Terry Riley: liar or master trickster?

I was recently preparing to play my intro-to-microtonality-class some Just
Intonation stuff. I was going to play them the 3rd movement of the "Harp
of New Albion" of Riley. I thought, this sounds great, it's got that
characteristic JI "purr" in spades, and is a great example of the sound
of the 7-limit.

Except that it isn't.

I was shocked when I read that the piece is in the 5-limit!! So I
decided to investigate the matter further.

The moment in question first occurs around :38 seconds or so into the 3rd
movement. there's a chord that sounded like 7-limit quintad (with a
"ninth" in there), or I'll be a monkey's left shoe. I mean, he must be
lying and there is a 7-limit interval somewhere in that tuning!!

So I figured out where the chord occurred in Riley's tuning.

Here is his complete tuning:

C# D D# E E# F# G G# A A# B B#
1/1 16/15 9/8 6/5 5/4 4/3 64/45 3/2 8/5 5/3 16/9 15/8

The chord in question is a "D" 8:9:10:12:14 chord, but not quite.

The ratios for it, in Riley's tuning, are:

16/15 : 6/5 : 4/3 : 8/5 : 15/8

But 15/8:8/5 is not a 7/6.

It's a 75/64.

The error between the 75/64 and the 74.66666/64 (a perfect 7/6) is
75/74.6666, or 7.713 cents.

So this small error explains why I was fooled into thinking that it was
indeed 7-limit.

With hindsight, I guess I can hear that it sounds a little off. . . or
maybe not. That first time that it appears, it sounds DANGED resonant.
You could fool me. Later he goes on to "jam" all up and down on the
keyboard on this sonority, and here it gets little weaker, but I don't
know if that's me hearing the "error", or just "sound coolness fatigue".

But anyway, it's sort of interesting how one can "fake" intervals of
higher limits within lower ones. I imagine he didn't plan to do this.
. . probably just layed his fingers on the keys and found this resonant
chord, which happens to "almost" be a 7-limit quintad.

I never really considered this possibility, I mean, the common line of
thought is, if you're using JI, then you HAVE to tune EVERYTHING
PERFECTLY.

But of course that's silly, if you've got, say 43 tones per
octave, you're bound to be able to approximate a lot of things very well.

Thoughts?

> But 15/8:8/5 is not a 7/6.
>
> It's a 75/64.

The difference being 225:224, a very famous comma around here.
In fact, I think The Harp of New Albion was even mentioned in
the "12-tone subsets of the 7-limit" thread back in '98/99.

> I never really considered this possibility, I mean, the common
> line of thought is, if you're using JI, then you HAVE to tune
> EVERYTHING PERFECTLY.

On tuning-math we're studying what happens when you allow JI
to be imperfect.

> But of course that's silly, if you've got, say 43 tones per
> octave, you're bound to be able to approximate a lot of things
> very well.

Yep.

-Carl

Hello Christopher!
yes also two 16/15s added together also. it is not uncommon for JI people to do such things.
and you don't have to tempter them out via unison vectors either. Partch is an example ( as a 41
tone system with two added tones). I have seen more than one JI composer become obsessed over the
the sounds at the far end of their tuning.

tuning@yahoogroups.com wrote:

>
>
> Message: 3
> Date: Tue, 6 May 2003 20:12:01 -0400 (EDT)
> From: Christopher Bailey <cb202@columbia.edu>
> Subject: Terry Riley: liar or master trickster?
>
> I was recently preparing to play my intro-to-microtonality-class some Just
> Intonation stuff. I was going to play them the 3rd movement of the "Harp
> of New Albion" of Riley. I thought, this sounds great, it's got that
> characteristic JI "purr" in spades, and is a great example of the sound
> of the 7-limit.
>
> Except that it isn't.
>
> I was shocked when I read that the piece is in the 5-limit!! So I
> decided to investigate the matter further.
>
> The moment in question first occurs around :38 seconds or so into the 3rd
> movement. there's a chord that sounded like 7-limit quintad (with a
> "ninth" in there), or I'll be a monkey's left shoe. I mean, he must be
> lying and there is a 7-limit interval somewhere in that tuning!!
>
> So I figured out where the chord occurred in Riley's tuning.
>
> Here is his complete tuning:
>
> C# D D# E E# F# G G# A A# B B#
> 1/1 16/15 9/8 6/5 5/4 4/3 64/45 3/2 8/5 5/3 16/9 15/8
>
> The chord in question is a "D" 8:9:10:12:14 chord, but not quite.
>
> The ratios for it, in Riley's tuning, are:
>
> 16/15 : 6/5 : 4/3 : 8/5 : 15/8
>
> But 15/8:8/5 is not a 7/6.
>
> It's a 75/64.
>
> The error between the 75/64 and the 74.66666/64 (a perfect 7/6) is
> 75/74.6666, or 7.713 cents.
>
> So this small error explains why I was fooled into thinking that it was
> indeed 7-limit.
>
> With hindsight, I guess I can hear that it sounds a little off. . . or
> maybe not. That first time that it appears, it sounds DANGED resonant.
> You could fool me. Later he goes on to "jam" all up and down on the
> keyboard on this sonority, and here it gets little weaker, but I don't
> know if that's me hearing the "error", or just "sound coolness fatigue".
>
> But anyway, it's sort of interesting how one can "fake" intervals of
> higher limits within lower ones. I imagine he didn't plan to do this.
> . . probably just layed his fingers on the keys and found this resonant
> chord, which happens to "almost" be a 7-limit quintad.
>
> I never really considered this possibility, I mean, the common line of
> thought is, if you're using JI, then you HAVE to tune EVERYTHING
> PERFECTLY.
>
> But of course that's silly, if you've got, say 43 tones per
> octave, you're bound to be able to approximate a lot of things very well.
>
> Thoughts?
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, Christopher Bailey <cb202@c...> wrote:

