TUNING digest 1211

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