This work dates from a transition period, when he was attracted by the serial technique as used by Webern and neoclassical trends. But he was always attracted by counterpoint an canonic techniques. This sonatina canonica is clearly on the neoclassical side, but its clarity of writing makes it quite attractive.
The new music Tonal Scale is as thus: 12 7 5 2 3 : 1 4 5 9 14 Not 12 with 7 & 5 BUT 14 with 9 & 5 [2^(1/14)] These are the Tonal Scales growing from f (by cycles of fifths): All Scales build from the first mode: equivalent to Lydian f White keys are = & Black keys are | 12 with 7 & 5 [2^(1/12)] =|=|=|==|=|= {1,8,3,10,5,12,7,2,9,4,11,6} 1thru7are= 8thru12are| 7 with 5 & 2 [2^(1/7)] ===|==| {1,3,5,7,2,4,6} 1thru5are= 6&7are| 5 with 2 & 3 [2^(1/5)] =||=| {1,3,5,2,4} 1&2are= 3thru5are| Now evolving up the other end 5 with 4 & 1 [2^(1/5)] ==|== {1,3,5,2,4} 1thru4are= 5is| 9 with 5 & 4 [2^(1/9)] =|=|=|==| {1,8,3,7,5,9,2,4,6} 1thru5are= 6thru9are| 14 with 9 & 5 [2^(1/14)] =|=|===|=|===| {1,12,3,14,5,7,9,11,2,13,4,6,8,10} 1thru9are= 10thru14are| Joseph Yasser is the actual originator of the realization, that scales develop by cycles of fifths. www.seraph.it/blog_files/623ba37cafa0d91db51fa87296693fff-175.html www.academia.edu/4163545/A_Theory_of_Evolving_Tonality_by_Joseph_Yasser www.musanim.com/Yasser/ The chromatic scale we use today is divided by 2^(1/12) twelfth root of two Instead of moving to the next higher: the 19 tone scale 2^(1/19) nineteenth root of two I decided to go all the way down and back up the other end: So 12 - 7 is 5 & 7 - 5 is 2 & 5 - 2 is 3 Now we enter to the other side: 2 - 3 is (-1)* & 3 - (-1) is 4* & (-1) - 4 is (-5)* & 4 - (-5) is 9* & (-5) - 9 is (-14)* ignoring the negatives we have * 1 4 5 9 14 Just follow the cycles how each scale is weaved together, as shown above. Each scale has its own division within the frequency doubling, therefore the 14 tone scale is 2^(1/14) fourteenth root of two
I liked the "Schumann part" of the sonatina!
The canonic art has always been a source of inspiration for Dallapiccola, before his encounter of the world of Webern and serial canonism§
This work dates from a transition period, when he was attracted by the serial technique as used by Webern and neoclassical trends. But he was always attracted by counterpoint an canonic techniques. This sonatina canonica is clearly on the neoclassical side, but its clarity of writing makes it quite attractive.
The new music Tonal Scale is as thus: 12 7 5 2 3 : 1 4 5 9 14
Not 12 with 7 & 5 BUT 14 with 9 & 5 [2^(1/14)]
These are the Tonal Scales growing from f (by cycles of fifths):
All Scales build from the first mode: equivalent to Lydian f
White keys are = & Black keys are |
12 with 7 & 5 [2^(1/12)] =|=|=|==|=|= {1,8,3,10,5,12,7,2,9,4,11,6}
1thru7are= 8thru12are|
7 with 5 & 2 [2^(1/7)] ===|==| {1,3,5,7,2,4,6} 1thru5are= 6&7are|
5 with 2 & 3 [2^(1/5)] =||=| {1,3,5,2,4} 1&2are= 3thru5are|
Now evolving up the other end
5 with 4 & 1 [2^(1/5)] ==|== {1,3,5,2,4} 1thru4are= 5is|
9 with 5 & 4 [2^(1/9)] =|=|=|==| {1,8,3,7,5,9,2,4,6} 1thru5are= 6thru9are|
14 with 9 & 5 [2^(1/14)] =|=|===|=|===| {1,12,3,14,5,7,9,11,2,13,4,6,8,10}
1thru9are= 10thru14are|
Joseph Yasser is the actual originator of the realization,
that scales develop by cycles of fifths.
www.seraph.it/blog_files/623ba37cafa0d91db51fa87296693fff-175.html
www.academia.edu/4163545/A_Theory_of_Evolving_Tonality_by_Joseph_Yasser
www.musanim.com/Yasser/
The chromatic scale we use today is divided by 2^(1/12) twelfth root of two
Instead of moving to the next higher: the 19 tone scale 2^(1/19) nineteenth root of two
I decided to go all the way down and back up the other end:
So 12 - 7 is 5 & 7 - 5 is 2 & 5 - 2 is 3
Now we enter to the other side:
2 - 3 is (-1)* & 3 - (-1) is 4* & (-1) - 4 is (-5)* & 4 - (-5) is 9* & (-5) - 9 is (-14)*
ignoring the negatives we have * 1 4 5 9 14
Just follow the cycles how each scale is weaved together, as shown above.
Each scale has its own division within the frequency doubling,
therefore the 14 tone scale is 2^(1/14) fourteenth root of two
Schumann op. 3