why thee two, Lou?

Greetings,
I have read that Lou Harrison preferred the Kirnberger II tuning above
all others. Can anybody tell me why? What was it about that particular
version of Kirnberger's ideas that was so attractive, in contrast to say, his III or
even the Werckmeister tunings?
Thanks,

Ed Foote RPT
www.uk-piano.org/edfoote/
www.uk-piano.org/edfoote/well_tempered_piano.html
<A HREF="http://artists.mp3s.com/artists/399/six_degrees_of_tonality.html">
MP3.com: Six Degrees of Tonality</A>

----- Original Message -----
From: <a440a@aol.com>
To: <tuning@yahoogroups.com>
Sent: Wednesday, May 21, 2003 5:32 PM
Subject: [tuning] why thee two, Lou?

> Greetings,
> I have read that Lou Harrison preferred the Kirnberger II tuning
above
> all others. Can anybody tell me why? What was it about that particular
> version of Kirnberger's ideas that was so attractive, in contrast to say,
his III or
> even the Werckmeister tunings?
> Thanks,
>
> Ed Foote RPT

i haven't looked into Kirnberger II, and
so can't say anything about it. :(

but in case you haven't seen my page on
Kirnberger III, you might want the URL:

http://sonic-arts.org/dict/kirnberger.htm

i go into pretty good detail about that one.

-monz

In a message dated 2003:05:21 05:33:10 PM, Ed Foote RPT (a440a@aol.com)
writes:

> I have read that Lou Harrison preferred the Kirnberger II tuning above
>all others.

Well, *this* side of JI that is.
"Just Intonation is the Best Intonation." - Lou Harrison

> Can anybody tell me why? What was it about that particular
>version of Kirnberger's ideas that was so attractive, in contrast to say,
>his III or even the Werckmeister tunings?

Good question(s) considering Harrison's love of Early Music/preBaroque
musics. AFAIK one would think Harrison would have liked either one of the French
_temperament ordinaire_ or one of the Italian hyperchromatic, irregular
tunings.
Maybe he just liked the simpler, "user-friendliness" of Kirnberger II tuning
more out of pragmatic choice than aesthetics.
Kirnberger's tunings IMMHO are rather pale, bland and near-comatose like
tragically over-cooked vegetables, but then again I grew up with much
"spicier" sounding musics (i.e. Chinese, Indonesian, Indian, Central Asian, all sorts
of folk-music, even Maori chants and Bob Dylan).

>Thanks

Ya most Humbly Welcome(d).

---
Hanuman Zhang, the "Yves Klein Bleu Aardvark"

"The wonderousness of the human mind is too great to be transferred into
music only by 7 or 12 elements of tone steps in one octave." - shakuhachi master
Masayuki Koga

"There's a rabbinical tradition that the music in heaven will be microtonal
=)" - one annotative interpretation of Talmudic writings

What strange risk of hearing can bring sound to music - a hearing whose
obligation awakens a sensibility so new that it is forever a unique, new-born,
anti-death surprise, created now and now and now. .. a hearing whose moment in
time is always daybreak. - Lucia Dlugoszewski

According to Daniel Wolf, Mr. Harrison like KII because it had a
perfect ditone diatonic and almost a syntonic diatonic in JI (one
tone is a half comma high). Mr. Harrison's Piano Concerto in KII is
beautiful.

Gabor

I don't understand the question. Lou Harrison wrote a single composition in
Kirnberger II and it is beautiful. What is the problem? Theory aside, the
piece is a beautiful work and is written exquisitely with this particular in
mind. Of course, Keith Jarrett didn't get it. But that's another story.

best, Johnny Reinhard

--- In tuning@yahoogroups.com, a440a@a... wrote:
> Greetings,
> I have read that Lou Harrison preferred the Kirnberger II
tuning above
> all others. Can anybody tell me why? What was it about that
particular
> version of Kirnberger's ideas that was so attractive, in contrast
to say, his III or
> even the Werckmeister tunings?
> Thanks,
>
> Ed Foote RPT

it's because kirberger II is 11 notes of an essentially just,
pythagorean/schismic tuning, plus the single extremely tempered note
A, which (just barely) makes it into a well-temperament. no other 12-
tone well-temperament has so much "just intonation" (or nearly so).
joseph pehrson made this observation in an article he published some
time ago.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_43792.html#43807

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, a440a@a... wrote:
> > Greetings,
> > I have read that Lou Harrison preferred the Kirnberger II
> tuning above
> > all others. Can anybody tell me why? What was it about that
> particular
> > version of Kirnberger's ideas that was so attractive, in contrast
> to say, his III or
> > even the Werckmeister tunings?
> > Thanks,
> >
> > Ed Foote RPT
>
> it's because kirberger II is 11 notes of an essentially just,
> pythagorean/schismic tuning, plus the single extremely tempered
note A, which (just barely) makes it into a well-temperament. no
other 12-tone well-temperament has so much "just intonation" (or
nearly so). joseph pehrson made this observation in an article he
published some time ago.

