We found almost ad nauseam information related to the golden ratio in general and her relationship to music in particular, and we found almost ad nauseam that this information is present almost ad nauseam the idea that this proportion is almost ad nauseam in nature primarily for reasons of efficiency and utility, is efficient and useful to have as this share tree branches to the sun from reaching many of their leaves is efficient and useful to take the form of snail snail and thus meets the proportion, is efficient and useful for the sea star being a star with these proportions ... Arguably, moreover, that our senses are educated , to perceive all that nature that we part, knowing how good that which responds to the golden ratio, as it is good be naturally be efficient because it means increasing the chances of survival, which is good . Well.
Almost ad nauseum in general
"If I divide a line into two how many items we have?
-Dos.
"No, three.
- Why?
"Because I get part A, part B and all ...
- Aaaah!
- and how to relate, from the point of view of the proportions between the elements, A, B and everything?
-Eeeeh ...
- Yes, Φ !
- Φ ?
- Yes, Φ , Phi!
-Fi
"Yes, Phi, the Greek letter represents an irrational number that is obtained as:
-Dos.
"No, three.
- Why?
"Because I get part A, part B and all ...
- Aaaah!
- and how to relate, from the point of view of the proportions between the elements, A, B and everything?
-Eeeeh ...
- Yes, Φ !
- Φ ?
- Yes, Φ , Phi!
-Fi
"Yes, Phi, the Greek letter represents an irrational number that is obtained as:
- What for?"
Not at all, Φ is absolutely inefficient and useless, but at first it seems quite the opposite. Represents the ratio of the proportion golden ng, which is neither more nor less than to relate how the three elements that we were talking about: the segment we call A, the other segment B and all the line.
- Could you tell me more please?
"Sure, I can give you information about ad nauseam. We give you an example: if the line was divided into two parts so that part A and part B measure exactly the same, there will be a relationship between those parties of equal that could be expressed as 1:1, but none of these parties maintained the same relationship to the whole, since he is the double of each, and this proportion is expressed as 2:1, then on the one hand we have a 1:1 ratio and the other a 2:1 ratio and fail to establish a unique relationship between the three elements: A, B and everything. In contrast, the proportion ng golden is one that divides everything into two unequal parts , and that the largest and the smallest part maintain a ratio that is exactly the same that keep the whole with the larger part. This provides linking the three elements: A, B and everything.
- Aaaah!
- Φ , as I said, is a ratio that arises from the division between the two parts together or at all with the largest share. In other words, if we divide the values \u200b\u200bof two related parties and the ratio will result Φ, such parties will be in proportion ng golden.
- Ooooh!
"As this ratio is in many living beings in nature and many natural beings attach it to a creation of God, that proportion took the name it has: proportion ng golden or divine proportion ng.
- uuuuh!
"That is why many artists took this kind of mathematical rule to build according to her works. Painters, architects, sculptors and musicians for centuries were paying attention to the irrational Φ . Φ, that useless, if something useful is that if we multiply the value of all the decimal part of Φ ie 0.618033989 ... get the golden point by which to divide the whole into two parts divinely, of course provided. Am I?
-Y ...
Not at all, Φ is absolutely inefficient and useless, but at first it seems quite the opposite. Represents the ratio of the proportion golden ng, which is neither more nor less than to relate how the three elements that we were talking about: the segment we call A, the other segment B and all the line.
- Could you tell me more please?
"Sure, I can give you information about ad nauseam. We give you an example: if the line was divided into two parts so that part A and part B measure exactly the same, there will be a relationship between those parties of equal that could be expressed as 1:1, but none of these parties maintained the same relationship to the whole, since he is the double of each, and this proportion is expressed as 2:1, then on the one hand we have a 1:1 ratio and the other a 2:1 ratio and fail to establish a unique relationship between the three elements: A, B and everything. In contrast, the proportion ng golden is one that divides everything into two unequal parts , and that the largest and the smallest part maintain a ratio that is exactly the same that keep the whole with the larger part. This provides linking the three elements: A, B and everything.
- Aaaah!
- Φ , as I said, is a ratio that arises from the division between the two parts together or at all with the largest share. In other words, if we divide the values \u200b\u200bof two related parties and the ratio will result Φ, such parties will be in proportion ng golden.
- Ooooh!
"As this ratio is in many living beings in nature and many natural beings attach it to a creation of God, that proportion took the name it has: proportion ng golden or divine proportion ng.
- uuuuh!
"That is why many artists took this kind of mathematical rule to build according to her works. Painters, architects, sculptors and musicians for centuries were paying attention to the irrational Φ . Φ, that useless, if something useful is that if we multiply the value of all the decimal part of Φ ie 0.618033989 ... get the golden point by which to divide the whole into two parts divinely, of course provided. Am I?
-Y ...
Almost ad nauseum
particularly tonal system, and most of the organizational Heights sounds, bases its existence on an axiom: the octave interval is the cycle for the human ear. In turn, this system divides the interval into twelve equal semitones. To divide the octave into golden ratio within the tonal system can apply the formula as follows:
Since there is 7.4 semitones in the system say that the golden point of the eighth is in the 7 semitones (perfect fifth), so it is possible to divide it in two ways:
The eighth divided into golden ratio.
