RE: how about 22et vs 19et ?

Neil Haverstick did a nice job talking about 19et. That's partially
because the existing musical terminology makes sense in 19et. Which
means, essentially, that traditional ways of composing and performing
music work in 19et. When 12et was adopted, 19et was a viable, known
alternative (Salinas, Costeley) but 12et won out for convenience's sake.
In 19et, most Renaissance, Baroque, and some classical music will sound
great. But, as Neil points out, the diatonic b7ths are unbelievably far
from forming nice 7-limit tetrads, so dominant sevenths (and arguably
half-diminished sevenths) sound better in 12et than in 19et.

What Neil doesn't point out, and what I would recommend he explore in
his playing, is that using the #6th instead of the b7th leads to a much
better set of septimal intervals. For example, in 12et, playing a B and
an F together is ambiguous as to whether the root is G or C#. In 19et,
the root is much more clearly C#, while a B and an E# will evoke a root
of G. It sounds to me like Neil, when playing a blues in G or D, is
sticking to the diatonic F in some places where an E# might be much more
consonant. I very often hear blues or pop music which, if transposed to
the key of D, uses a septimal E# over the G (IV) chord, and slightly
less often I hear the #6 over the I chord. Weighing against the
acoustical superiority of the #6th is the familiarity and symmetry of
the traditional diatonic scale, and the fact that 19et's 7-limit
intervals often deviate from JI in the opposite direction than 12et's
approximations of the same intervals, leading to a very strong initial
"that's out-of-tune" reaction.

31et is just like 19et but more so (i.e., 7-limit intervals based on the
augmented sixth chord are nearly just; those based on the diatonic b7
are worse than 12et but not as bad as the same in 19et.) It also has
great 11-limit approximations.

22et is completely non-traditional. The fact that the product of four
perfect fifths does not approximate a 5:1 ratio throws a wrench into the
works. You have to scrap the usual notions about how to tune the guitar,
scales, chords, and keys (not to mention repertoire!), or at least
retreat to a much more bare-bones set of definitions in order to build
an understanding of the tuning back up. You can read my paper on John
Starrett's web site to see at least one approach. 34et is
non-traditional as well, but the inequality between major and minor
whole tones is much less noticeable than in 22et, and making a "comma"
adjustment, often necessary when trying to force traditional chord
progressions into non-traditional tunings, is more disturbing when the
adjustment is as large as 1/22 octave.

So 22et forces you to abandon much of what you have learned about how
music works. It has much better 7-limit approximations than 19et, and
will even get you as close to the 11-limit as Harry Partch's own voice
could (max. error 20.1 cents). 34et is not consistent beyond the
5-limit.

15et and 27et are also nice, non-traditional tunings. 26et is
"traditonal" in a sense but turns 12et's deviations from 5-limit JI
upside-down. 26et's leading tone of 138 cents (3/26 oct) is certainly
unusual-sounding, and it can even sound better to use a harmonically
false leading tone to get a more familiar interval of resolution (92
cents or 2/26 oct). But 26et has a nice way of introducing 7-limit
harmony (two diatonic scales tuned a half-octave apart will each contain
the 7-limit completion of all of the other's 5-limit triads!) and is
even consistent through the 13-limit. Finally, 29et is worth considering
since it is consistent all the way through the 15-limit.

If you want to get really non-traditional, try 24.6063et, which gives
you great approximations of all ratios of odd numbers through 13, but
forget about even numbers!

As for fingering, it does help if you already have calloused fingers,
otherwise your finger will just mash over several frets and probably
dampen the string's vibrations somewhat. You need to get some hardened
part of your fingertip (or side) to press the string down between two
frets, and that can be a lot easier on an electric guitar, since the
tension and action are lower. Don't expect to be able to pull off your
usual set of flashy licks and tricks without a long period of slowly
re-training your fingers.


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From: jpff@maths.bath.ac.uk
Subject: Re: Music Notation Software & Synth query
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