7/4 not?

When posting descriptions of the scales i've used for several pieces here, several people (i think) have repeatedly claimed that the 947 cent interval in 19TET can not be used as a 7/4. (which leaves the question to what other ratio it is closer to?)

A just 7/4 is 969 cents, so the 19TET approximation is 22 cents flat. This would be enough to make it "unrecognizable". But this hasn't been a problem with the 12TET 5/4 which is almost as out of tune.

Also, the 3 and 5 is already 7 cents flat, so measured from them (instead of the 1/1) the 7/4 is only 15 cents flat.

Whether somebody considers it a stable enough 7/4 or not, the 947 cent interval is very useful, in (otherwise) diatonic contexts and in the other scale types that i have described in previous posts. (a full run-down of these will come some day).

Inconsistency is an issue which is always drawn up in ET harmonic approximations, IMO it is being given more importance than it really has. I think most ears are going by the sound of the 947 cent interval as being "different" (from the regular diatonic minor seventh, minor third or whereever it occurs) rather than being particularly close to the 7th harmonic.

Point being, if 947 is assumed to be the 7th harmonic, it can be practically used as such. And it gives particularly interesting flavors together with 5-limit intervals-such as using the regular minor third with subminor seventh, or subminor third with regular seventh. Also these differ from quarter tones because all of these intervals are actually contained in the diatonic system, only the combinations extend beyond the definitional limits.

-=-=-=-=-=-=-
MATS �LJARE
http://www.angelfire.com/mo/oljare

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Hi Mats,

The 19-tET augmented sixth may be unrecognisable as a 4:7 dyad, but I
agree that in a large enough otonal context, like an approximate
4:5:6:7 or 5:6:7:9, 7s can work in 19-tET.

> Inconsistency is an issue which is always drawn up in ET harmonic
> approximations, IMO it is being given more importance than it really
has.

This question is not relevant to the use of 4:7s in 19-tET because
19-tET _is_ 9-limit consistent.

-- Dave Keenan

--- In tuning@y..., "Mats Öljare" <oljare@h...> wrote:
>
> When posting descriptions of the scales i've used for several
pieces here,
> several people (i think) have repeatedly claimed that the 947 cent
interval
> in 19TET can not be used as a 7/4.

> Inconsistency is an issue which is always drawn up in ET harmonic
> approximations, IMO it is being given more importance than it
really has.

But 19-tET _is_ consistent in the 7-limit!

> I
> think most ears are going by the sound of the 947 cent interval as
being
> "different" (from the regular diatonic minor seventh, minor third
or
> whereever it occurs) rather than being particularly close to the
7th
> harmonic.

Well if that's the case, then you're not talking about using it as a
7/4 anyway, and thus you're not talking about ET harmonic
approximations.
>
> Point being, if 947 is assumed to be the 7th harmonic, it can be
practically
> used as such.

Well, if anything is assumed to be anything, it can be practically
used as such. Whether you get the musical result you wanted is a
different question.

19-tET is great, no doubt about it. Lots of very interesting MOS
scales, etc. An adaptive 7-limit program applied to 19-tET
compositions could be very interesting (as would one applied to 22-
tET compositions).