the passion of the list

Yow...for a bunch of math guys, the folks around here can get pretty
hot under the collar...(a joke, of course...print on a screen does not
convey certain things too well). This is an opportune time for me to say
a couple of brief things about the list...first, I have, and have always
had, the higest respect for math...interestiingly enough, my dad,
brother, and uncle are all very good mathematicians, so it's been around
in my life a lot...it just isn't me. This sort of speculation gets deep,
because I believe I got my "right brain" sort of attitude from my mom's
side, where a great uncle was conductor of the Kansas City Symphony at
one time, and my granny was a classical pianist...I find genetics quite
fascinating, why we are the way we are. I am also an enormous Einstein
fan...here's an interesting guy, who obviously knew something about
math, but also had an ability (with his thought experiments), to bring
very tough concepts down to a very simple place...that's for me.
People do change, hopefully for the better...I apologize here and now
for any past bad vibes directed towards the math folks...I now feel very
at peace with all that...all you theory guys who love lattices and all
that...go for it, it's most likely a blast for you, and I'm sure it is
very meaningful....it sure isn't causing me any harm. On the other hand,
the SOUND of music is my thing, and a knowledge of any sort of tuning
theory is absolutely non essential for producing great music. Sure, it
can point some paths to check out, but the 2 are unrelated. My analogy
is martial arts...I studied many years with some very tough dudes, and I
have a lot of theories about fighting..however, I AM NOT going to get
into the ring and test my theories...I enjoy watching martial arts
contests from the safety of my living room. And, I also must mention
that I studied music theory very deeply for many years with a great
bebop sax player....I love theory, I love speculation and learning new
concepts...it's just that, as I am aging and developing more as a
person, that my more intuitive side is gaining more prominence. We all
have a balance of yin/yang, and I believe my approach to life is more
yin at this point. Again, I have no problem with the math
guys...Starrett is one of my best compadres in all of this, and he
surely qualifies as a math guy...yet, we meet in a place where the
sounds of music take precedence, and we have, and will continue to, make
some great (I hope so) music together.
I am always sorry to see folks calling each other foul names...geez,
when that happens, of COURSE the other party is going to have a heated
response...that is a line that should not be crossed, and when someone
does it, in an earlier time (or read Dune), one could be "called out,"
and loss of life was emminent. A respect for each other as humans is
essential, and those that disrespect it have a problem that they need to
deal with, post haste.
As far as yin/yang, we often see Partch's name mentioned as a great
pioneer, and rightly so...but, Ivor Darreg was also a great pioneer, and
rarely recieves mention here...I believe he was yin to Partch's yang,
and the basic tone of this list is very yang and intellectual...thus,
Partch. Ivor was a great influence on me because of his basic concepts,
the most important being that each tuning has it's own MOOD, or
feeling...indeed, this is a profound concept, quite true, and points the
way towards the making of music...Ivor was not much of a technician, to
be sure, but his "Detwelvulate" CD is a favorite of mine because of the
FEELING in it.
And, that brings me to a parting suggestion...how about all you math
guys talking about your passion for music itself, separate from the
math? What moves you in the field of music? What are you wanting to
experience, feel, when you put a CD on? For example, when I listen to
Bartok's "Music for Strings, Percussion and Celesta," it's like seeing
the storm of WW 2 brewing on the horizon in Europe...it's an experience
beyond music itself...same when I hear Hendrix play "Machine Gun;" it's
like seing a battlefield in the Vietnam war. Marty Robbin's music is
like going to the movies for me, it's totally visual...I could go on.
So, what do some of you other folks get from listening? Thanks for
reading this, I hopwe folks chill out and get into the peaceful and
profound pursuits which music and tuning can provide all of us...Hstick

Very inspiring post, Neil. I'd love to share a few words on the topic.

I got into music because it seems so cool- it's only there (like all art
I guess) because it's beautiful. It's a way for humans to share what we
find beautiful. It seems unlike the other arts, though (and I'm not the
first to point this out), in that it takes sound to a whole new level on
this earth. A visual artist may show us something that's never been seen
(like the fantasy of a Roger Dean painting) or even a new way to see (like
a Picasso or Van Gough), but it never really seems to compare to the
fantastic visual detail around us. Computer graphics are getting there,
I guess (if you've ever seen the movie Antz). Architecture gives us a
new way to live -- an artificial environment -- but on balance, I've
always preferred the woods (where my waste is recycled and the food and
air are fresher, and, the latest science informs us, more healthful).

Music, on the other hand, is definitely at the top of its game. There
are those who may prefer the sound of a running stream, or a traffic jam,
but I'm not one of them. To me the greatest sound on this earth is the
sound of human voices singing in just intonation. I like to imagine that
animals like dogs and cats experience pure bliss when they hear human
music. I even played a concert about this, called _Chorus in the Cello_.
I used the cello register of my piano, which can sound a lot like a tenor
voice, and tried to play what a human choir might sound like if you
couldn't understand the words. There are many stories of angelic choirs.
For an agnostic like me, angelic choirs are human ones.

I'm allergic to cats, and I don't really like them. But when I lived in
Berkeley and had no piano to play, and my neighbor let me use his
Steinway, I had to put up with his cat. But I soon grew to love that
cat, because when I played, it stretched out on top of the piano, on its
back, and hung its head over the fall board, and looked right at me with
its blue eyes. It would stay there for hours while I played. I would
try to imagine what it must be like to hear that, while feeling it
vibrate all around and through you. And if I ever wanted the cat to
leave, I would simply switch to harpsichord (they _hate_ it!). :)

For me, music is one of the richest things in life. Take Beethovan's
late string quartets, a good Bach fugue, or some extended YES tunes.
I've also heard "ethnic" music from Africa, India, and Persia that I
simply couldn't believe.

The kind of thing I'm saying seems to be supported, somewhat, by recent
experiments where listening to "complex" music (Mozart is only one
example) temporarily improves scores on spatial reasoning tests. I
first learned of those experiments from an article Erv Wilson gave me.
He's into this aspect of music, too.

I guess what I'm saying is, I see music as one of the best things about
being human, and thus as one of the best things to be involved with as a
human, to improve humanity if such is possible. Take Beethovan's Ode to
Joy -- a celebration of the fact that all humans experience, from time to
time, the feeling of joy, and isn't that great? Sure, the work is over
played, but if I can live 150 years after it was written and still get
that out of it, then wow!

I got into tuning because it seems like the natural concern of a good
musician. From my earliest memory, I can remember wondering what gave
Barbershop quartets and boys' choirs that special sound. When I found
out about just intonation, I was shocked. I can still remember the first
time I heard the familiar Barbershop, not as a timbre, but as a locked
7-limit chord. I was _really_ shocked. I can still remember the first
time Denny played his 15-limit slide guitar for me. I was blown away.
I knew I was on to something, but that I'd have to learn as much as I
could if I was going to synthesize these new materials into good music
in my lifetime.

You said, Neil, that theory didn't have anything to do with making good
music, and I can see what you're saying. But it only applies to the guy
who's had a 19-tone guitar dropped in his lap -- or, for that matter, a
12-tone one! I've made outstanding music on the top of an empty can of
Pavich organically-grown Jumbo Thompson seedless raisins... but I think I
prefer polyphonic instruments that approximate just intonation (with a
raisin-can holding down the beat, of course!).

A 19-tone guitar may be about the same as a 12-tone one, but consider the
piano. The white keys make a strong statement. They suggest there's
something special about the diatonic scale. I'm a keyboardist in search
of an instrument, and it will be expensive. I want to choose carefully.
That's why I'm on this list, trying to understand all this stuff. I still
believe that the raw materials of 11-limit JI are enough to keep me
occupied making awesom music for many years, but I'm becoming convinced
that organizing these materials a bit before I start will be worth my
time. When I get there, we'll have to jam!

-Carl

Neil and Carl, wonderful testimonials, both of you! Here's my stab.

Music has been a passion for me since long before I knew the meaning
of the word "passion". At about age three, in church, I remember a
particular passage from "Onward Christian Soldiers", where the words
are "forward into battle", and the dyads are something like F-A,
(falling) C-G, A-F, (then back up) C-G, F-A; that progression seemed
very vivid and lovely. The rest of church was a complete and utter
bore to me (something which, for good or ill, has changed little over
time).

