How do you find the inversion of the number?
What if we apply Mod 12 to this idea?
What is the pitch class set for a C major triad? (0,4,7). What is the inversion? (0,8,5).
The chord made is a F minor triad, because we directly flipped the intervals around C.
When you have to transpose and invert a PC set, the formula is TnI().
OR
The SECOND OPTION is correct. By transposing first, it changes the axis you invert over. You have to invert first, THEN transpose. You have to wait to find normal form until AFTER you invert the PC set.
Shortcut:
### Set Class Think of pitch class, it is a combination of pitches, thus a PC set. So set class, is a collection of pitch class sets.
Heirarchy:
A set class for (0,4,7), a major triad, all of its transpositions and inversions create 24 PC sets, making one large set class. This includes all major and minor triads in interger notation.
Inversion, like transposition, is often associated with motion that connects similar objects. You need to be able to (1) invert a collection of pitches and (2) determine the inversional relationship between two collections of pitches.
This passage above from Debussy’s “Sunken Cathedral” is an example. Just as was the case in the [transpositionally-related passages][transposition], these two gestures have the same intervallic content—and so, our ears recognize them as very similar. (Debussy underscores that similarity by giving both of the gestures the same rhythmic setting.) Unlike transposition, however, the interval content of these two gestures is not arranged in the same way.
Both have the same intervals, but the {A,D,E} collection has the +5 on the bottom instead of on the top.
Inverting something is a two-step process, performed in this order: (1) Reflect the pitch classes in an object around the 0-6 axis of symmetry, and then (2) transpose it. I’ll illustrate first on a clock, and then show you an easier way:
Fortunately, there is a much quicker way to invert a pitch or collection of pitches! Given any collection of pitch classes and a TnI, simply subtract the the pitch classes from n:
Conversely, to determine the TnI that relates two collections of pitch classes, find a common value to which they all sum. That is the n in TnI: