source file: mills2.txt Date: Sun, 24 Nov 1996 14:13:24 -0800 Subject: Re: Thoughts on Brian M's Non-Octave Thoughts From: Gary Morrison <71670.2576@CompuServe.COM> (Gag! This is the third time I've written this message; CompuServe Information Manager keeps kicking the bit-bucket on me. This message only though. Weird...) First of all, let me acknowledge right off that Brian has experience with more nonoctave tunings than I do. My nonoctave experience is mostly limited to 88CET tuning, although my experience with 88CET is fairly significant. Regarding coming close to an octave being sufficient to elicit the feeling of octave equivalence: I absolutely agree with that, but I'd like to add that it doesn't necessarily mean that it will sound like a CORRECT octave. Best I've been able to see, speaking in very overgeneralized approximations, an interval within about 75 cents of an octave will sound like an octave rather than having a musical meaning of its own. And if it's more than, say, 10 cents off from a proper 2:1, it will sound pretty dreadfully out of tune. That too is a big overgeneralization, and both of those generalizations apply only to approximately-harmonic timbres. On a related note, Paul E recently pointed out that neither he nor I have been able to get a pitch-classing effect from a P12 (3:1). I may have inadvertently misrepresented my findings there. That is certainly true when it comes to compounding intervals by a twelfth, meaning that I haven't been able to find much similarity between, for example, a major third and a major fourteenth. I have, however, been able to get a sense much like that of leading-tone resolution to other intervals, including the P5. In doing that though, I have to avoid the tuning's closest representations of an octave, because aluding to the octave almost immediately destroys the sense the P5, or whatever, is the most "basic" interval. Regarding Enrique Moreno's (or Brian's attribution of Enrique Moreno's) view that using traditional interval nomenclature for non-octave tunings' pitch relationships: I can certainly see value in avoiding them. When I was in the throes of devising my 88CET notation system, I initially devised an 88CET-specific interval nomenclature, but later decided that there really wasn't a whole lot of value to it, and that it was more likely to confuse than enlighten. But certainly a strong case can be made for avoiding classifying some intervals in terms of traditional nomenclature. 9:7 is probably in that category, in that it somewhat stretches the boundary between thirds and fourths. I find it to be more clearly a third than a fourth, but there are certainly some contexts where it clearly has a fourth-like sound. One is the scenario where you let a pickup note rise by a 9:7 into the opening downbeat in a moderate-to-fast-tempo melody. That is probably a case of social conditioning: it probably gives that fourth-like sensation (or it often does for me anyway), because that's a VERY common melodic use for a P4. But that brings to mind the first of two caveats to accepting Enrique's view that traditional nomenclature shouldn't apply to nonoctave tunings. Is this sort of social conditioning (this sort of sensation is a third, this sensation is a fifth, etc.) hopeless to try to overcome? It is certainly deeply engrained. My other caveat is that this sort of motivation for not applying traditional interval nomenclature to non-octave tunings' resources is not in any specific to non-octave tunings. Any tuning that 9:7s (again, as an example) may benefit from avoiding classifying that interval as a third or a fourth. If his concern in particular is that you need to come up with a new set of interval nomenclature based upon the interval and its non-octave duplicates (e.g., coming up with a name for the sensation of Pierce-Bohlen's 9:7 and its 3:1-displaced equivalent, then I personally would be skeptical about the value in that, because I have only managed to get a pitch-classing effect from other intervals in very limited ways. But then again, that may be partly due to the fact that, like Carlos' Alpha and Beta tunings, 88CET doesn't really have a natural interval of repetition (although its 7:4, 3:2, 5:2, and 8:1, in order of decreasing preference, are good candidates). Regarding Brian's question about how one goes about determining a non-octave tuning's most consonant interval: Brian approached the question, appropriately I'd say, in terms of what intervals work for doubling. In that regard, I have found that intervals that work for doubling are heavily dependent upon the intervals in the original chord. In particular, most any interval that is "bland" compared to the other intervals in the chord seems to work fairly well for doubling. Even intervals as flavorful as a 5:2 seem to produce a quite satisfactory doubling effect for chords whose harmonies are comparatively complex, like 7:6s or 11:9s for example. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Sun, 24 Nov 1996 23:12 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA06177; Sun, 24 Nov 1996 23:14:25 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA06239 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id OAA22606; Sun, 24 Nov 1996 14:14:22 -0800 Date: Sun, 24 Nov 1996 14:14:22 -0800 Message-Id: <961124221020_71670.2576_HHB43-8@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu