Yahoo Tuning Groups Ultimate Backup tuning Monzo on Elster's analysis of Johnston 6th Quartet

> From: <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, July 01, 2001 8:45 PM
> Subject: [tuning] Re: Ben Johnston String Quartet CDs
>
>
> I was wondering if you could help me with one thing, Monz??
>
> At the end of the Fonville "Guide" Fonville states: "A complete
> listing (notation, ratios, and cent values) of all the lattice
> structures up to 31, including all possible combinations Johnston has
> used, is available from the author."
>
> The author being Fonville, not Johnston, in this case... I was
> wondering how to contact Fonville?? Or is it possible that
> the "miraculous monz" would *also* have such a similar chart??
>
> I shore would like one of 'em.... (will pay $$)

You can try contacting John Fonville at his email address
at UCSD: <jfonville@ucsd.edu>. He's the department chair,
and pretty busy these days, but give it a shot. Keep in
mind that he may not even be around during the summer.
During the school year I see him from time to time, and
will ask about this next time we run into each other if
you haven't gotten it by then.

I do have a lot of charts of Johnston lattice structures,
but none of them are as complete as Fonville's. I'd be
happy to send you copies, but it may take a while to assemble
them all. Actually, maybe I'll just scan them and put
them up on my website. My charts generally have Johnston's
notation and MIDI-pitch-bend ("cawapus"), which reflects
my use of them to input MIDI-files of Johnston's music.
But many also include my HEWM notation and other info.

For an easy and available start on Johnston's notation with
a 5-limit system, Joe, take a look in the back of my book...
should be the first appendix, just before the one giving
the long list of prime numbers.

There's a one-page 3^(-4...4)*(5^(-2...2) 5-limit system
(hmmm... which, it turns out, is a 45-note Euler genus...)
with each cell in the diagram giving for that note:

- an early version of my HEWM notation, in which the
basic cardinality was designated by the 7 diatonic
letter-names and only the #, b, x, bb ...etc. accidentals
(instead of the full 72-EDO set I use now), accompanied
by the list of prime-factors and their exponents;

- the Johnston notation;

- the ratio;

- the Semitone value (i.e., cents);

- the nearest 12-EDO pitch and the amount of MIDI pitch-bend
necessary to obtain the ratio, expressed in terms of the
software I was using at the time, which only had a maximum
resolution of 64 (= 2^6) units per semitone, which is
equivalent to 768-EDO (quite a bit coarser than the
2^12 "cawapus" which Cakewalk lets me use now).

- finally, a tabulation of the nearest 24, 31, 41, 53, and 72-EDO
pitches and the amount of cents adjustment necessary to obtain
the ratio.

So at least to get an idea of a 5-limit system that would include
lots of Johnston's pitches, you can view many other approximations
and notations of those pitches here.

> I thought I was really doing something by finding harmonies through
> common tones in a blackjack lattice, but this is all CHILD'S PLAY
> compared with the intricate and elaborate pre-compositional structure
> that Johnston sets up for the 6th String Quartet as explained, rather
> clearly I might add, by Steven Elster...

I know what you mean, Joe. I consider the *combination* of the many
different pre-compositional aspects of this piece to be among the
most complicated and sophisticated I've ever seen.

> Now the question is whether this pre-compositional activity for the
> 6th String Quartet isn't perhaps a bit "over cooked..." Well, what
> I'm saying is that of ALL the quartets it was actually my LEAST
> favorite....

Hmmm... I haven't yet had the benefit of hearing the other
Johnston quartets (except the 4th), but I like the 6th very much.

I'm quoting this next bit out of order, so that the rest will
lead naturally into my analysis, which I found and copied below.

> Things get a little freer about the middle of the quartet and then,
> this is just my theory, Johnston becomes conceptually exhausted and
> runs the ENTIRE THING BACKWARDS in a giant palindrome!

Johnston has used palindrome structures in many of his pieces.
It's been a favorite device of his.

OK... now back to the order of Joe's post...

