How do you call such chord?

Chords, scales, harmony, melody, etc.
22906 posts since 20 Oct, 2007 from not here

Post Sun Sep 26, 2021 2:33 pm

Check it out, here is what the concern with pitch-class analysis of music looks like.

[Allen] Forte’s work has been guided by a cartographic impulse that can conceal the deeper value of his innovations. In the present work, for instance, he tirelessly maps out the surface of several dozen individual movements by Webern, in many cases relating each and every note to a matrix consisting of octatonic subsets grouped together according to which of the three forms of p.c. set class 8-28 they evoke. As often is the case with Forte, the actual analytical insights are often concealed below the surface of the analyses. Insights are here in abundance, however, especially in Forte’s treatment of the later works of Webern’s atonal oeuvre, opp. 12–16. Paradoxically, it is in discussing these works that Forte makes his case for the centrality of the octatonic to Webern’s music most convincingly, even though (as Forte himself admits) his octatonic Swiss army knife works less infallibly here than in the earlier opus numbers due to Webern’s introduction of an increasing number of non-octatonic surface formations. ... perry.html

(Forte is about everybody's go-to regarding Webern, or at least among the chief referents when one is going to embark on that kind of work. Forte was innovative in that he decided there was such an ethos to this music that the structure as a whole may be known, rather than it being individual wild hairs ad culum.)

here's a picture: Image

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803 posts since 4 Feb, 2021

Post Sun Sep 26, 2021 2:50 pm

Oh, note staffs and not piano rolls with integers. Big surprise that is :wink:
Tribe Of Hǫfuð "First rule: From one perfect consonance to another perfect consonance one must proceed in contrary or obligue motion." Johann Joseph Fux 1725.

22906 posts since 20 Oct, 2007 from not here

Post Sun Sep 26, 2021 4:51 pm

There it is.

22906 posts since 20 Oct, 2007 from not here

Post Sun Sep 26, 2021 6:09 pm

There is something called pitch-class set (often attributed to Forte) which would not be 0-11; if it was let's say the far end of 'basic' (eg., 3 to 9 tones), ie., variable minor or a synthetic scale with a real 9 it would be 0-8. This attribution to Forte arrives later than pitch class theory, going back a couple decades to 1953 and Babbitt, afaik,

A problem with set theory for tonal music arises with inversions of harmonies. I'm going to just leave that there.

The usefulness of thinking in terms of sets within a set, abstractly, can in part be demonstrated in simple terms:
I like this intervallic bit, eg: "B-C-Eb", I like the sound of it, evocative.
In this 'theory', we're looking for equivalences. So this intervallically can be duplicated at 11 other starting points, and it can be flipped, eg., F D C#. B C Eb. F D C#. Bb A F#. Ab G E. (the last three is an inversion); now we've a 12-tone row.

So we have abstracted a little musical germ with the aim of internal cohesion by reiterating equivalence.
It's an abstraction of intervals; talking in terms of sets and suchlike is not unexpected as a mode of operation. If we look at that germ, its most 'packed' form is simply + 1 semitone, then plus 3 more.
So the tighter interval for this class is a semitone, in which case B is said to be 0.

So the choice of notes in a 12-tone row have to do with smaller segments, typically. Was Webern thinking in terms of six or 4; or manipulating from an abstraction from octatonic symmetrical, with say a derived 3-note class...
The crux of pitch class theory is segmentation because the meaning is revealed in the finer workings, segmentation.

In tonal, functional music (let alone the simplicity of modal activity), these things are not as abstract as that, the notes will have a meaning in the tonal realm (or the modal meanings relating to the central tone) and ramifications that have to be fit to the tonal (or modal) fabric. You don't extrapolate things out of tonality abstractly like that for long or you've exceeded the tonal framework.

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