My grandfather had huge 78 RPM records, 14 or 15 inches across, with
various light classics. One passage, I think from a Sousa march (!),
always made me think of a graveyard at night with some spirit floating
nearby - again very vivid.

My dad rebuilt an old reed pump organ, and I played by ear, hymns and
popular tunes. I figured out tonic, subdominant, dominant relationships
(without, of course, knowing their names). Relative minors (ditto).
Inversions. Sharps and flats associated with each key. Perfect and
plagal cadences. It's all right out there for intuitive understanding.
Piano lessons did not stick: I found the drills stiflingly boring, when
I could already play songs by ear, with harmony. Of course, I missed
out on learning good keyboard fingering technique by failing to follow
through on lessons!

Somewhere, long ago, my older brother Emerson introduced me to the math
of Just Intonation. I have no idea where he found it, or exactly how
old we were. Teenagers, I suppose. But I didn't actually hear JI
till much later, in my 40's, when I used pitch bends to produce it on a
Korg M1. Beginning in the early '90's, and working completely in a
vacuum, I started writing real-time dynamic retuning software. A year
and a half ago I found the tuning list, learned words like "5-limit" and
"7-limit" for the first time, and abandoned for the moment real-time
tuning in favor of "leisure" tuning (having the whole sequence available
for consideration).

I am by now completely hooked on the sound of (quasi) JI, and listen to
it every day. My own works, such as they are, and retunings of
sequences I happen to like. Especially when well tuned, music has a
sweetness and purity which, to me, no other living experience
approaches. It has no calories, won't get anyone pregnant or sick; it
does not fatigue; it requires no exertion yet demands one's willing
attention; it engages, relaxes, and satisfies like nothing else.

JdL

Neil Haverstick wrote,

> As far as yin/yang, we often see Partch's name mentioned as a
greatpioneer, and rightly so...but, Ivor Darreg was also a great
pioneer, and rarely recieves mention here...I believe he was yin to
Partch's yang, and the basic tone of this list is very yang and
intellectual...thus, Partch.

Great post Neil! I really like your Partch/Darreg analogy, and I
agree -- though I might've said Partch via Helmholtz; there was an
awful lot to Partch (so to speak), and for the most part it's the
Helmholtz part that most frequents the list... In fact, with the
pro/con harmonic entropy threads making so many headlines lately
<grinning thing>, some might find it instructive to check out chapter
X (specifically the "degree of harmoniousness of consonances" section)
of Helmholtz' "On the Sensations of Tone".

In this one bit he offers amongst other things a dyadic "intensity of
influence" measure; that's 100/(n*d) for short (see p. 187), and what
I'm sure must be the original "one footed bride"/"harmonic entropy"
styled attempt to model dyadic consonance (or "concordance") across
the pitch continuum. Of these beautiful and -- to anyone who's been
following the harmonic entropy threads -- familiar looking graphs (see
p. 193) he wrote, "to obtain a general graphical representation of the
complicated relations which co-operate to produce the effect, I have
made such a calculation, knowing that diagrams teach more at a glance
than the most complicated descriptions". I can just see Joe Monzo
nodding his head in approval now! (BTW -- note to Joe Monzo: I think
paragraphs three and four on page 194 would offer an excellent
"classic" psychoacoustic definition of discordance and concordance;
all the more so as he uses the terms dissonance and consonance...
perhaps it would be a good way to set up the distinctions in the
tuning dictionary?).

Anyway, I think it is this prudent, scientific influence in the
tradition of Helmholtz, or Partch via Helmholtz, that probably best
typifies the Erlichian or Keenanesque vibe of the list. Personally I'm
grateful for the degree of quality control that results from the
occasionally curt "technical policing"... but then again I'm also the
type who would like to know if something I'm saying or doing tuning
theory wise is technically out of whack, and I don't think I could
find a better place for that than this very list (thanks in large part
to Paul Erlich's persistency and diligence). The occasional clashing
of the "technocrats" and the "feel" guys is always going to occur, and
I think (and as David Finnamore just pointed out) that simply by its
very nature this type of a forum better sustains technical, as opposed
to aesthetic, discourse... but I see no reason why there wouldn't be
room enough for everyone who's got something to say to say it on the
list the way the it presently operates. I also think of John
Starrett's mp3.com site as an indispensable tuning list "satellite".
Many a list member has their music there to be shared in the same way
that the technical oriented discourse is shared at the tuning list
proper.

Former tuning lister Jeff Collins kindly sent me an Ivor Darreg
"video" a while back, and it was chockfull of quirky homespun warmth
and about a bazillion wonderful oddly detwelveulated devices! Neil
definitely hits the mark when he says "he was yin to Partch's yang"!
But that's not to say that he wasn't an effective or astute author of
tuning theory, as that's hardly the case; Brian McLaren has sent me
some photocopies of Darreg's written material, and I've always found
it to be clear and very informative. But the very idea that he could
coin an archetypal tuning term at once as nebulous and inimitably
useful as "moods" speaks volumes for his experience based,
straightforward approach. Lots of fun and very inspiring.

Anyway, keep yingin' and keep yangin'!,

- dan

John A. deLaubenfels wrote:

>Music has been a passion for me since long before I knew the meaning
>of the word "passion". At about age three, in church, I remember a
>particular passage from "Onward Christian Soldiers", where the words
>are "forward into battle", and the dyads are something like F-A,
>(falling) C-G, A-F, (then back up) C-G, F-A; that progression seemed
>very vivid and lovely. The rest of church was a complete and utter
>bore to me (something which, for good or ill, has changed little over
>time).

This is a particularly stark manifestation of the "horn fifth"
device, so called because it's so idiomatic in writing for pairs
of natural horns. So the passage from the hymn:

soprano: A G F G A G F G
(interval)3 5 6 5 3 5 6 5
bass: F C A C F C A C
for-ward in- to bat- tle

corresponds to the following partials for paired horns:

10 9 8 9 10 9 8 9
8 6 5 6 8 6 5 6

The horn fifth phenomenon was really the only usage of hidden
fifths between outer parts that was considered to be not only
acceptable, but even desirable, in the 18th century. I'm sure this
has something to do with how "catchy" its sound is to the ear;
John's relation of his experience of it as being the one thing that
was interesting to him about a church service when he was a toddler
is a nice testament to that catchy effect.

But what I'm wondering is, why *is* it so catchy? Is it merely that
the device is isomorphic to a goodly portion of the harmonic series,
or could any of the following factors have something to do with it:

--the alternation of imperfect and perfect consonances?
--the implied alternation between two triads a fifth apart?
--the similar motion of the two parts?
--the expanding and contracting size of the interval?

And I wonder if anyone else would agree that the particular instance
of the horn fifth in this hymn is more catchy than just any old horn
fifth because of the fact that the implied two triads a fifth apart
are the tonic and subdominant in the key (whereas the same device
on the tonic and dominant doesn't seem to me like it would have quite
the same effect). In other words, does the tonal implications of the
passage as more-or-less a prolongation of the dominant harmony in the
hymn contribute to the catchiness?

I think if the answer is "yes" this demonstrates an important
relationship between music and those two other things that together
with it form a great triumvirate of passions in my life: food and sex.
For while the music has a great urge to move toward the dominant and
finally come to a rest on the tonic after "see his banners flow,"
the vacillation between the subdominant and the contrapuntal tonic
chord has an irresistable quality all its own, much like the moment
just as one takes a swig of a good beverage right after a heavy meal,
or like the moment just prior to an orgasm. Pretty carnal, passionate
stuff for a Protestant hymn, eh?

D.S.

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

http://www.egroups.com/message/tuning/13356

HELMHOLTZ:
to anyone who's been
> following the harmonic entropy threads -- familiar looking graphs
(see p. 193) he wrote, "to obtain a general graphical representation
of the complicated relations which co-operate to produce the effect,
I have made such a calculation, knowing that diagrams teach more at a
glance than the most complicated descriptions".

