Mi against Fa - Hexachords

[SeanKBrennan]

Hello there,

I've recently been reading Joseph Fux's Gradus Ad Parnassum and have some encountered some confusion with modes and hexachords in first species counterpoint. The cantus firmus supplied is in E Phygian (no sharps or flats, beginning and ending on E). In the example given (which can be found below), a B against G is marked incorrect for the following reason:

mi against fa
is the devil of musica

This mi against fa you have written in the progression from the sixth to seventh bar by a skip of an augmented fourth or tritone which is hard to sing and sounds bad, for which reason it is forbidden in strict counterpoint.

When I look at the hexachords I see that G is sol, re, ut and B is mi. I don't understand how this is mi against fa, could anyone further explain this?

Thanks.

[Gamma-UT]

The problem is not the two notes together but the way that the counterpoint line moves from F to B: that's what Aloysius has marked. I had a similar problem with that bit the first time I saw it.

[SeanKBrennan]

I was aware that having two notes together that make a tritone is incorrect, but does the same go from moving from one not to another? Thank you very much for your help.

[Gamma-UT]

In the context of this style of counterpoint, yes it does. It's mostly to do with the way the hexachords were used in singing in Palestrina's time. By Fux's time, I think this idea was well on its way out. But when Palestrina was writing, the hexachord system was how singers ordered their singing.

In the case of F and B, the 'mi' and 'fa' come from different hexachords and singers could only switch from one to the other easily at certain points. In the soft hexachord, the only one that contains both F and B, the B is flat because F is ut and B is fa (it's also why it's called the soft hexachord).

[SeanKBrennan]

I still don't understand why you can't use mi from one hexachord fa from a different one. Isn't it like saying "In the key of C, D is the third of Bb major therefore you can't use it within certain contexts"? Or am I wrong to be thinking of these hexachords in a tonal center type of context?

I suppose what I'm trying to say is that am I true in saying you can't move from A to C because A is mi in the soft hexachord and C is fa in the hard hexachord?

[Gamma-UT]

I still don't understand why you can't use mi from one hexachord fa from a different one. Isn't it like saying "In the key of C, D is the third of Bb major therefore you can't use it within certain contexts"? Or am I wrong to be thinking of these hexachords in a tonal center type of context?

Hexachords were primarily a practical tool for singing kind of grafted onto a medieval theory. We can use in effect any note from any hexachord, partly because we have equal temperament but also because we use a slightly different type of solmisation that covers a full octave. Palestrina and, to some extent, Fux predate tonal centres. From a historical point of view, you can look up Gradus as Fux's way of stopping the rise of new-fangled tonal music.

For the moment though I wouldn't worry about it other than to avoid hidden tritones when doing that style of counterpoint.

[SeanKBrennan]

Thank you for the clarification, it is much appreciated.

[Ogg Vorbis]

Berstein ignored this rule in "Westside Story" when he wrote "Maria." The first two notes of the melody is "mi against fa."

He was hit by a train 2 days later.

[psenior]

I am very pleased to see a discussion on the ancient rules for composing modal music. I am aware that these rules existed but never knew the little details as described above.

[SeanKBrennan]

I am very pleased to see a discussion on the ancient rules for composing modal music. I am aware that these rules existed but never knew the little details as described above.

The Alfred Mann translation of Gradus ad Parnassum is the book for you then! =]

[psenior]

Thanks for the info. I will definitely check out this book in the near future!