> 75/74.6666, or 7.713 cents.

7.7115 cents to be more precise.

> So this small error explains why I was fooled into thinking that it
was
> indeed 7-limit.

as carl mentioned, this "anomaly" of 225:224 and its exploitation by
just intonation composers has been a persistent theme on this list.
for example, right around the time this list moved from the mills
server, carl and others were discussing carl's 12-tone just tuning
which made use of these same 225:224 "cheats" -- and turned out to be
quite similar, if not identical, to an important 12-tone just scale
of fokker's (from his book on ji singing) with the same property. if
you don't mind such errors on the fringes of the tuning, but wish to
keep the center absolutely just, you can even implement blackjack as
a simple ji periodicity block:

/tuning/files/perlich/scales/blackjust4.g
if

where the errors in the consonant intervals on the "fringes" are all
either 225:224 (7.7115 cents), 2401:2400 (0.7212 cents), or
16875:16807 (6.9903 cents). in the diagram, the just consonances are
shown in color, and the "trick" consonances are uncolored, with the
ratio by which they deviate from just clearly (i hope) indicated.

of course you could just use 72-tone equal temperament and all the
errors will be 3 cents or under . . . but some will prefer to have
some true just intonation resources instead and allow for greater
errors in chords "far" from the "1/1" . . . it seems to be a matter
of taste, and of endless debate . . .

hi Chris,

my vote: master trickster.

i really loved reading this post, mainly because
the interval in question (75:64), *and* its resemblance
to 7:6, have been the subject of posts i submitted
here years ago in reference to my JI retuning of
my piece _3 Plus 4_.

i tried searching for those posts, but can't find
them. maybe someone else can?

... anyway, here's the piece:
http://sonic-arts.org/monzo/3plus4/3_plus_4_by_monz.mp3

the 75:64 occurs at the end of the main part of
the tune, just before the "hook", where it lands
on the D#-minor chord; it first occurs at time 0:21.

the point behind these posts was how i found it
interesting that while 75:64 is closer in size to
7:6 than it is to 19:16, to my ears the effect
75:64 gave at this point in my piece was more like
the latter than the former.

(i've made reference to these tuning-list posts
so many times that one of these days i really should
assemble them into a webpage, so that i can point
to that instead of trying to find the old posts.)

-monz

----- Original Message -----
From: "Christopher Bailey" <cb202@columbia.edu>
To: <tuning@yahoogroups.com>
Cc: <chris@music.columbia.edu>
Sent: Tuesday, May 06, 2003 5:12 PM
Subject: [tuning] Terry Riley: liar or master trickster?

