Various major seconds

Gerald Eskelin wrote,
>
>>It would be very interesting to know (as I mentioned earlier) to know if
>>experienced ears can consistently hear 8:9 as scale steps 1-2 and 9:10 as
>>scale steps 2-3.

Paul Erlich offered:
>
> This would imply scale step 3 is consistently 5:4 above scale step 1. What
> happened to your "high third"?

Paul, I'm not married to the "high third." I'm just curious about it.

> Furthermore, if steps can really be heard as
> ratios in this way,

I'm pretty sure I can. But perhaps I'm thinking 2-3 context instead of
"phantom fundamental." That's why I propose a blind experiment to test my
thesis and objectify the matter.

> wouldn't it be kind of natural to interpret the "high
> third" as the product of two 8:9 steps, i.e., a Pythagorean major third?

Intellectually, perhaps. Likely not "naturally" (perceptually). I'm more
concerned about what causes, or contributes to, the "high third" experience
as I have described it here many times--which I suspect has little or
nothing to do with major seconds, neither intellectually nor naturally.

> That is the usual take on Indian music, where the just (5/4) and Pythagorean
> (81/64) major thirds are sruti #s 7 and 8 out of a 22-sruti octave. Now it
> is true that the Pythagorean major third wouldn't lock harmonically as part
> of a triad, so for the third time I suggest the possibility of
> 1/24:1/19:1/16 for your locked major triad with high third.

For now the second time in a post to you (and the third if you count another
to someone else) I am requesting a clarification of what appear to be
fractions separated by colons. Please unlock the code. For example, how does
the expression 4/5 relate to the expression 4:5? Also, what does 1/x
represent? I really would like to know what you are saying here. Can someone
whose math training ended at college algebra have a fighting chance of
understanding? I hope this is simply a matter of form rather than of depth.

Thanks,

Jerry