Wowzer. Those *really* are the Harmonic Entropy graphs, Dan. I
forgot *all* about those! They've been "around" a while! (1885)

> tuning theory, as that's hardly the case; Brian McLaren has sent me
> some photocopies of Darreg's written material, and I've always found
> it to be clear and very informative. But the very idea that he could
> coin an archetypal tuning term at once as nebulous and inimitably
> useful as "moods" speaks volumes for his experience based,
> straightforward approach. Lots of fun and very inspiring.
>

Does this "moods" business that Darreg is talking about have any
relationship to the similar descriptions in Indian music that we have
been reading about?? Was Darreg influenced by such things? Please
inform, since I really know virtually nothing, unfortunately, about
Darreg...
________ ___ _ __ _ _
Joseph Pehrson

Joseph Pehrson wrote,

> Wowzer. Those *really* are the Harmonic Entropy graphs,
Dan. I forgot *all* about those! They've been "around" a while!

Yes indeed, and it's interesting to note that the minutia of this
particular model continues to fascinate (and evolve) even as the 20th
century says goodbye. In any event, I think he saw it as a way to show
the deep "valleys" and shallow "cols" that would result if a dyadic
continuum were fluidly (as opposed to incrementally) traversed by a
harmonically rich timbre.

> Does this "moods" business that Darreg is talking about have any
relationship to the similar descriptions in Indian music that we have
been reading about?? Was Darreg influenced by such things? Please
inform, since I really know virtually nothing, unfortunately, about
Darreg...

Well I don't know much more than nothing myself, but I'll give it a
go... I remember reading about him hearing some particular 19-tET
music and being vexed by the sound of these pieces, which he
understandably attributed to their composer, only to later discover
upon actually tuning and playing in 19 that he could easily recreate
the vibe he had originally attributed to these pierces by simply
playing the tuning. So, in other words, what he had originally felt
probably had as much to do with the character of the tuning as it had
the character of the pieces.

A simple way to test dive the "mood" theory is to try and play in a
like family of equal tunings. Start simple - say 5 and 10 equal. Once
you've assimilated five, got it good and happening in your ear, can
you then hear its characteristic "mood" in 10? Try the same with say 7
and 14 equal... This is the basic idea.

Try rumaging around in the Brian Mclaren archives at:

<http://www-math.cudenver.edu/~jstarret/mclarens_posts.html>

Brian is (to my mind) an engaging and prolific writer on the topic of
microtonality. He was also close to Darreg and is definitely carrying
on in the "moods" tradition of microtonal exploration. Be forewarned
though: If you though Jeff Harrington was a loose canon polemicist...
or that Jacky Ligon's parting post was a red-hot earful... or that
things couldn't get much worse on the list than they were last week...
well, you ain't seen nothing yet!

- dan

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

http://www.egroups.com/message/tuning/13409

>
> Try rumaging around in the Brian Mclaren archives at:
>
> <http://www-math.cudenver.edu/~jstarret/mclarens_posts.html>
>
> Brian is (to my mind) an engaging and prolific writer on the topic
of
> microtonality. He was also close to Darreg and is definitely
carrying on in the "moods" tradition of microtonal exploration. Be
forewarned

Actually, I'se been there before... and, fortunately, the sign didn't
say "no tresspassin'!" Thanks for the remind and further elaboration.

> though: If you though Jeff Harrington was a loose canon
polemicist...
> or that Jacky Ligon's parting post was a red-hot earful... or that
> things couldn't get much worse on the list than they were last
week... well, you ain't seen nothing yet!
>
>
> - dan

Hmmm. I just can't wait...
__________ ____ __ __ _
Joseph Pehrson

Joseph Pehrson wrote:

> --- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:

on Brian Mclaren:

> > though: If you though Jeff Harrington was a loose canon
> polemicist...
> > or that Jacky Ligon's parting post was a red-hot earful... or that
> > things couldn't get much worse on the list than they were last
> week... well, you ain't seen nothing yet!
> >
> >
> > - dan
>
> Hmmm. I just can't wait...

Very opinionated.

--
* D a v i d B e a r d s l e y
* 49/32 R a d i o "all microtonal, all the time"
* http://www.virtulink.com/immp/lookhere.htm

Joseph Pehrson wrote,

> Hmmm. I just can't wait...

Yeah, the interpersonal bad is real bad... no doubt about it. But I'm
of the opinion that the good is rare and that his good is good... so
I'm also of the opinion that there's an awful lot there that's *WELL*
worth a look... what a prolific guy.

FWIW, Brian's own "A Brief History of Microtonality in the 20th
Century" mightily stoked my imagination many years ago as it seemed to
paint a world just bursting at the seems with possibilities... and for
better or worse, I have a feeling that this is not always the
impression one might get if they were to land on this list still
unsure of themselves and exactly what it is that they wanted to do
tuning wise (see Haverstick's point about the tenor of the list being
"yang heavy" so to speak).

Skip the interpersonal mayhem posts and check out the worthwhile
business... there's plenty of it.

- dan

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
> http://www.egroups.com/message/tuning/13409
>
> Joseph Pehrson wrote:
> >
> > Does this "moods" business that Darreg is talking about have
> > any relationship to the similar descriptions in Indian music
> > that we have been reading about?? Was Darreg influenced by
> > such things? Please inform, since I really know virtually
> > nothing, unfortunately, about Darreg...
>
> ... Try rumaging around in the Brian Mclaren archives at:
>
> <http://www-math.cudenver.edu/~jstarret/mclarens_posts.html>
>
> Brian is (to my mind) an engaging and prolific writer on the
> topic of microtonality. He was also close to Darreg and is
> definitely carrying on in the "moods" tradition of microtonal
> exploration. Be forewarned though: If you though Jeff Harrington
> was a loose canon polemicist... or that Jacky Ligon's parting
> post was a red-hot earful... or that things couldn't get much
> worse on the list than they were last week...
> well, you ain't seen nothing yet!

I'm not sure how much of a connection there is between the Indian
'moods' concepts and Darreg's. Darreg's main contribution to
tuning theory in this particular area was a recognition that
each tuning (I can only recall him saying this about ETs) has
a particular mood. I think his main point was that there was
no reason to not explore a certain ET, just because 'theory'
says that it's useless from the standpoint of JI approximations,
etc. Every ET has compositional possibilities because each
one has its own valid mood to explore.

McLaren is no doubt the main person carrying on the Darreg
tradition - indeed he has devoted a *lot* of work to assembling
Darreg's work into a website that hopefully we'll see some day
soon. Brian has also collected a ton of Darreg's music on
various CDs he's made as part of his 'Microtonal Record Shelf'
series.

If you write to Brian and express a sincere interest in
microtonal music, you can expect a generous flood of CDs and
articles in your mailbox.

Brian McLaren
2462 SE Micah Pl
Corvallis, OR 97333-1966

And Dan's warning about the vitriolic attitude of Brian's writing
is right on the mark: the fantastic piece he sent me that inspired
me to write the post I sent yesterday about the complexity of
human musical perception is a direct attack on at least one branch
the New York academic music-theory establishment, and is entitled
'MTO TALK gets a Drano enema'.

So that gives you some idea of the inflammatory language he uses
in his attempts to unclog the thought processes of what he sees as
block-headed academic theorists going on and on about generalities
that supposedly concern music but that take no account of results
of modern psychoacoustic research. But he backs up every word
he writes with copious (and I do mean copious) references to the
literature, and about 85% of his quotes are from the 1990s.

Darreg himself was no slouch when it comes to written theory.
I've been told by those who knew him that he considered it a
form of therapy to wake up at 6 am and sit at his typewriter
for 5 hours EVERY DAY. When I mentioned letters from Ivor to
Johnny Reinhard, Johnny said 'wait a minute' and returned with
a BOX of letters from Darreg - he was that prolific. A lot of
his work was reprinted in various issues of _Xenharmonikon_,
and quite a bit of McLaren's can also be found there.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

It's the passion on the list that best speaks to the intensity with which we
care about what we do. Sometime people don't like each other all that much
but they work together for the common good (or at least their mutual good).
Much more often, there are friends to be made and new ideas to explore.

Being on this list is like looking carefully into the mirror to see all
that's there, over and over, again.

I would suggest that statistically, some will leave for whatever reasons.
And some will come back. Yes, the e-mail medium is often mistaken for overly
passionate declarations (some even seeming to rant) but they are all primary,
firsthand examples of feedback to one's work, and very important in the long
run.

