Re: Neutral thirds.

In-Reply-To: <Pine.GSO.4.10.10111051215310.18051-100000@konichiwa.cc.columbia.-
edu>
Christopher asked:

> What are the most common representations of the "neutral third" in JI?
>
>
> 11/9 ?
> 39/32 ?

I'd go for 11/9 every time. It's simpler and closer. Although, in strict
JI (or RI), you need two kinds of neutral thirds to make up the fifth.
With 11/9, that'd be 27/22.

Graham

Some people find bare neutral thirds to be sort of consonant, and not
too dissonant. This applies to me for dyads in mellow timbres in a
medium pitch range. The harmonic entropy model with an appropriate s
value (anywhere around 1.25% to 1.75%) predicts that 11/9 is more
consonant that all ratios whose complexity (numerator times
denominator) is _lower_, down to as little as half the complexity of
11/9:

/tuning/files/perlich/stearns2.jpg

Of course, 11/9 also becomes "consonant" in a higher register in
chords like 4:5:6:7:9:11, but that's a very different sort of
consonance, (and a much smaller value for s would be
appropriate) . . .