The 1235 tetrachord yields two Major 2nds (C-D & D-E), one minor 3rd (E-G), one Major 3rd (C-E), one Perfect 4th (D-G) and one Perfect 5th (C-G). The first 2 lines of which (in bold) would look like this when notated:Īnd so on (.the other 12 permutations are all in the book). That being said, if we were to order the numbers 1,2,3 & 5 as permutations, we would get the following 24 different groupings of those four numbers: While 24 is already a challenge for the average non-android to handle with ease, imagine having to deal with 120! Add to that the fact that, as the vast majority of Western music is in 4/4 time, phrases built with groups of 4 notes fit more naturally and evenly in a 4/4 measure than groups of 5. In other words, 4 notes yields 24 unique permutations, while the 5 note Pentatonic Scale produces 120 permutations of 5 notes each.
Mathematically speaking, any group of 4 unique items yields 24 mutually exclusive arrangements of those same 4 items. So, why only four and not five note permutations?
It's actually the first four notes of a Pentatonic Scale (C-D-E-G-A), which itself can be viewed as a series of consecutive Perfect 5ths (C-G-D-A-E), and is based on the natural overtone series. The 1235 tetrachord (C-D-E-G in C), whether played or sung, is probably the most common and recognizable note grouping in Western music, irrespective of style.
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