My aim is to be as courteous and I can be on the conscious level, to the
degree that's possible. Somethings can be tough to take, but
misunderstanding complexities is something none of us need apologize for.
None of us is the list without the others.

Johnny Reinhard

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/13443

> If you write to Brian and express a sincere interest in
> microtonal music, you can expect a generous flood of CDs and
> articles in your mailbox.
>
> Brian McLaren
> 2462 SE Micah Pl
> Corvallis, OR 97333-1966
>

Thanks a lot, Monz, for the reference, and I will immediately write
to him...

Does he have e-mail as well??

>
> And Dan's warning about the vitriolic attitude of Brian's writing
> is right on the mark: the fantastic piece he sent me that inspired
> me to write the post I sent yesterday about the complexity of
> human musical perception is a direct attack on at least one branch
> the New York academic music-theory establishment, and is entitled
> 'MTO TALK gets a Drano enema'.
>

I could use a little work in the plumbing department, so I'm looking
forward to it!
____________ ____ __ __ _
Joseph Pehrson

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

http://www.egroups.com/message/tuning/13444

> It's the passion on the list that best speaks to the intensity with
which we care about what we do. Sometime people don't like each
other all that much but they work together for the common good (or at
least their mutual good). Much more often, there are friends to be
madeand new ideas to explore.
>
> Being on this list is like looking carefully into the mirror to see
all that's there, over and over, again.
>
> I would suggest that statistically, some will leave for whatever
reasons. And some will come back. Yes, the e-mail medium is often
mistaken for overly passionate declarations (some even seeming to
rant) but they are all primary, firsthand examples of feedback to
one's work, and very important in the long run.
>
> My aim is to be as courteous and I can be on the conscious level,
to the degree that's possible. Somethings can be tough to take, but
> misunderstanding complexities is something none of us need
apologize for. None of us is the list without the others.
>
> Johnny Reinhard

I very much enjoyed "boss" (AFMM) Johnny Reinhard's post! I agree
with it 200%! Whoops... there's my math again... it was ASCAP that
wanted 200% royalties (....)
_____________ ____ __ __ _
Joseph Pehrson

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
> --- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> http://www.egroups.com/message/tuning/13443

[Brian McLaren's address]

>
> Does he have e-mail as well??

As far as I know he only gives to people at his own discretion,
so I'm sorry but I won't pass it along.

He appreciates it when people go thru the trouble of writing
a letter and putting it in a mailbox, and if you do that,
he will reward you with a package of goodies. You can count
on it. His 'Introduction to Microtonality' CD is worth asking
for specifically, as well as the 'Drano enema' paper.

> [me, monz]
>
> And Dan's warning about the vitriolic attitude of Brian's writing
> is right on the mark: the fantastic piece he sent me that inspired
> me to write the post I sent yesterday about the complexity of
> human musical perception is a direct attack on at least one branch
> the New York academic music-theory establishment, and is entitled
> 'MTO TALK gets a Drano enema'.
>
>
> [Joe Pehrson]
>
> I could use a little work in the plumbing department, so I'm
> looking forward to it!

OK, but be forewarned!!

Look at the last word in that title: he's talking about
unclogging *HUMAN* plumbing with Drano, not the kind that's
made of iron!

McLaren's choice of words is a force to be reckoned with !!!!!!
If any microtonalist has the passion alluded to in the thread
title, it's him!

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Neil wrote,

>And, that brings me to a parting suggestion...how about all you math
>guys talking about your passion for music itself, separate from the
>math? What moves you in the field of music? What are you wanting to
>experience, feel, when you put a CD on?

Music . . . I am at a loss for words to put in into . . . it just goes
beyond the trappings of daily experience . . . it's more powerful than any
other form of art or communication. Every style is wonderful and
transcendent in its own way . . . Both Yes and Debussy have made me cry . .
. Eric Clapton and Jimi Hendrix have made me value playing guitar more
highly than even speaking . . . I hear a good African beat and I start to
dance, it's as basic as breathing and eating and sleeping . . . when I put a
CD on, I want to feel something, whether it's intellectual wonderment or
anger or loveliness . . . good music gets you right to the feeling, and you
forget where you are, who you are, or who's making the music . . . even
playing can be like that sometimes.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/13492
>
> . . . when I put a CD on, I want to feel something, whether
> it's intellectual wonderment or anger or loveliness . . . good
> music gets you right to the feeling, and you forget where you
> are, who you are, or who's making the music . . . even playing
> can be like that sometimes.

In my experience, playing can bring about the *strongest*
feelings of forgetting where and who you are (too bad it's
only the rare moments when inspiration is really running high,
that it gets like that) - far stronger than anything I feel
from merely listening, altho the best recorded performances
can do it too to a lesser extent.

The best moments I can remember like this were when I used
to play in a biker band (rock 'n' roll) back in the early 1980s.
There were times when we were jamming (in improvisational
sections moreso than the 'worked out' parts) and it really
felt like we were all tapped into some kind of cosmic vibe
that dictated what we played while we just followed along.

Music is the only art-form I know of that can do that.
I think it's more akin to a great sporting event, when the
team is really hot, than to its art cousins like painting,
cinema, etc. - altho being in the audience at a *really* good
poetry reading can come close to this feeling too.

Among the multitude of other amazing results of psychoacoustic
research documented in McLaren's 'MTO TALK gets a Drano enema',
one of the most fascinating is this:

> [Brian McLaren]
>
> ... modern brain research into music listening systematically
> disproves the antique canard that a melodic arc or rhythm or
> timbre is perceived and analyzed raionally by the [detail-
> oriented logical word-centered] left brain hemisphere. On
> the contrary, a large body of modern brain research proves
> that listeners primarily use their emotional wholistic
> large-scale-pattern-perceiving right brain hemisphere when
> listening to music...

The primary reference he gives to this particular topic is:

Antonio R. and Hanna Damasio. 1977.
'Musical Faculty and Cerebral Dominance',
in _Music and the Brain: Studies in the Neurology of Music_
ed. MacDonald Critchley and R. A. Henson.
William Heinemann Medical Books Limited, London, p 145-152.

This seems to me to support very well what I quoted Paul as saying.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

Sound Chaser

Faster moment spent spread tales of change within the sound,
counting form through rhythm electric freedom
moves to counterbalance stars expound our conscience
all to know and see the look in your eyes.

Passing time will reach as nature relays to set the scene,
new encounters spark a new fruition,
guiding lines we touch them, our bodies balance out the waves
as we accelerate our days to the look in your eyes.

From the moment I reached out to hold I felt a sound,
and what touches our soul slowly moves as touch rebounds.
And to know that tempo will continue
lost in trance of dances
as rhythm takes another turn,
as is my want, I only reach to look in your eyes.

-Anderson, Howe, Moraz, Squire, and White

In response to Neil's post I will name some music which has struck
me strongly in the past several years. I made a list of musicians
or groups that I considered to be my greatest musical discovery in
the pop/world category in a particular year, hearing it on the
radio, via friends or otherwise. I don't like the term "world music"
but use it in absence of a better term. All music is world music,
isn't it? If you think your musical taste may be similar to mine,
then pay attention, because obviously I regard this to be a set of
very good tips!

1991: Lamine Konte�
Griot from Senegal. Sings very melodious songs accompanying himself
on the kora.

1992: Madredeus
Folk group from Portugal. Probably doesn't need an introduction since
it is very successful.

1993: Varttina (with umlaut on both a's)
Finnish group singing lively, cheerful songs, many traditional.
The slower songs are beautiful too.

1994: Padma Talwalkar
Classical Indian singer. Use a sunny morning to hear her singing
raga Jaunpuri and feel a "cosmic joy", also for lack of an adequate
term.

1995: Natacha Atlas
Former Trans-Global Underground singer. She makes pop music with a
strong Arabic component. Quality songs in Arabic intonation.

1996: Hijas del Sol
Two sunny sisters from Ecuatorial Guinea. They're so cute.

1997: Geeta Dutt
My favourite Indian popular film music singer. Even if you don't like
the genre you have to admit she sings this nostalgic music from the
50's and 60's beautifully.

1998: Min Xiao-Fen
Virtuoso Chinese player of pipa and ruan.

