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Can anybody explain me from the understandable way cause im not a pro at mathematics ?
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Because a perfect 12th is 3 times the frequency of the fundamental tone, and a 5th is an octave below it.
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Can anybody explain me from the understandable way cause im not a pro at mathematics ?
It's pretty hard to explain without going into mathematics but here's a simplified explanation. When the ratio of two frequencies are related as a fraction where neither the top or bottom number is large those frequencies will sound in harmony with one another, if you can't express it as a simple fraction the notes will sound dissonant. 2/1 is the octave, 3/2 is a fifth, 4/3 is a fourth etc. To add intervals you multiply the fractions together so a fourth plus a fifth is 4/3 * 3/2 which is 2/1, or an octave. The major scale is actually a set of frequency ratios that work well together so that there is a pair of notes which creates each of the intervals 2/1 , 3/2, 4/3 5/4, 6/5. The fifth note in that scale has a ratio of 3/2. These exact fractions only work well if you only need to play in one key, in order to produce a piano that plays equally well in all 12 keys the intervals are adjusted slightly so that no key contains perfect fractional intervals but they are all pretty close to where they should be.
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Can anybody explain me from the understandable way cause im not a pro at mathematics ?
It's pretty hard to explain without going into mathematics but here's a simplified explanation. When the ratio of two frequencies are related as a fraction where neither the top or bottom number is large those frequencies will sound in harmony with one another, if you can't express it as a simple fraction the notes will sound dissonant. 2/1 is the octave, 3/2 is a fifth, 4/3 is a fourth etc. To add intervals you multiply the fractions together so a fourth plus a fifth is 4/3 * 3/2 which is 2/1, or an octave. The major scale is actually a set of frequency ratios that work well together so that there is a pair of notes which creates each of the intervals 2/1 , 3/2, 4/3 5/4, 6/5. The fifth note in that scale has a ratio of 3/2. These exact fractions only work well if you only need to play in one key, in order to produce a piano that plays equally well in all 12 keys the intervals are adjusted slightly so that no key contains perfect fractional intervals but they are all pretty close to where they should be. Thank you. 
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Great explanation.
This was actually one of the purposes of Bach's introduction of the Well-Tempered Clavier.
He was experimenting with temperaments which could reasonably utilize each key in tune. This is why he wrote a prelude and fugue in the major and minor of each.
Today's equal temperament is the modern extension of Bach's Well Temperament.
(I usually tune my 5ths with about a 2-3 beat rate per 8-10 seconds)
Earlier tunings would take common keys (C major, F Major, G major), and tune the fourths, fifths - and in some temperaments even thirds - in perfectly. While this sounded quite nice in C major, it compromised many keys. For example, in the meantone temperament, c-sharp and g-sharp beat like crazy.
(To my ear, the augmented fourth sounds even more diabolical in early tunings)
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Thank you. Really? That answered it?  I wouldn't have thought this was a "Why" at all.......it sort of just is. I think Chris' reply just explained "what," but not "why." But maybe "What" was all you meant. Or maybe I'm making too much of the difference between what and why.  I thought maybe what you were asking was, why do we hear certain frequency ratios the way we do -- and I wouldn't think that has an answer either. It just is. BTW......we had a discussion of this a few months ago, and somehow it got pretty tense..... 
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(also, those ratios are simply in their purest form... lowest divisible or whatever. In other words - C#550:A440 = 5:4. Of course, that particular frequency relationship is a purely consonate 3rd, which only occurs in meantone)
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In essence the Fifth is the 5th note on the Major and Minor scales ... the Perfect Fifth is called the Dominant ... harmonizing smoothly.
With 12 notes to the basic keyboard "octave" (not 8, folks)... what is pertinent is the fact that the so-call Perfect Fifth (G above C) ... happens to involve an interval of 7 semitones/ against the total 12 ... a proportion of 1.7 ... within a touch of THE GOLDEN SECTION(1.6).
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I wouldn't have thought this was a "Why" at all.......it sort of just is. I think Chris' reply just explained "what," but not "why." Right on. The real answer to the original question is really "because people agreed to define it that way". Specifically, we've adopted a convention, when talking about certain musical intervals, of using "perfect" as a shorthand for "involving ratios of relatively small whole numbers". That doesn't necessarily make the intervals perfect in the everyday sense of the word. If they're so darn good, let's see them make a circle of fifths that's exactly equal to a whole number of octaves!
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^^ Yes ^^ -- thanks, MathGuy. We've had questions like this before, and funnily, it seems the OP is always satisfied with replies like those ones above, even though.....well, what we said. Maybe when people ask "why," sometimes they really only mean "what."
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The monocord, supposedly invented by Pythagorus but probably known in ancient Egypte, is the ideal instrument to understand the notions of the intervals. The length of its single string allows one to concretely visualize the relationships of tones.
