Consistency (was: Chain-of-4:7s tunings)

[Paul Erlich TD236.7]
>Dave Keenan wrote,
>
>>Of those with reasonable consistent 5-limit intervals, we only have 0, 22,
>>24, 26, 27, 29, 31, 34, and 36 and above. Looking at all 7-limit intervals
>>and enforcing consistency we lose 24, and 29 and 34 look pretty marginal.
>
>34 is not consistent in the 7-limit, but 29 is consistent all the way
>through the 15-limit.

It's important to remember:
(a) that inconsistency isn't a sufficient reason for rejection;
(b) that consistency can always be enforced to any limit by using a
non-best approximation to some interval(s);
(c) that an otherwise inconsistent ET with consistency enforced in this
way, may be more accurate than another naturally consistent ET.

Regards,
-- Dave Keenan
http://dkeenan.com

On Fri, 2 Jul 1999, David C Keenan wrote:
> It's important to remember:
> (a) that inconsistency isn't a sufficient reason for rejection;

Not for you, perhaps. For Paul E. it is. I actually restrict myself to
ETs that are level-2 (or higher) consistent. (I know, it doesn't leave
me many options.)

> (b) that consistency can always be enforced to any limit by using a
> non-best approximation to some interval(s);

Well, yes, it can. To me it seems a rather perverse thing to do, but if
floats your boat, hey, go for it.

> (c) that an otherwise inconsistent ET with consistency enforced in this
> way, may be more accurate than another naturally consistent ET.

Only if the second ET has a larger--generally significantly
larger--stepsize.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
O
/\ "Hey--do you think I need to lose some weight?"
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Dave Keenan wrote,

>> It's important to remember:
>> (a) that inconsistency isn't a sufficient reason for rejection;

Paul Hahn wrote,

>Not for you, perhaps. For Paul E. it is.

Only for ETs below 35. Above that, the second-best approximation for some
interval may still be within 1% of JI. I've discussed inconsistent ETs such
as 76 where the same JI interval has different approximations depending on
what scale you use!