source file: mills3.txt Date: Tue, 16 Dec 1997 06:33:28 +0100 Subject: 19-tone Equal Notation From: Gregg Gibson 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. SMTPOriginator: tuning@eartha.mills.edu From: Gregg Gibson Subject: Re: Levy's Book PostedDate: 16-12-97 06:57:54 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 16-12-97 06:55:49-16-12-97 06:55:49,16-12-97 06:55:29-16-12-97 06:55:29 DeliveredDate: 16-12-97 06:55:29 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125656F.00209291; Tue, 16 Dec 1997 06:57:43 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA16573; Tue, 16 Dec 1997 06:57:54 +0100 Date: Tue, 16 Dec 1997 06:57:54 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA16571 Received: (qmail 17217 invoked from network); 15 Dec 1997 21:57:51 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 15 Dec 1997 21:57:51 -0800 Message-Id: <34967A86.147F@ww-interlink.net> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu