mem@sii.UUCP (Mark Mallett) (08/25/83)
b Can anybody tell me, or point me to literature describing, why certain combinations of tones are pleasing and some aren't? That is, I'd like to know some of the physics of harmony. For instance, why are major thirds, fourths, fifths & major triads pleasant? I can tell the ratio of the frequencies of all the notes involved, and that the base-10 logarithms of those ratios are rather interesting. Any real information would be appreciated. Mark E. Mallett decvax!sii!mem
DCP@MIT-MC@sri-unix.UUCP (08/27/83)
From: David C. Plummer <DCP @ MIT-MC> Part of it is physics, part of it is history/culture, and part of it is psychoacoustics. Physics: I don't know of a good literary reference. "Horns, Strings and Harmony" (I'd give you more info but I can't find my copy at the moment) may help. It has mostly to do with where the overtones fall. I think you can safely punt the logarithms. For example, take a major triad which has a Pythagorean ration of 4:5:6 and a minor triad with ratios 6:7:9 and look at the overtones (assume C is 256 for convenience). First note that each of these has a major and minor interval. One major interval is in a ratio of 4:5 and the other is 7:9, or .8 vs. .777. The minor intervals are 5:6 and 6:7, or .833 and .857. This more or less shows that the Pythagorean system is bankrupt for practical uses. Anyway, you will find that in the major triad more strong overtones of the root (say the first 10) overlap with overtones of the other notes than in the minor triad. History: In the Medieval days (of Western culture) they really didn't care about major scales and minor scales; they had modes. Very few people of recent days (probably as far back as 100 years) have used modal harmonies, unfortunately. As I recall, the Beatles were actually the most popular to revive some of it. But back in the Medieval days they were highly concerned with God and the devil. If something didn't sound quite right, it was the devil's doing and was to be avoided. Tritones, minor seconds and major sevenths immediately fell into this class. Major seconds and minor sevenths were't far behind. Then minor thirs/major sixths. The only universally accepted intervals were the octave, perfect fourth and perfect fifth. Even the major third and minor sixth were sometimes avoided; you will often find cadences that are perfect fifths and octaves with no thirds. As the years went on the rules got looser but the underlying philosophical base didn't sway quite so quickly. Also note that India and Japan have completely different tonal systems than the West. We may find their music unpleasant or uninteresting because we do not understand it. This has been true throughout history (read up on Beethoven or Stravinsky, for example). Psychoacoustics: You say that major triads/intervals are pleasant, implying minor triads/intervals are not. Why? Why do people generally consider minor triads "sad"? (It is often the case, but not always; perhaps because of the composer's will, not the listener's.) Why is the key of E major "brighter" than E-flat major? Why is C major the most "crystaline" major key? How many people believe in the Nyquist theory when applied to music? Example: is 44.1 Ksamples per second really sufficient for digital audio disks? (I say no. This gives a Nyquist frequency of 22K and with filters the upper range is diminished to around 20K. People will say that you can't hear above 20K anyway. So what? You can't hear below 16Hz either. You can FEEL below 16Hz, so there is no reason there are not some subtle interactions above 20K.) There is only so much physics and music theory you can put into practice before the subjective aspects show their heads, for better of for worse.
steve@brl-bmd@sri-unix.UUCP (09/02/83)
From: Stephen Wolff <steve@brl-bmd> As DCP has pointed out, you've mixed physics and psychoacoustics. There are some of us, for example, who assert the major triad is not pleasant but merely trite, and that one of the most interesting chords is the fundamental- fifth-octave because of the ambiguity and mystery of the "missing" major/minor third. Your discussion of logarithms implies you're thinking of "equal temperament" which did not enter widespread use until the 19th century. For a concise discussion of other tunings (`Pythagorean', `just', `mean-tone') look up those terms and also `Intervals, calculation of' in the Harvard Concise Dictionary of Music (Belknap/HUP,1978). And there are some early music buffs who claim that 16th century string and keyboard music (that of John Dowland, for example) doesn't sound `right' unless the instruments are tuned in one of the mean-tone temperaments that were in common use at that time. But frankly my ears aren't that well-trained!