User:Akselai/FM scale: Difference between revisions
Created page with "A '''frequency-modulated scale (FM scale)''' is a scale with steps generated by a frequency modulation function. Such a scale is usually aperiodic, but is periodic under some..." |
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An '''FM scale of the second kind''' is a function from the ''real numbers'' to musical intervals. Since these are usually continuous functions, it is meaningless to talk about scale steps of an FM scale. The x-th "scale step" in such a scale is called the x-th '''spec''' (pl. '''specs'''), which comes from the phrase "tone spectrum". | An '''FM scale of the second kind''' is a function from the ''real numbers'' to musical intervals. Since these are usually continuous functions, it is meaningless to talk about scale steps of an FM scale. The x-th "scale step" in such a scale is called the x-th '''spec''' (pl. '''specs'''), which comes from the phrase "tone spectrum". | ||
It is defined as the integral of the FM function: | It is defined as the integral of the FM function: | ||
<math>\text{FM}(i) = \displaystyle \int_0^t f( | <math>\text{FM}(i) = \displaystyle \int_0^t f(x) dx</math> | ||
Unlike a usual scale, which is mathematically a function from the ''integers'' to musical intervals, here we have a scale with continuous scale degrees. So, we cannot put such a scale into Scala or a usual DAW retuning plugin; however, audio synthesis software such as Csound and SuperCollider provide good environments for continuous scales. | Unlike a usual scale, which is mathematically a function from the ''integers'' to musical intervals, here we have a scale with continuous scale degrees. So, we cannot put such a scale into Scala or a usual DAW retuning plugin; however, audio synthesis software such as Csound and SuperCollider provide good environments for continuous scales. | ||