> Getting to the Elster... what was PARTICULARLY fascinating to me was
> his presentation of SERIAL CHARTS in HARMONIC SERIES ORDER. I
> capitalize these words, because this really made a BIG impression
> with me. Like many people, I have studied serial rows and matrices
> up the wazoo, but *never* did I see them organized by harmonic series
> principles.
>
> This idea, and I believe this is *probably* at the CORE of Ben
> Johnston's serialism, was VERY striking to me... and I think that
> Elster VERY clearly demonstrated it.

The combination of Partchian tonality and serialism really struck
me too.

> Also, there was a very neat chart which showed all the common tones
> from the hexachords... and these common tones are used in the piece
> to join hexachords together. Actually, it looks as though he uses a
> LOT of common hexachords between rows such as Retrograde and
> Retrograde Inversion...
>
> Elster points out the important structure of the two complementary
> hexachords of the row (used to be called "combinatoriality") with
> transposition by that all important 135/128... a combination of
> a "chromatic" adjustment with "justice..." our syntonic comma. Very
> cool...
>
> Man, that's neat.

OK, here's my commentary on Elster and the quartet. Print this
and keep it with Elster's article, as it corrects several errors.

ELSTER'S ANALYSIS OF JI SERIALISM IN BEN JOHNSTON'S 6TH QUARTET
===============================================================

by Joe Monzo

--- In tuning@egroups.com, "Joseph Pehrson" wrote:
> http://www.egroups.com/message/tuning/13889
>
> As somebody who only VERY OCCASIONALLY dips into a bit of
> serialism, I assume that eventually I might "dip into"
> xenharmonic patternings as well. I believe Neil
> Haverstick has also done a bit of work in this direction...
>
> so there *are* people interested in your explorations!

INTRODUCTORY
------------

Reference:

Steven Elster, 1991.
'A Harmonic and Serial Analysis of Ben Johnston's
String Quartet No. 6'.
_Perspectives of New Music_, v 29 # 2, p 138-165 [Summer].

I've written about this here often before, so a search of
the archives might turn up more.

+/- are the only additional symbols from Ben Johnston's notation
which I can accurately reproduce in ASCII, so I'll give the
letter-names of the pitches in my adaptation of 72-tET, along
with the prime-factors in the form |a b c d| where a, b, c, d
are the exponents of the prime-bases 3, 5, 7, and 11 respectively.
Also, I use Semitones instead of cents (but they mean the same
thing). Johnston's notational system is based on C = 1/1.

I will use lattice diagrams to help illustrate the pitch
relationships, based on my lattice formula described at
http://www.ixpres.com/interval/monzo/lattices/lattices.htm

The otonal structure represents identities as follows:

11
\
\
\ 9
\ /
\ /
\ /
\ 3
\ /
5 \ /
'-._\ /
' 1 --------- 7

And the utonal structure is the exact mirror image:

7 --------- 1
/\ '-._
/ \ ' 5
/ \
3 \
/ \
/ \
/ \
9 \
\
\
11

JOHNSTON'S BASIC 12-TONE SERIAL ROW AND ITS HEXACHORDS
------------------------------------------------------

Elster opens with:

> This paper presents an analysis of Johnston's extended just
> harmonic structures as organized by serial processes in String
> Quartet No. 6.

The _6th Quartet_ is a serial 11-limit JI composition.
Johnston divides the prime row into 2 hexachords.

The first hexachord gives odentites 3-1-11-5-7-9 of the
10/9 otonality ('D-' in Johnston's notation), as follows:
(intervals between pitches are given below; I use my 72-EDO
notation for the pitches):

5/3 - 10/9 - 55/36 - 25/18 - 35/18 - 5/4
A- D- G> F#< Cv E-
8.84 1.82 7.34 5.69 11.51 3.86
\/ \/ \/ \/ \/ \
-3:2 +11:8 -11:10 +7:5 -14:9 +5:4
7.02 5.51 1.65 5.83 7.65 3.86

The second hexachord gives udentities 3-1-11-5-7-9 of the
75/64 utonality ('d#'):

25/16 - 75/64 - 75/44 - 15/8 - 75/56 - 25/24
G#< D#< A+ B- E# C#<
7.73 2.75 9.23 10.88 5.06 0.71
/ \/ \/ \/ \/ \/
+5:4 -4:3 +16:11 +11:10 -7:5 +9:7
3.86 4.98 6.49 1.65 5.83 4.35

(In his 'Example 3', Elster incorrectly gives the 11-udentity
of this hexachord as 225/128; the correct ratio is 75/44.)

