source file: mills3.txt Date: Tue, 21 Oct 1997 18:17:44 +0200 Subject: Dictionary Devils From: Carl Lumma >>I like equal-step tunings as much as the next guy. I even like 12. I am >>always amazed at how good it sounds, and at how powerful it is... > >Okay, so to you, 12-TET tunings are powerful (and this is cause for >amazement, presumably because of the high integer ratios it employs) I call it powerful because it gets a lot done with only 12 pitches. There is a difference between consonance and utility. 12et's intervals aren't very consonant, but they do provide a huge musical framework for being only 12 (providing 144 of Partch's "senses"). >>Consonance is a factor of the size the number in an intervals ratio. > >In a sense, yes, because the interval itself is a factor of the sizes of >the numbers in the ratio. What? >But in another sense, no: the Random House Dictionary and the New Harvard >Dictionary of Music agree that consonance is a factor of cultural conventions >and the "mind of the beholder" (or the musical equivalent of that). Here's your problem! You are using the Random House Dictionary and New Harvard Dictionary of Music as references. Consonance is not a factor of the mind, it is an acoustic phenomenon having to do with the superposition of waveforms. Make the perception of this phenomenon as subjective as you like. >>An interval 16 cents flat of the sublime 6/5 has frequency ratio >>19723/16585. This, of course, is our quite dissonant 12et minor third. > >So, 6/5 is sublime, and 19723/16585 is quite dissonant, yet powerful. I did not call any interval in 12 equal powerful. I called the tuning powerful. If you listen to the 300 cent third, you can hear it beat. This is dissonance. >>An interval 18 cents flat of the 6/5 bears ratio 19/16. It is a very >>consonant minor third found in the duple 16-32 of the harmonic series... > >And 19/16 is very consonant. It seems this comment was designed to make fun of me, based on your Random-House-school-of-Cognitive-Psychology definition of consonance. If consonance is so subjective, why don't you offer a description of the 19/16? What's that? You've never heard it? >Colleagues of the tuning list, the evidence suggests that musical beauty >is in the ear of the hearer. All forms of beauty are subjective. That this is so, I think, is beautiful. >I see many claims that low integer ratios produce more "natural" and "perfect" >harmonies, but little proof that people actually respond this way. The fact that you've heard many claims seems to suggest that people respond that way. For more evidence, check out Arthur Benade's "Special Relationships" study, written up in his book "The Fundamentals of Musical Acoustics" and in Doty's excellent "Just Intonation Primer". Or you could do your own study. I've done demos with over 15 people and have yet to find someone who doesn't prefer his subjective experience of Just Intervals. Or you might ask why a capella choirs sing in Just Intonation. You can't get any more direct a measure of how humans like their sound than how they tend to use their voices in a group. >This makes the tuning list sometimes read like some medieval treatise on the >nature of God. Why be amazed then, that the Devil incarnate, 12TET, wields >such power? I don't know who we've got on this thing, but I thought it was more than numerologists. There's nothing inherently good about the low integers. Tuning to them only makes sense because they occur in the timbres of most acoustic instruments. If you have an instrument (like the Hammond Organ) that produces tempered harmonics, then it would be a mistake to tune it in Just Intonation (it's also impossible to re-tune tonewheel organs). As for my use of "amazed", you've probably got me. I'm actually amazed at how such beautiful patterns can come out of almost any tuning, Just or not. That's why I got into Xenharmonics. Not because I was on a numerological crusade, but because tuning can be one of the most powerful resources for musicians. Carl SMTPOriginator: tuning@eartha.mills.edu From: James Kukula Subject: MIDI file formats PostedDate: 21-10-97 19:53:32 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 21-10-97 19:52:45-21-10-97 19:52:46,21-10-97 18:53:24-21-10-97 18:53:24 DeliveredDate: 21-10-97 18:53:24 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C1256537.0062332E; Tue, 21 Oct 1997 19:52:36 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA23110; Tue, 21 Oct 1997 19:53:32 +0200 Date: Tue, 21 Oct 1997 19:53:32 +0200 Received: from ella.mills.edu by ns (smtpxd); id XA23124 Received: (qmail 6851 invoked from network); 21 Oct 1997 10:53:28 -0700 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 21 Oct 1997 10:53:28 -0700 Message-Id: <199710211747.KAA11860@sunatg3> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu