tag:blogger.com,1999:blog-5748784285539605706.post4436433539423808396..comments2024-03-08T08:38:53.587-05:00Comments on Software Reflections: The Math of Music (Part 1)David Buckhttp://www.blogger.com/profile/14309364915707457568noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-5748784285539605706.post-23560659205647837182013-07-30T20:12:18.802-04:002013-07-30T20:12:18.802-04:00The half steps you are used to are a result of the...The half steps you are used to are a result of the equal tempered scale. From a musical point of view, they produce music that's slightly out of tune. The equal tempered scale is a compromise that allows you to play songs in any key and they all sound relatively good.<br /><br />The groups of two and three black keys aren't just a convenience. They derive from the math behind the equal tempered scale. When you crunch the numbers, it naturally breaks the keyboard into 12 semitones with groups of 2 and 3 sharp/flat notes. It's not just a coincidence or a convention. It's dictated by the math.<br />Davidhttps://www.blogger.com/profile/07044995997965805073noreply@blogger.comtag:blogger.com,1999:blog-5748784285539605706.post-55546638317426770062013-07-22T08:58:21.902-04:002013-07-22T08:58:21.902-04:00> I was never able to understand, however, why ...> I was never able to understand, however, why the<br />> piano keys are the way they are.<br />> Why is there no E# or Fb note? Why no B# or Cb?<br />> Why is the same key sometimes called F# and <br />> sometimes called Gb?<br /><br />Because there is nothing special about the black keys on a piano. They are all half steps, same as the white keys. The keys were laid out this way for a couple of reasons, all related to stupid humans. One, if all the keys were white, it would be impossible to tell which key is which. If each pair of white keys had a black key between them, it would be equally impossible. So the twelve keys per octave are split up into seven white keys and five black keys, and the black keys are arranged in two groups, a group of two and a group of three. The identity of each white key can then be ascertained by its relationship to the black keys. The white key to the left of two black keys is a C. The white key to the left of three black keys is an F. The white key to the right of three black keys is a B. Etc through the entire keyboard. The other reason they are laid out this way is to enable humans to play octaves. If you want to play a C4 and a C5 with one hand, it would be impossible without black keys; with 12 white keys, the hand would not be large enough to reach.<br />Anonymoushttps://www.blogger.com/profile/01846767035521562730noreply@blogger.com