***Thanks, Paul, for coming to the rescue on this. I was going to
respond last night that Harrison liked the way he could use 12 notes
and come as close to JI as possible, but I was looking for an
electronic version of my article and couldn't find it. The article is
based upon the program notes that Lou wrote for the performance of
the Piano Concerto with Ursula Oppens in Carnegie Hall, October 15,
2000.

Well, finally I found the print version. Here's the salient section:

"The most noticable feature of the concerto is the fact that it is a
big "alternately tuned" piece. It is *not* in the standard 12
tempered pitches per octave for which we are accustomed in the West.
Instead, the piano and orchestra are tuned in "Kirnberger II" a "well
temperament." Johann Philipp Kirnberger (1721-1783) was a student of
J.S. Bach and musician for Frederick the Great, and he constructed
this tuning, a pretty easy one to effect. Essentially, almost all
the perfect fifths (and therefore fourths) of the tuning are "just"
(meaning no beats), with some tempering of a final "A" at the end of
the tuning cycle. This tuning has some extraordinary features: just
intonation major triads on C and G and just intonation minor triads
on E and B. It is no wonder that Lou Harrison is so enamored of this
tuning -- it is about as close as one can come to "just intonation,"
music with no interval beating, and still use only 12 pitches per
octave."

J. Pehrson

I hafta admit, I probably have Kirnberger II mixed up with some other
meantone or well-temperament.

In a message dated 2003:05:22 06:25:17 PM, jpehrson@rcn.com writes:

>***Thanks, Paul, for coming to the rescue on this. I was going to
>respond last night that Harrison liked the way he could use 12 notes
>and come as close to JI as possible, but I was looking for an
>electronic version of my article and couldn't find it. The article is
>based upon the program notes that Lou wrote for the performance of
>the Piano Concerto with Ursula Oppens in Carnegie Hall, October 15,
>2000.
>
>Well, finally I found the print version. Here's the salient section:
>
>"The most noticable feature of the concerto is the fact that it is a
>big "alternately tuned" piece. It is *not* in the standard 12
>tempered pitches per octave for which we are accustomed in the West.
>Instead, the piano and orchestra are tuned in "Kirnberger II" a "well
>temperament." Johann Philipp Kirnberger (1721-1783) was a student of
>J.S. Bach and musician for Frederick the Great, and he constructed
>this tuning, a pretty easy one to effect. Essentially, almost all
>the perfect fifths (and therefore fourths) of the tuning are "just"
>(meaning no beats), with some tempering of a final "A" at the end of
>the tuning cycle. This tuning has some extraordinary features: just
>intonation major triads on C and G and just intonation minor triads
>on E and B. It is no wonder that Lou Harrison is so enamored of this
>tuning -- it is about as close as one can come to "just intonation,"
>music with no interval beating, and still use only 12 pitches per
>octave."

Intriguing. I hafta dig up some music in K II then... Thanx.

Possibly idea(s): Would a well-tempered "mutation" of the 22-tone Indian
_shruti_ work interestingly 0_o? or how about a more extreme, "extended"
_temperament ordinaire_ - some variety of irregular temperament somewhere between
22tET and authentic _shruti_?

---
Hanuman Zhang, the "Yves Klein Bleu Aardvark"

Brett Campbell writes:
>>"After prolonged exposure to the rich, kaleidoscopic world of microtones,
>>retuning to equal-tempered music was for me like going back to black and
>>white after spending a weekend immersed in color".

"There's a rabbinical tradition that the music in heaven will be microtonal
=)" - one annotative interpretation of Talmudic writings

NADA BRAHMA - Sanskrit, "sound [is the] Godhead"
LILA - Sanskrit, "divine play/sport/whimsy" - "the universe is what happens
when God wants to play" - "joyous exercise of spontaneity involved in the art
of creation"

czhang23@aol.com a �crit :

> In a message dated 2003:05:21 05:33:10 PM, Ed Foote RPT (a440a@aol.com)
> writes:
> > I have read that Lou Harrison preferred the Kirnberger II tuning above
> >all others.
>
> Well, *this* side of JI that is.
> "Just Intonation is the Best Intonation." - Lou Harrison
>
> > Can anybody tell me why? What was it about that particular
> >version of Kirnberger's ideas that was so attractive, in contrast to say,
> >his III or even the Werckmeister tunings?
>
> Good question(s) considering Harrison's love of Early Music/preBaroque
> musics. AFAIK one would think Harrison would have liked either one of the French
> _temperament ordinaire_ or one of the Italian hyperchromatic, irregular tunings.
> Maybe he just liked the simpler, "user-friendliness" of Kirnberger II tuning
> more out of pragmatic choice than aesthetics.

