19-tone Equal Notation

Bob Lee said:
> Again, I'm new to the list. Please forgive me if this is covered in a FAQ I
> haven't read.
>
> How is 19TET music notated? Gregg Gibson's recent writings on the subject
> have been quite enlightening, but I don't understand how music would be
> communicated if the octave were divided differently. What becomes of our
> familiar A B C D E F G? Has a system been developed, or is this "left as an
> exercise for the reader"?

19-tone equal temperament is actually more easily and logically notated
in terms of our traditional notation than is 12-tone equal temperament.
I will be happy to explain.

Here is the cycle of fifths in the 19 system:

Ascending from C:
C G D A E B F# C# G# D# A# E# B#

Descending from C:
C F Bb Eb Ab Db Gb Cb Fb

In the 19-tone equal, the cycle of fifths closes at E#/Fb (which are the
same pitch) and B#/Cb (also the same pitch). All the other sharps and
flats are distinct pitches. In our traditional notation, two such notes
as D# and Eb are notated differently, even though in the 12-tone equal,
which came into universal use (late 19th century) only long after the
invention of our notational system (in the 14th century, I believe) such
notes as D# and Eb are the same pitch. You can see that as far as our
notation is concerned, which expects 21 distinct pitches, 19-tone equal
is far more natural.

Here are the 19 notes in order:

C C# Db D D# Eb E E#/Fb F F# Gb G G# Ab A A# Bb B
B#/Cb C

In the 19 system, every time we sharp a note, we raise it by 1/3 tone
(instead of by 1/2 tone), and every time we flat a note, we lower it by
1/3 tone. So, for example, Fbb=E, Bx=C, Dbb=C#, Abbb=G.

Roughly 95% of the music you are likely to encounter can therefore be
played very easily in 19-tone equal. The other 5% consists of music
where a note such as Fb is equated with E in a consonant chord; this
kind of modulation sounds merely artificial in 12-tone equal, but
perfectly horrid in 19-tone equal. Since most music was not habitually
written for 12-tone equal until well into the 19th century, and since
rock and other popular music is as a rule perfectly oblivious to the
more extreme 12-tone modulations, one can happily use 19-tone equal for
just about any music one pleases. I rarely use anything else.

If you have any additional questions , or if anything puzzles you about
this, please feel free to inquire of me further.

I'm quite new to this list myself, but most everyone seems friendly
enough, provided you don't call anything 'worthless'. Welcome.


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From: Gregg Gibson
Subject: Re: Levy's Book
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