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On music intervals, and other updates
cognitivefun | 12 years ago Reply Link me
On music intervals, and other updates
Apologies for the delayed updates. Most of the updates over the past week or so were to allow stats to show within the test application for logged-in users. As for testing-related changes, since last week, we have a simple music interval test. A number of users have quickly pointed out that there are design problems with this test. In particular, the 6-semitone interval could span 4 or 5 white keys, depending on which root note is used. If this is all old information for you, feel free to skip the next two paragraphs, in which I will briefly explain this interval business (which is more about music than cognitive science).

The "intervals" we are talking about is simply the distance between any two musical notes. The "root" note is the foundation on top of which we build this interval. In this interval test, it is always the lower note, which is also the leftmost key that lights up on the piano display. Now, while you may have no problem hearing the highs and lows in a song, in order to talk about "how much higher" and "how much lower" with each other, musicians invented the language of intervals. That's right: this is a vocabulary, just like how you say "trumpet" when you see a trumpet, or how there are "two heads" between the heights of Mr. Eightheadstall and Mr. Sixheadstall.

There are different ways to talk about intervals: you can use difference in whole tones, semitones, microtones, or maybe even Hertz, just as you may use feet, inches, centimeters etc., to measure height differences. Here's where the memory task comes in. If most people in the world differ by regular intervals of height, say, between half a head to four heads, you would quickly begin to generalize: 2 heads between Mr. Sixheadstall and Mr. Fourheadstall, and 3.5 heads between Ms. Fiveheadstall and Ms. Eightandahalfheadstall. If we switch to inches, we could say, 24 inches between Mr. Sixheadstall and Mr. Fourheadstall instead: same distance, different language. This test tries to use the language more commonly used in Western music theory; if you've never heard of it, no big deal, because you can learn it just like you learn about inches and centimeters.

Back to the ambiguity problem. As jimmydean9 pointed out, tritones (6 semitones) would span 4 white keys with C as the root, or 5 white keys with F as the root. If we are concerned only about relative distances, then the test should accept both answers, but it didn't. I wrestled with this problem a bit

This test is administered in the spirit of a stimulus differentiation task. To keep the stimulus-reponse as short as possible, an interval test seemed reasonable. To make all responses one keystroke, the exact "white key interval" was used without respect to augmentedness or diminshedness (whether there is an extra half-tone put in or taken out). The problem with accepting both 4 and 5 as valid responses to the tritone (Aug4 and dim5) is that the stimulus would resolve to two valid responses, which could lead to interference. But as this test is about relative pitch, I may be completely wrong.

Based on feedback, you can now select the maximum interval the test asks. As for the ambiguity, I will sidestep the issue for now: the test will simply not ask about Aug5 and dim5.

Finally, a basic day/week/month aggregation function is now available in your personal stats (thanks, sygenator).
cognitivefun | 12 years ago Reply
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