Visualizing intonation

[timothy42b]

For the people here there won't be anything new in this video, but I'll share it anyway because smalin does such a good job of visual presentation accompanied by sound. I've been following him for a couple of decades and he gets more creative all the time.

[mgladdish]

I wrote this up for my own benefit a while back. I created graphs and everything.

https://martingladdish.co.uk/personal/just-intonation/

[AndrewMeronek]

I agree: nice visualization. Stuff like this IMHO should be included in every high school music class. Combine with some grade-level algebra and it's a pretty quick path to getting students into actually doing these calculations and deepening understanding from more than 1 perspective. (That is, not just music or math class, but combining them.)

[LeTromboniste]

That's a really clever way of displaying it! I'll be using that video and tool for sure.

[AndrewMeronek]

I wrote this up for my own benefit a while back. I created graphs and everything.

https://martingladdish.co.uk/personal/just-intonation/

Also nice.

For those who like the math side of things, it is not a far stretch at all to figure out how to calculate the intervals for a 1/4-comma meantone temperament.

[robcat2075]

I agree intonation is under-taught, at least among us winds.

From beginner band through graduate school I had no instruction on intonation except that occasionally a teacher would intone, "You must learn to use your ear," as if that was the beginning and end of what could be conveyed.

Intonation was regarded like pubic hair... eventually it would develop.

Rarely, it would be mentioned that equal temperament wasn't quite right so you have to "lower the third" but no one ever demonstrated the difference.

When I got my Commodore 64 in the 1980s I found that it could produce any frequency on demand and it was very interesting to implement a comparison of a ET major chord vs. a just-tuned chord and finally hear what the fuss was about.

But difficult to ever apply that in a band setting where no one is ever exactly in tune.

The string world is rather different. They are being taught to tune fifths from the start and any note they play can be tested against a neighboring string so learning to tune all intervals is potentially a thing for them.

[LeTromboniste]

My experience is exactly the opposite. I was taught in my very first higher ed trombone lesson at 17 what pure intervals are and how much to adjust (and in which direction) for each possible harmonic role within a chord. With my first teacher, we'd spend 10-15 minutes at the start of every trombone or brass ensemble session just playing through a chord matrix, where voices take turn moving chromatically, changing the harmonic role of everyone else and having to adjust intonation as your role changed (you get the point immediately the first time you're playing a pure minor third, and the the fundamental shifts down a semitone and suddenly you need to lower your note 30 cents!). Every wind player I've known throughout my studies and professional life has at least known the basics of how intonation works, and playing pure chords is the bread and butter of orchestral players.

Meanwhile, until I moved to early music (and even then...), I had known very few string players who had more than a very superficial (and often completely wrong) knowledge and understand of how intonation works.



I have a presentation I've regularly given on quarter-comma meantone that I should record and upload at some point.

[Wayne]

Robocat, I should have been your band teacher. I won't oversell the success of my groups but they did know what to listen for to be "in tune". It was a pretty simple cue- if your sound disappears into the sound next to you that is in tune. If the sounds are fighting, you are not in tune. We played with lowering and raising pitches to learn what those effects were. However, we mostly avoided adjusting the instrument except for large differences. We focussed on making a great sound with the best posture and suspension habits possible. Those great sounds were either in tune or easy to tune to.

I echo Maximillian in that at university my individual teacher and small ensemble coaches did a lot of work on tuning- unison, chords, minor vs major. Maybe that's why I didn't ignore it as a band teacher.