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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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brandy said: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.Redbelly98 said: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
Redbelly98 said: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
turbo-1 said: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.
brandy said: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?
Jeff Reid said: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.
Phrak said: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)?jim mcnamara said:Try playing js bach as he would have heard it with a=~410.
brandy said: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?
The mathematical basis for why chords sound pleasant lies in the relationship between the frequencies of the individual notes within a chord. When these frequencies are in a simple mathematical ratio, such as 1:2 or 2:3, the resulting sound is perceived as harmonious and pleasant to the ear.
These ratios create a pleasant sound by producing a phenomenon known as harmonic resonance. When two frequencies are in a simple mathematical ratio, they reinforce each other and create a sense of unity and coherence in the sound.
The human brain processes the mathematical relationships in chords through a complex network of neurons and brain regions responsible for auditory perception. These neurons detect and analyze the frequencies of the individual notes within a chord, and the brain interprets this information as a harmonious sound.
Yes, there are cultural and personal factors that can influence the perception of pleasant chords. For example, different cultures may have different preferences for certain types of chords, and personal experiences and memories can also influence one's perception of pleasant chords.
No, not all chords follow simple mathematical ratios. Some chords, such as dissonant or atonal chords, do not follow these ratios and may be perceived as unpleasant or discordant to the ear. However, these chords can still be used effectively in music for creating tension and contrast.