When a stretched string is separated into two equal portions, both parts sound at the octave of the full string. The ratio between the length of the full string and its octave is 2:1 .
When the string is separated into two portions of which the first is twice as long as the second, the longer part sounds at the fifth of the full string. The ratio between the length of the full string and that of the fifth is 3:2.
After the octave, the fifth has always been considered as the consonant interval par excellence in western music.
For this reason the fifth played an essential role in the foundation of the scales that we know today.
The perfect fifth, a fascinating subect.
Last edited by landorrano; 09/03/10 05:43 AM.
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Specifically, we've adopted a convention, when talking about certain musical intervals, of using "perfect" as a shorthand for "involving ratios of relatively small whole numbers". I disagree with the sense of the arbitrary that you give to the idea of a perfect fifth. Not all intervals are considered perfect or just, and there are solid reasons why the fifth has this title.
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Specifically, we've adopted a convention, when talking about certain musical intervals, of using "perfect" as a shorthand for "involving ratios of relatively small whole numbers". I disagree with the sense of the arbitrary that you give to the idea of a perfect fifth. Not all intervals are considered perfect or just, and there are solid reasons why the fifth has this title. You've got a point, as most sources do restrict the perfect intervals to be the unison (1:1), fourth (4:3), fifth (3:2), and octave (2:1). That's equivalent to saying the intervals involve ratios of whole numbers that are both less than 5, rather than just saying (as I did above) that they involve small whole numbers. Either way, this numeric stuff isn't very satisfying musically, but things seem to get slippery if you try to characterize that set of perfect/just intervals any other way. You often see it stated that the perfect intervals are the ones that are most consonant, but if you try to get to the bottom of what that means, it comes back once again to ratios of small whole numbers. "Most consonant" might also be taken as a synonym for "sounds the best", but I would venture to guess that most people actually think thirds and sixths sound better than open fourths and fifths. So maybe the replies that discussed what instead of why (as Mark put it) really are more interesting!
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Here's how I understand the "why" question (if we take "why" literally): Why is it that those intervals that have such "pure" sounds happen to be the intervals with such simple ratios of their frequencies?And that's the one that I don't think has an answer. It just "is" -- and it's fascinating. IMO..... if there really is an answer -- very IMO, so IMO that I better say IMO a few more times..... the answer lies in evolutionary Darwinism (or God's creationism -- whichever one prefers, it doesn't matter). Maybe some sounds in nature with those particular ratios are especially important for beings to take particular note of -- and if so, there would be an adaptive advantage to hearing those intervals in a special way. I can't think offhand of any 'sounds of nature' that would fit this, but maybe somebody else can. P.S. Whoever can, there might be a Nobel Prize in it for you.
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Great explanation.
This was actually one of the purposes of Bach's introduction of the Well-Tempered Clavier.
He was experimenting with temperaments which could reasonably utilize each key in tune. This is why he wrote a prelude and fugue in the major and minor of each.
Today's equal temperament is the modern extension of Bach's Well Temperament.
Bach didn't invent well temperament. A lot of time and various tuning developments happened between Bach's day and the universal adoption of equal temperament much later, so I think it's a bit of a stretch to say that it is the "extension" of well temperament.
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Specifically, we've adopted a convention, when talking about certain musical intervals, of using "perfect" as a shorthand for "involving ratios of relatively small whole numbers". I disagree with the sense of the arbitrary that you give to the idea of a perfect fifth. Not all intervals are considered perfect or just, and there are solid reasons why the fifth has this title. You've got a point, as most sources do restrict the perfect intervals to be the unison (1:1), fourth (4:3), fifth (3:2), and octave (2:1). That's equivalent to saying the intervals involve ratios of whole numbers that are both less than 5, rather than just saying (as I did above) that they involve small whole numbers. Either way, this numeric stuff isn't very satisfying musically, but things seem to get slippery if you try to characterize that set of perfect/just intervals any other way. You often see it stated that the perfect intervals are the ones that are most consonant, but if you try to get to the bottom of what that means, it comes back once again to ratios of small whole numbers. "Most consonant" might also be taken as a synonym for "sounds the best", but I would venture to guess that most people actually think thirds and sixths sound better than open fourths and fifths. So maybe the replies that discussed what instead of why (as Mark put it) really are more interesting! I think it has much to do with overtones (which correspond to the ratios). I am not savvy enough about it to really discuss it intelligently, but even in my ignorant state, it makes perfect sense to me that the upper note of a perfect fifth is vibrating at exactly the same speed as the second-strongest overtone from the octave-lower fundamental of the other note, and that exact physical correspondence is something we have chosen to label as "consonance". Or something like that...
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IMO..... if there really is an answer -- very IMO, so IMO that I better say IMO a few more times..... the answer lies in evolutionary Darwinism Evolutionary Darwinism? As opposed, maybe, to stationary Darwinism?
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