Note the dualistic symmetry inherent in Johnston's division
of the row into an otonal and a utonal hexachord.

Here are the 12 pitches of the row arranged as a scale, which
Elster points out is not the way Johnston uses them:

ratio prime-factor ~Semitones 72-tET

35/18 |-2 1 1 0| 11.51 Cv
15/8 | 1 1 0 0| 10.88 B-
75/44 | 1 2 0 -1| 9.23 A+
5/3 |-1 1 0 0| 8.84 A-
25/16 | 0 2 0 0| 7.73 G#<
55/36 |-2 1 0 1| 7.34 G>
25/18 |-2 2 0 0| 5.69 F#<
75/56 | 1 2 -1 0| 5.06 E#
5/4 | 0 1 0 0| 3.86 E-
75/64 | 1 2 0 0| 2.75 D#<
10/9 |-2 1 0 0| 1.82 D-
25/24 |-1 2 0 0| 0.71 C#<

D- otonality hexachord:

G>
\
\
\ E-
\ /
\ /
\ /
\ A-
\ /
F#< \ /
'-._\ /
' D- --------- Cv

D# utonality hexachord:

E# --------- D#<
/\ '-._
/ \ ' B-
/ \
G#< \
/ \
/ \
/ \
C#< \
\
\
A+

Putting them together gives the 12-tone 'prime row', which the lattice
clearly shows is based on an Euler genus with a fundamental of 10/9
and a guide-tone of 75/64:

E# --------- D#<
/ \'-._
/ \ ' B-
G> / \ /
\ G#< \ /
\ / '-._ \
\ / ' E-\
\ / / \
\C#< / \
\ '-._ / \
/ \ ' A- \
/ \ / A+
F#< \ /
'-._ \ /
' D- --------- Cv

ERRATA IN ELSTER
================

Elster's 'Example 8' gives a chart of common-tones in Johnston's
tuning. There are three discrepancies from the values I calculated:

- 'C-' = |-4 1 0 0| = 160/81 should be rounded to 1178 cents, not 1179.

- 'C7^b' == 1134 cents is incorrect and seems to appear on the
chart for no reason, since it is included in the header column
but not in the body of the chart itself. Elster gives a ratio
of 77/40 == 1134 cents, which is correct, but the prime-factoring
indicated by Johnston's notation would actually be |1 -2 1 1|
with a ratio of 231/100 == 249 cents.

- 'A7b-' = |-6 1 1 0| == 743 cents should have ratio 1120/729,
not 1126/729, but is incorrect here anyway, since it is the
9-odentity of the G7b- = |-4 0 1 0| otonality and in Johnston's
notation should be 'A7b' (without the minus sign) = |-2 0 1 0|
== 765 cents, with ratio 14/9.

