quantum mechanics

Thinking a bit more about quantum mechanics and oscillators... the problem of
the quantum behavior of a vibrating string is essentially the same as the
problem of electromagnetic radiation in a cavity, the thermodynamic aspect of
which led Planck to his original hypothesis at the very origin of quantum
mechanics, back around 1900.

Classically we would describe the motion of a string by providing amplitudes
and phases for each of the modes of osciallation. As the string is coupled to
its environment, these amplitudes would slowly and steadily decrease as the
string vibrates a sounding board which radiates the sound.

Quantum mechanically, each mode of oscillation would not have a continuous
range of possible amplitudes, but a discrete range. These amplitudes would
not steadily decrease, but somehow they jump discretely from one amplitude
level to a lower level.

So it's the diminuendo, not the glissando, that gets broken into minute
steps!

Jim


SMTPOriginator: tuning@eartha.mills.edu
From: Aline Surman
Subject: Wilson scale
PostedDate: 30-12-97 08:42:36
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: 30-12-97 08:40:20-30-12-97 08:40:20,30-12-97 08:39:44-30-12-97 08:39:44
DeliveredDate: 30-12-97 08:39:44
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 C125657D.002A2109; Tue, 30 Dec 1997 08:42:06 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA27666; Tue, 30 Dec 1997 08:42:36 +0100
Date: Tue, 30 Dec 1997 08:42:36 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA27650
Received: (qmail 13304 invoked from network); 29 Dec 1997 23:42:34 -0800
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 29 Dec 1997 23:42:34 -0800
Message-Id: <34A8ADFC.3376@dnvr.uswest.net>
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu

Stellated two out of 1 3 5 7 hexany, also dekatesserany, mandala,
tetradekany
0: 1/1 0.000 prime, unison
1: 21/20 84.46723 minor semitone
2: 15/14 119.4428 major diatonic semitone
3: 35/32 155.1396 septimal neutral second
4: 9/8 203.9100 major whole tone
5: 5/4 386.3139 major third
6: 21/16 470.7811 narrow fourth
7: 35/24 653.1849 septimal diminished fifth
8: 3/2 701.9553 perfect fifth
9: 49/32 737.6521
10: 25/16 772.6278 classic augmented fifth
11: 105/64 857.0950 septimal neutral sixth
12: 7/4 968.8264 harmonic seventh
13: 15/8 1088.269 classic major seventh
14: 2/1 1200.000 octave
This is the lattice with factors 2 ignored, the zero indicates the 1/1
position.

hor > 3/1 - ver ^ 5/1 - hor >> 7/1

| * | | |
* | * * | * * * | |
. | 0 * * | * * | * |
| | * | |

Imagine the four layers on top of one another for a 3D image.

Manuel Op de Coul coul@ezh.nl


SMTPOriginator: tuning@eartha.mills.edu
From: Aline Surman
Subject: various
PostedDate: 30-12-97 18:10:52
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: 30-12-97 18:08:35-30-12-97 18:08:36,30-12-97 18:07:59-30-12-97 18:08:00
DeliveredDate: 30-12-97 18:08:00
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 C125657D.005E27A0; Tue, 30 Dec 1997 18:10:21 +0100
Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA28211; Tue, 30 Dec 1997 18:10:52 +0100
Date: Tue, 30 Dec 1997 18:10:52 +0100
Received: from ella.mills.edu by ns (smtpxd); id XA28196
Received: (qmail 11701 invoked from network); 30 Dec 1997 09:10:49 -0800
Received: from localhost (HELO ella.mills.edu) (127.0.0.1)
by localhost with SMTP; 30 Dec 1997 09:10:49 -0800
Message-Id: <34A93363.15ED@dnvr.uswest.net>
Errors-To: madole@mills.edu
Reply-To: tuning@eartha.mills.edu
Originator: tuning@eartha.mills.edu
Sender: tuning@eartha.mills.edu