source file: mills3.txt Date: Sun, 19 Oct 1997 20:37:57 +0200 Subject: Re: TUNING digest 1211 From: Larry.Polansky@Dartmouth.EDU (Larry Polansky) Re: fretless... there are a couple of other fretless players out there... and my new marchione guitar is fretless.... not sure what exactly i'm gonna play with it but if anybody's got a cool piece.... lp SMTPOriginator: nowitzky@pacificnet.net From: Mark Nowitzky Subject: Analysis of Vicentino's "Madonna" PostedDate: 20-10-97 01:54:43 SendTo: tuning@eartha.mills.edu CopyTo: CN=coul1358/OU=AT/O=EZH,kami@interlinx.qc.ca,armandtatevossian@prodigy.com,Klynt@wardlawclaims.com,msrotman@aol.com,peterp7878@aol.com,saxqtet@aol.com,matchframe@instanet.com,tom.nowitzky@globalstar.com,nowitzky@calarts.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: 20-10-97 01:54:29-20-10-97 01:54:30,20-10-97 00:55:10-20-10-97 00:55:10 DeliveredDate: 20-10-97 00:55:10 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 C1256535.008351FC; Mon, 20 Oct 1997 01:54:22 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA21278; Mon, 20 Oct 1997 01:55:14 +0200 Received: from polaris.pacificnet.net by ns (smtpxd); id XA21280 Received: from pm3d-28.pacificnet.net (pm3d-28.pacificnet.net [207.171.18.173]) by polaris.pacificnet.net (8.8.5/8.8.5) with SMTP id QAA14575; Sun, 19 Oct 1997 16:54:43 -0700 (PDT) env-from (nowitzky@pacificnet.net) Date: Sun, 19 Oct 1997 16:54:43 -0700 (PDT) Message-Id: <2.2.16.19971019165149.3f9762ce@pacificnet.net> X-Sender: nowitzky@pacificnet.net X-Mailer: Windows Eudora Pro Version 2.2 (16) Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" To: tuning@eartha.mills.edu From: Mark Nowitzky Subject: Analysis of Vicentino's "Madonna" Cc: Manuel.Op.de.Coul@ezh.nl, kami@interlinx.qc.ca, armandtatevossian@prodigy.com, Klynt@wardlawclaims.com, msrotman@aol.com, peterp7878@aol.com, saxqtet@aol.com, matchframe@instanet.com, tom.nowitzky@globalstar.com, nowitzky@calarts.edu This posting may be found in its entirety, complete with hyperlinks to MIDI examples, at: http://www.pacificnet.net/~nowitzky/justint/madonna.htm (and I apologize for its length)... Analysis of Vicentino's "Madonna", by Mark Nowitzky, 10/19/97 Inspired by this posting to the TUNING list: (From TUNING Digest 1210, Topic 2) ... beginning of forwarded message... Date: Fri, 17 Oct 1997 13:52:06 +0200 From: Manuel.Op.de.Coul@ezh.nl To: tuning@eartha.mills.edu Subject: Vicentino enharmonic madrigal I have made a short MIDI file with the first page of Nicola Vicentino's madrigal "Madonna il poco dolce". Vicentino wrote this madrigal as an example of a composition that employs the three modes diatonic, chromatic and enharmonic. The microintervals of the enharmonic mode are minor dieses. I have rendered it in 5-limit just intonation with minor diesis of 128/125. Thanks to Kami Rousseau for putting it in his website. Download http://www.interlinx.qc.ca/~kami/music/madonna.mid or go to his music page http://www.interlinx.qc.ca/~kami/ and follow the link "MIDI files". No special equipment needed. Manuel Op de Coul ... end of forwarded message... My thoughts and analysis of Manuel's MIDI file: This work by Vicentino sounds like an excellent example for testing out tuning theories. When I first played it, it sounded like the third chord in the piece was too sharp. But I wasn't sure, because I had some similar surprises when I experimented with a Moussorgsky work. (Click here for details on that experiment.) Anyway, I took a "microscope" to the file to understand what was happening. I found that the tuning was accomplished by using MIDI "pitch bends" on the notes, to adjust them from equal temperament to just intonation. (I used the same tuning method on the aforementioned Moussorgsky work.) ... a short digression into how pitch bending works...: A MIDI pitch bend mimics the "pitch wheel" found on many electronic keyboards. As an example, to get a "justly intoned" C Major chord, you'd sharpen the G (via a positive pitch bend), and flatten the E (via a negative pitch bend): C Major chord ------------------------------ Equal tempered Justly intoned -------------- -------------- G+0 G+80 E+0 E-561 C+0 C+0 The notation used here is the note name, followed by the positive or negative pitch bend value. The values are based on a semitone having 4096 pitch bend units. ... back to the Madonna MIDI file...: So, I found that the first four chords were tuned as follows: Manuel's 5-limit just intonation rendering ------------------------------------------ G minor G Major D Major F Major ------- ------- ------- ------- G+80 G+80 F#+1281 F+1602 D+160 D+160 D+1842 C+1682 Bb-160 B-481 A+1041 A+1041 G+80 G+80 D+1842 F+1602 You can see from the above that the transition from the first chord to the second is smooth, because most of the notes don't change (G+80 remains G+80, and D+160 remains D+160). The only change is from Bb-160 to B-481. But the third chord (D Major) is a different story. The D+160 becomes a much sharper D+1842 (which explains the "sharpness" I heard when I first played the file). But I wondered; is this how it "should" be? ... another digression, this time into 5-limit just intonation...: A classic way to help visualize 5-limit just intonation is by placing the notes in a two-dimensional table. This is the so-called Duodenarium, from Ellis' translation of Helmholtz' On the Sensations of Tone. The notes are arranged as follows: ascending Perfect Fifths are written over one another vertically ascending Major Thirds are written to the right horizontally Theoretically, the Duodenarium can extend infinitely in the vertical and horizontal directions. Using the "note + pitch bend" notation, the center of the Duodenarium looks like this (with C+0 at the very center): Duodenarium with "note + pitch bend" notation