From: Hatunen on 11 Aug 2006 12:57 On Fri, 11 Aug 2006 08:34:32 -0500, barney2(a)cix.compulink.co.uk wrote: >In article <v8mod29jovghn6ns4jerg1n4g48funs1nb(a)4ax.com>, >mxsmanic(a)gmail.com (Mxsmanic) wrote: > >> *From:* Mxsmanic <mxsmanic(a)gmail.com> >> *Date:* Fri, 11 Aug 2006 12:17:30 +0200 >> >> Martin writes: >> >> > The pink oboe? >> >> I simply wanted to know if it was equal temperament (such as a piano) >> or not (such as a violin). > >Now that you know, are you going to answer my enquiry as to why a major >triad with far-from-integer ratios among the frequencies is nevertheless, >in the West, broadly considered a 'pleasing' sound? The ratio of 1.259921 in the even-tempered scale is the best approximation to a ratio of 5:4 of the diatonic scale; the ideal 5:4 ratio would be the ideal harmonic. The well-tempered scale is simply a good approximation the well-tempered scale having a number of practical advantages over the diatonic scale. ************* DAVE HATUNEN (hatunen(a)cox.net) ************* * Tucson Arizona, out where the cacti grow * * My typos & mispellings are intentional copyright traps *
From: Hatunen on 11 Aug 2006 13:00 On Fri, 11 Aug 2006 09:24:36 -0500, barney2(a)cix.compulink.co.uk wrote: >In article <9t2pd218v75s89pn4vequsson0313ptjf7(a)4ax.com>, >mxsmanic(a)gmail.com (Mxsmanic) wrote: > >> *From:* Mxsmanic <mxsmanic(a)gmail.com> >> *Date:* Fri, 11 Aug 2006 15:54:01 +0200 >> >> barney2(a)cix.compulink.co.uk writes: >> >> > Now that you know, are you going to answer my enquiry as to why a >> > major triad with far-from-integer ratios among the frequencies is >> > nevertheless, in the West, broadly considered a 'pleasing' sound? >> >> Because it approaches integer ratios. > >Why, then, was an augmented fourth e.g. C4-F#4 long considered among the >worst of dissonances, despite being closer to an integer ratio than the >frequently-used and entirely-acceptable perfect fifth e.g. C4:G4? > >> At one time, many pianos were tuned to make the more popular ratios >> exact, and the less popular ones relatively inaccurate. This was >> abandoned as popular piano playing broadened to include all sorts of >> music, and not just a few popular hits. > >What are the differences in the piano repertoire before and after equal >temperament? The problem with a diatonic tuned piano is taht the diatonic scale is base one note, perhpas C; that piano can't be used to play in another key. ************* DAVE HATUNEN (hatunen(a)cox.net) ************* * Tucson Arizona, out where the cacti grow * * My typos & mispellings are intentional copyright traps *
From: dgs on 11 Aug 2006 13:00 Dave Frightens Me wrote: > On Fri, 11 Aug 2006 12:18:51 +0200, Mxsmanic <mxsmanic(a)gmail.com> > wrote: > > >>Dave Frightens Me writes: > > >>>Intelligent people live in the same world as anyone else. >> >>But they are smarter than other people are. > > > Not necessarily. You can be intelligent, but not very smart. Like, for instance, those with Asperger's syndrome, perhaps? -- dgs
From: Mxsmanic on 11 Aug 2006 13:06 Hatunen writes: > The ancient Greeks demonstrated the rleationship between harmony > and integer ratios, although, of course, they knew nothing of > frequency and did it by the measurementof instrumental string > lengths. It's lucky for them that they didn't post their findings on this newsgroup. -- Transpose mxsmanic and gmail to reach me by e-mail.
From: barney2 on 11 Aug 2006 13:21
In article <pfdpd2d9uvs94du0bnlb352a7p91kkeb9d(a)4ax.com>, hatunen(a)cox.net (Hatunen) wrote: > *From:* Hatunen <hatunen(a)cox.net> > *Date:* Fri, 11 Aug 2006 09:57:44 -0700 > > On Fri, 11 Aug 2006 08:34:32 -0500, barney2(a)cix.compulink.co.uk > wrote: > > >In article <v8mod29jovghn6ns4jerg1n4g48funs1nb(a)4ax.com>, > >mxsmanic(a)gmail.com (Mxsmanic) wrote: > > > >> *From:* Mxsmanic <mxsmanic(a)gmail.com> > >> *Date:* Fri, 11 Aug 2006 12:17:30 +0200 > >> > >> Martin writes: > >> > >> > The pink oboe? > >> > >> I simply wanted to know if it was equal temperament (such as a piano) > >> or not (such as a violin). > > > >Now that you know, are you going to answer my enquiry as to why a > major >triad with far-from-integer ratios among the frequencies is > nevertheless, >in the West, broadly considered a 'pleasing' sound? > > The ratio of 1.259921 in the even-tempered scale is the best > approximation to a ratio of 5:4 of the diatonic scale; the ideal > 5:4 ratio would be the ideal harmonic. So the reason that C4-G4 sounds 'better' than C4-F#4 is that the ratio of the former, 1:1.498303, is closer to 10:15 than the latter, 1:1.41421, is to 10:14? (This is a genuine question.) |