[mycroftiv]

I'm also a music theorist and educator. I'm interested in your perspective on whether it is a good idea to try to introduce students to the acoustic/mathematical derivation of the scale. To provide context for non-technical readers, the physical basis of harmonic intervals is integer ratios of frequencies, and European tempered tuning systems create scales and chords as a pragmatic adjustment of mathematically pure tuning to the necessity of using a finite number of predetermined pitches for instruments such as the piano.

I am still unsure as to whether the deeper understanding of scales, chords, keys, tuning, and temperament is something I should push to make students study and understand. Many students have a negative reaction to even the simplest math, but other students get a lot of benefit from understanding exactly how and why a given set of pitches fit together to form chords and scales. In the context of group instruction, deciding how much time to devote to this material is a dilemma for me.

[alexophile]

>whether it is a good idea to try to introduce students to the acoustic/mathematical derivation of the scale

I did this when I was teaching my roommate about theory, but he has a degree in math, so it seemed like the logical approach.

That said, teaching theory is incredibly good practice, so I like to do it whenever possible, and in my experience, the best time to explain the mathematical foundations of music is when they start to ask questions about it. It's like the matrix - if they're not ready for it, it's just too much.

[fab13n]

My guess is that it would lose and scare all of the many people for whom mathematics aren't a native language. Do it for mathematically minded people, I'd say with at least a A level in sciences, but avoid it for "normal" people.

There might be a non-mathy way to show that something fishy happens with Pythagorean scales, similar to the post, with well chosen computer-generated sounds; but this would mainly interest people with a couple years of musical practice.

[icarus_drowning]

I think it would be worth doing with older students as a supplement to the curriculum. One of the bad things about my "major scale-centric" approach is that I never explain why a major scale is WWHWWWH, which is actually a barrier to some students, who are either curious or who need more context for their information.

I teach mostly middle-school and high-school kids, and we barely have enough time to get through what I have, so I skip it. I wish I didn't have to.

[nitrogen]

Do you ever tell them something like, "There's a bunch of cool stuff you can learn about this, if you go to the web site, or look for _____ on Wikipedia?"

[nandemo]

Although I'm not a music educator, in my opinion it's better to teach scales primarily by ear, without teaching too much theory at the beginning.

I've seen something like this elsewhere on the web: teach the C major scale until the student is familiar with it, can play the scale and its chords/arpeggios on their instrument, sing it given the tonic, etc. Then play the scale starting on G. G, A, B, C, D, E, will sound "right", that is, just like the C, D, E, F, G, A. Only the seventh (F) will sound "off". So we "fix" it by raising it a halftone. You can go all thru the circle of fifths this way.

If the student wants to know the reasons behind it you can teach it, but just like in math and CS I believe it's better to teach the concrete before the abstract.

[kbutler]

> To provide context for non-technical readers,

I love the fact that I'm a "non-technical" reader in this discussion!

[zwieback]

I think it's very helpful to work back to the math, if the students are capable of understanding it. You can start with the familiar white-piano-keys scale and build forward, exactly like the article shows. Eventually, though, it's important to understand the math and how the different tempers were derived.

Instead of math maybe show pictures of sine waves and how they relate. My kids learned that in elementary school and it seemed to make sense to them. You can even demonstrate it pretty easily with long strings and a cheap strobe or the 60Hz lighting in the room.