Music Notation and the Abacus

Music Notation and the Abacus
Andre Willers
15 Sep 2010

"No stave , no symphony ." Christopher Page
www.historytoday.com/music

Synopsis :
The synthesis of music with the abacus by Guido of Arezzo (circa 1010 AD) led to the Stave Musical notation . This opened up entire new ecologies of music composition and reproduction . Architecture and religious memes were severely affected .

Discussion :

1.History :
Without a musical notation , large groups of humans are limited to chorus effects or individual artistes . Complex coordination is not possible .
Examples are the Greek theatrical chorus , any chorus like work chantys , anthems ,etc .

This was the state of play around 753 AD , when Pippin of France and Pope Stephen II signed a "pacis foedera" at Pippin's Farm Palace near Ponthion in the Champagne . A mutual aid pact .

Included in this deal (probably much against his will ) was Simeon (of Greek or Syrian descent) , who was second in charge of the Roman Schola Cantorum .
(Nobody remembers the name of number one . The dangers of academic politics .)
The Gregorian Chant (Frank-Roman chant) rose from Simeon's teachings .

Fast forward to the early 11th Century AD .
The climate and civilization had improved . Populations exploded . Useless younger sons were sent off to the capital to get some polish and out of underfoot . Many of them ended up in the Choir , to the music-master's despair .
This person was Guido of Arezzo .
At first , he could only teach them by exposing them to all the thousands of tunes that had accumulated and requiring them to memorize them .

His students had no talent , lots of money and an aristocratic hauteur , but he had to deliver people who could sing in tolerable harmony . The usual academician's nightmare .

But many of them came from commercial backgrounds , and were intimately familiar with the Abacus . Some of them started using the positions of the counters on the abacus to represent tunes as an aide-memoire .

Guido gratefully seized on this . To give him his due , he never claimed that he invented the notation , only that it gave his students more time for " prayer , for the recitations of Psalms , for nocturnal vigils and other duties they can perform cum puritate" .("Epistola ad Michahelem" ) . Right .

It was a communal academic effort , and their academic master seems to have been a fairly nice guy in not grabbing all the glory for himself (as would happen today) .

The signature is that there is no fixed date . (Processes never have fixed dates , but glory-hounds always have.)

What happened then ?
His students spread all over Europe , returning to their roles as minor aristocracy , but still remembering having being part of something grand and world-changing . Symphonies and Orchestras flowed out of this . Also Cathedrals and Opera houses .
A tradition of Culture .
Still lasting to this day .
Not bad .

Printing and Composers :
There was an insatiable demand for new tunes . These could be printed . The bread and butter of printing houses and composers . The underlying demand that made moveable-type printing profitable .

New Instruments :
This led to demand for new instruments like the clavier .

Cathedrals:
The explosion of cathedral building was a direct result of heavenly choirs in huge acoustic environments . The choirs were only possible because of the musical accompaniment . And this was only possible because they read the music .

But notice the role of the dirigent . Rieux , von Karajan and backward to Guido of Arezzo .

Opera Houses:
Culture with a vengeance .

The concept of Heaven :
Playing the harp in concert with the chorus .
I presume the electric-guitarist playing "Bad moon arising" must be a Protestant .

The Algorithms :
1.Music-to–Abacus .
The abacus would be decimal , with Roman subsections on V . Hence the 5 staves on left and right .Call the Set of Rules Alg(M,A)
A musical tune can be expressed as a single number by using the abacus number algorithm . (Eg 67387665) (ie treating the notes on the bars as numbers )
Cf Godel numbers .

2.The inverse:
Abacus-to-Music.
This is a typical trapdoor function .
A single number cannot easily be translated back into a tune . But it is handy for indexing purposes . Hence the later habit of calling new compositions by number .

Generating new tunes:
Generate a set of numbers from popular tunes from the Set of Rules Alg(M,A).
Inverse it with a Genetic algorithm to give appealing tunes .
Add a small spice of random mutation , and the we have new tunes of life .

Andre