> I was recently preparing to play my intro-to-microtonality-class some Just
> Intonation stuff. I was going to play them the 3rd movement of the "Harp
> of New Albion" of Riley. I thought, this sounds great, it's got that
> characteristic JI "purr" in spades, and is a great example of the sound
> of the 7-limit.
>
> Except that it isn't.
>
> I was shocked when I read that the piece is in the 5-limit!! So I
> decided to investigate the matter further.
>
> The moment in question first occurs around :38 seconds or so into the 3rd
> movement. there's a chord that sounded like 7-limit quintad (with a
> "ninth" in there), or I'll be a monkey's left shoe. I mean, he must be
> lying and there is a 7-limit interval somewhere in that tuning!!
>
>
> So I figured out where the chord occurred in Riley's tuning.
>
>
> Here is his complete tuning:
>
> C# D D# E E# F# G G# A A# B B#
> 1/1 16/15 9/8 6/5 5/4 4/3 64/45 3/2 8/5 5/3 16/9 15/8
>
>
>
> The chord in question is a "D" 8:9:10:12:14 chord, but not quite.
>
> The ratios for it, in Riley's tuning, are:
>
> 16/15 : 6/5 : 4/3 : 8/5 : 15/8
>
> But 15/8:8/5 is not a 7/6.
>
> It's a 75/64.
>
> The error between the 75/64 and the 74.66666/64 (a perfect 7/6) is
> 75/74.6666, or 7.713 cents.
>
> So this small error explains why I was fooled into thinking that it was
> indeed 7-limit.
>
> With hindsight, I guess I can hear that it sounds a little off. . . or
> maybe not. That first time that it appears, it sounds DANGED resonant.
> You could fool me. Later he goes on to "jam" all up and down on the
> keyboard on this sonority, and here it gets little weaker, but I don't
> know if that's me hearing the "error", or just "sound coolness fatigue".
>
> But anyway, it's sort of interesting how one can "fake" intervals of
> higher limits within lower ones. I imagine he didn't plan to do this.
> . . probably just layed his fingers on the keys and found this resonant
> chord, which happens to "almost" be a 7-limit quintad.
>
> I never really considered this possibility, I mean, the common line of
> thought is, if you're using JI, then you HAVE to tune EVERYTHING
> PERFECTLY.
>
> But of course that's silly, if you've got, say 43 tones per
> octave, you're bound to be able to approximate a lot of things very well.
>
>
>
> Thoughts?

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

> as carl mentioned, this "anomaly" of 225:224 and its exploitation by
> just intonation composers has been a persistent theme on this list.

If you take a 5-limit scale, and look for approximations under 10
cents, the one you seem to run into by far the most often is 225/224.

--- In tuning@yahoogroups.com, Christopher Bailey <cb202@c...> wrote:
> I was recently preparing to play my intro-to-microtonality-class
some Just
> Intonation stuff.

Speaking of your class, did you get my CD?

> I never really considered this possibility, I mean, the common line of
> thought is, if you're using JI, then you HAVE to tune EVERYTHING
> PERFECTLY.

Yow. Where have you been? We've certainly discussed microtemperaments
in relation to JI here before.

> But of course that's silly, if you've got, say 43 tones per
> octave, you're bound to be able to approximate a lot of things very
well.

Try 45 tones of ennealimmal and you can change that to very, very well.

--- In tuning@yahoogroups.com, Christopher Bailey <cb202@c...> wrote:

/tuning/topicId_43658.html#43658

> But anyway, it's sort of interesting how one can "fake" intervals
of higher limits within lower ones. I imagine he didn't plan to
do this. . . probably just layed his fingers on the keys and found
this resonant chord, which happens to "almost" be a 7-limit quintad.
>

***I believe we have had discussions on this list concerning this in
relation to Paul Erlich's ideas of Harmonic Entropy... Yes??

> I never really considered this possibility, I mean, the common line
of thought is, if you're using JI, then you HAVE to tune EVERYTHING
> PERFECTLY.
>
> But of course that's silly, if you've got, say 43 tones per
> octave, you're bound to be able to approximate a lot of things very
well.
>
>
>
> Thoughts?

***Well, Ezra Sims claims he can't hear the difference between 72-tET
and just and Ted Mook feels the same.

And *me?* Well, I would say the same, too, except that Johnny
Reinhard would kick me off the board of the AFMM, so let's say I
write strictly in 72 rather than in approximated *just...* :)

J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> And *me?* Well, I would say the same, too, except that Johnny
> Reinhard would kick me off the board of the AFMM, so let's say I
> write strictly in 72 rather than in approximated *just...* :)

Do you listen to sustained chords when comparing?

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
> --- In tuning@yahoogroups.com, Christopher Bailey <cb202@c...>
wrote:
>
> /tuning/topicId_43658.html#43658
>
> > But anyway, it's sort of interesting how one can "fake"
intervals
> of higher limits within lower ones. I imagine he didn't plan
to
> do this. . . probably just layed his fingers on the keys and
found
> this resonant chord, which happens to "almost" be a 7-limit
quintad.
> >
>
> ***I believe we have had discussions on this list concerning this
in
> relation to Paul Erlich's ideas of Harmonic Entropy... Yes??

well, you need go no further than good old 12-equal to see how you
can "fake" some pretty resonant chords. this is really no different
in nature.

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

/tuning/topicId_43658.html#43869

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > And *me?* Well, I would say the same, too, except that Johnny
> > Reinhard would kick me off the board of the AFMM, so let's say I
> > write strictly in 72 rather than in approximated *just...* :)
>
> Do you listen to sustained chords when comparing?

