1/0: Difference between revisions

1/0 is an "interval" with an undefined numeric value. As a ratio, it can be taken to refer to the distance between any [[note]] and the note with a frequency of 0 Hz (equivalent to silence), or with an infinite frequency (which does not exist).   

As a fraction, the value of 1/0 is undefined due to the fact that 0*n=0, causing all other intervals to vanish (as the resulting ratio can be simplified down to 1/0), which, if defined, causes absurdities.

For example, you could take a descending 1/0 from 440Hz to 0Hz, and then an ascending 1/0 from 0Hz to 660Hz, seemingly implying that a [[3/2|perfect fifth]] is the same as a [[unison]]. This problem is solved by declaring that 1/0 cannot be used to make any mathematical statements, leaving it mathematically undefined. However, it can be represented as a [[ratio]] between any number and 0.  

Building a scale out of 7 of [[21edo]]'s sharp fifths (of about 742.857 cents) gives a scale that can be interpreted as a [[diatonic]] scale with large steps of size 5 and small steps of size -2 (note that this means "ascending" small steps are actually descending). When attempting to make an [[Antidiatonic|antidiatonic scale]] with the same relative step sizes, it always lands on the unison (as there are 2 large steps and 5 small steps, 5*2+(-2)*5 = 0), and as such, the sizes of the steps go to infinity - the [[generator]] for this scale is, in fact, 1/0, and the scale is represented by [[0edo]].

While 1/0 cannot be physically played, it might still be possible to imply it in a piece of music.