Hi Zhang & Ed Foote !
Why ? more ideas : Ovbiously, Kirnberger II resolves the 3/2 � 9/8 � 5/3 � 5/4
dilemma by touching a minimum of 3/2, and is the simplest form of temperament,
if ever we can call it so : replace meantone G-A by a 19/17 (192,56 c.) or a
341/305 (193,15 c.) and it�s a JI tuning.
But another quality of that arrangement I have been interested in for a diatonic scale
is also to present a maximum of differencial coherence between second intervals,
A � G being almost equal to F# three octaves below.
Applying Lou Harrison�s precept that "Just Intonation is the Best Intonation", this
property can even be improved by using the 13-limit meantone interval * 143/128 *
(191,85 c.) between A & G, as
143 � 128 = 15 = 120 / 8 = Kirnberger II F# precisely.
Best choice would be of course to have both 143 and 144, which would cover all
situations with more melodic difference tones :
120 128 143-144 160
8 15 16
Considering the highly consonant links 143 offers with 11 & 13 limit intervals (and
therefore arab & persian spices), the metaphor of an occidental temperament
being healed by � oriental � colors quite pleases me as well.

--- In tuning@yahoogroups.com, czhang23@a... wrote:

> Possibly idea(s): Would a well-tempered "mutation" of the
22-tone Indian
> _shruti_ work interestingly 0_o?

yes indeed! i recently came up with interesting ways of well-tempering
higher-dimensional just periodicity blocks along various dimensions,
in private e-mails involving dave keenan. i haven't even posted this
to the tuning-math list yet! but if you wish, i'll post some 22-tone
examples when i get back to the office next week.

> or how about a more extreme,
>"extended"
> _temperament ordinaire_ - some variety of irregular temperament
>somewhere between
> 22tET and authentic _shruti_?

i think you'll find just such a tuning system described near the end
of my paper:

http://www-math.cudenver.edu/~jstarret/22ALL.pdf

--- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:

> and is the simplest form of
temperament,
> if ever we can call it so : replace meantone G-A by a 19/17 (192,56
c.) or a
> 341/305 (193,15 c.) and it's a JI tuning.

kirnberger actually used ratios of 161 for this purpose -- the
syntonic comma is split in "half" into 160:161 and 161:162, as i
learned at johnny's house.

In a message dated 2003:05:23 05:34:57 PM, paul e quotes me & writes oh so
neatly:

>--- In tuning@yahoogroups.com, czhang23@a... wrote:
>
>> Possibly idea(s): Would a well-tempered "mutation" of the
>>22-tone Indian _shruti_ work interestingly 0_o?
>
>yes indeed!

yippy! A vote o' confidence...

>i recently came up with interesting ways of well-tempering
>higher-dimensional just periodicity blocks along various dimensions,
>in private e-mails involving dave keenan. i haven't even posted this
>to the tuning-math list yet!

Hmm, chalk this up to synchroncity? Or mayhaps great minds... ;)
or at least hyper-minds...

>but if you wish, i'll post some 22-tone examples when i get back to the
office next >week.

Oh thanx in advance ::VeRY BiG GRiNNie::

>> or how about a more extreme, "extended"
>> _temperament ordinaire_ - some variety of irregular temperament
>>somewhere between 22tET and authentic _shruti_?
>
>i think you'll find just such a tuning system described near the end
>of my paper:
>
>http://www-math.cudenver.edu/~jstarret/22ALL.pdf

oh I have that paper. I am still chewin' * on the first 1/2 dozen pages...

* _not_ literally ;) OKAY!
yes, I am part Cantonese ** but I am also part Indonesian ;)

** translation and paraphrase of Mandarin sayin': "The
too-smart-for-their-own-good Cantonese will eat anything that moves or isn't locked down/nailed
down."

---
Hanuman Zhang, the "Yves Klein Bleu Aardvark"

Brett Campbell writes:
>>"After prolonged exposure to the rich, kaleidoscopic world of microtones,
>>returning to equal-tempered music was for me like going back to black and
>>white after spending a weekend immersed in color".