1999: Urna Chahar-Tugchi
or simply "Urna". Female singer from Inner-Mongolia with a fabulous
voice. Accompanied by Mongolian and Chinese traditional instruments
and electric zither.

Manuel Op de Coul coul@ezh.nl

--- In tuning@egroups.com, Neil Haverstick <STICK@U...> wrote:
> can point some paths to check out, but the 2 are unrelated. My
analogy
> is martial arts...I studied many years with some very tough dudes,
and I
> have a lot of theories about fighting..however, I AM NOT going to
get
> into the ring and test my theories...I enjoy watching martial arts
> contests from the safety of my living room. And, I also must mention

I don't blame you. I heard there were four guys with broken hands
from the latest Dog Brothers Gathering (a meeting of martial arts
enthusiasts who get together for stick fighting with minimal
protection allowed as well as grappling). Such an event is not a
tournament; there are no prizes other than perhaps friendship and
respect. This is the lengths some people will go to, to test their
fighting skills and theories. All I have done is one full contact
sparring session (tae kwan do rules) and the wrestling-type practice
of Judo and that is as far as I care to take it - I want to retain
the use of my hands for music making. :)

> pioneer, and rightly so...but, Ivor Darreg was also a great
pioneer, and
> rarely recieves mention here...I believe he was yin to Partch's
yang,

Darreg was the guy who really planted the seeds of interest in
microtonality in my head. Not in person but at the posthumous
release party for his CD "Detwelvulate!". I even got to see a
microtonal rock band at the party featuring Jonathan Glaser on 19-
tone tuned keyboard and some long-haired dude on 19-tone electric
guitar who also played some mean slide licks on a Megalyra. I don't
know why the "seed" didn't take root right away - otherwise I would
have never left San Diego.

> And, that brings me to a parting suggestion...how about all you
math
> guys talking about your passion for music itself, separate from the
> math? What moves you in the field of music? What are you wanting to
> experience, feel, when you put a CD on? For example, when I listen

I'm not really a math guy. :) But I must say I was moved by much of
the music in the movie "Kama Sutra: A Love Story" that was shown on
Bravo tonight. I had a similar reaction to the music of "The Last
Temptation Of Jesus Christ".

Paolo

--- In tuning@egroups.com, phv40@h... wrote:
> http://www.egroups.com/message/tuning/13621
>
> Darreg was the guy who really planted the seeds of interest in
> microtonality in my head. Not in person but at the posthumous
> release party for his CD "Detwelvulate!". I even got to see a
> microtonal rock band at the party featuring Jonathan Glaser on
> 19-tone tuned keyboard and some long-haired dude on 19-tone
> electric guitar who also played some mean slide licks on a
> Megalyra. I don't know why the "seed" didn't take root right
> away - otherwise I would have never left San Diego.

It's Jonathan *Glasier*. And the 'long-haired dude' on guitar
was probably Jeff Stayton - does that name ring a bell?
If not, perhaps it was John McBryde AKA Brink McGoogy.

BTW, I wanted to mention Brink earlier in response to the post
asking about others who use these non-'8ve' ET scales. He and
Brian McLaren both use them.

It's too bad Brink's music isn't better known - he's recorded
some *really* rocking stuff in very oddball tunings.

McLaren uses such tunings as 31^(1/37), 17^(1/21), and
5^(1/31) in his pieces.

Another very famous use of a tuning like this was 5^(1/25)
(I think that's it - can't find a reference) by Stockhausen
in _Gesange der Ju"nglinge_, back around 1955-56.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

I wrote:
> http://www.egroups.com/message/tuning/13630
>
> McLaren uses such tunings as 31^(1/37), 17^(1/21), and
> 5^(1/31) in his pieces.
>
> Another very famous use of a tuning like this was 5^(1/25)
> (I think that's it - can't find a reference) by Stockhausen
> in _Gesange der Ju"nglinge_

I thought some of you who aren't familiar with these
non-'8ve' ETs, and who don't have the liner notes to
McLaren's CD, would be interested in knowing a little
more about those cryptic numbers.

Curtain please....

'ratio' ~decimal ~cents ~deg/8ve name

31^(1/37) 1.09725 161 7.468 37th root of 31
17^(1/21) 1.14444 234 5.138 21st root of 17
5^(1/31) 1.05329 90 13.351 31st root of 5
5^(1/25) 1.06649 111 10.767 25th root of 5

The 1st column gives the clearest mathematical expression
of the exact interval of the basic 'step size' in each scale
- 'ratio' is in quotes because the value is by definition an
irrational number.

The 2nd column gives an approximate decimal value for the
'ratio' of the basic step-size.

The 3rd column gives the approximate cent value of the basic
step-size.

The 4th column gives the approximate number of degrees that
span an '8ve', which is here defined as the 1:2 ratio.

The last column gives the name of the 'ratio' in words, which
is the form used to describe the tuning.

The McLaren tunings are used on tracks 7, 15, and 22, respectively,
on his CD _Microtonal Music, Volume 2_.

Lots of info on Stockhausen's piece can be found in the literature
on modern music.

(Except that in all the books *I* have, I can't find one damn
reference to the tuning of this piece!... ARRRGH!!! ... I know
it's here somewhere!...)

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

> Curtain please....
>
> 'ratio' ~decimal ~cents ~deg/8ve name
>
> 31^(1/37) 1.09725 161 7.468 37th root of 31
> 17^(1/21) 1.14444 234 5.138 21st root of 17
> 5^(1/31) 1.05329 90 13.351 31st root of 5
> 5^(1/25) 1.06649 111 10.767 25th root of 5
>
Thank you, Monz, for this help. Actually, I *WAS* kind of "getting
it" from the formula... but this really "spells it out"
specifically...

STOCKHAUSEN:
>
> (Except that in all the books *I* have, I can't find one damn
> reference to the tuning of this piece!... ARRRGH!!! ... I know
> it's here somewhere!...)
>

Are you certain that the tuning you mention wasn't used in his
earlier electronic STUDIE... rather than in GESANGE (??) Maybe it
was used in both... but I am pretty certain about the former...
___________ ___ __ _ _
Joseph Pehrson

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/13636

> Curtain please....
>
>
>
> 'ratio' ~decimal ~cents ~deg/8ve name
>
> 31^(1/37) 1.09725 161 7.468 37th root of 31
> 17^(1/21) 1.14444 234 5.138 21st root of 17
> 5^(1/31) 1.05329 90 13.351 31st root of 5
> 5^(1/25) 1.06649 111 10.767 25th root of 5
>
>
> The 1st column gives the clearest mathematical expression
> of the exact interval of the basic 'step size' in each scale
> - 'ratio' is in quotes because the value is by definition an
> irrational number.
>
> The 2nd column gives an approximate decimal value for the
> 'ratio' of the basic step-size.
>
> The 3rd column gives the approximate cent value of the basic
> step-size.

I had to make another comment on this. On looking at the cents
values... my first reaction is to say "that's warped!"

Of course, "warped" is a high compliment in my lexicon...

I note that the values for his step sizes are PRETTY CLOSE to our
"accepted" 12-tET in all of the cases. (Well, I mean, contrasted
with so many other microtonal scales with smaller step sizes.)

Could it be that McLaren... with his extensive background and
knowledge of microtonality... has come to the conclusion that the
scales that are really the MOST ASTONISHING are those that
APPROXIMATE our traditional 12-tET, but that are slighly "askew??"...
particularly regarding the non-equivalent octave (??)

That's playing with our tradition, perception, and perhaps it also
indicates that there is a kind of "natural" step size to scales
(somewhere around 100 cents maybe) that make pitch differentiation
meaningful.

Dunno. Just something to think about.
_______________ ___ __ _ _
Joseph Pehrson

Joseph wrote,

>Could it be that McLaren... with his extensive background and
>knowledge of microtonality... has come to the conclusion that the
>scales that are really the MOST ASTONISHING are those that
>APPROXIMATE our traditional 12-tET

I don't see in what way a scale of 161- or 234- cent intervals could be said
to approximate 12-tET!

Someone using Paul Erlich's email wrote:

> Music . . . I am at a loss for words to put in into . . . it just goes
> [snip]
> forget where you are, who you are, or who's making the music . . . even
> playing can be like that sometimes.

