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1/1 17/16 425/384 153/128 51/40 1377/1024 17/12 119/80 51/32 17/10
85/48 119/64 2/1
0 105.0 175.6 308.9 420.6 512.8 603 687.5 806.9 918.6
989.3 1073.8 1200
Pat hi and gracious greetings to you
my first observation is that you have related most of the intervals to the
17/16 directly or near-directly, and that the tonic is not as directly
related.
You've used 3s 5s 7s & 17s as factors in the generative process - sometimes
very high numbers - these seem to me to be the outcome of chains of fifths
or in one case two thirds, over and above the 17/16.
425 = 17 x 5 x 5
153 = 17 x 3 x 3
119 = 7 x 17
1377 = 17 x 3 x 3 x 3 x 3
85 = 5 x 17
51 = 3 x 17
Just a few arithmetical reflections
In fact to illustrate my point about the intervals relating most directly to
the 17/16, here's the tuning measured in relation to the 17/16 pitch:
Original PP-DB-er
1/1 17/16 425/384 153/128 51/40 1377/1024 17/12 119/80 51/32 17/10
85/48 119/64 2/1
In rel to 17:16:
25/24 9/8 6/5 81/64 4/3 7/5 3/2 8/5 5/3 7/4 32/17 2/1
in rel to the original 153/28:
the 17/12 is a 7/6
the 51/32 is a 4/3
If I were designing a scale in response to yours, I might look at some
multiples of lower primes in relation to the tonic as well as to the 17:16.
That way the tonic might feel a bit happier, having a few friends to whom it
might relate more directly - otherwise the 17 guys might get a bit cliquey
......who knows, and then there will only be one 17 ratio left (the 32/17).
I might use:
PP/DB:1/1 17/16 425/384 153/128 51/40 1377/1024 17/12 119/80 51/32
17/10 85/48 119/64 2/1
LB: 1/1 17/16 425/384 153/128 51/40 21/16 17/12 3/2 51/32
17/10 7/4 119/64 2/1
now you have the 17:16 and the 3:2 and the 51/32 breathing together, an
interesting tetrad chord
I would use a 7:4 (delicious), which locks in the 3/2 and the 21/16 into a
great business: 3,7 and 21 go well together and also makes a wonderful party
with the 17, the 51 and the 119.
You've got me interested now I'll have to try yours AND my
variation..........
Its amazing there are 66 relationships between 2 notes, 220 between 3 notes
......(in a "12" tuning that is), so many interrelationships, (knew it for a
million years but I just started thinking about it).
LaMonte Young uses only chains of 3:2 and 7:4 in The Well-Tuned Piano as
generator intervals, so that each note is either a chain of fifths or a
chain of harmonic 7ths (7:4s), or both, away from the tonic.
Will listen later to how my Korg sounds with your tuning, .......no album
though!
Looking forward to hearing your music on CD enormously
R & E (& B)
your cyberfriend
Lawrence
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