source file: m1365.txt Date: Thu, 26 Mar 1998 08:55:21 -0600 (CST) Subject: 88CET Ear-Training CDs, part 5 From: mr88cet@texas.net (Gary Morrison) 88CET? Wuzzat? --------------- Before I go into more detail about the sorts of exercises that make sense on such a CD, I need to explain a bit more about 88CET tuning itself. Some of the exercises won't make a lot of sense without this background information. Indeed, some of the exercises on these 88CET CDs aren't likely to make much sense on, for example, a 34TET ear-training CD. I did a series of tuning-list postings on 88CET tuning about 3 years ago or so. Even though it's been that long, I'll paraphrase the qualities of 88CET tuning a lot here, since that's not the main thrust of this series. I am working on some really killer web pages about 88CET tuning, but they're only about 1/3 done now. So in the meantime (not to be confused with "meantone"!), if you'd like to learn more, I can send any of you who might be interested in more details about 88CET, the text of those postings (assuming that I can find them all!). Most basically, "88CET" stands for "88-Cent [per step] Equal Temperament". It's an equal-temperament whose primitive step size is 88 cents. The 1200 cents in an octave's span clearly don't divide evenly by 88, so 88CET is a nonoctave tuning. No two notes on an 88CET instrument are exactly an octave apart, nor exactly two octaves apart. But the fact that it does not approximate octaves is not, in itself, quite as critically important as several other attributes. For the purposes of this series, here's what's most important about 88CET tuning: 1. 88CET has no traditional major or minor thirds. Instead it has three nontraditional thirds: subminor (7:6), neutral (11:9), and supramajor (9:7). 2. It has no approximation to a traditional major or minor scale. 3. Since it has no octave, 88CET has no octave-compound intervals. That means that, rather than getting "octave-equivalent" intervals in each octave's span, you instead get an different set of harmonic resources. 4. 88CET has a pretty good approximation to a 4:6:7:9:10:11:15 harmonic-series fragment chord, or (obviously) any fragment of that chord. 5. Since it's an equal temperament, it can also play that same structure inverted, meaning a that same subharmonic-series fragment. 6. Also because it's an equal-temperament, you can build other chords as stacks of any one of those intervals, such as a neutral triad, which is a stack of two 11:9 neutral thirds. That in the same sense that a major triad is a minor third atop a major third. 7. Since 88CET has no approximation to the octave, it has two intervals that come close to an octave. They are far enough to sound "out of tune", and close enough not to sound like anything in their own right. They are, in short, "off octaves" and I find that they pretty much have to be avoided in most forms of harmony (for approximately-harmonic timbres that is). 8. In addition to "off-octaves", 88CET also has a similarly dreadful- sounding off twelfth (3:1 ratio), and off double-octave (4:1). Other harmonic frequencies (5:1, 6:1, 7:1, etc.) seem to be either sufficiently well-represented, or are harmonically remote enough to be tolerable. Again I'm brutally paraphrasing here, so I'm not coming even close to doing justice to the importance of any of these qualities of 88CET tuning. Here is a table of frequency-ratio approximations in 88CET music: ------------------------------------------ Number of 88CET Ratio Steps Interval Name ------------------------------------------ 1:1 0 Perfect Unison 10:9 2 "Minor" Wholetone 7:6 3 (Septimal) Subminor Third 11:9 4 Neutral Third 9:7 5 Supramajor Third 10:7 7 (Large Septimal) Tritone 3:2 8 Perfect Fifth 5:3 10 Major Sixth 7:4 11 Subminor Seventh 15:7 15 Neutral Ninth 9:4 16 Major Ninth 5:2 18 Major Tenth ------------------------------------------