Who are you, and what have you done with Paul?!

:-)

--
David J. Finnamore
Nashville, TN, USA
http://members.xoom.com/dfinn.1
--

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13664

> Joseph wrote,
>
> >Could it be that McLaren... with his extensive background and
> >knowledge of microtonality... has come to the conclusion that the
> >scales that are really the MOST ASTONISHING are those that
> >APPROXIMATE our traditional 12-tET
>
> I don't see in what way a scale of 161- or 234- cent intervals
could be said to approximate 12-tET!

Hi Paul!

You _would_ pick the ones that are the furthest from 100 cents for
your example!! I meant that the scale step size is "roughly" similar
to the 100 cent steps we are "used" to, only the system would be a
little "wacky" due to the elimination of the octave. Let's say, in a
generalized sense as compared with a 25 cent interval for 48-tET or
some such.
________________ ____ __ __ _
Joseph Pehrson

Joseph wrote,

>You _would_ pick the ones that are the furthest from 100 cents for
>your example!! I meant that the scale step size is "roughly" similar
>to the 100 cent steps we are "used" to, only the system would be a
>little "wacky" due to the elimination of the octave.

Even a scale with 90-cent steps would have almost nothing in common with
12-tET, as regards its musical properties. Think of Gary Morrison's 88-¢et
scale. Think of 13-tET.

I once suggested that a nice set of six guitars would be in all the ETs from
26 to 31. Dan Stearns asked, why so many similar scales? I replied, these
scales couldn't be more different, and span the gamut as regards musical
properties.

Paul Erlich wrote,

> I once suggested that a nice set of six guitars would be in all the
ETs from 26 to 31. Dan Stearns asked, why so many similar scales? I
replied, these scales couldn't be more different, and span the gamut
as regards musical properties.

Frettings that is... "similar frettings". In other words, so many
similar modes of interface. Interface matters (well to me anyway).
BTW, I think this type of "confusion" is typical of some of the
"problems" that occur onlist; different folks can simply read the same
thing quite differently.

- dan

--- In tuning@egroups.com, "Joseph Pehrson" <pehrson@p...> wrote:
> http://www.egroups.com/message/tuning/13647
>
> --- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> http://www.egroups.com/message/tuning/13636
>
> > 'ratio' ~decimal ~cents ~deg/8ve name
> >
> > 31^(1/37) 1.09725 161 7.468 37th root of 31
> > 17^(1/21) 1.14444 234 5.138 21st root of 17
> > 5^(1/31) 1.05329 90 13.351 31st root of 5
> > 5^(1/25) 1.06649 111 10.767 25th root of 5
> >

Closeness of McLaren's non-'8ve' ETs TO 12-ET?
----------------------------------------------

> [Joe Pehrson]
>
> I note that the values for his step sizes are PRETTY CLOSE to our
> "accepted" 12-tET in all of the cases. (Well, I mean, contrasted
> with so many other microtonal scales with smaller step sizes.)

Well... the ~161-cent step size of 31^(1/37) is a lot closer
to a '3/4-tone' interval [= 150 cents] than to anything 12-tET;
McLaren's composition in this tuning doesn't sound at all like
a 12-tET piece. The nearest low-integer ratios to it are 11/5
[= ~165 cents], 35/32 [== 5^1*7^1 = ~155 cents], and 12/11
[= ~151 cents].

But you're right to observe that the other ones are rather
closer, maybe not so much to 12-tET, but to ratios we know.
It's interesting to observe what familiar intervals these
'weird' ones approximate...

The 5^(1/31) step-size of ~90 cents is nearly identical to
the 256/243 [== 3^-5] 'limma' version of the 'semitone' in
Pythagorean tuning.

The 5^(1/25) step-size of ~111 cents is very close to the
16/15 semitone of 5-limit JI [= ~112 cents].

But note that neither of these non-'8ve' ETs has any special
resemblance to the respective JI approximations *as a whole*,
because both Pythagorean and 5-limit scales have *two* versions
of the semitone, and McLaren's scales only have one.
So they still sound 'weird' (and beautiful).

The 17^(1/21) step-size of ~234 cents is quite close to the
septimal 'whole tone' of 8/7 [= ~231 cents]. So this tuning
sort of resembles a 'septimal whole tone scale', altho it's
also somewhat like 5-tET [step-size of 240 cents].

McLaren playing with tradition?
-------------------------------

>
> Could it be that McLaren... with his extensive background and
> knowledge of microtonality... has come to the conclusion that
> the scales that are really the MOST ASTONISHING are those that
> APPROXIMATE our traditional 12-tET, but that are slighly
> "askew??"... particularly regarding the non-equivalent octave (??)
>
> That's playing with our tradition, perception, <...>

(I'm treading in dangerous water here, presuming to speak for
McLaren... quick, what's the antidote if you swallow Drano?!...)

I'd guess that what you're saying here may be a part of why
he likes these scales so much. One thing Brian absolutely
*revels* in is totally trashing what he perceives as worn-out
'old wives tales' and traditions, and the more gasoline he
can pour on the flames, the better.

But I think that really his main point is just to explore the
sound of as many different tunings as he can discover. Brian
and Johnny Reinhard stand out as the two who have composed in
more different kinds of tunings than anyone else I know of.

Brain has also composed pieces in every ET from 5 to 53, and
if you think La Monte Young uses high-prime JI, track 12 of
McLaren's _Microtonal Music, Volume 6_ is in 641-limit JI,
and track 15 is in 3067-limit JI!

(In case Paul Erlich is ready to dispute the relevance of a
JI limit this high, I'll emphasize now that this is *precisely*
McLaren's point: we can't hear anything in these tunings
that has anything to do with their supposed numerical qualities,
because these large numbers are too close to the small ones
which *do* have such a powerful affect.)

Mostly he just likes to find an interesting mathematical construct,
then tune up his intruments and compose pieces expoloring what
they sound like. Mostly I see him as a great adventurer, sort
of a Magellan of microtonality. His intent is definitely to
open up the 'Western' world's ears to *non*-12-tET in every
way possible.

I think McLaren's real point of departure is Darreg's observation
that each tuning has its own 'mood', and that regardless of
supposed psychoacoustical relevance or irrelevance, *every*
tuning has more-or-less unique compositional possibilities.

I say 'more-or-less unique' because when one begins working
with as many different tunings as McLaren (and Reinhard, and
Dan Stearns), one begins to perceive the 'family' relationships
between different tunings. For example, 5-, 10-, 15-, 10-,
and 25-tET all have some intervals in common, so there are
sounds common to all of them that can be used to portray these
'familial' relationships.

A 'natural' step-size for scales?
---------------------------------

> <...> and perhaps it also indicates that there is a kind
> of "natural" step size to scales (somewhere around 100 cents
> maybe) that make pitch differentiation meaningful.
>
> Dunno. Just something to think about.

That's an interesting observation. But if anyone asked me what
I thought was a 'natural' scale step size, I'd probably be
inclined to answer in terms of some kind of pentatonic scale
system, because a *lot* of music all over the world and for
centuries (millenia?), right down to present-day pop music,
has made use of pentatonic scales most of the time. So I'd
be much quicker to say that the 'natural' step size is somewhere
between a 'major 2nd' [= ~200 cents] and 'minor 3rd' [= ~300
cents].

I think it's perhaps even more interesting that I can't make
a decision between these two: the 'natural' scales seem more
often to contain *two* step-sizes rather than one, whether
they're pentatonic or heptatonic (= diatonic). Of course I'm
generalizing here, but the concept is one worth exploring
- Dan Stearns posts a lot on this.

