Removed floating we in temperament post
Getty Ritter
7 years ago
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| 145 | 145 | As an interesting aside: the existence of Pythagorean comma is also the reason for one of the odd vestigial features of musical notation: namely, the existence of \em{enharmonically equivalent notes}. When learning modern music notation, you quickly learn that there are some odd redundancies in staff notation, including the fact that some notes can be expressed more than one way: for example, A♭ and G♯ are two ways of writing the same note. That's true with modern tunings and notation, but one reason for having both notations is that they \em{did} used to connote different notes in tunings like the Pythagorean tuning: if we use A♭ as our root note, then we'd write our close-to-the-root-but-not-quite note as G♯, and the two would differ from each other by the Pythagorean comma. This distinction is no longer made, but we're still stuck with the notation. |
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Back to the scale we're generating, where we have have to decide what to do with the not-quite-the-root note: we could include our it in the scale we're creating, and maybe even continue generating new frequencies from our \tt{3:2} generator. This would build a scale that includes more and more notes, but in addition to requiring some a physically unwieldy keyboards, our scales are already getting diminishing returns from including these new notes: our goal was to choose a set of notes that sounded good together. Already, we've confused would-be composers to including two very-nearly-the-same notes when all the other notes are nicely distinct, and that new root isn't going to sound nearly as nice when played with some of the notes we generated earlier. Anyway, since |
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| 147 | Back to the scale we're generating, where we have have to decide what to do with the not-quite-the-root note: we could include our it in the scale we're creating, and maybe even continue generating new frequencies from our \tt{3:2} generator. This would build a scale that includes more and more notes, but in addition to requiring some a physically unwieldy keyboards, our scales are already getting diminishing returns from including these new notes: our goal was to choose a set of notes that sounded good together. Already, we've confused would-be composers to including two very-nearly-the-same notes when all the other notes are nicely distinct, and that new root isn't going to sound nearly as nice when played with some of the notes we generated earlier. Anyway, since our new note is \em{almost} just the original root note, we could just leave it off, stop the scale with only twelve notes. Sure, that means that one of our intervals is gonna be a \em{teeny} bit less consonant than the others, but most of them sound great, right? | |
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| 149 | 149 | As it turns out, that's exactly what Western music did for about two thousand years. |
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