> On 27 May 2016, at 08:16, Michael Hendry <hendry.mich...@gmail.com> wrote:
>> Don't forget, G# and Fb are NOT the same note. > > This is where my lack of formal musical education shows me up - I’m a > self-taught amateur guitarist. F# and Gb look and sound the same on the > guitar (and on the piano), but it seems that this is because these > instruments have been constructed to sound equally bad in all keys. The Pythagorean tuning, used since Medieval times, has pure octaves P8 equal to the ratio 2, and pure fifths P5 the ratio 3/2, so for frequencies, but on plucked strings like the guitar, or stricken, as on a piano, it gets a bit stretched. Then these are iterated. So it has two generators P5 and P8, which is also what LilyPond has internally in order to make produce staff notation transpositions. Think of the white keys of a piano keyboard: the short distances, the minor second m, gets a bit narrow, to about 90 cents instead of the 100 cents the guitar usually has. The major second M, the large distances, becomes slightly wider, and so the sharp that raises with M - m, as F# is a P5 = m + 3M above B and F is 2m + 2M above the same note, which is also what the flat lowers with. Between F# and Gb is then (M - m) - (M - (M - m)) = M - 2m which is called the Pythagorean comma, around 20 cents. Change the value of P5 to get other tunings, like (extended) meantone tunings. > Other instruments are constructed and tuned so as to sound good in certain > keys and not so good in others, so it’s feasible that an orchestra could > sound better playing in sharp keys. Only the strings section provide absolute pitch references in the form of open strings tuned in Pythagorean tuning. For the other orchestral instruments, woodwinds and brasses, even though are designed as though being in E12 (12 equal temperament), one must adapt the pitches on each individual note. > Other mysteries (to me!) may also be explained in a similar way: > > Why aren’t trumpets and clarinets made a bit shorter, so that they don’t have > to have transposed parts? Clarinets come in A and Bb because limitations of the mechanics: the former is better in sharps, the latter in flats. Blatter says there so little difference in tone color a composer could not rely on it, as it varies more between performers. With the modern Boehm mechanics, it does not matter so much, as on the flutes, which can play just about anything chromatically, so it is a tradition. > Why is the G string on my guitar the one I most commonly check because > although it sounds perfectly in tune in the context of a G major chord, it > can sound out of tune in other contexts? It is a tricky to put the frets on a guitar in the right positions, as it depends on type of strings used: thinner strings will increase more in pitch when pressed. So the manufactures guess what the users might use. There are various methods to get around this: first decide what type of strings you would want use, and then adjust the guitar after that. _______________________________________________ lilypond-user mailing list lilypond-user@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-user