What strange risk of hearing can bring sound to music - a hearing whose
obligation awakens a sensibility so new that it is forever a unique, new-born,
anti-death surprise, created now and now and now. .. a hearing whose moment in
time is always daybreak. - Lucia Dlugoszewski

The gods aren't cool enough to have invented dissonance

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> kirnberger actually used ratios of 161 for this purpose -- the
> syntonic comma is split in "half" into 160:161 and 161:162, as i
> learned at johnny's house.

The difference between the two being 25921/25920, at 0.0668 cents.
This comma, as well as 162/161 and 161/160 are 23-limit, and are
commas of the {2,3,5,7,23} subgroup. Did Kirnberger somehow use this
fact when tuning, or is it a mere accidental side effect?

In the Scala collection, we find the following for Kirnberger 2. Is
there a JI version which is more authentic? Would that make
895.11186 cents into 13041/8192 or into 32805/20608?

! kirnberger2.scl
!
Kirnberger 2: 1/2 synt. comma. "Die Kunst des reinen Satzes" (1774)
12
!
135/128
9/8
32/27
5/4
4/3
45/32
3/2
405/256
895.11186
16/9
15/8
2/1

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

> yes indeed! i recently came up with interesting ways of well-tempering
> higher-dimensional just periodicity blocks along various dimensions,
> in private e-mails involving dave keenan. i haven't even posted this
> to the tuning-math list yet! but if you wish, i'll post some 22-tone
> examples when i get back to the office next week.

So where have you been? Don't forget to post your well-tempered blocks!

wallyesterpaulrus a �crit :

> --- In tuning@yahoogroups.com, jacques dudon <aeh@f...> wrote:
> > and is the simplest form of
> temperament,
> > if ever we can call it so : replace meantone G-A by a 19/17 (192,56
> c.) or a
> > 341/305 (193,15 c.) and it's a JI tuning.
>
> kirnberger actually used ratios of 161 for this purpose -- the
> syntonic comma is split in "half" into 160:161 and 161:162, as i
> learned at johnny's house.

I wonder if Lou knew that, he would have probably loved that 7th harmonic.
I love 161 for other reasons : 28 - 23 = 5 which is half a comma away,
as you mention, of their product - rare, rare harmony !

G = 144
A = 161
B = 180
C = 192 etc.

161 - 144 = 17 and 180 - 161 = 19 : same differential-coherent fractal series :
128 136 144 152 161 170 180 ... that converges towards 1, 057 453 770 738 38
& which produces in fact a "5/4" of 1.250 390 199... (386, 854 c.)

--- In tuning@yahoogroups.com, czhang23@a... wrote:

> >i think you'll find just such a tuning system described near the
end
> >of my paper:
> >
> >http://www-math.cudenver.edu/~jstarret/22ALL.pdf
>
> oh I have that paper. I am still chewin' * on the first 1/2
dozen pages...

let me know if i can help you break any of that down into plain
english -- i know it's written very densely and can get stuck to your
teeth . . .

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> > kirnberger actually used ratios of 161 for this purpose -- the
> > syntonic comma is split in "half" into 160:161 and 161:162, as i
> > learned at johnny's house.
>
> The difference between the two being 25921/25920, at 0.0668 cents.
> This comma, as well as 162/161 and 161/160 are 23-limit, and are
> commas of the {2,3,5,7,23} subgroup. Did Kirnberger somehow use this
> fact when tuning, or is it a mere accidental side effect?

kirberger was simply tempering out the syntonic comma, in this case
by distributing it among only two fifths, and using "just
temperament" as margo would say.
>
> In the Scala collection, we find the following for Kirnberger 2. Is
> there a JI version which is more authentic?

johnny's got it at home in his copy of kirnberger's book. somehow the
number 161 was right there in the ratio for A -- perhaps he took D as
1/1, i don't remember.

In a message dated 2003:05:25 12:06:09 AM, paul e writes:

>> >i think you'll find just such a tuning system described near the
>> >endof my paper:
>> >http://www-math.cudenver.edu/~jstarret/22ALL.pdf
>
>> oh I have that paper. I am still chewin' * on the first 1/2
>>dozen pages...
>
>let me know if i can help you break any of that down into plain
>english -- i know it's written very densely and can get stuck to your
>teeth . . .

Thanx I most definitely will - offlist ;) Luckily I have Monzo's on-line
dictionary bookmarked and I can always politely pester ;) John Chalmers and
Warren "the Scarlet Aardvark" Burt as well.

