Inversus: Sankyo 20-Note Moebius Strip Plays Inverse Music
by Roland Tremblay (030204 MMDigest)

tremblay_MoebMelo.jpg (92 kb)

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,
4 Feb 2003 14:40:22 -0500

tremblay_Inversus.doc  (54 kb,  MS-Word 97/98)
  MIDI files:
tremblay_BrunoInv.mid (6 kb)
tremblay_CalDrmIn.mid  (4 kb)
tremblay_ForlorIn.mid  (4 kb)
tremblay_SoWhatIn.mid (4 kb)
tremblay_NobodyIn.mid (5 kb)
tremblay_ScarboIn.mid (4 kb)

tremblay_MoebHow.jpg (17 kb)

tremblay_LoopLink.jpg (18 kb)

tremblay_Smalworl.jpg (34 kb)

tremblay_moeband.jpg (50 kb)

tremblay_MoebMelo.jpg (92 kb)

tremblay_SpacerDm.jpg (44 kb)

tremblay_SpacerC.jpg (45 kb)

tremblay_SmalSpacer.jpg (55 kb)

A mathematician named Klein
Thought the Möbius Loop was divine
    Said he, "If you glue
    The edges of two
You get a weird bottle like mine."
 -- anonymous

Three jolly sailors from Blaydon-on-Tyne
They went to sea in a bottle by Klein.
Since the sea was entirely inside the hull
The scenery seen was exceedingly dull.
 -- Frederick Winsor, "The Space Child's Mother Goose"

16 February 2003