be
>> given piping intonation. Tunes in G are never pipe tunes. So this
>> [slightly flattened thirds] is exactly what you *would* expect if
> the choice were a musical one.
> There are pipe tunes in G.
Like what? The only one I can recall ever seeing is David Glen's
bizarre arrangement of "Dalkeith Fair" (possibly an A pipe tune
long ago, but filtered through an 18th century flute/fiddle setting).
Which G is the root? - they are never an octave apart on the pipes.
> More importantly it is impossible for a fiddler to play in the "piping
> intonation" or any intonation either than the "just" one.
Objective measurements in recent decades (using equipment your pal
Helmholtz couldn't buy, like the Stroboconn) show that the intonation
string players (e.g. in string quartets) tend to use instinctively is
mostly Pythagorean. Playing in meantone is routine among early music
players; I dare say David Greenberg could do that even without any cues
from a keyboard. Indian fiddlers can play in any raga possible within
the 22-shruti system. Turkish classical players use Western fiddles to
play in any of a couple of dozen makams built from a 24-note unequally-
tempered set of intervals defined in Pythagorean units. The restriction
you're suggesting is not built in either into the fiddle hardware or the
player's brain.
Assuming you have the Dover edition of Helmholtz, I suggest you look at
the table starting on p.453 (among the translator's appendices) which
shows the awe-inspiring variety of whole-number ratios that somebody,
somewhere, has played, sung, or thought we ought to play or sing. The
Highland bagpipe features in a different table on p.515; its scale turns
out to be almost identical to an Arabic one, first described by the
lutenist Zalzal and surviving as modern "meshAqah", which suggests that
widely separated cultures both found some logic in it.
(Another table is pertinent to a discussion we had a few weeks ago;
the lists of historic fundamental pitches beginning on p.495 show how
fantastically implausible it is that anyone in Britain in the mid-to-
late 18th century would have used a pitch below A=390, even for such
an obscure instrument as the guittar, without saying explicitly that
they were doing something really, really weird and foreign).
> It is impossible for a fiddler/violinist [or a trombonist or a singer]
> to play/sing in "another sort of intonation". Quoting L. Lloyd , "It is
> easy to play out of tune, it is a superhuman feat to play 'off the note'
> with exactly the mistuning required for equal temperment, for we may be
> sure that the player has no physical means of reproducing equal
> tempertment with accuracy".
However other kinds of intonation provide harmonic feedback that equal
temperament doesn't, so playing in those isn't a superhuman feat. Barber-
shop quartets are a pretty dramatic example of amateur-feasible music
with an alternate temperament (often the fundamental pitch shifts during
the performance, a bug/feature of just-intonation-by-ear first noticed
during the 16th century in critiques of Zarlino's theoretical scheme).
The barbershop repertoire makes my toes curl but I have to admire the
technique.
And if you've got a reference instrument playing with you, like a gamelan,
a set of smallpipes, or a harpsichord tuned in meantone, almost any
adjustment is possible.
> As I said in an earlier e-mail the ear can measure the "just intonation"
> intervals but it can't measure deviations from them nor can it measure
> intervals which would produce other than just intonation ratios.
The point is that there are great many alternate whole-number ratios
that could be considered to represnt intervals like "third" or "seventh";
just intonation (the rule "pick the smallest numbers you can with prime
factors less than 7") has not historically often been the popular option.
Measuring small deviations is easy: count beats or listen for difference
tones. But that isn't what people do when playing; you have an intuitive,
not measured, feel for when you've got the right sound, and you can develop
that intuition for any one of several different tuning systems. There are
early music singing groups these days that can switch between different
intonation systems in the same concert, from Pythagorean for mediaeval
repertoire to just intonation for the early Renaissance to meantone for
the Baroque.
> Consider also that when you've tuned your fiddle in fifths, you have
> preselected the pitch of four and sometimes five of the notes in the
> diatonic scale in the most-used fiddle keys and they are all in the
> "just intonation" scale.
If you tune in pure fifths you do *not* get just intonation pitches for
the open strings, but Pythagorean ones; assuming you start at the bottom,
only the G and D will be right. (Classical players don't tune in pure
fifths but adjust things a bit). But for playing pipe tunes, there are
only three relevant open strings - D, A and E - for all of which, if we
assume we're playing in A, the pipe scale coincides with just intonation.
The B is dead on too. The weird shit comes in with C#, F#, and the Gs
at each end of the chanter scale, all of which are fingered notes on a
conventionally-tuned fiddle.
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