Someone nominated me for Junior Council President. Granted, I'm abroad all of next year, so I can't do it, but it's still flattering. And surprising. Oh, well
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Happy hexachordsldmoonflowerApril 18 2005, 00:33:14 UTC
Thanks!
As for the theory, you asked for it, so here:
You probably remember that there were different modes (eight of them: Dorian, Hypodorian, Phrygian, Hypophrygian, Lydian, Hypolydian, Mixolydian, Hypomixolydian) used in the composition of Gregorian chants. That was all good and well for composers to know, but not terribly important to singers. A guy named Guido D'Arezzo is credited with inventing what is called hexachordal theory, which involves solmization (what we call solfege in post-Renaissance theory). As you may have noticed when singing in chorus, singers tend not to think about the specific notes when they're singing; instead, they know how the notes are supposed to be related to each other in the scale. That's why you can sing, say, "Happy Birthday" in C just as easily as you can in G as long as someone gives you a note to start on. So what happens in hexachordal theory is that there are three hexachordal modes: natural, hard, and soft. Natural runs from C to A, ut re mi fa sol la. I don't know why "ut" (pronounced "oot") is now "do" in modern parlance, but there you are. Soft and hard modes exist because the problem posed by B. B is a problem because F-natural to B-natural creates a tritone (augmented 4th/diminished 5th). The tritone was known as the "diabolus in musica" back in the Middle Ages because of the dissonance it created. The diabolus in musica must be avoided at all costs. To avoid the diabolus in musica, you would flat the top note of the interval, namely B, in this case. So in Medieval music, you could have either a "hard B" (B-natural) or a "soft B" (B-flat), depending on whether there is a risk of diabolus in musica. Hard mode runs from G to E, and soft mode runs from F to D with the B flatted. As you know, a mode/scale has seven notes and not just six, so if you tried to sing up a mode on one hexachordal mode, you'd go "ut re mi fa sol la" and get stuck on what we would now call "ti," which didn't exist then. So to continue up the mode, you need to mutate from one hexachordal mode to the other so you can finish your mode. Take Dorian mode, for example. That has the whole/half-step patterns you would get if you only used natural notes starting on D: D E F G A B C D (whole step, half, whole, whole, whole, half, whole). You can start in natural mode and names the notes as follows: D---E---F---G---A---B---C---D re--mi--fa--sol--la
Uh oh, we've hit B. It's a B natural, so that makes it a hard B, so we'll mutate to hard mode. ****** D---E---F---G---A---B---C---D Natural: re--mi--fa---sol/ *********** Hard: ut---re--mi--fa--sol
As for the theory, you asked for it, so here:
You probably remember that there were different modes (eight of them: Dorian, Hypodorian, Phrygian, Hypophrygian, Lydian, Hypolydian, Mixolydian, Hypomixolydian) used in the composition of Gregorian chants. That was all good and well for composers to know, but not terribly important to singers. A guy named Guido D'Arezzo is credited with inventing what is called hexachordal theory, which involves solmization (what we call solfege in post-Renaissance theory). As you may have noticed when singing in chorus, singers tend not to think about the specific notes when they're singing; instead, they know how the notes are supposed to be related to each other in the scale. That's why you can sing, say, "Happy Birthday" in C just as easily as you can in G as long as someone gives you a note to start on.
So what happens in hexachordal theory is that there are three hexachordal modes: natural, hard, and soft. Natural runs from C to A, ut re mi fa sol la. I don't know why "ut" (pronounced "oot") is now "do" in modern parlance, but there you are.
Soft and hard modes exist because the problem posed by B. B is a problem because F-natural to B-natural creates a tritone (augmented 4th/diminished 5th). The tritone was known as the "diabolus in musica" back in the Middle Ages because of the dissonance it created. The diabolus in musica must be avoided at all costs. To avoid the diabolus in musica, you would flat the top note of the interval, namely B, in this case. So in Medieval music, you could have either a "hard B" (B-natural) or a "soft B" (B-flat), depending on whether there is a risk of diabolus in musica. Hard mode runs from G to E, and soft mode runs from F to D with the B flatted.
As you know, a mode/scale has seven notes and not just six, so if you tried to sing up a mode on one hexachordal mode, you'd go "ut re mi fa sol la" and get stuck on what we would now call "ti," which didn't exist then. So to continue up the mode, you need to mutate from one hexachordal mode to the other so you can finish your mode.
Take Dorian mode, for example. That has the whole/half-step patterns you would get if you only used natural notes starting on D: D E F G A B C D (whole step, half, whole, whole, whole, half, whole). You can start in natural mode and names the notes as follows:
D---E---F---G---A---B---C---D
re--mi--fa--sol--la
Uh oh, we've hit B. It's a B natural, so that makes it a hard B, so we'll mutate to hard mode.
****** D---E---F---G---A---B---C---D
Natural: re--mi--fa---sol/
*********** Hard: ut---re--mi--fa--sol
And we're finished! Hooray!
And that's how you mutate hexachordal modes.
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