===========

COMPLETE SET OF PITCHES FOR JOHNSTON 6TH QUARTET
------------------------------------------------

ratio prime-factor ~cents

160/81 |-4 1 0 0 | 1178
35/18 |-2 1 1 0 | 1151
40/21 |-1 1 -1 0 | 1116
77/81 |-4 0 1 1 | 1112
15/8 | 1 1 0 0 | 1088
225/121 | 2 2 0 -2 | 1074
50/27 |-3 2 0 0 | 1067
11/6 |-1 0 0 1 | 1049
20/11 | 0 1 0 -1 | 1035
25/14 | 0 2 -1 0 | 1004
16/9 |-2 0 0 0 | 996
225/128 | 2 2 0 0 | 977
140/81 |-4 1 1 0 | 947
75/44 | 1 2 0 -1 | 923
5/3 |-1 1 0 0 | 884
44/27 |-3 0 0 1 | 845
45/28 | 2 1 -1 0 | 821
128/81 |-4 0 0 0 | 792
25/16 | 0 2 0 0 | 773
14/9 |-2 0 1 0 | 765
55/36 |-2 1 0 1 | 734
50/33 |-1 2 0 -1 | 719
3/2 | 1 0 0 0 | 702
121/81 |-4 0 0 2 | 695
40/27 |-3 1 0 0 | 680
225/154 | 2 2 -1 -1 | 656
35/24 |-1 1 1 0 | 653
10/7 | 0 1 -1 0 | 617
45/32 | 2 1 0 0 | 590
25/18 |-2 2 0 0 | 569
112/81 |-4 0 1 0 | 561
15/11 | 1 1 0 -1 | 537
110/81 |-4 1 0 1 | 530
75/56 | 1 2 -1 0 | 506
4/3 |-1 0 0 0 | 498
55/42 |-1 1 -1 1 | 467
35/27 |-3 1 1 0 | 449
225/176 | 2 2 0 -1 | 425
5/4 | 0 1 0 0 | 386
100/81 |-4 2 0 0 | 365
11/9 |-2 0 0 1 | 347
40/33 |-1 1 0 -1 | 333
98/81 |-4 0 2 0 | 330
25/21 |-1 2 -1 0 | 302
32/27 |-3 0 0 0 | 294
75/64 | 1 2 0 0 | 275
7/6 |-1 0 1 0 | 267
225/196 | 2 2 -2 0 | 239
55/48 |-1 1 0 1 | 236
25/22 | 0 2 0 -1 | 221
9/8 | 2 0 0 0 | 204
10/9 |-2 1 0 0 | 182
88/81 |-4 0 0 1 | 143
15/14 | 1 1 -1 0 | 119
35/33 |-1 1 1 -1 | 102
25/24 |-1 2 0 0 | 71
28/27 |-3 0 1 0 | 63
45/44 | 2 1 0 -1 | 39
55/54 |-3 1 0 1 | 32
225/224 | 2 2 -1 0 | 8
1/1 | 0 0 0 0 | 0

I made a lattice of the entire pitch set, USING JOHNSTON'S
NOTATION, but not in ASCII, so here it is:
/tuning/files/monz/6thq-latbig.gif

-monz
http://www.monz.org
"All roads lead to n^0"

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>Thanks so much, Monz, for your extended commentary and >corrections on
>the Elster, and I have saved your comments! I really >appreciate all
>the work that you've put into this.

>It rather looks as though Andy Stefic has a chart of >the complete
>Johnston from the 9th Quartet, but I would urge you to >put anything
>up on your Website.

Andy Stefik (hehehe - close though) - One guy spelled it Stefixx once (one more X and I would have been a porn star! LOL)

I really dont understand why someone would want a complete lattice or chart of one of his quartets. I dont have any idea how that will help you understand the music. His music is based alot on modulations by microtonal intervals and etc. Its MUCH MUCH MUCH easier to think about it from this perspective. Like for example being in the key of D- and then modulating to A major or whatever realizing that these are microtonal keys. His music relatively traditional in that way, a chunk of it at least, and its a whole hell of alot easier to analyse it from that perspective. Or if its serialist make a twelve tone row and modulate it microtonally ... no need for huge charts.

Besides these huge lattices are more like trivia. How many tones did he use here or whatever. Do you actually think he writes huge charts and diagrams before writing some music? There is no way he could keep track of all those numbers and ratios and things and still pay attention to the real music.

If the charts are helpful someone ... well thats cool I'm glad and I'll send it if you want it Joe, but I really dont get how its helpful because it has nothing to do with how he writes the music. Correction it does, but is far far under the surface ... in the same way that when I write a 12 TET piece I dont write out all the logarithms and frequencies in every octave...

>In fact, I would urge Tuning List members to contact >Andy and Ben
>Johnston to get a copy of the string quartet CD... >then, after we all
>listen to it, we can have a similar experience for >commentary...

>Ben Johnston is selling this double CD set for $20, >and will only
>give one to a "customer..." but, believe me, it's >worth it.

