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Presented here are a batch of NEVER-BEFORE-HEARD waltzes composed by Wolfgang Amadeus Mozart. How can that be??? you ask. Where'd they find 'em??? This is some kind of trick, right? You mean Hank Mozart, or somebody, right?
No, we're talking about W. A. the man, himself. The waltzes were generated with his Musikalisches Wuerfelspiel (musical dice game). Mozart wrote the original for piano in C major and it has been transcribed into A major for guitar. See credits further down this page.
The waltz has 17 measures: two 8-measure sections plus a 2nd ending measure for the A section. The first and second endings of the A section are always the same. For some reason, Mozart wrote only two alternatives for the final measure. For each of the other 14 measures he wrote 11 alternatives; 11 because that's how many different sums you can get by tossing two dice (from 2 to 12). So, in total, Mozart wrote 11 x 14 + 2 = 156 measures for the Musikalisches Wuerfelspiel.
To find the total number of distinct waltzes that can be generated from these 156 measures, we multiply 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 11 x 2.
That works out to precisely 759,499,667,166,482 (760 trillion) unique waltzes. (Ok, to be honest, some of these might sound a tad like some of the others.) While the figure is nowhere near the 100,000,000,000,000,000 (100 quadrillion) figure estimated by a modern publisher, it's nothing to be sneezed at, either.
The cost of disk space being what it is, I've only provided you with a starter set of about 200 different waltzes in guitar tablature. If that's not enough to satiate you - or, if you're the selfish sort who wants to make sure he's playing waltzes nobody else has ever played - I've put up a BASIC program to generate them. Knock yourself out.
In the key of A, the waltzes fit much better on the guitar with the 3rd string tuned down to F#. This gives the presentation in tablature slightly more justification, for those who look with disdain on tablature. Of course, the main reason is I can generate tablature; I can't generate music.
It's about time we had a go at the table of contents. We'll continue the discussion later.
1. Randomly generated waltz sets - each measure used once per set.
In each of the nine sets here, there are 11 randomly generated waltzes. However, each time a measure is randomly selected, it is removed from the pool so it can't be selected again. Thus, the 11 waltzes in each set very neatly use up all of Mozart's measures, and use each one exactly once. (In the interest of playing never-before-heard Mozart, don't start at the beginning - jump in the middle somewhere!)
Set 1 / Set 2 / Set 3 / Set 4 / Set 5 / Set 6 / Set 7 / Set 8 / Set 9
2. Randomly generated waltz sets - measures may appear multiple times in the set.
In each of the nine sets here, there are 11 randomly generated waltzes. A used measure is not removed from the pool, so it could very well pop up in several waltzes in the set. This is more in line with the original dice-tossing selection method. The downside is that you will see some measures popping up several times, while others don't get used at all. See discussion further down.
Set 1 / Set 2 / Set 3 / Set 4 / Set 5 / Set 6 / Set 7 / Set 8 / Set 9
3. Non-randomly constructed waltzes.
In defiance of the Wuerfelspiel instructions, I have hand-crafted some waltzes by picking and choosing desired measures. For example, you get the most- and least-notey waltzes; the highest- and lowest-pitched waltzes; the "blockiest" waltz; and a few others with certain constraints on melodic motion. This gives a taste of the extremes you would encounter among the gazillion possibilities.
4. Index of measure alternatives.
An index to all the measures Mozart wrote for the Musikalisches Wuerfelspiel is presented in the form of a set of 11 waltzes, each using a specified alternative for all the measures. Waltz 1 uses alternative 1 for all of its measures, waltz 2 uses alternative 2 for all of its measures, etc. This will help you to pick and choose measures to custom design a waltz, if so desired. The computer program allows you to do this.
5. Musikalisches Wuerfelspiel computer program.
Here is the computer program which generates Mozart waltzes. It's written in BASIC. I promise you, it's easy to use. Guaranteed virus-free.
Further Discussion
The 1802 edition of the Musikalisches Wuerfelspiel doesn't actually use those words as the title or anywhere else. The mundane title Instruction is given in four languages, each quadrant of the cover devoted to a given language. Here are the German and English quarters of the title page.
ANLEITUNG
Walzer oder Schleifer mit zwei
Wuerfeln zu componiren, so
viele man will, ohne
etwas von der Musik
oder Composition
zu verstehen.
PAR
INSTRUCTION
To compose without
the least knowledge
of Music so much German
Walzer or Schleifer as
one pleases, by throwing a
certain Number with two Dice.
My 1936 "Grove's Dictionary of Music and Musicians" treats Schleifer as a synonym for Ländler, "a national dance popular in Austria, Bavaria..." Grove's calls it the "real ancestor" of the modern waltz, which "first made its appearance about 1780."
