Fw: [tuning] 29 in a fifth?

Tony Taylor wrote:

> Isn't that basically 50-edo stretched out?

Well, quite heavily stretched :-) ... Octaves don’t work this way.

Petr

--- On Tue, 5/5/09, Petr Pařízek <p.parizek@...> wrote:

From: Petr Pařízek <p.parizek@chello..cz>
Subject: [tuning] 29 in a fifth?
To: "Tuning List" <tuning@yahoogroups.com>
Date: Tuesday, May 5, 2009, 10:02 AM

Hi tuners,

yesterday I made an experiment by taking two pure fifths and splitting each
of them into different intervals -- i.e. one became 4:5:6, the other was
6:7:9. When I took that as a single 4:5:6:7:9 chord and I started
subtracting one-step intervals again and again, after a while, I found two
small intervals which I could temper out. So the four intervals used were
1296/1225, 25/24, 3136/3125, and 420175/419904. This means that one mapping
for the 3/2 was "2 7 2 0" and another was "5 3 0 2". When I subtracted these
to get the 1/1, I got a mapping of "3 -4 -2 2". And when I then subtracted
multiples of the fifth's mappings to get the required amounts of tempering
for the large and small intervals, I got "29 0 -6 14" and "0 29 10 -4". So
it turns out that's actually 29 equal steps to a fifth, where the large
interval has a size of 4 steps and the small interval size is 3 steps. I
don't have a chance to try it out but it seems it must work pretty well
because the two commas I tempered out are really small ... Anyone who has
something to say about 29-ED3/2? :-D

Petr

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