Those who wrote about playing "in reverse" might be interested to know
how it can be used on simple instruments like the Sankyo 20-key
manivelle musical box and Mr. Christmas book music model.  I use Piet
Paardekam's "Midiboek" program to print my arrangements.

This posting is focused on the first "M" in MMD, ("Mechanical How to").
If you are interested in the second "M" ("Musical Why"), look for my
article "Inversus.doc" in the archives.  I also sent many JPEG and MIDI
files.

Playing a tune on a Sankyo paper strip, we go from the beginning to the
end, printed side up.  There are these alternatives:

- "Inverse".  From the beginning with the paper upside down.  The
notes are reversed (treble to bass, and vice versa).

- "Retrograde".  From the end to the beginning with the paper upside
down.  The rhythm is reversed, but not the notes.

- "Inverse-retrograde".  From the end to the beginning with the
printed side up; both notes and rhythm are reversed.

Let's apply the "inverse" process to the Sankyo 20-key system.

Playing the paper band upside down from the beginning, the notes are
reversed in mirror, pivoting around the midpoint of the scale.  To play
non-stop, I punch a strip of flexible photo paper and twist it 180
degrees before splicing it with two-faced tape.  (See: "MoebHow.jpg",
LoopLink.jpg.)

We get a Moebius band (See Moeband.jpg, and keyword "Moebius" in MMD
archives).  It integrates its two sides in one continuous rectangle.
When the red "underwear" of the strip is appearing on top, "Diabolus
est Deus inversus"!

A process similar to the one was used by Slonimsky in "Moebius Strip
Tease": the music rotated endlessly around the head of two singers, as
the inside went outside and vice versa.  His instructions: "Copy the
music on a strip of card stock 68 inches long and give the strip a half
twist to turn it into a Moebius strip."  :)

When we invert a standard Sankyo strip, we get on both sides a G scale
of white notes.  Many Celtic tunes use that scale, like the melody
"Forlorne", followed by an inverted variation of the tune, and then
again the melody, to get a whole tune out of a single punched chorus:
"ForlorIn.mid"

To invert in the more common C Major key, we have to modify the paper
band so it shifts down one note.  I cut out from the treble edge of a
Sankyo band a strip the width of a hole track, 3 mm.  (See Smalworl.jpg).
I replace the cutout paper by a resilient plastic spacer of the same
thickness on the treble side of the strip guide (MoebMelo.jpg).  When
the strip plays printed side up, the 20 notes stay aligned with their
star wheels.  Played upside down, all holes shift one note lower on the
tracker guide, so the band is pivoting around central E and chord C
remains C.

You can test that on pre-punched C songs.  "It's A Small World",
(Smalspacer.jpg) doesn't sound bad.  But any tune will sound better
when arranged especially for inversus.  Listen to a five-note Spiritual
(Nobodinv.mid).  I composed a tune with inversus in mind: "BrunoInv.mid"

Bewitched by mirror thinking :), I cut out the other edge of a strip,
-- the bass side instead of the treble -- and placed a spacer on the
bass side of the guide (SpacerDm.jpg).  We get a scale in D minor for
folk tunes (ScarboIn.mid).  That scale is used by Miles Davis
(SoWhatIn.mid).

The Yunsheng 15-Note movement we see in the MMD archives would play
Inversus in A minor (CalDrmIn.mid).

I am now experimenting with retrograde, used alone or combined with
inversus by J. S. Bach and W. A. Mozart.  To be continued?

Roland Bruno Tremblay,
Montreal

 [ Merci, Roland.  I will place your article and the images at the
 [ MMD Tech site, http://mmd.foxtail.com/Tech/   -- Robbie