AUTHENTICITY: It should be mentioned that some grumpy Gusses out there doubt the Mozart attribution. A card in the Library of Congress card catalog says, "Although it is known from his sketchbooks that he experimented with this idiom, the attribution is doubtful."
C'mon, man! It's in his sketchbook; it sounds just like him; and the cover from the 1802 edition says "W. A. Mozart" as big as life. What more d'ya want?
A 1957 edition of the Musikalische Wuerfelspiel by B. Schott's So"hne had this to say:
Das musikalische Wuerfelspiel ist 1793, also erst nach Mozarts Tod, bei J.J. Hummel in Berlin-Amsterdam erschienen. N. Simrock in Bonn druckte das Spiel 1796 nach; dieser Druck wurde unsere Ausgabe zu Grunde gelegt. Es ist durchaus mo"glich, dass Mozart das musikalische Wuerfelspiel selbst entworfen hat, da er sich gelegentlich mit derartigen Spielereien befasst hat, wie es z.B. [zum Beispiel] das Skizzenblatt zum Adagio KV 516 beweist. Dieses entha"lt eine Skizze zu einer Menuettstimme, deren Takt-gruppen durch Buchstaben in einer a"hnlichen Form wie in dem vorliegendem musikalischen Wuerfelspiel angeordnet sind.
Don't laugh at my high-school German, but this is what I see: "The Musical Dice Game was published [appeared] in 1793, thus only after Mozart's death, by J.J. Hummel in Berlin-Amsterdam. N. Simrock in Bonn later printed the game in 1796; this printing [edition] becoming the basis of our edition. It is by all means possible that Mozart himself designed [sketched] the Musical Dice Game, since he had occasionally occupied himself with such trivialities, as demonstrated, for example, by the sketch page for the Adagio KV 516. This contains a sketch for a minuet melody whose measures were arranged by means of letters in a similar form as in the musical dice game under consideration."
Of course, the naysayers will point out that Schott has an interest in people believing Mozart wrote it.
The 1936 Grove's devotes half a page to "The spurious and doubtful works" of Mozart. It mentions "the large number of spurious piano pieces" but doesn't bring up the Musikalische Wuerfelspiel.
RANDOMIZATION: The original instructions were for the player to throw two dice to randomly select an alternative for each measure. This method, of course, does not give each measure alternative an equal chance of getting picked, since 7 shows up much more frequently than 2 or 12, for example. The selection process used here gives an equal chance to each of the 11 alternatives. (From the start, even before the days of personal computers, I used a dodecahedron with numbered sides instead of dice.)
Quick quiz: about how many times would you have to throw a conventional 6-sided die before you'd expect each of the 6 numbers to appear? Think about it before clicking on the answer here.
I suspect most people would not have guessed an answer that large based on intuition. The point is, random selection is an extremely inefficient - downright lousy, even - way to exhaust a set of possibilities. What this has to do with Mozart is that, if you want to hear each of his 11 alternatives for a given measure, you would expect to have to randomly pick 33.2 times, on the average, to finally nail all 11. Think about it like this: even after you've struggled to snag 10 different alternatives, you would expect to have to pick 11 more times just to snag the remaining one. (The situation would be much worse with dice.) This is the main reason for generating waltzes in sets of 11 with no measure reused. It's very satisfying to think that playing through one set of 11 waltzes covers everything Mozart (or that impostor) wrote.
KOECHEL NUMBERS: The Koechel number for the Musikalisches Wuerfelspiel is K. 516f. For each unique waltz, I generate a unique "decimal" which is appended to K. 516f. It's in quasi-base 11 representation, where A represents 10, B represents 11, and there is no 0. The decimal is 15 "digits" long, one for each measure for which Mozart wrote alternatives - that is, all measures except the 1st and 2nd endings. The digits simply represent, measure by measure, which of the 11 alternatives was selected. Given just the Koechel number - K516f.899135A22AB6131, for example - one could construct the unique waltz by piecing together the specified measures given in the "Index of measure alternatives".
THE FINAL MEASURE: This one is curious. Mozart wrote only two alternatives for the last measure. Moreover, they are given completely lopsided representation. One alternative is given one time, while the other is given ten times. The good news is that the rare one transcribes very poorly to the guitar, punching out A notes at four different octaves. We can only give it two. The other final measure fares a little better, but really wants to descend to the next lower A rather than come back up to our 5th string.
ORNAMENTS AND SYMBOLS: Mozart wrote three trills and one turn in the Musikalisches Wuerfelspiel.
" = trill. Starts on the main note.
~ = turn. Main note => upper neighbor => main => lower => main.
^ = arrowhead indicating strum or arpeggiation.
He didn't write the guitaristic arpeggiation, of course.
The tuning of the 3rd string to F# provides the best possible shot at playing the turn but, even so, an inverted mordent (main note to upper neighbor and back down) is about all I can comfortably fit in.
