
You've heard of Find the Lady; the card shark trick? Well this is a game of Find the Nonsense.
It has to do with inversions adding up to nine, but first I'll give you a better known example.
Three guys buy a pizza. It costs 25. They each throw in 10, and receive 5 pound coins in change. They each take one of the 5 pound coins, and while wondering how to divide the remaining 2, one of the guys notices an odd thing.
They each paid 10. They each took back 1. That means that up to now the pizza has cost each of them 9. There's 2 remaining. 3x9=27 add the remaining 2 and you get 29. Where's the other pound gone?
It's the kind of thing that confuses you if you've had a few, and even sober, it takes a bit of thought at least for some of us to spot where the nonsense actually happens.
For those who haven't already worked it out, or don't care to, it's that the 2 should be subtracted from the three 9's not added. That's where the nonsense is.
Where is it in this musical example?
This had me confused for a while. If you're into math or computing, you'll probably spot it easily.
Okay, so you know that musical interval inversions always add up to 9? For example, AB is a 2nd. The inversion is BA (7th).. 2+7=9. AC 3rd. CA 6th. 3+6=9. AD 4th. DA 5th. 4+5=9, and so on.
If you forget about music for a minute, and just look at the number side of things, it's easy to see what's happening. Write out 19 over and over:
123456789123456789 ad infinitum.
You can see that 2 could be said to be one to the right of 1, or eight to the left. 1+8=9. 5 is two to the right of 3, or 7 to the left. 2+7=9 etc. Obviously each number is nine digits away from the next occurrence of that same number. 1 is always 9 away from 1 in either direction, 2 is always 9 away from 2, and so on. So any time you put a marker in between, you're dividing 9 in two, and so the two bits will of course always add up to 9.
Now let's return to music for the game of Find the Nonsense.
In music we have AG rather than 19. If we write it out as we did above:
ABCDEFGABCDEFG
We can see that the interval inversion thing works in much the same way as it did for digits 19. B is 1 to the right of A, or 6 to the left. C is 2 to the right of A, or 5 to the left. But hold on,1+6=7. 2+5=7. What's happened to 9? Ah right, there are now only seven symbols, AG, instead of nine 19.
Well if that's the case then why is it that a 2nd inverted becomes a 7th, 2+7=9. A 3rd inverted is a 6th, 3+6=9. 9 has returned, even though we now only have seven symbols. Where's the nonsense?