In the previous post I've used the word "pitch" to refer to the frequency of a musical note, to make it clear that I was not referring to the voice of the instrument, which is more commonly recognized as being the province of harmonics.
Henceforth, I may revert to using "tone", or use them interchangeably.
Friday, December 29, 2006
musing about the problem space
It's not as though scales composed of harmonics are really all that unfamiliar.
Woodwind instruments naturally produce pitches that are harmonics (integer multiples) of some fundamental frequency, determined by the size and shape of the instrument's resonant cavity. Brass instruments also produce harmonics, and those with either valves or slides are capable of altering the fundamental frequency by modifying the resonant cavity, making available pitches which fall between those which would otherwise be possible. Generally speaking, the notes either can produce are mapped onto the equal tempered scale, although it's quite a stretch in some cases.
Non-fretted strings can produce any pitch whatsoever within their ranges. Orchestras, dominated by woodwinds and strings, may gravitate towards scales that could be accurately described in terms of harmonics, although the scores they work from are based on the equal tempered scale. Those scores may include pitch bending cues to encourage this, even if the harmonic nature of the tonal target is obfuscated to the point of being conceptually absent.
Pianos and most modern fretted instruments, guitars included, are designed to support the equal tempered scale, but many electronic keyboards can be programmed for a wide variety of scales, mapping their keys to pitches that are a little higher or lower than they represent in the equal tempered scale.
The twin problems have always been building instruments offerring a wide enough selection of discrete pitches to support a wide variety of scales without tempering, and creating a notation that represents harmonic relationships in music compactly and in a manner that can be read quickly enough for performance.
The historical upshot of the first of these was that a musician with a repertoire spanning many scales would have to carry many instruments. The latter meant that no such notational system ever became commonplace, so it wasn't really possible to write down the music; it could only be preserved by passing along the knowledge of playing it.
Programmable devices (keyboards...) are solving the former, and opening the way to address the latter. We can easily record sound these days, of course, but that's not the same thing. Say you had available a performance instrument (or interface to a synthesizer) capable of a wide range of pitches in any given configuration and of being reconfigured on the fly, how could a composition best be represented to enable you to play while reading along.
While some variation on standard musical notation, read left to right with higher notes appearing higher on the staff, might be made to work, I think the same technology which is delinking sound production from physical constraints may also provide some interesting possibilities for the presentation of music as a performable abstraction. I have some ideas along these lines, but nothing yet so well developed that it doesn't seem better to leave it to your imagination.
Given a system which represents pitches as integer multiples of the frequency of some fundamental, or in all but the simplest cases, as integer ratio (e.g. 4/3 or 5/4) multiples of the frequency of some reference pitch, what sort of notation would encapsulate such relationships among the simultaneous/sequential notes that comprise a musical piece such that someone familiar with the notation could follow along quickly enough to reproduce the piece while reading?
Woodwind instruments naturally produce pitches that are harmonics (integer multiples) of some fundamental frequency, determined by the size and shape of the instrument's resonant cavity. Brass instruments also produce harmonics, and those with either valves or slides are capable of altering the fundamental frequency by modifying the resonant cavity, making available pitches which fall between those which would otherwise be possible. Generally speaking, the notes either can produce are mapped onto the equal tempered scale, although it's quite a stretch in some cases.
Non-fretted strings can produce any pitch whatsoever within their ranges. Orchestras, dominated by woodwinds and strings, may gravitate towards scales that could be accurately described in terms of harmonics, although the scores they work from are based on the equal tempered scale. Those scores may include pitch bending cues to encourage this, even if the harmonic nature of the tonal target is obfuscated to the point of being conceptually absent.
Pianos and most modern fretted instruments, guitars included, are designed to support the equal tempered scale, but many electronic keyboards can be programmed for a wide variety of scales, mapping their keys to pitches that are a little higher or lower than they represent in the equal tempered scale.
The twin problems have always been building instruments offerring a wide enough selection of discrete pitches to support a wide variety of scales without tempering, and creating a notation that represents harmonic relationships in music compactly and in a manner that can be read quickly enough for performance.
The historical upshot of the first of these was that a musician with a repertoire spanning many scales would have to carry many instruments. The latter meant that no such notational system ever became commonplace, so it wasn't really possible to write down the music; it could only be preserved by passing along the knowledge of playing it.
Programmable devices (keyboards...) are solving the former, and opening the way to address the latter. We can easily record sound these days, of course, but that's not the same thing. Say you had available a performance instrument (or interface to a synthesizer) capable of a wide range of pitches in any given configuration and of being reconfigured on the fly, how could a composition best be represented to enable you to play while reading along.
While some variation on standard musical notation, read left to right with higher notes appearing higher on the staff, might be made to work, I think the same technology which is delinking sound production from physical constraints may also provide some interesting possibilities for the presentation of music as a performable abstraction. I have some ideas along these lines, but nothing yet so well developed that it doesn't seem better to leave it to your imagination.
Given a system which represents pitches as integer multiples of the frequency of some fundamental, or in all but the simplest cases, as integer ratio (e.g. 4/3 or 5/4) multiples of the frequency of some reference pitch, what sort of notation would encapsulate such relationships among the simultaneous/sequential notes that comprise a musical piece such that someone familiar with the notation could follow along quickly enough to reproduce the piece while reading?
Saturday, December 02, 2006
back burner != forgotten
Rumor has it that Apple has a tablet computer with a touch sensistive screen in the works. This is very interesting to me because it could simplify creating user interfaces in software for virtual instruments which present their tonal options in terms of harmonics, rather than force-fit to the equal-tempered scale. It might even be possible to create a usable performance instrument within the constraits of such a device, without having to migrate it to a larger display or custom-built gadget. I certainly intend to try.
Meanwhile, you can learn more about harmonic-based music at the wesite of The Just Intonation Network.
Meanwhile, you can learn more about harmonic-based music at the wesite of The Just Intonation Network.
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