Pitch Axis Theory

Explained well here:
http://en.wikipedia.org/wiki/Pitch_Axis_Theory

Yes and yes. Which one would you like:

a) real pitch axis theory - a compoistional tool developed by Bela Bartok in the early 1900s as part of his explorations of musical symmetry... or

b) Satriani's, which has little to do with actual pitch axis, and even less to do with music theory?

That Wikipedia entry is actually pretty awful.

You might start with this thread

What do you call what Satriani and many others do, using different scales with the same bass or root note? It seems to be very different from what you describe. Parallel modes? Meandering aimlessly?

That makes good sense. I just reread Noteboat's other post as well (lots there; took a while to sink in.) Interesting that what Satriani calls pitch axis is not quite the same thing. "Parallel scales" seems fairly simple, conceptually. Applying it to make interesting music is another story, of course.

Hi NoteBoat. Can you recommend any piece of music that demonstrates the use of pitch axis? Was Bartok the only major composer to use it or did it continue to find favour among later composers? (leaving Joe aside for the moment :D )
The serial composers employed melodic symmetry too. Is it the same principle?

My problem with it is that, although it 'looks' clever, I'm not sure how well that symmetry can be appreciated when heard in music. I'm not questoning the undoubted importance of symmetry in music in general (balanced phrases, tonality, form, etc.) - just wondering if that kind of melodic symmetry seems a bit contrived.

What's your opinion on its use in actual music?

That thread about pitch axis is really interesting, I kind of thought of that idea myself a few days ago.

You guys might find this interesting. What I did was make a scale by taking the tonic (I guess you call it keynote in this context) and then went up a half step, then a whole step, then 3 half steps etc. to make a 6 note run that always moves by one more halfstep than the previous interval, you end up with some locrian licks that dare I say sound good.

But I thought of using pitch axis (though I wasn't calling it that) to move the same way the other direction for variety, ill definetly experiment with it some more...I had almost forgotten about it.

I don't really need a big explantion for this, but the idea with tone rows is to use all 12 tones before repeating any tone that you have already played correct?

Fretsource, I think of pitch axis as just another compositional technique. Like any other technique - tone rows, etc - the value is in generating ideas that are related to the motif in some way. But also like any other technique, the results have to be examined for practicality; pitch axis is intellectually intriguing, but that doesn't mean the results are automatically aesthetically good.

Bartok was the originator, and was obsessed with musical symmetry. But many other 20th composers used the same concept at times: Berg, Stravinsky, Webern, Crumb, and Tenney that I know of. Some analysts point to segments of Debussey - or even Bach - as evidence of the technique... I kinda doubt it.

The problem with looking at a piece after the fact and saying "Aha - Pitch Axis at work!" is that it's a lot like literary analysis. I remember sitting through classes where teachers went on and on about a particular book saying "this symbolizes the working class, that symbolizes the rise of capitalism, and this character over here stands for the emerging banking cartel of the early 19th century.." I often thought the symbolism was only in the minds of the literature professors; the writers cared about story, plot, character, and scene. If they'd spent their time thinking about symbolism and jamming the literary elements into that mold, the stories wouldn't have been nearly as good.

As an analytical tool, in my view, pitch axis is a dead end. It's been supplanted by set theory... (warning to others: theory geekery ahead)

Conceptually, Bartok's compositional technique can be thought of as a matrix. If the tones involved in a melody are C-Db-E-F#, you have:

C Db E F#
Db E F# C
E F# C Db
F# C Db E

This gives you the available axes (left column) and the intervallic relationship of the pitch axis to the other pitches in the melody (across each line). With that as a starting point, you can perform the standard serial technique of inversion to generate the pitches of each axis.

Now you've got what the transformed tones are - if you started with row 3, you have E, down a major 2nd to D, down a diminished fifth to G#, down a minor 2nd to Fx. Rearrange the tones to put E back in third place, and you have the transformation on pitch axis: G#-Fx-E-D.

The hot topic in today's theory world is set theory. If you let C=0, the original set is 0-1-4-6; the transformation would be 9-8-5-3. Calculate the interval vector of each: each has one semitone (0-1, 8-9), one whole tone (4-6, 3-5), one minor third (1-4, 5-8 ), one major third (0-4, 5-9), one perfect fourth (1-6, 3-8 ), and one tritone (0-6, 3-9). [edited to get rid of the 8 )= 8) sunglasses

Forte's set analysis would identify the two as inversionally related and transposed - put the transformation in retrograde and you have D-E-Fx-G#, exactly one whole step higher than the original melody of C-Db-E-F#.

Since Forte's work is hot stuff among today's students, I have no doubt that pitch axis is being widely used today... but the composers are probably not thinking along the same lines as Bartok. If a z-related set (one with an identical interval vector) is treated as a tone row, the result will be identical to Bartok's pitch axis as long as the sets are not complimentary (i.e, there is at least one common tone between the sets).

Since Forte's work encompasses the same results, most modern analysis of pitch axis is going to take the set theory approach. If Erno Lendvai had sold more books, the opposite might be true today.

Dneck, yes - a tone row uses all 12 tones in order before starting over. If you're working with a smaller set of tones (diatonic scale, hexachord, etc.) the term for the same technique is "cell".

But you can repeat a tone if you'd like - if your row/cell starts C-D-Eb, you can play C-D-D-Eb-Eb... as long as the repetitions are immediate.

Thanks NoteBoat - informative and helpful as always.

I just had a look at the Wikipedia article. I see what you mean about its quality. It's like they're talking about something completely different. Bartok doesn't even get a mention.:shock: