source file: mills3.txt Date: Mon, 27 Oct 1997 22:54:29 +0100 Subject: RE: harmony and small integer frequency ratios From: "Paul H. Erlich" > > >Just intervals of small interval ratios have a uniquely pure > > sound. > >Yup. > > >This purity is not always desirable. > >Right. If an n:1 frequency ratio is tuned too purely in sustained harmonic >timbres, the upper note will disappear. > > >Differences of tuning as small as 1 cent do affect the sound > >of the chord. I'm unable to try smaller intervals at present. > >Real musicians playing acoustic instruments don't have this level of control. > > >When an interval is detuned by more than a few cents, this > > detuning has more of an impact on the sound of the chord than > > the particular ratios involved, provided the latter are small > >(I haven't worked out how small yet). > >It depends what you're listening to. If the chord occurs as a result of >simultaneous melodic lines in a piece of music, I don't think you're right, >unless you'd allow 20 cents to be considered a few cents. If you're listening >for beats, then yes, you're exactly right. > > >All of the above depends strongly on timbre > >Amen. Volume as well. > > >The idea that dissonance increases with prime limit is > >erroneous. > >I agree. The odd limit is a much better indicator. I bought a copy of >Partch's book while in San Francisco (I last read it many years ago) and on >virtually every page there is evidence, often strong, emphatic evidence, that >his definition of "limit" was the odd, not prime, definition. All the Partch >"experts" using the prime definition frustrate me to no end as they clearly >have not listened as much as Partch and yet fail to understand the ideas he >derived from years of listening. And for those using the prime limit >definition to describe the resources of a tuning system rather than >consonance/dissonance issues, what information is contained in the knowledge >of the highest prime one is using that is more important than knowing any of >the other primes one is or is not using? > >>The 3-5-7 limits happen to get progressively out >>of tune in 12tet, though, which may be the origin of this. > >3, 5 and 7 are successive odd numbers, so I don't think one has to resort to >12tet to explain the increasing dissonance of their respective intervals >(which I clearly hear). However, since you're using a "prime," not "odd" >definition, of limit, I think you're right; for example, 9:8 and 16:9 are >more familiar, due to 12tet conditioning, than 8:7 and 7:4, but the latter >would be more consonant if one could erase the conditioning. Many who cannot >undo their conditioning therefore conclude that prime limit 3 is more >consonant than prime limit 7, but I would say that this is not true; it is >only true that odd limit 3 is more consonant that odd limit 7. Odd limit 9 is >naturally slightly more dissonant that odd limit 7, though this ordering may >be culturally altered. However, what is considered "in tune" and "out of >tune" may have much more to do with familiar scalar intervals than familiar >harmonic intervals, and some pure 7s hidden in inner voices will sound just >fine to even the most culturally conditioned of listeners. SMTPOriginator: tuning@eartha.mills.edu From: William Sethares Subject: psychoacoustic foundations PostedDate: 28-10-97 16:15:45 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: 28-10-97 16:14:52-28-10-97 16:14:53,28-10-97 15:15:27-28-10-97 15:15:28 DeliveredDate: 28-10-97 15:15:28 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 C125653E.0053BE30; Tue, 28 Oct 1997 16:14:41 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA29748; Tue, 28 Oct 1997 16:15:45 +0100 Date: Tue, 28 Oct 1997 16:15:45 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA29534 Received: (qmail 1901 invoked from network); 28 Oct 1997 07:15:32 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 28 Oct 1997 07:15:32 -0800 Message-Id: <199710281513.AA03194@eceserv0.ece.wisc.edu> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu