Play the GIF to check your results.Chromatic Aberration Chromatic AberrationĪ lens will not focus different colors in exactly the same place because the focal length depends on refraction and the index of refraction for blue light (short wavelengths) is larger than that of red light (long wavelengths).The amount of chromaticaberration depends on the dispersion of the glass. Now that you've finished counting the intervals "From C," try finishing the rest of the table. Check out the GIF again to see how couting from C-G clockwise gets the number (interval) 7 (a perfect fifth), but counter-clockwise reveals the number 5 (a perfect fourth) - the inversion of a perfect 5th. The benefit of using the chromatic cirlce is that you can easily invert an interval by just counting counter-clockwise. A perfect fifth, or a "7," now becomes a perfect fourth, a "5." For more help with inversions, check out my music inversion calculator. Therefore, any time that you get an interval higher than a tritone, 6, it needs to be inverted. ICVs top out at tritone because tthey're greatest distance from any one note once inversions are taken into account. But why? Well, "7" is too high because it represents a perfect fifth, an interval greater than a tritone, and ICVs "top out" at tritones.
However, seven is too high and has no place on our ICV. If you followed my process, you will have found seven half-steps from C to G. Play the GIF to see how I like to visualize the process. Now that we have the number "3," write three in the first box on our table, directly next to "From C." Next, do this for the remaining intervals from C: C-E and C-G. Therefore, the pitch-classes C and A ultimately boil down to a minor third rather than a major sixth.ģ.1: Counting with the circle method: C to E and C to G On the other hand, the pitch-class "A" represents all As, from A0 through A7 and beyond. A440 is not the same pitch as an A below middle C. A pitch, such as A440, is the A above middle C, also known as A4. This is why the tritone is always the farthest distance from any given pitch-class.įor example, the pitches C and A may at first appear to represent an interval of a major sixth, however, this assumption implies specific pitches rather than pitch-classes. This is because any interval greater than a tritone can be inverted and thus becomes in an interval smaller than a tritone. The largest interval represented by ICVs is a tritone. Why does an ICV only go up to tritones and not perfect 5ths and above? This digit represents the number of tritones in a collection. In this case, there four perfect fourths. This digit represents the number of perfect fourths in a collection. This digit represents the number of major thirds in a collection. This digit represents the number of minor thirds in a collection. This digit represents the number of major seconds in a collection. This digit represents the number of half-steps in a collection.