The 'complete set' of McLaren non-'8ve' ETs
-------------------------------------------

Here's a table of all the non-'8ve' ETs used by McLaren in the
CDs I have by him:

(The 'vol.trk' column gives the volume number of the CD in
McLaren's 'Microtonal Music series, and track number of the
composition. Other columns formatted as above, except that
I decided that one decimal place was good enough for 'deg/8ve'.)

vol.trk 'ratio' ~decimal ~cents ~deg/8ve name

1.4 3^(1/13) 1.08818 146 8.2 13th root of 3
1.6 3^(1/15) 1.07599 127 9.5 15th root of 3
1.7 3^(1/16) 1.07108 119 10.1 16th root of 3
1.8 3^(1/17) 1.06676 112 10.7 17th root of 3
2.7 31^(1/37) 1.09725 161 7.4 37th root of 31
2.15 17^(1/21) 1.14444 234 5.1 21st root of 17
2.22 5^(1/31) 1.05329 90 13.4 31st root of 5
3.7 7^(1/38) 1.05254 89 13.5 38th root of 7
4.1 5^(1/25) 1.06649 111 10.8 25th root of 5
4.15 5^(1/33) 1.04998 84 14.2 33rd root of 5
4.16 31^(1/53) 1.06694 112 10.7 53rd root of 31
6.3 17^(1/28) 1.10648 175 6.9 28th root of 17

Notes about the step-sizes:

- 3^(1/13) and 31^(1/37) are close to 2^(3/24) ['3/4-tone'].

- 3^(1/15) and 3^(1/16) are close to 2^(5/48) ['5/8-tone'].

- 3^(1/17), 5^(1/25), and 31^(1/53) are nearly the 16/15 ratio.

- 17^(1/21) is close to the 8/7 ratio.

- 5^(1/31), 7^(1/38), and 5^(1/33) are close to the 'limma'.

- 17^(1/28) is nearly identical to 2^(7/48) ['7/8-tone'].

Joe, you've composed pieces in '1/8-tones'... you should find
some of these tunings quite interesting.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13672

> Joseph wrote,
>
> >You _would_ pick the ones that are the furthest from 100 cents for
> >your example!! I meant that the scale step size is "roughly"
similar to the 100 cent steps we are "used" to, only the system
would be a little "wacky" due to the elimination of the octave.
>
> Even a scale with 90-cent steps would have almost nothing in common
with 12-tET, as regards its musical properties. Think of Gary
Morrison's 88-¢et scale. Think of 13-tET.
>
> I once suggested that a nice set of six guitars would be in all the
ETs from 26 to 31. Dan Stearns asked, why so many similar scales? I
replied, these scales couldn't be more different, and span the gamut
as regards musical properties.

Hi Paul...

Well, I would be the first to admit that most probably you have
developed a "heightened sensitivity" due to your increased exposure
and to your having studied all the xenharmonic stuff in such great
detail.

HOWEVER, I would still submit that one of the reasons that the
Bohlen-Pierce scale is so intriguing is due to the fact that the
scale steps are _somewhat_ similar to what we have grown "used" to in
12-tET, only "wacked out" due to the lack of octave equivalence...

Actually, I would also maintain that you *OWN* choice of 22-tET,
particularly when you divided it up into TWO 12 note scales (well, OK
you left out the E or whatever) was due to the fact that you wanted
to emulate 12-tET to a degree in PRACTICE, while retaining all the
xenharmonic benefits of the sonorities of 22...

So, the point is, the comparisons to 12-tET are apt and, in fact,
some of the most interesting and useful scales are similar to it...
only a little "off..." 19 is a little like that too.

That's just my cursory "take..."
______________ ___ __ _ _
Joseph Pehrson

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/13679

> (The 'vol.trk' column gives the volume number of the CD in
> McLaren's 'Microtonal Music series, and track number of the
> composition. Other columns formatted as above, except that
> I decided that one decimal place was good enough for 'deg/8ve'.)
>
>
> vol.trk 'ratio' ~decimal ~cents ~deg/8ve name
>
> 1.4 3^(1/13) 1.08818 146 8.2 13th root of 3
> 1.6 3^(1/15) 1.07599 127 9.5 15th root of 3
> 1.7 3^(1/16) 1.07108 119 10.1 16th root of 3
> 1.8 3^(1/17) 1.06676 112 10.7 17th root of 3
> 2.7 31^(1/37) 1.09725 161 7.4 37th root of 31
> 2.15 17^(1/21) 1.14444 234 5.1 21st root of 17
> 2.22 5^(1/31) 1.05329 90 13.4 31st root of 5
> 3.7 7^(1/38) 1.05254 89 13.5 38th root of 7
> 4.1 5^(1/25) 1.06649 111 10.8 25th root of 5
> 4.15 5^(1/33) 1.04998 84 14.2 33rd root of 5
> 4.16 31^(1/53) 1.06694 112 10.7 53rd root of 31
> 6.3 17^(1/28) 1.10648 175 6.9 28th root of 17
>
>
I think the confusion here has to do with the fact that I'm being
"gross" (ahem) and not really specific.

OF COURSE, I *do* realize that each tuning system is different... I
was just saying that in a "gross" way it would seem that any system
that has a basic unit that is in the vicinity of 100 to 200 cents,
would be a LITTLE akin to the 12-tET we know, or to some readily
acceptable "smallest cultural unit" as you seem to also be
attesting...

I'm just contrasting that in a general way with teeny-tiny scale
steps that you would get with 31-tET or 72 or whatever... and saying
that the alteration from expected tradition has something to do with
why I find these kind of scales so intriguing and peculiar.

It seems, Joe, that you found at least a GRAIN of truth or interest
in some of my comments on this. These were just the MOST GENERAL
observations... but they seem to be what I'm hearing after messing
around more with [ADVERTISEMENT] Graham Breed's MIDI RELAY...
_____________ ____ __ _
Joseph Pehrson

Music??? Bah, humbug!

I'm still waiting for someone to take up my challenge to find a smaller
5-limit interval than:
3^94848 / ( 2^95605 * 5^23569 ) (numerator and denominator are both 45254
digits)

Now, that's real beauty; so who needs music!

--- In tuning@egroups.com, "Kees van Prooijen" <kees@d...> wrote:

http://www.egroups.com/message/tuning/13693

>
> Music??? Bah, humbug!
>
> I'm still waiting for someone to take up my challenge to find a
smaller
> 5-limit interval than:
> 3^94848 / ( 2^95605 * 5^23569 ) (numerator and denominator are
both
45254
> digits)
>
> Now, that's real beauty; so who needs music!

Kees, Milton "Bah"-bitt advanced this (general) argument here in the
U.S. many years ago!
_________ ___ __ _
Joseph Pehrson

Hi Joseph,

I hope you realize that I don't consider this an argument at all. In fact my
remark was so ridiculous that I didn't even thought it necessary to put an
:-) there.
I like a lot of Babbitt's stuff though. And the challenge still stands :-)

Kees

----- Original Message -----
From: "Joseph Pehrson" <josephpehrson@compuserve.com>
To: <tuning@egroups.com>
Sent: Wednesday, September 27, 2000 7:32 PM
Subject: [tuning] Re: the passion of the list

> --- In tuning@egroups.com, "Kees van Prooijen" <kees@d...> wrote:
>
> http://www.egroups.com/message/tuning/13693
>
> >
> > Music??? Bah, humbug!
> >
> > I'm still waiting for someone to take up my challenge to find a
> smaller
> > 5-limit interval than:
> > 3^94848 / ( 2^95605 * 5^23569 ) (numerator and denominator are
> both
> 45254
> > digits)
> >
> > Now, that's real beauty; so who needs music!
>
> Kees, Milton "Bah"-bitt advanced this (general) argument here in the
> U.S. many years ago!
> _________ ___ __ _
> Joseph Pehrson
>
>
>
>
> You do not need web access to participate. You may subscribe through
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>
>

--- In tuning@egroups.com, "Kees van Prooijen" <kees@d...> wrote:

http://www.egroups.com/message/tuning/13707

> Hi Joseph,
>
> I hope you realize that I don't consider this an argument at all.
In fact my remark was so ridiculous that I didn't even thought it
necessary to put an :-) there.

> I like a lot of Babbitt's stuff though. And the challenge still
stands :-)
>

Actually, I like the electronic Babbitt... where there's enough
"machinery" to keep his head busy... then he becomes a little more
"romantic!"

But the happy (:)/ sad :() [that's the extent of my math] part of it
is the fact that Babbitt truly believed it, in his famous essay "Who
Cares If You Listen..." (Probably Monz has the citation)

Partly this was born of composer frustration... partly mathematical
enthusiasm...

Personally, I've had the good fortune to get to know Milton Babbitt a
little bit...