I have been reading the Lou Harrison Reader recently and feel like there
are striking similarities betwixt my learning from some of this list's
"heavyweights" and that of Harrison's learning from Cowell: "...that an exchange of
ideas with a more experienced colleague might be a stimulant to someone who
already knew where he was going..."
Again humble thanx, ya peeps.

---
Hanuman Zhang, the Yves Klein Bleu Aardvark

"O wise humanity, terribly wise humanity! Of thee I sing. How inscrutable is
the civilization where men toil and work and worry their hair gray to get a
living and forget to play!" - Lin Yutang, _The Importance of Living_

"...So what is life for? Life is for beauty and substance and sound and
colour; and even those are often forbidden by law [socio-cultural conventions].
. . . Why not be free and live your own life? Why follow other people's rules
and live to please others?..." ~Lieh-Tzu/Liezi, Taoist Sage (c. 450- c. 375
BCE)

"...we may be able to prove conclusively that all men are born with
potentially brilliant intellects...and that the source of cultural creativity is the
consciousness that springs from social cooperation and loving interaction...the
majority of us live far below our potential, because of the oppressive nature
of most societies." - John Blacking

=> To Thine Own Self Be True <=

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Don't forget to post your well-tempered blocks!

well, you asked for it! i looked and couldn't find the original
message i sent out, which described the formula i used to create
these. so a challenge for you is to try to reverse engineer them. 41-
toners they were:

> > hi folks . . .
> >
> > if one of the four periodicity blocks i sent out works better for
aaron's
> > scale, please let me know.
> >
> > here's an example of irregular tempering for a more just center.
> >
> > start with the periodicity block (if you wish, assume 1/1 = D as
dave
> > suggests)
> >
> > cents numerator denominator
> > 0 1 1
> > 21.506 81 80
> > 62.961 28 27
> > 84.467 21 20
> > 111.73 16 15
> > 140.95 243 224
> > 182.4 10 9
> > 203.91 9 8
> > 231.17 8 7
> > 266.87 7 6
> > 294.13 32 27
> > 315.64 6 5
> > 357.1 896 729
> > 386.31 5 4
> > 407.82 81 64
> > 435.08 9 7
> > 470.78 21 16
> > 498.04 4 3
> > 519.55 27 20
> > 561.01 112 81
> > 582.51 7 5
> > 617.49 10 7
> > 638.99 81 56
> > 680.45 40 27
> > 701.96 3 2
> > 729.22 32 21
> > 764.92 14 9
> > 792.18 128 81
> > 813.69 8 5
> > 842.9 729 448
> > 884.36 5 3
> > 905.87 27 16
> > 933.13 12 7
> > 968.83 7 4
> > 996.09 16 9
> > 1017.6 9 5
> > 1059.1 448 243
> > 1088.3 15 8
> > 1115.5 40 21
> > 1137 27 14
> > 1178.5 160 81
> >
> > applying two different schemes irregular 7-limit schismic
temperament, this
> > becomes
> >
> > scheme 1
> >
> > 0
> > 24.98
> > 62.00
> > 87.19
> > 115.87
> > 141.43
> > 180.56
> > 204.36
> > 231.72
> > 265.75
> > 293.02
> > 317.82
> > 356.48
> > 383.27
> > 409.98
> > 436.28
> > 471.41
> > 497.92
> > 521.80
> > 560.36
> > 585.25
> > 614.75
> > 639.64
> > 678.20
> > 702.08
> > 728.59
> > 763.72
> > 790.02
> > 816.73
> > 843.52
> > 882.18
> > 906.98
> > 934.25
> > 968.28
> > 995.64
> > 1019.44
> > 1058.57
> > 1084.13
> > 1112.81
> > 1138.00
> > 1175.02
> >
> > scheme 2
> >
> > 0
> > 24.64
> > 61.64
> > 86.00
> > 115.81
> > 141.65
> > 181.24
> > 204.18
> > 232.12
> > 265.59
> > 293.23
> > 317.14
> > 356.51
> > 383.89
> > 410.41
> > 436.44
> > 470.95
> > 497.96
> > 521.09
> > 559.92
> > 584.39
> > 615.61
> > 640.08
> > 678.91
> > 702.04
> > 729.05
> > 763.56
> > 789.59
> > 816.11
> > 843.49
> > 882.86
> > 906.77
> > 934.41
> > 967.88
> > 995.82
> > 1018.76
> > 1058.35
> > 1084.19
> > 1114.00
> > 1138.36
> > 1175.36
> >
> > how do these look, especially as the scale from D (which is
really the
> > *center*)? note that the smallest step is 23.80 cents in the
first scale,
> > 22.94
> > in the second.
> >
> > if we need to start from a different periodicity block, let me
know.