By Eric Garneau
In his eighth lecture on 'Introduction to Pitch Systems in Tonal Music', John Crooks returns to the idea of tuning an instrument by building, in his words, 'a diatonic set with in-tune major and minor triads.' Since we now know the mathematical ratios behind both major and minor triads, that should be easy, right?
Spoiler alert, guys: the answer is no. It turns out that if you try to align major and minor I-IV-V (i-iv-v) triads to form a scale using the math we've learned (you calculate majors with a 4:5:6 ratio and minors with a 10:12:15 ratio), somewhere along the line you're left with one note that ends up with two different frequency values - it's one tone in the major V triad but another, just a few Hz off, in the minor iv. According to Crooks, this is called a 'comma,' which results when two pitches, ostensibly the same note, are ever so slightly off in frequency. It's a weird phenomenon, and Crooks doesn't show all his math to prove that he's right, but I suppose we can trust him (also, he does encourage at-home users to check the math themselves with a calculator).
So where does this leave us? We saw a few weeks ago that we can't build in-tune triads with a Pythagorean scale, and now it turns out we can't build an in-tune scale using perfect triads. How can we tune our instruments now? The answer, as it turns out…
WILL BE REVEALED IN NEXT WEEK'S EPISODE!
Find schools that offer these popular programs
- Music Composition and Theory
- Music History and Literature
- Music Merchandising and Management
- Music Pedagogy
- Music Performing
- Musical Conducting
- Musicology and Ethnomusicology
- Piano and Organ
- Stringed Instruments
- Voice and Opera
Is OCW Like TV?
And this brings me to a point that's been stewing in my head since we began this OCW journey - how much are these video lectures like television shows, or at least like Internet television shows? It's certainly a comparison that Crooks himself invites; he constantly refers to these productions as 'episodes' and often offers teasers for the next lesson's content. Weeks ago I joked that it reminded me of the 1960s Adam West Batman TV show, but I actually think that's pretty accurate. 'CAN we learn how to tune a piano? WILL basic mathematics save us? WHICH actress will be playing Catwoman next week?!'
Obviously our sample size is pretty small here - we're only looking at one class - but I wonder if this isn't a compelling way to think about OCW content delivery in general. Consider that these videos are constructed to appeal specifically to at-home Internet users; that's probably why, with only one exception in week two, none of these installments have run longer than about 12 minutes. That stands in stark contrast to actual university classes - if we cautiously guess that each installment of Crooks' course has lasted an average of 14 minutes, we might have only spent 112 minutes learning this stuff so far. That's one 2-hour Wednesday class!
Of course users have the option of watching videos more than once, pausing to take notes, etc., but still it seems that economy of time is a real concern here. Could that be because the purveyors of OCW recognize that, when it comes to Internet media, they've got to get in and get out with maximum efficiency? Would the temptation be too great, in a 50-minute lecture pulled straight from a classroom, to click away from your screen and check out YouTube or Facebook or whatever?
Maybe it's just me, but I think it's interesting to look at the business philosophy behind OCW's presentation. Granted, the University of California - Irvine probably doesn't have much to gain financially from people watching their videos, at least not in the short-term. But anyone who releases a product like this wants to make sure that product gets maximum exposure, right? So it seems to me that, like other Internet video sites before them, the school (or at least Crooks) is specifically structuring this class into short episodes with compelling teases for later installments to appeal to the largest possible audience. And, at least for me, it works.
Now, make sure you join us next week on OCWednesday to solve THE MYSTERY OF THE UNTUNABLE INSTRUMENT.
While you're (channel) surfing the 'net, check out these other great music blogs.