Jazz II.

Jazz II
Andre Willers
22 Mar 2011

Synopsis:

Cultures are perfusing via music .

Discussion:

Before 1020 AD all music was freeform . There was no generally accepted notation .
Pupils learned by listening and playing .

Then stave notation was developed from the abacus in the 11 the century AD.
See http://andreswhy.blogspot.com "Music Notation and Abacus" Sep 2010
(Repeated in Appendix A for your convenience , and the glorification of Guido of Arezzo .)

Music became repetitive on demand . The only creative licence allowed was for the composer , under strict control of the politicians (nobility , patrons).

Certain composers achieved staggering reputations , because they were the only ones allowed to innovate . Their music was replicated by printing press , orchestras , conductors and arrangers . The whole bureaucratic panoply . (Beethoven , etc)

Meanwhile , back at the farm , the serfs were generating new tunes . The most successful ones got replicated by word of tune .

Remember , all humans can hear and compose in their heads .
See http://andreswhy.blogspot.com "The Squat and the Wobble" Oct 2004
Rhythm is programmed literally into the fingertips .

Jazz is where the two worlds collide and fuse .
Formalism with individual creativeness .
Repetitiveness with room .

The division of 1020 AD and fusion after 1800 AD created enormous energies and vigour .

Light Jazz
Composers went out and listened to Eastern European folk music , teased out the melodies and synthesized them into opera's and light classical music .
Liszt (Hungarian Rhapsodies) , Verdi (all) , Bizet (Carmen) etc .
These were Jazz artists .And suitably reviled in their time .

Later , in the 1900's , other cultures fused in .
First African , because of the large African-American population in the US.
Classical jazz . Jazz as we know it.

Other cultures like Chinese , Japanese , Cambodian , Indian , Laotian , Australian , etc
are beginning to transfuse in .

The Algorithm
The problem is to keep enough of the old to be recognizable , and enough of the new to give that "Aha" feeling .

Luckily , we know how to calculate that ratio fairly exactly .
It is our old friend ,
Reserves , as found in http://andreswhy.blogspot.com "NewTools : Reserves" Nov 2008 .

The old tune has to retain 1/3 of it's characteristics . The artist can then add on 2/3 's , while retaining identity .

Really great artists can change the first 1/3 or portions of it .
Portions measured in 1/3 of 1/3 of 1/3 to n'th 1/3 .

The Jazz of Asian and Western and African music is inevitable . It sounds delicious .

All that Jazz!

Andre
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Appendix A
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

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