***Well, this is a good point and it probably *is* audible, although
will all the vagaries of live performance it *could* be hard to
tell. Johnny says if I want just I should really specify the cents
so the performer will do it accurately. I suppose that's a good
point. However, it makes the process much more complicated for the
performer, I believe, so it seems I would prefer the "near just" of
strict 72-tET.

JP

In a message dated 5/26/03 10:48:12 AM Eastern Daylight Time,
jpehrson@rcn.com writes:

> Johnny says if I want just I should really specify the cents
> so the performer will do it accurately. I suppose that's a good
> point. However, it makes the process much more complicated for the
> performer, I believe, so it seems I would prefer the "near just" of
> strict 72-tET.
>
>

Not true. Why should it be any more difficult for a player to read cents and
play exact just than exact 72-tET? Johnny

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

/tuning/topicId_43658.html#43882

> In a message dated 5/26/03 10:48:12 AM Eastern Daylight Time,
> jpehrson@r... writes:
>
>
> > Johnny says if I want just I should really specify the cents
> > so the performer will do it accurately. I suppose that's a good
> > point. However, it makes the process much more complicated for
the
> > performer, I believe, so it seems I would prefer the "near just"
of
> > strict 72-tET.
> >
> >
>
> Not true. Why should it be any more difficult for a player to read
cents and
> play exact just than exact 72-tET? Johnny

***Hi Johnny,

Well, when the performer is playing 72, he is only playing *three*
inflections from 12-equal: the quarter-tone, the sixth-tone and the
twelfth-tone throughout the range.

He doesn't have to think about anything but these *three*
inflections, so anything additional adds to the process...

JP

In a message dated 5/26/03 12:28:50 PM Eastern Daylight Time,
jpehrson@rcn.com writes:

> ***Hi Johnny,
>
> Well, when the performer is playing 72, he is only playing *three*
> inflections from 12-equal: the quarter-tone, the sixth-tone and the
> twelfth-tone throughout the range.
>
I understand, Joseph. However, you seem to think that "normal" notes are
like buttons to be pressed.

In brass, just intervals are most natural to play as a result of the
harmonics. Computing ET quartertones, sixthtones, and twelfth tones, is as hard or
harder than playing pure relationships.

Strings have no points of reference other than harmonics. They too can
negotiate from harmonics easier than ET divisions.

Woodwinds merely need different fingerings. The instruments were based on
these just relationships, with keys added to them in order for them to navigate
12-tET. In some ways, these are the easiest instruments of all for just
because the fingerings put the player (albeit once discovered) right in the ball
park. And the training of the ear to just is a more laudable ability for
harmony than any temperament can be. This may seem a value judgment, but it comes
from a polymicrotonalist that uses all possibilities of intervals for their
idiosyncratic characters.

>He doesn't have to think about anything but these *three*
>inflections, so anything additional adds to the process...

JP

Once again, are you speaking for the players here? As a player I have to
disagree. There is much to think about of which the non-player has no idea.

best, Johnny Reinhard

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Well, this is a good point and it probably *is* audible, although
> will all the vagaries of live performance it *could* be hard to
> tell. Johnny says if I want just I should really specify the cents
> so the performer will do it accurately. I suppose that's a good
> point. However, it makes the process much more complicated for the
> performer, I believe, so it seems I would prefer the "near just" of
> strict 72-tET.

If you want something where it's really very hard to hear any
difference, 171-et does the job, up to the 7-limit anyway. I suspect
many people would actually prefer the sound of 72-et to 171-et or JI
anyway, if we did a head-to-head.

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

/tuning/topicId_43658.html#43887

> --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
wrote:
>
> > ***Well, this is a good point and it probably *is* audible,
although
> > will all the vagaries of live performance it *could* be hard to
> > tell. Johnny says if I want just I should really specify the
cents
> > so the performer will do it accurately. I suppose that's a good
> > point. However, it makes the process much more complicated for
the
> > performer, I believe, so it seems I would prefer the "near just"
of
> > strict 72-tET.
>
> If you want something where it's really very hard to hear any
> difference, 171-et does the job, up to the 7-limit anyway. I suspect
> many people would actually prefer the sound of 72-et to 171-et or JI
> anyway, if we did a head-to-head.

***Hi Gene!

Well, it sounds as though you are saying that maybe people would hear
72-tET as more *integrated*, *symmetrical* or whatever. That's an
interesting contention, and sure to raise the hackles of the JI
religioso...

J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:

> Well, it sounds as though you are saying that maybe people would hear
> 72-tET as more *integrated*, *symmetrical* or whatever. That's an
> interesting contention, and sure to raise the hackles of the JI
> religioso...

What I'm saying is that it doesn't have that characteristic, locked-in
slab-like purity of true JI, which some people prefer and some people
might not. On the other hand, 612-et *does* sound like JI to me.