TETRACHORDSA tetrachord is a four note scale arranged with the following steps: whole-whole-half. Each major scale is made up of two tetrachords. I could not understand fully how certail scales have certain sharps or flats, except to start out from the Key note and count the steps which revealed the sharps or flats. In looking at tetrachords I found a pattern that helped to shape the scales in my mind and this is what I've discovered. If you began writing out notes of four starting from C and just kept going in notes of four it revealed a pattern for determining which key had 2 sharps or 3 sharps, etc. It all seemed random to me. First I will write out the tetrachords for the keys that have sharps.
|_||G#||A#||B#||C#||The first column lists the number of sharps for that particular chord (beginning with the first note). If you took the first two rows that make up the C chord you can see that the first tetrachord can be divided in to the even numbers of sharps. For example C-D-E-F is equal to 0-2-4-6 sharps in those keys. The second half of the tetrachord on the C scale G-A-B-C are the odd number of sharps 1-2-5-7 for those keys. One note however is that the F note should be the key of F# and the high C is the key of C#.|
The flats too form a pattern but in descending order. Here are the tetrachords for the flats.
|0||C||D||E||F||The first column lists the number of flats in that key. Again using the C scale the number of flats fall into an odd and even number pattern in descending order. C-D-E-F have 7-5-3-1 flats and G-A-B-C have 6-4-2-0 flats.|
You can also see that all the naturals in the sharp scales are flatted in the flat scales, while all the sharps in the sharp scales are naturals in the flat scales.