source file: m1368.txt Date: Sat, 28 Mar 1998 16:08:10 -0600 (CST) Subject: 88CET Ear Training CDs, Part 6 From: mr88cet@texas.net (Gary Morrison) 88CET Notation -------------- The other important aspect of 88CET to learn a bit about in order to understand the exercises on my 88CET ear-training CDs, is my notation system. This is one of those non-auditory, "intellectual", memorization exercises I mentioned earlier. As powerful as it is to be able to conjure up the sound of any 88CET interval in your mind at will, you still can't tell what E up to G sounds like without the strictly intellectual knowledge of what the interval between those two notes is! Without an octave to organize a tuning around, you have to choose some other interval. Two intervals stand out as most likely candidates, because they are very intuitively basic to our ears, and because you can build interesting scales around them. The first such interval is the 3:2 perfect fifth, and the second is the 7:4 subminor seventh. As you can see from the earlier-presented table of frequency-ratio approximations, in 88CET tuning 8 steps forms a perfect fifth, and 11 steps is a subminor seventh. Since this series is not basically about 88CET Music Theory, I'll just say that using those two intervals to form a cyclic scale pattern of 2122121 (2 meaning two 88CET steps - a small whole step, and 1 meaning a half step). This 2122121 pattern repeat in 7:4s rather than octaves, meaning that two As are not octaves 7:4s apart. The pattern also maps nicely to a traditional piano (or MIDI) keyboard if you imagine away the G#/Ab key, and leave a half-step between G and A: A# C# Eb Gb A B C D E F G A On my 88CET MIDI instruments, I make the G#/Ab key play the same pitch as the adjacent A key, but it doesn't really matter, since I never use that key anyway. Perhaps skipping over the G#/Ab key seems odd, but this structure is really a lot more intutive, audibly speaking, than not skipping the G#/Ab key. The entire 7+5 structure of a traditional keyboard corresponds to a pattern of tritones wrapping within a span of a not-very-accurate neutral seventh (11:6). Perhaps you'll just have to listen to those two pairs of intervals for yourself, but when you do, I think you'll have to agree that 3:2 and 7:4 are much more intuitive, simple, and meaningful to our ears than 10:7 and 11:6! Once you establish this 2122121 pattern, you have a system of "pseudokeys", each with its pseudokey signature. Then again, they're not like any key signature you've probably ever seen before though! Although these pseudokeys don't necessarily suggest a tonality (thus "pseudo"keys rather than a true key), it turns out that they can be used that way. When you do use them to suggest a tonality, you promptly find that related keys, even in as such a nontraditional tuning, are still fifths apart. Since this scale pattern is cyclic in fifths, you find that related keys have pseudokey signatures that differ by a single sharp or flat.