source file: mills3.txt Date: Mon, 8 Dec 1997 23:35:10 +0100 Subject: Reply to Gregg Gibson From: "Paul H. Erlich" It is interesting that you began with a question about Arabic music. Arabic modes use neutral seconds (which bisect minor thirds) and neutral thirds (which bisect perfect fifths) which are not present in 19-equal. So much for studying "all the modes melodically distinct to the ear!" Septimal intervals, the next logical step in consonance after the 5-limit intervals in triads, are far better represented in 31-equal than 19-equal. If you really believe that the 31-equal dieses are too small for use in melody, no one will force you to use them! Even avoiding them, you will have more melodic variety than in 19-equal, plus you will get much better 7-limit harmonies, far better 11-limit harmonies, and even those Arabic modes (just add 1 to the size of each of the heptatonic steps in an Arabic scale in 24-equal and you get a pretty good 31-equal approximation). 22-equal, far from being worthless, has occupied me for the last six years; see my paper at http:/www-math.cudenver.edu/~jstarret/microtone.html under "Notes on Microtonality." Worthless for diatonicism, maybe; for escaping the diatonic hegemony, it may be our only hope. In a rare moment of compositional inspiration, I wrote a piece where the top voice moves down through 20 of the 22 tones. You can hear this on the Tuning-List Tape. Despite the 54.5 cent steps, I can sing this melody in the shower (but only if I clearly imagine the harmony). >>Of the heptatonic modes, the familiar seven of the diatonic genus >>have consonant chords on six of the seven degrees, as is universally >>known. More subtly, every one of these degrees is part of at least one >>consonant chord (actually, of at least two) within the untransposed >>diatonic order. No other heptatonic modal genus has above four of its >>seven degrees which are the roots of consonant chords within the genus, >>all of whose degrees are included within at least one consonant chord. >>These genera are four in number, including 28 modes. On C these are: > >>C D E F G Ab B C >>C D E F G Ab Bb C >>C Db E F Gb A Bb C >>C D E F G# A B C > >This looks interesting, but it sounds like you're saying there are four of >something that there are none of. Can you clarify please? > >Anyway, I recall someone posting about a psychology experiment back in the >50s or 30s where subjects were trained to listen to melodies whose interval >sizes were gradually decreased, over the course of months, to something like >tenths of tones. The subjects became quite comformtable with these melodic >sizes, could distinguish them quite clearly, and when exposed to conventional >Western music again, found the intervals very large. > >Someone with a lot of 12-equal training is likely to consider two notes >separated by 40 cents "the same", and two notes separated by 60 cents >"different." It doesn't take a genius of psychology to explain that. However, >both listeners and musicians are able to learn and enjoy considerably smaller >intervals, as many on this list can attest from personal experience. SMTPOriginator: tuning@eartha.mills.edu From: DMB5561719 Subject: Re: Tuning into the FUTURE. PostedDate: 09-12-97 00:35:57 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: 09-12-97 00:34:05-09-12-97 00:34:06,09-12-97 00:33:53-09-12-97 00:33:54 DeliveredDate: 09-12-97 00:33:54 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 C1256567.00817491; Tue, 9 Dec 1997 00:34:00 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA10114; Tue, 9 Dec 1997 00:35:57 +0100 Date: Tue, 9 Dec 1997 00:35:57 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA10112 Received: (qmail 22174 invoked from network); 8 Dec 1997 15:35:54 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 8 Dec 1997 15:35:54 -0800 Message-Id: <6fc37828.348c8122@aol.com> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu