Conductor's Knowledge, pt. 2: String Harmonics, Counterpoint basics

being a string player i didn't think that i would really need to brush up on these, but when they showed up on the test i was embarrassingly unsure of everything and ended up not really writing any harmonics. here is a brief tutorial on their notation and sounding pitches.

natural harmonics: the ones you can get by placing only one finger on the string. these have basically the most confusing notation ever, but here is the clearest way of laying it out.
you can think of the natural harmonic in two ways in terms of finger placement: you are either dividing the string into one of several simple ratios which produce the natural harmonic, or you are putting your finger lightly upon a place which would produce a different pitch if you held it down firmly. most string musicians tend to just think of it in this latter way, which is why we get so confused when we don't see a clear notation. when we think of it like this, it's difficult to remember whether what we're seeing is the finger configuration or the actual sounding pitch.

the clearest notation i have found so far is to put a solid notehead on the *open string* that one is using, and a harmonic diamond notehead on the *place on the string* that one would put the finger. if one wants to be super clear, they can put the sounding pitch in parentheses above that.

here's a pretty good diagram of the g string on the violin, using this notation.

an alternative would be to not include the g string real notehead, but instead to label the string above the staff; for example "sul G."
for a more tabulated form of the same information in the picture:
string division (finger at the _____) - sounding pitch above open string/fundamental
1/2 (finger at octave) - octave above
1/3 (finger at fifth OR octave + fifth) - octave + fifth above
1/4 (finger at fourth OR two octaves) - two octaves above
1/5 (finger at major third OR two octaves + major third) - two octaves + major third

artificial harmonics are made by stopping the string with one finger (acts as if the string were shortened) and usually use the 1/3 or 1/4th string division (i.e. placing the harmonic finger either a fifth or fourth above the stopped note. the 1/5th division (placing the finger a major third above the note) is also possible, but doesn't get used so much in violin playing because it's so fuzzy. the 1/2 division is not really possible on any instrument unless you shorten the string so much you can reach halfway across it. the noise that comes with this usually makes it a pretty bad idea.
so we can obtain generally, with stopped harmonics, pitches that are either an octave + fifth or two octaves above the fundamental (the stopped pitch). these are easier to notate; the same as above, with a solid note on the fundamental/stopped pitch, and the open diamond head on the touched place.

i was going to do counterpoint but i really can't remember most of the rules so far. i just sort of guess. my feeling is that there are way too many rules for me to learn in one week's time, so for basics:
a "cantus firmus" is a given melodic phrase that is to be "given contrapuntal treatment" in the form of counterpoint. counterpoint is any other part other than the cantus firmus.
intervals (both melodic, between two notes of the same voice, and harmonic, between two notes at the same time in different voices) are classed as follows:
   perfect consonance: unison, fifth, octave
   imperfect consonance: third, sixths
   dissonances: second, fourth, seventh
generally all of these in all forms (major/minor, dimished/augmented) are allowed for melodic progression except the major/minor seventh. all of them are allowed as harmonic intervals within about a billion guidelines.
there are five species, and the number generally refers to how many notes the counterpoint has per note of the cantus firmus.
   first species: one note per cantus firmus note
   second species: two notes per
   third species: four notes per (three notes per, for example when the cantus is given in a 3/2 bar and there are three half notes in the counterpoint per cantus note, is a category of second-species)
   fourth species: two notes syncopated (perhaps think of as one note, offset by half the value of the cantus firmus)
   fifth species: any combination thereof
there is also a type where there is no cantus firmus and instead two equally moving lines. since the cantus firmus is almost always given in whole notes, it'll be fairly obvious when this is the case (and not just a first species counterpoint). this is known as second species in both parts.

general voice leading rules apply, but usually they are taken to the extreme - for example it's usually forbidden to cross voices, and there shouldn't ever be too many steps or skips in a row (the safest way to write is whenever there is a skip, leave it by step in the opposite direction. avoid tritones; avoid perfect intervals except in the beginning and last bars, open and end with perfect intervals.
too many to learn in a week, so i'll just leave it at this and do the rest by guessing... i'll have to take a real counterpoint class at some point.