Tuning the Horn - 7th Harmonic

Hello and welcome to Michael's Microtonal Method Episode 3. The 7th Harmonic. So let's start right in with the F horn. Harmonics 1 2 3 4 5 6 7 and we get some of these intervals here. The interval between the 4th harmonic and the 7th. 7 to 4 5 to 7 7 to 5 6 7 7 6 Narrow minor 3rd. We're here at the augmented. Sorry, the diminished fifth. And now we're here. So the wide major 2nd. 8 to 7. Wide major 3rd. 9 7. And the augmented 4th. 10 to 7. And we'll stop there. If we go higher to the 11th harmonic, we then come into the realm of the 11 limit intervals. And we'll do that in the next episode. So we've got some nice intervals associated there. And now let's just explore what happens with, so this 7th harmonic on the horn, it's a written B flat. And the other intervals, the other ways of playing a B flat using the limits we had in previous episodes. So the 3 limit B flat has worked like this. So I've tuned the E flat horn. To the F. So we go C to F and F to B flat. And there's our B flat. That's 3 limit 1. That's the ratio 16 to 9. So here's a 5 limit 1. So what I'm going to do here is that's on the F horn. C and G. Now I'm adjusting the B flat horn, the technically the A flat horn. The first slide I've pushed in. So they match. The two G's match. And now the B flat will be up there nice and high. This is the ratio 9 to 5. You hear the difference between the 3 limit and the 5 limit. And now here's the 7 limit. So in descending order of high to low. Low to high. Some nice shifts there just by a simple little bit of tuning. All right. Now there's lots of 7th harmonics we can use on the double horn. So each of these, well there's 16 tube lengths. They've each got their own 7th harmonic. And so what can be nice to do is the intersection between the 3rd harmonic or the 6th harmonic, usually in the octave we need it, the 5th harmonic and the 7th harmonic. And I'll play you a few. So here's the one we just have. Even if I just put the slide back to normal. So we've got, here we have and using the 10th harmonic of the B horn. It's actually sharper than we'd expect. We'd expect it to be low. But all three slides together. So maybe this one's the least useful one. Because it's not quite working how we want. But if we go semi, like let's go tone lower. So we use this note here. The 6th harmonic of the G flat horn. The 5th harmonic of the A horn. So this is a written A flat or a G sharp on the horn. And then we use the 7th harmonic of the E flat horn. We get some nice shifts that way. You can do that a semitone lower. The lowest one we can do sort of really effectively is here. So that's a written F for us. That's the 6th harmonic. That's the 5th harmonic of the G flat horn. And the 7th harmonic of the C horn. And the 7th harmonic of the C horn is not as flat as we'd expect. So with a bit of care, but we can easily shift that with a little left. That's not hard to shift that one. And the highest one we can go up to is up here. So we've got this note for us, a written E flat. I'm playing this on the G flat horn or the F sharp horn. It's the 9th harmonic. And therefore we can play the 10th harmonic of an E horn. Easy to play. And the 7th harmonic of the B flat horn. There's a nice little shift there. There's a whole bunch of them. I'm putting a transcript of this and you'll see a slightly bigger chart there going through the ones that are possible. So you just have to work out the written pitch. So if it says, you know, the last one we did is all written, our written E flat. Top space with a treble clef. So you can work it out from there. So look, the other beaut thing we can do is we can do things like tuning parts of the horn to a 7th harmonic. So let's say for instance, we've got we want to tune the E flat horn 8th harmonic to that. So a bit sharp, pull it out a bit further. So look, the slide doesn't have much further to go. You can see it there, pulled out. A little tiny bit sharp, but that's about it. It's going to pull out soon. And then we can go down another tone. And then we get that really close interval between our written A flat, which is on the, so it's basically the 49th harmonic of a, you know, it's the 7th harmonic of a 7th harmonic, compared to where we started. So that interval there, very narrow interval, 37 cents if you're interested, or we could call it the ratio 49 to 48. So you can do nice neat things like that on the horn without much trouble at all really. So we'll leave it there for this episode. There's some beautiful chords and things. I think I'll do that in a separate video at some stage, play a few chords, show what's nice in chord spacings, you know, harmonics 4 and 6 and 7. And, or 6 7 8, or 6 7 9, this sort of thing. So some nice ones to play, and we'll set up a different video for a few different chords, all right? So there's a short introduction to the 7th harmonic and some of the possibilities on the standard double horn.