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found periodicity block, now what?

🔗Robert C Valentine <BVAL@IIL.INTEL.COM>

12/24/2000 11:54:30 PM

I just went through Paul Ehrlichs tutorial on periodicity
blocks again. I certainly hope it is online so that
newbies and/or slowpokes (like myself) have access to it.

I've decided to look at systems built from 3 primes which
don't match either a strict prime or odd limit. As an
example, I decided to find a periodicity block for
3, 5 and 11.

I built the following matrix representing the unison
vectors

5/4 11/8 3/2 UV
-1 2 -1 121/120
-1 0 4 81/80
1 1 3 55/54

which suggested that a 19 tone periodicity block exists.

By inspection I think I found 2.

27/16
' |
' | 99/64
' | '|
27/22 | ' |
| | ' |
| 9/8-----45/32
| , | | |
| , | 33/32 |
| , | '| |
18/11 | ' | |
| | ' | |
| 3/2-----15/8
| ' | | |
| ' | 11/8 |
| ' | '| |
12/11 | ' | |
| | ' | |
| 1/1----- 5/4
| ' | | |
| ' | 11/6 |
| ' | ' | |
16/11 | ' | |
| |' | |
| 4/3------5/3
| ' |
| ' 11/9
| '
64/33

and
99/64
'|
' |
' |
9/8 |
'| |
' | 33/32
' | '|
18/11 | ' |
| |' |
| 3/2---------15/8
| '| | '|
| ' | 11/8 ' |
| ' | '| ' |
12/11--------15/11 |
| |' | | |
| 1/1------|---5/4
| '| | | '|
| ' | 11/6 | ' |
| ' | ' | ' |
16/11---------20/11 |
| | ' | |
| 4/3------|---5/3
| ' | '
| ' | '
| ' | '
64/33---------40/33

My questions are :
Did I do it right?
What do I do with it now?
Do tiles 'share' nodes with the next tile?
How do these relate to MOS/regular/proper and
other magic words?
Is there a transformation from periodicity block to
et, or from unison vector to et?

Thanks to Paul for putting together this tutorial, and
also to the Fokker site which has his paper on 7 limit
periodicity blocks. Happy whatever-your-solstice-holiday-is
to everyone on the list(s).

Bob Valentine