If while looking for the golden ratio of the fifth (7 semitones) we get the major third (4 semitones):
perfect fifth interval.
We got to get through dividing the octave and the fifth golden ratio, the two configurations simultaneous sound foundation of harmony tonal system: major and minor chords.
As in a line have two golden points (dividing it into major-minor and minor-major) in the eighth, musical line, too:
The two golden points in the eighth.
Vista and the eighth and makes us tetrachords think of the ancient Greeks and how to construct these scales, with symmetry as a primary parameter. If both produce a golden level between C5-sol4 and forth between FA4-C4 (4 * 0 , 618 033 989 = 3 , 090169944), looking for symmetry between the two quarters disjoint contained in the eighth, we arrived, surprise surprise, a pentatonic scale:
Pentatonic scale, symmetrical and golden.
a melody built on this scale, seeking to locate in its most important moments (beginning and end of sentence) notes providing the eighth in a golden, will be making a formal organization associated with this equation:
Melody symmetrical pentatonic scale based in Golden.
note that in the first sentence, marked in the example with a bracket, is the equivalent of 16 eighth notes in duration. "We provide?
So the equivalent of 6 and 10 eighth notes correspond to the minor parties over 16, just the duration of the first and second hemifrases, marked in the example with ligatures. The second sentence is the replica of the first, a more serious tetrachord. Aspects
harmonic, melodic, rhythmic and formal dancing around the golden ratio in the tonal system (and elsewhere). Who use this system if you have never even heard of the golden ratio, will be using it. Almost
tired of tonality in particular and nature in general
"Tell me, you being a musician, Why do they always say Mozart, Bach, Beethoven, Debussy, Bartok and others used in his music the golden ratio? "Because
used. All of them used the tonal system (in the case of Bartók is a key extended in many ways but no longer in the key base more traditional), and the tonal system appears to be built on the golden ratio.
"Excuse me for interrupting, but one word in his speech that makes me a bit of noise: appears. Does not tonal system is perhaps built on the golden ratio?
"Good point. I can only confirm their suspicions. The tonal system divides the octave into 12 equal semitones cultural after a long walk was through various tuning systems and many types of temperaments, all proceeds of the compositional needs of each era and none of them responding to nature. In equal temperament, except the eighth, nothing is according to the nature of sound, nothing is, shall we say, refined. So take as unit of measurement of the eighth as the tempered semitone is already taking a unit of non-natural, arising cultural practices of centuries, so the golden ratio of the eighth deduced from these semitones is the golden ratio of the eighth, but the golden ratio of the tonal system.
"I understand, I think ...
-Rinse the shade does not represent the nature, say something else interested me.
"You say. "That
believe that the golden ratio holds all of nature is at least innocent, to believe that the golden ratio is the only way of nature is not to realize that nature has an overwhelming number of possibilities, and some is manifest, others are lost and others are latent. I think it is more appropriate to speak of natures, and in the plural, rather than the nature.
"I know where it goes.
- Where do you think I?
-Towards a cry for help.
- Yeah, dude, did you right! Death to the golden ratio! I want to see and hear other natures! I do not resign ourselves to seeing only one possibility! I want other colors, I want another pitch! ... Perhaps, after all, not so much the death wish of the golden ratio. What do you think?
-Y ...
used. All of them used the tonal system (in the case of Bartók is a key extended in many ways but no longer in the key base more traditional), and the tonal system appears to be built on the golden ratio.
"Excuse me for interrupting, but one word in his speech that makes me a bit of noise: appears. Does not tonal system is perhaps built on the golden ratio?
"Good point. I can only confirm their suspicions. The tonal system divides the octave into 12 equal semitones cultural after a long walk was through various tuning systems and many types of temperaments, all proceeds of the compositional needs of each era and none of them responding to nature. In equal temperament, except the eighth, nothing is according to the nature of sound, nothing is, shall we say, refined. So take as unit of measurement of the eighth as the tempered semitone is already taking a unit of non-natural, arising cultural practices of centuries, so the golden ratio of the eighth deduced from these semitones is the golden ratio of the eighth, but the golden ratio of the tonal system.
"I understand, I think ...
-Rinse the shade does not represent the nature, say something else interested me.
"You say. "That
believe that the golden ratio holds all of nature is at least innocent, to believe that the golden ratio is the only way of nature is not to realize that nature has an overwhelming number of possibilities, and some is manifest, others are lost and others are latent. I think it is more appropriate to speak of natures, and in the plural, rather than the nature.
"I know where it goes.
- Where do you think I?
-Towards a cry for help.
- Yeah, dude, did you right! Death to the golden ratio! I want to see and hear other natures! I do not resign ourselves to seeing only one possibility! I want other colors, I want another pitch! ... Perhaps, after all, not so much the death wish of the golden ratio. What do you think?
-Y ...
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