Thanks Joe. Ben would appreciate that. I do as well. I spent MANY MANY MANY MANY hours remastering those tracks. The old tapes were in, lets say, pretty poor shape. This wasnt Bens fault of course tapes just degrade over time. The first quartet took forever to clean up, but I was pretty happy with how the audio came out.

>Now, getting to the "soup to nuts" of this whole >business,
>the "bottom line" is whether music like this can >actually be played
>accurately and, even if it is, whether the >xenharmonicism is actually
>AUDIBLE.
>I'm not depricating Johnston's amazing (and graceful) >work in any
>way... I'm just thinking about my *own* direction and >positing some
>ideas...

Well Joe I think that you are very much in the right track of thinking here - or perhaps I would sound less dogmatic if I said I agree. As for accuracy: It is possible to test performances like these and this work should be done not just in reference to Bens work but for rock music, punk music, etc. Did you know that some Rage Against the Machine scores notate Qaurter tones? I wonder if they really play them and how accurately. That would be fun work to test!

With Ben's music specifically there are ways to increase accuray. For starters computer realizations should be made to help players. Relying on the ears alone is a mistake future generations should not have to make. Obviously neither Ben Partch or many others had that option. Myself whenever I work with Ben's material I use an FM synth algorithm (its a really basic and simple one) but the accuracy is superb and there is no audible beat frequency (to my ears) with intervals that suposedly dont have one... as there can be in some of the MIDI recordings I've heard.

I will go into this further at a later date.

Anyway this question of accuracy is VERY important for me as well. In fact I think it is one of the most important questions that can be asked about microtonality.

Besides suppose someone comes along and discovers players perform Ben's music with an average error of +/- 13 cents per tone. Big deal it surely doesn't lighten his work. Its better to just know because this info could be very helpful to other composers potentially.

>For *me* personally, the 2nd Quartet, particularly the >3rd movement,
>has the most AUDIBLE xenharmonic effects. Maybe the >intonation in
>some of the other quartets is too subtle for my ear at >this point.
>That's not an impossibility! :) However, like I >maintained
>previously, for all the elaborate infrastructure, >frankly, I don't
>hear it.

I dont know exactly what you mean by xenharmonic in this context could you explain?

As for audibility. Do you mean the elaborate structures of huge lattices with tons and tons and tons of tones? Ben doesn't hear it that way either. As I said at the top there are easier ways to think about it which relate alot to standard theory and ear training.

>In addition, I really don't think the ideas that >Elster has on how
>performers should learn to play Johnston are >practical. No
>performers that *I* know are going to do this. Maybe >somebody
>connected with some University theory department >might, but it's a
>stretch. The problematic performance history of these >string
>quartets... when there is one, helps substantiate my >postulate...

>I'm running back to 72-tET, REALLY FAST, if you >please...

What does he say about method. I know Ben's music well, and I've read a bunch of articles, but I haven't read that one.

Or you could just make up your own tuning system.

>Anyway, without a doubt, Johnston's accomplishment is >incredibly
>substantial, and sets up a paradigm for new directions >in music and
>tuning...

>How or if these ideas will work for other people is a >separate
>question... certainly Johnston has been very >successful in his own
>right.

Sure. This is almost a question of influence. I've never been much concerned with these kind of questions really. Like, "What is John Cages Value?", "Or how can Beethovens music benefit me as a composer?" or "How will Johnston's music influence the future?" I really dont know answers to these kind of questions, and so I try to ignore them and ask different questions instead. Perhaps "What time is it and why am I still writing email?" hehehehehehe

>I just wish these string quartets were on a commercial >CD!

Yaa who knows maybe eventually, but as for right now thats what he wanted. If I wouldn't have opened my big mouth I dont know if he would have released them at all. He cares alot more about just continuing to write music, then publicizing or things like that. Hell he wouldn't even let me make a CD Cover for the CD's!! He just has other things he'd rather be doing, and thats ok too.

Cheers!

Andy

Monzo on Elster's analysis of Johnston 6th Quartet

🔗monz <joemonz@yahoo.com>

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