Name that interval: Brahms 1st Symphony Horn solo

Originally posted on Quora, but they've stopped allowing updates.

I have an obsession with pitch and timbres which brings me to this ramble.

We start with the Big Ben chimes:

Compare with this horn solo part of the 4th movement of the Brahms 1st symphony:

It is similar.

But the part I want to focus on is is the interval between the 8th and 9th notes which is not in the clock chimes. In the Brahms symphony is it is between a B natural and a Bb. By the way, when you listen to the solo flute repeat the theme, you can hear a little pitch glitch and between the 5th and 6th notes (a D and E) and you can see what's going on when the fingers go between 011-000 and 110-110. I am always fascinated by such little glitches that give a little character to the sound.

But now I get to the part that fascinated me. I had heard that Brahms horn parts were not for the modern valve horns you seen the Youtube clip, but are for a hand horn. And this instrument doesn't play that interval as perfectly.

In my mind I got that this interval was slightly less than the equal-temperament note. When I mentioned it an eminent musicologist, he said, well you know in the harmonic series, you have it wrong. That note should be slightly greater than equal temperament.

Brahms wrote Clara Schumann in a letter that he got this theme from listening to Alpine Horns when he was on vacation in the Alps. So I went to check out what the alpine horn does. See

and he is right! It is slightly flatter then equal temperament. If you map this to the natural overtone sequence this is harmonics 12, 11, 9 (G, F#, D). And even more undisputable, listen to this, 7 seconds in:

and even played with a C crook 4 minutes in :

you will hear it less flat, but not sharp as it was in my memory. So what gives with my bad memory? Is it just more senility?

Possibly. It could be that I was just hearing it as the intervals between F#, E, C. Or more likely translating the slight less than half step between C and B in the natural horn when the B is muted with the hand. With hand adjustments, the French Horn no longer strictly follows the harmonic series.

Or just wrong. I’ve updated my memory on this though.