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brandy
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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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so 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
The actual ratio between adjacent piano keys is
[tex]
2^{1/12} = 1.059... [/tex]
or roughly 89/84. :yuck:
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
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.
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?
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.
But 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.
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.
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?