Here are some suggestions for the trills:
___ ___ _______ ___ _____
| | | | | | |-|-|-| | | | |-| | |
___________ ________________ ______________
|_0_______| |_0____________| |_0__________|
|_________| |_______2___2__| |_____0_2_0__|
|_____"5__| ==> |_____5___5___5| or |____________|
|______2__| |_____2________| |_____2______|
|_________| |______________| |____________|
|_0_4____4| |_0_4_________4| |_0_4_______4|
___ ___ ___ ___ _______ ___
| | | | | | | | |-|-|-| | |
_______________ __________________
|_____________| |_______0___0____|
|_4___"4______| ==> |_4___4___4___4__|
|_0___________| |_0______________|
|_____________| |________________|
|_2_2__1_2_0_2| |_2_2_1___2___0_2|
|_____________| |________________|
___ ___ ___ ___ _______ ___ ___ _______ ___
| | | | | | | | |-|-|-| | | | | |=|-| | | |
_______________ __________________ __________________
|_____________| |________________| |________________|
|_2___"2______| ==> |_2___2_3_2_3_2__| or |_2___2_3_2______|
|_____________| |________________| |________________|
|_2__________1| |_2_____________1| |_2_____________1|
|_0____0_2_4__| |_0___0___2___4__| |_0___0_____2_4__|
|___4_________| |___4____________| |___4____________|
CREDIT: The Musikalisches Wuerfelspiel was published in a guitar version by Carousel Publishing Corp. as Melody Dicer in 1976. The transcription from piano to guitar in standard tuning was by Miguel Coelho. I had a lot of fun with that. Thanks, Miguel!
More recently, I noticed that the waltzes were easier to play with the 3rd string tuned to F#. I translated the Melody Dicer measures into tablature for that tuning and wrote a program to randomly generate waltzes.
Looking for a bit of background information, I discovered that the Library of Congress had an edition from 1802. (Just another LC thrill, ho hum.) Comparing that with the Melody Dicer version, I found about 17 measures where original piano notes could be restored, thanks to the F# tuning. Having access to the original also allowed me to work up slightly different solutions in several other places. All in all, I was quite amazed at how faithful the guitar transcription was.
The only place where I willfully altered Mozart was in a few of the alternatives for measure 13. His bass part was often just two E notes, dropping from e on beat 1 to E on beat 2 or 3. In the guitar transcription, starting with the low E gives a better connection from measure 12. Where that change was made, I usually shifted the second E up an octave.
RHYTHM VALUES: have been doubled from Mozart's original which was in 3/8. The ascii tab can easily handle 16th notes, but they look best with a little filling in by hand. The 3/4 time avoids 16th notes completely.
THE MODERN TABLATURE: This tablature uses the spaces, rather than lines, to represent the strings of the instrument. The main reason for this choice is that the fret numbers are more visible in the spaces than on the lines. A simple change to the computer program will cause it to generate tablature with frets-on-the-lines, if you want.
PRINTING OUT: The layout of the tablature within the web pages was based on considerations of print technology back in the 1990s. It was designed for a page break every 66 lines, counting from the first title line. You can probably fiddle around and find a perfectly acceptable way to print it using the technology at your disposal, but here is one way.
1. In the Internet Explorer browser: click View; click Source. The web page comes up in Notepad.
2. Delete all material before the title line, "Walzer - Musikalische Wuerfelspiel 1 of 11"
3. Delete all material below the last line of tablature at the end of the file.
4. Click File; click Save As... and save the file as a .TXT file, wherever you want, named however you want. Close Notepad.
5. Open that .TXT file with Microsoft Word. If you scroll down or hit Print Preview, you will see the page breaks are not quite right.
6. Select all text with ^A (control A); choose font style Lucida Console. The page breaks are still not right.
7. Click File, then Page Setup.
8. Set Top margin to 0.9".
9. Set Bottom margin to 0.9". Click OK.
10. Observe that all page breaks are now precisely above the line that gives the page number. Hit Print Preview to doublecheck.
11. If happy, then Print.
If you want to give a bit more breathing room between the two waltzes on a given page, it seems to work out that for every line you add between the two, you need to reduce the top and bottom margins by a total of 0.2" (inches). For instance, if you add a line, change each margin to 0.8". Apparently, Lucida Console at font size 10 runs five lines per inch. There is no describing, even all these years later, how much pain and suffering I endure because of modern computing's obsession with proportional spaced type. I really needed that. Like a hole in the head. Thanks, Bill.
REAL THANKS: Mas Frank, of Java, pointed me in the right direction regarding "Schleifer", and corrected my translation of "erst" in the paragraph from the Schott edition. Not "first after Mozart's death", but "only after..."
COPYRIGHT: the pieces presented here and the computer program may be copied freely by anybody. Help yourself.
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