Quote For The Fourth Of February

In an interview published in 1990 he said he had never seen Howard Hanson's 'Harmonic Materials of Modern Music', and downplayed the influence of Forte on his own work. And while Carter may have benefited from the works he did consult, he clearly found them inadequate, otherwise he would never have undertaken the laborious task of compiling the Harmony Book.

An iconoclasitc desire to go his own way may have been one motivating factor, particularly given his attempts to distance himself from the 12-tone practice of Babbitt, Martino and others in the 1960s and 70s. But Carter had other reasons as well. One has to do with his working methods.

Carter sketches incessantly, often making a thousand or more pages of sketches for a single twenty-minute composition. Frequently he will re-copy a passage several times as it takes shape, preferring to put on paper changes that he could easily keep track of in his head. Looking through Carter's manuscripts one gets the feeling that the act of putting musical ideas on paper - of moving the pencil across the page - is his preferred method of getting to know his materials, and an important stimulus for his imagination.

Writing out the chords of the Harmony Book himself may have served a similar purpose, giving Carter the opportunity to become thoroughly familiar with each chord through the process of writing out its subsets and supersets.

From pg20 of Elliott Carter's Harmony Book.

A Portly Chord Courtesy of Berio

This chord appears at the end of Berio's 1954 piece 'Nones.'

It's quite heavy and caught my ear. Below I have included the relevant score fragment and a quickly thrown together graphic PC set analysis (it might look like I drew it in pencil crayon, but actually they are watercolour crayons I'll have you know and I would use them like that by brushing on some water if I had some thicker paper and/or more time/will power).

I am a long way from being any sort of analyst but one thing is clear from a cursory look at the thing, all pitches are present except for G (or 7 if you prefer).

B (11) is the most prevalent pitch appearing five times at the bottom end of the texture, in the contrabassoon, the tuba, the timpani, the cello and the double bass.

The woodwind PC set and the brass PC set look quite similar at first glance, I think they are transposed inversions of each other, give or take a pitch or two. The string pitches look like a subset of the same PC set (three of four pitches fit that scheme)

I'll have to look more closely at it and will probably edit this a bit later if i'm wrong about any of this (so no one will know unless you happen to check my blog in the meantime, in which case, don't tell anyone I wasn't absolutely certain from the off, I don't want to be blackballed at the Music Theory and Analysis Society of Balsall Heath, the dinner and dance evenings are just too good to miss plus there is bingo on a Sunday).

EDIT: Alright, I looked at it more closely, yes, the two sets used in the woodwind and the brass are the same set, 6-Z11 and the strings appear to contain a subset of the same. This helps provide some structure and sense to the dense chromatic harmony.

Of course much remains unanalysed, such as the precise registers (pitches not pitch classes) and the intervals used (in vertical order), but then as I said, I am not an analyst (so sue me, oh and I claim fair use of the tiny score and music fragments, please don't sue me about that)

The score fragment doesn't have the instruments or clefs listed (I should have photoshopped them in when I prepared the image, never mind) here they are...

Instruments as written in the score (top to bottom)

Woodwinds:

Ott
Fl.
Ob.
Cl.
Sax.
Fag. (bass clef)
C.Fag (bass clef)
Cor
Cor

Brass:

Trb
Trb
Trbn (bass clef)
Trbn (bass clef)
Tuba (bass clef)

Percussion

Timp (bass clef)
G.C.
Tamb.
T.T.
Vibr.
Arpa (two staves, treble and bass)

Strings:

Vni A
Vni B
Vni C
Vle (alto/viola clef)
Vc (bass clef)
Cb. (bass clef)

The Sound of Root Rectangles

Following on my previous post/geometry quiz (won by Tom from Geneva, his prize is currently being considered) here is a musical rendering of that pattern, well, the root rectangles aspect anyway.


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[Text below copied from NetNewMusic video uploads section]

This PC Set/Chord is based on simple root rectangles (approximate, could go microtonal for more accuracy perhaps). Intonation isn`t great, most of the instruments are new (to me). Working with projective geometry now which is yielding some interesting results (has a counterpoint and register aspect too). Will come back to this root rectangles thing (it has a dominant 7th in it which I didn`t expect, a bit like the Spanish Inquisition). Also I need more hats and sunglasses.