Re: European Follow-On

--- In MakeMicroMusic@yahoogroups.com, "hstraub64" <hstraub64@t...>
wrote:
> --- In MakeMicroMusic@yahoogroups.com, "M Gould" <mark.gould@a...>
> wrote:
> > A little while back I posted a link to an amusing item in 10 EDO.
> > It was connected with decimilisation. Now that there will be 25
> > members of the EU as from Saturday, I thought that we should try
> > to write a piece in 25EDO.
> >
>
> He he - then talk about the meaning of consonance and dissonance
> will get a political touch and eventually become dangerous...
>
> But looking at that tuning, I see it has two interesting
properties.
> It contains 5TET, and it appears to have quite nice thirds and
> harmonic sevenths, which makes it a candidate for some kind of 7-
> limit tetrad tonality, as in Paul's article on 22TET.

It can be seen as a bug or a feature, but 25-equal isn't consistent
(Kurt, are you paying attention?) in the 7-limit. For example, the
closest approximation to 3:2 is 15 steps; to 7:6, 6 steps. Put the
two intervals together, and you would expect to see 7:4 as 21 steps.
But the best approximation to 7:4 in 25-equal is 20 steps, not 21.

on 4/30/04 3:28 PM, wallyesterpaulrus <paul@stretch-music.com> wrote:

> --- In MakeMicroMusic@yahoogroups.com, "hstraub64" <hstraub64@t...>
> wrote:
>> --- In MakeMicroMusic@yahoogroups.com, "M Gould" <mark.gould@a...>
>> wrote:
>>> A little while back I posted a link to an amusing item in 10 EDO.
>>> It was connected with decimilisation. Now that there will be 25
>>> members of the EU as from Saturday, I thought that we should try
>>> to write a piece in 25EDO.
>>>
>>
>> He he - then talk about the meaning of consonance and dissonance
>> will get a political touch and eventually become dangerous...
>>
>> But looking at that tuning, I see it has two interesting
> properties.
>> It contains 5TET, and it appears to have quite nice thirds and
>> harmonic sevenths, which makes it a candidate for some kind of 7-
>> limit tetrad tonality, as in Paul's article on 22TET.
>
> It can be seen as a bug or a feature, but 25-equal isn't consistent
> (Kurt, are you paying attention?) in the 7-limit. For example, the
> closest approximation to 3:2 is 15 steps; to 7:6, 6 steps. Put the
> two intervals together, and you would expect to see 7:4 as 21 steps.
> But the best approximation to 7:4 in 25-equal is 20 steps, not 21.

Yes, yes, now I remember this use of the word consistency in the context of
ETs. However the context I was talking about pretty sure wasn't about ETs.
But I'll reply about that in the other thread later.

-Kurt