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From: Hatunen on 11 Aug 2006 12:07 On Fri, 11 Aug 2006 09:14:08 +0100, The Reid <dontuse(a)fell-walker.co.uk> wrote: >Following up to Mxsmanic > >>Frequencies of sound that relate to each other in small integer ratios >>are pleasing to the ear. The larger the integers in the ratio, the >>less pleasant the combination of frequencies. Non-integer ratios are >>even worse, and frequencies that are relatively prime to each other >>sound worst of all. > >so you are claiming the musicality of sound is dependant upon the >counting base we selected? Sounds like total bollox to me, but I >only ever read one music theory book. A. Harmony is a matter of frerquency ratios, and rations are independent of the counting base used. Even-tempered scales do not allow the nice even ratios that a diatonic scale does. Bach wrote The Well-Tempered Clavier to demonstate that the use of even tempered scales could sound almost as good as diatonic scales. Almost. B. Primeness of a number is independent of the counting base used. C. The quality of beign an integer is independent of the counting base used. ************* DAVE HATUNEN (hatunen(a)cox.net) ************* * Tucson Arizona, out where the cacti grow * * My typos & mispellings are intentional copyright traps *
From: barney2 on 11 Aug 2006 12:05 In article <789pd2p8b3iiuu4s9j689bmmrv3gvnm86h(a)4ax.com>, mxsmanic(a)gmail.com (Mxsmanic) wrote: > *From:* Mxsmanic <mxsmanic(a)gmail.com> > *Date:* Fri, 11 Aug 2006 17:42:02 +0200 > > barney2(a)cix.compulink.co.uk writes: > > > 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? > > Perhaps because they were not exact ratios? Please answer the question. Both pairs of notes are in non-integer ratios. Why, then, is one acceptable and the other not; and why is the more acceptable one the one that is /further/ from an integer ratio, apparently contradicting the implication of your suggestion that a major triad is pleasing because "it approaches integer ratios"? > > What are the differences in the piano repertoire before and after > > equal temperament? > > Apparently a lot of popular songs at one time were in a small subset > of keys, and some tuners chose to tune pianos to favor these keys, to > the detriment of others. Well, not just songs. But I still don't understand your meaning in writing "popular piano playing broadened to include all sorts of music, and not just a few popular hits" - there was an extremely large and varied keyboard repertoire /long/ before equal temperament.
From: Hatunen on 11 Aug 2006 12:42 On Fri, 11 Aug 2006 12:00:01 +0100, The Reid <dontuse(a)fell-walker.co.uk> wrote: >Following up to Mxsmanic > >>> so you are claiming the musicality of sound is dependant upon the >>> counting base we selected? >> >>No. Read what I wrote. I didn't say anything about base. > >But I did, I'm talking about the likelihood of integer values >depending on counting base, not the musicality of the notes. > >For instance, when dividing, base 12 gives a lot more integer >results than base ten. Rubbish. Integers are integers regardless of the counting base. >I don't see any relationship between the *base* and *scale* >dependant accident of integers and musicality. The diatonic scale is based on integral ratios between two notes; this gives the most harmonious sounds. For harmonious spound it doesn't matter what the frequencies themselves are so long as they bear a simple integer relationship to each other. The even-tempered scale is based on the twelfth root of an octave, and because it only delivers integer relataionships for the octaves, the harmony can neer be as perfect as it can for the diatonic scales. Unfortunately, it is basically impossible to change scales with diatonically tuned instruments; if the instrument is tuned for a diatonic scale based on C, it cannot be used on a musical piece written in F#. >Integers could be made to appear anywhere by manipulating the >scale intervals. they are a label, not the sound itself. Nonsense. Integers are integers. But Mixi is talking about integer ratios, not integers. By this he means frequency ratios like 2:1 and 5:3; the actual frequencies need not be integers, and, as a practical matter, never can be. 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. ************* DAVE HATUNEN (hatunen(a)cox.net) ************* * Tucson Arizona, out where the cacti grow * * My typos & mispellings are intentional copyright traps *
From: JohnT on 11 Aug 2006 12:47 "Martin" <me(a)privacy.net> wrote in message news:tv9pd2lrg6aka646ccrms86r93r3fdtaof(a)4ax.com... > On Fri, 11 Aug 2006 17:43:03 +0200, Mxsmanic <mxsmanic(a)gmail.com> > wrote: > >>Dave Frightens Me writes: >> >>> You seem to interpret this coupled with your shyness as >>> meaning you are highly intelligent. >> >>I haven't speculated on my own intelligence at all. > > Of course not! You know you are highly intelligent and superior in all > respects to Europeans and in particular to natives of your adopted > country. The really sad thing is that he probably does "know" that. JohnT
From: Hatunen on 11 Aug 2006 12:51
On Fri, 11 Aug 2006 15:00:12 +0100, The Reid <dontuse(a)fell-walker.co.uk> wrote: >Following up to Mxsmanic > >>The set of integers is of the same size in every >>base. > >I've read that four times and am deciding not to bother. Good thing; it's true. The size of the set of integers is the transfinite number aleph-null and it doesn't matter what number base you're using. if you'e going to give Mixi a hard time it's a good idea to know the subject. ************* DAVE HATUNEN (hatunen(a)cox.net) ************* * Tucson Arizona, out where the cacti grow * * My typos & mispellings are intentional copyright traps * |