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can anyone explain with mathematics/physics why chords or notes thirds (c & e, e&g, d&f, etc) or octaves sound better than say two consecutive tones???
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based off what he's saying, you'd want to have a combination of sound waves that do not have peaks that create internal frequencies (the spikes he is referring to) that causes odd freq sounds to occurso what would be the conditions in order for something to be "pleasant"
This is true on a piano, but an ochestra using multiple instruments can play a true C chord where E 5/4 above C and G is 3/2 above C.Contrast that to a major C chord:
C & E are a factor of 2^(4/12) = 1.260, pretty close to 5/4
C & G are a factor of 2^(7/12) = 1.498, pretty close to 3/2
Yuck indeed. A little calculator work tells me 18:17 is close. 1.0588., with .06% error. Still :yuck:The actual ratio between adjacent piano keys is
[tex]
2^{1/12} = 1.059... [/tex]
or roughly 89/84. :yuck:
Doh! you got me.12/11 is 1.09..., about 1 and one-half piano keys apart.
Contrast that to a major C chord:
C & E are a factor of 2^(4/12) = 1.260, pretty close to 5/4
C & G are a factor of 2^(7/12) = 1.498, pretty close to 3/2
In some traditions (ages zero through 5 or 8 or 10 and on up) dissonance is quite pleasant and intently practiced. It gets you a bottle, your diapers changed, etc.Tough one, because some musical traditions are more accepting of dissonance than others, and to some listeners, some tonal intervals are quite well accepted that in other traditions might be rejected.
there's an old USENET post of mine that speaks to this issue. i would repost it, but i was actually depending on the use of "ASCII art" to illustrate it and PF won't let me precede a line of text with spaces. be sure to read it with a mono-spaced font, otherwise intervals in the illustrations don't line up right.can anyone explain with mathematics/physics why chords or notes thirds (c & e, e&g, d&f, etc) or octaves sound better than say two consecutive tones???
Thanks, I have sometimes wondered if musicians ever do that.This is true on a piano, but an ochestra using multiple instruments can play a true C chord where E 5/4 above C and G is 3/2 above C.
Yes, and there are some intervals that can sound both pleasant orBut you asked 'why', not what is pleasant. I think you need to ask some rocket surgons, or brain chemists, or something.
What sounds pleasant are simple ratios between notes like 1 to2 (an octave), 2 to 3, and 3 to 5. Things like 6 to 7 begin to sound .... unpleasant. Two notes side by side on a piano are in the ratio of about 11 to 12.
Since about 1900. Try playing js bach as he would have heard it with a=~410.A is defined to be 440hz for most forms of music.
On another historical note (bad pun), how long ago did organs have presets to set them for "just intonation"? How long ago did organs have stops (affects multple presets with a single switch, commonly a foot operated button)?Try playing js bach as he would have heard it with a=~410.
"American Scientist" just had an article about this exact question:can anyone explain with mathematics/physics why chords or notes thirds (c & e, e&g, d&f, etc) or octaves sound better than say two consecutive tones???