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From: barney2 on 12 Aug 2006 10:40 In article <pe7qd25qudseo2cdgdbt1qh7eqocebh6fh (a)4ax.com>, hatunen(a)cox.net (Hatunen) wrote: > *From:* Hatunen <hatunen (a)cox.net>> *Date:* Fri, 11 Aug 2006 17:22:55 -0700 > > On Fri, 11 Aug 2006 12:21:56 -0500, barney2 (a)cix.compulink.co.uk> wrote: > > >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 > > I think you mean 2:3. Yes - extreme laziness on my part there. > > than the latter, 1:1.41421, is to 10:14? > > > >(This is a genuine question.) > > I may have to work this out. The notes on the well-tempered scale > are related to the twelfth root of two ( 2^1/12). In any case > 1:1.41421 is approximately 5:7. But yes, the ratio of 2:3 is more > harmonious. But is it more harmonious /because/ it is 2:3 and not 5:7, or is that just happenstance?
From: James Silverton on 12 Aug 2006 11:08 Hello, barney2 (a)cix.compulink.co.uk!You wrote on Sat, 12 Aug 2006 09:40:44 -0500: ??>>>> 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 ??>> ??>> I think you mean 2:3. b> Yes - extreme laziness on my part there. ??>>> than the latter, 1:1.41421, is to 10:14? ??>>> ??>>> (This is a genuine question.) ??>> ??>> I may have to work this out. The notes on the ??>> well-tempered scale are related to the twelfth root of two ??>> ( 2^1/12). In any case 1:1.41421 is approximately 5:7. But ??>> yes, the ratio of 2:3 is more harmonious. Pretty obviously you two, barney and hatunen, understand the mathematical bases of harmony but it might be worthwhile giving a reference to rather a good discussion that includes something of the physiological aspects: http://www.sciwrite.caltech.edu/journal03/A-L/hardesty.pdf I might just quote, for lesser mortals like me who don't know much about musical theory, "The frequency of the beats is just the difference between the frequencies of the two component waves. This phenomenon has great importance in harmony most people find rapid beats unpleasant (if not terribly annoying) and dislike intervals between tones with frequency differences substantial enough to produce rapid beats." Now why people find the rapid beats unpleasant is something else! James Silverton Potomac, Maryland E-mail, with obvious alterations: not.jim.silverton.at.comcast.not
From: Hatunen on 12 Aug 2006 17:23
On Sat, 12 Aug 2006 09:40:44 -0500, barney2 (a)cix.compulink.co.ukwrote: >In article <pe7qd25qudseo2cdgdbt1qh7eqocebh6fh (a)4ax.com>, hatunen(a)cox.net >(Hatunen) wrote: >> I may have to work this out. The notes on the well-tempered scale >> are related to the twelfth root of two ( 2^1/12). In any case >> 1:1.41421 is approximately 5:7. But yes, the ratio of 2:3 is more >> harmonious. > >But is it more harmonious /because/ it is 2:3 and not 5:7, or is that just >happenstance? I'm not really sure. ************* DAVE HATUNEN (hatunen (a)cox.net) ************** Tucson Arizona, out where the cacti grow * * My typos & mispellings are intentional copyright traps * |