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| appearson=[[Geogaddi]]}} | | appearson=[[Geogaddi]]}} | ||
− | + | '''A Is To B As B Is To C''' (sometimes abreviated to '''a:b::b:c''') is track number 17 on the [[Geogaddi]] album. The track title is an example of a golden ratio which is a concept of elementary geometry in design, both human and nature. | |
== Samples/Lyrics == | == Samples/Lyrics == | ||
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*''"So, those prophecies you've been describing"'' ... ''"And now to business [matters?]..."'' (reversed; sample source unknown) | *''"So, those prophecies you've been describing"'' ... ''"And now to business [matters?]..."'' (reversed; sample source unknown) | ||
*Towards the end of the track, a distorted voice repeating ''"It must be a musical computer!"'' sampled from [https://youtu.be/lYJrM9epx-0?t=110 Make a Joyful Noise!: introducing Colby!]<ref>{{#ev:youtube|lYJrM9epx-0|480||||start=110|false}}</ref> | *Towards the end of the track, a distorted voice repeating ''"It must be a musical computer!"'' sampled from [https://youtu.be/lYJrM9epx-0?t=110 Make a Joyful Noise!: introducing Colby!]<ref>{{#ev:youtube|lYJrM9epx-0|480||||start=110|false}}</ref> | ||
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== Comments == | == Comments == | ||
* [[A Is To B As B Is To C]] often written a:b::b:c. [DC] notes that this is just a mathematical statement that the ratio of a to b is the same as the ratio of b to c: a/b = b/c. If you take a rectangle whose dimensions are in the so-called [http://mathworld.wolfram.com/GoldenRatio.phpl golden ratio], e.g. a × b, where a = 1.618... and b = 1, then remove a 1x1 square from it, the remaining rectangle has dimensions b × c, where b = 1 and c = 0.618..., and you will indeed find that "a is to b as b is to c": 1.618/1.000 = 1.000/0.618. The above are rough figures. To be precise, the golden ratio φ is 1.618033989... — in fact, it is (1+√5)/2 — and if you use these exact numbers, then the relationship is perfect: φ/1 = 1/(1-φ), exactly. See interview quotes at head of Geogaddi comments on the use of the golden ratio in art and music. The golden ratio is also the limit of the ratio of consecutive Fibonacci numbers (a series where each number is the sum of the two previous numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,...). That is, the sequence of fractions 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, ... tends towards the golden ratio φ. These numbers all crop up in many places in nature. A simple example is the number of spirals seen in the composite flower of a sunflower plant; the number of spirals in one direction will be one fibonacci number, the number in the opposite direction, a different fibonacci number. So also in the cones of conifers, phyllotaxis (arrangement of leaves on stems), and related spirals occur in shells and elsewhere. Dr Math [http://mathforum.org/library/drmath/view/52679.phpl explains]. | * [[A Is To B As B Is To C]] often written a:b::b:c. [DC] notes that this is just a mathematical statement that the ratio of a to b is the same as the ratio of b to c: a/b = b/c. If you take a rectangle whose dimensions are in the so-called [http://mathworld.wolfram.com/GoldenRatio.phpl golden ratio], e.g. a × b, where a = 1.618... and b = 1, then remove a 1x1 square from it, the remaining rectangle has dimensions b × c, where b = 1 and c = 0.618..., and you will indeed find that "a is to b as b is to c": 1.618/1.000 = 1.000/0.618. The above are rough figures. To be precise, the golden ratio φ is 1.618033989... — in fact, it is (1+√5)/2 — and if you use these exact numbers, then the relationship is perfect: φ/1 = 1/(1-φ), exactly. See interview quotes at head of Geogaddi comments on the use of the golden ratio in art and music. The golden ratio is also the limit of the ratio of consecutive Fibonacci numbers (a series where each number is the sum of the two previous numbers: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,...). That is, the sequence of fractions 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, ... tends towards the golden ratio φ. These numbers all crop up in many places in nature. A simple example is the number of spirals seen in the composite flower of a sunflower plant; the number of spirals in one direction will be one fibonacci number, the number in the opposite direction, a different fibonacci number. So also in the cones of conifers, phyllotaxis (arrangement of leaves on stems), and related spirals occur in shells and elsewhere. Dr Math [http://mathforum.org/library/drmath/view/52679.phpl explains]. | ||
* A correspondent has said that he thinks the Steve Miller song "Fly Like an Eagle" is used in this track, that the same sounds occur in the first part of the song. To add to that: in what it probably just one of those odd coincidences, that the album of the same name (from which the song is taken) ends with a track called "The Window". | * A correspondent has said that he thinks the Steve Miller song "Fly Like an Eagle" is used in this track, that the same sounds occur in the first part of the song. To add to that: in what it probably just one of those odd coincidences, that the album of the same name (from which the song is taken) ends with a track called "The Window". | ||
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+ | == Video == | ||
+ | {{#ev:youtube|Kg3fsTjEY5c}} | ||
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+ | == References == | ||
+ | <references /> | ||
== External links == | == External links == | ||
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*[http://en.wikipedia.org/wiki/Golden_ratio Wikipedia article on the golden ratio] | *[http://en.wikipedia.org/wiki/Golden_ratio Wikipedia article on the golden ratio] | ||
*[http://en.wikipedia.org/wiki/List_of_backmasked_messages Wikipedia article listing backmasked messages] | *[http://en.wikipedia.org/wiki/List_of_backmasked_messages Wikipedia article listing backmasked messages] |
A Is To B As B Is To C | |
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Running time | 1:40 |
Appears on | Geogaddi |
A Is To B As B Is To C (sometimes abreviated to a:b::b:c) is track number 17 on the Geogaddi album. The track title is an example of a golden ratio which is a concept of elementary geometry in design, both human and nature.