So what does this all have to do with tuning?? "Who Cares if You
Listen??" That doesn't have anything to do with tuning?? Aw come on!
_____________ ____ __ _
Joseph Pehrson

Joseph wrote,

>Actually, I would also maintain that you *OWN* choice of 22-tET,
>particularly when you divided it up into TWO 12 note scales (well, OK
>you left out the E or whatever) was due to the fact that you wanted
>to emulate 12-tET to a degree in PRACTICE, while retaining all the
>xenharmonic benefits of the sonorities of 22...

Please enlighten me.

>That's just my cursory "take..."

Do you find "fifths" and "fourths" in McLaren's scales? Major and minor
triads? What about them reminds you of 12-tET? Playing them chromatically? I
hope that's not what 12-tET is to you -- the chromatic scale.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> http://www.egroups.com/message/tuning/13712
>
> [asking Joe Pehrson:]
> Do you find "fifths" and "fourths" in McLaren's scales? Major
> and minor triads? What about them reminds you of 12-tET?
> Playing them chromatically? I hope that's not what 12-tET is
> to you -- the chromatic scale.

For those who would like to look further into the resources
of the non-'8ve' ETs used by Brian McLaren, on which I posted,
here is a table giving cents-values of pitches in all the
non-'8ve' ETs used on volumes 1-6 of McLaren's 'Microtonal
Music' CDs, for a 6-'8ve' keyboard mapping. (This may not
be the same as the ranges used by McLaren.)

One can see, for example, that the 3^(1/15) tuning has an
intervals which resemble the 5-limit JI 'major 3rds' (= 5/4
= ~386 cents), because an interval made up of 3 degrees in
this scale, (3^(1/15))^3, is ~380 cents; or that 17^(1/21)
and 17^(1/28) both have intervals which are very close to
the Pythagorean 'perfect 5th' (= 3/2 = ~702 cents), because
(17^(1/21))^3 and (17^(1/28))^4 are both ~701 cents.

The numbers in the first row give the volume number of the CD
in McLaren's 'Microtonal Music' series, followed by the track
number, in the format volume.track; for example, '1.4' means
'Microtonal Music, volume 1, track 4'.

The numbers in the second row are a shorthand form which describes
the tuning, shortened so that all the columns would fit here.
The number before the slash is the root, and the number after
the slash is the base; for example, '13/3' means '13th root
of 3' or 3^(1/13).

The numbers in the first column (on the left) give the number
of steps away from the central pitch, which would most likely
be mapped to 'middle-C'. Thus the table gives the values for
the set of pitches from 36 degrees below 'middle-C' to 36 degrees
above it, which, if mapped to a regular 12-tone keyboard, would
be a range of 6 keyboard '8ves', 3 below and 3 above 'middle-C'.

The numbers in the body of the chart give the cent-values (rounded
to the nearest integer cent, and modulo 1200) of the pitches in
the scales.

v.tr 1.4 1.6 1.7 1.8 2.7 2.15 2.22 3.7 4.1 4.15 4.16 6.3
step 13/3 15/3 16/3 17/3 37/31 21/17 31/5 38/7 25/5 33/5 53/31 28/17
deg
-36 733 235 521 772 216 1192 364 408 788 560 762 894
-35 879 362 639 884 376 225 454 497 899 645 874 1069
-34 1026 489 758 996 537 459 544 586 1011 729 986 44
-33 1172 616 877 1108 698 692 634 674 1122 814 1098 219
-32 118 742 996 20 858 926 724 763 34 898 11 394
-31 265 869 1115 132 1019 1159 814 852 145 983 123 570
-30 411 996 34 244 1180 193 904 940 256 1067 235 745
-29 557 1123 153 355 140 426 993 1029 368 1151 347 920
-28 703 50 272 467 301 660 1083 1118 479 36 459 1095
-27 850 176 390 579 462 894 1173 6 591 120 571 70
-26 996 303 509 691 622 1127 63 95 702 205 684 245
-25 1142 430 628 803 783 161 153 184 814 289 796 421
-24 89 557 747 915 944 394 243 272 925 374 908 596
-23 235 684 866 1027 1104 628 333 361 1037 458 1020 771
-22 381 810 985 1139 65 861 423 450 1148 542 1132 946
-21 528 937 1104 51 226 1095 512 538 59 627 44 1121
-20 674 1064 23 162 386 129 602 627 171 711 157 96
-19 820 1191 141 274 547 362 692 716 282 796 269 272
-18 967 118 260 386 708 596 782 804 394 880 381 447
-17 1113 244 379 498 868 829 872 893 505 965 493 622
-16 59 371 498 610 1029 1063 962 982 617 1049 605 797
-15 205 498 617 722 1190 96 1052 1070 728 1133 717 972
-14 352 625 736 834 151 330 1142 1159 840 18 830 1148
-13 498 752 855 946 311 564 32 48 951 102 942 123
-12 644 878 974 1057 472 797 121 136 1063 187 1054 298
-11 791 1005 1092 1169 633 1031 211 225 1174 271 1166 473
-10 937 1132 11 81 793 64 301 313 85 356 78 648
-9 1083 59 130 193 954 298 391 402 197 440 190 823
-8 30 186 249 305 1115 531 481 491 308 525 303 999
-7 176 312 368 417 75 765 571 579 420 609 415 1174
-6 322 439 487 529 236 999 661 668 531 693 527 149
-5 468 566 606 641 397 32 751 757 643 778 639 324
-4 615 693 725 752 557 266 840 845 754 862 751 499
-3 761 820 843 864 718 499 930 934 866 947 863 674
-2 907 946 962 976 879 733 1020 1023 977 1031 976 850
-1 1054 1073 1081 1088 1039 966 1110 1111 1089 1116 1088 1025
0 0 0 0 0 0 0 0 0 0 0 0 0
1 146 127 119 112 161 234 90 89 111 84 112 175
2 293 254 238 224 321 467 180 177 223 169 224 350
3 439 380 357 336 482 701 270 266 334 253 337 526
4 585 507 475 448 643 934 360 355 446 338 449 701
5 732 634 594 559 803 1168 449 443 557 422 561 876
6 878 761 713 671 964 201 539 532 669 507 673 1051
7 1024 888 832 783 1125 435 629 621 780 591 785 26
8 1170 1014 951 895 85 669 719 709 892 675 897 201
9 117 1141 1070 1007 246 902 809 798 1003 760 1010 377
10 263 68 1189 1119 407 1136 899 887 1115 844 1122 552
11 409 195 108 31 567 169 989 975 26 929 34 727
12 556 322 226 143 728 403 1079 1064 137 1013 146 902
13 702 448 345 254 889 636 1168 1152 249 1098 258 1077
14 848 575 464 366 1049 870 58 41 360 1182 370 52
15 995 702 583 478 10 1104 148 130 472 67 483 228
16 1141 829 702 590 171 137 238 218 583 151 595 403
17 87 956 821 702 332 371 328 307 695 235 707 578
18 233 1082 940 814 492 604 418 396 806 320 819 753
19 380 9 1059 926 653 838 508 484 918 404 931 928
20 526 136 1177 1038 814 1071 598 573 1029 489 1043 1104
21 672 263 96 1149 974 105 688 662 1141 573 1156 79
22 819 390 215 61 1135 339 777 750 52 658 68 254
23 965 516 334 173 96 572 867 839 163 742 180 429
24 1111 643 453 285 256 806 957 928 275 826 292 604
25 58 770 572 397 417 1039 1047 1016 386 911 404 779
26 204 897 691 509 578 73 1137 1105 498 995 516 955
27 350 1024 810 621 738 306 27 1194 609 1080 629 1130
28 497 1150 928 733 899 540 117 82 721 1164 741 105
29 643 77 1047 845 1060 774 207 171 832 49 853 280
30 789 204 1166 956 20 1007 296 260 944 133 965 455
31 935 331 85 1068 181 41 386 348 1055 217 1077 630
32 1082 458 204 1180 342 274 476 437 1166 302 1189 806
33 28 584 323 92 502 508 566 526 78 386 102 981
34 174 711 442 204 663 741 656 614 189 471 214 1156
35 321 838 561 316 824 975 746 703 301 555 326 131
36 467 965 679 428 984 8 836 792 412 640 438 306

Tune up your synths and start exploring, y'all! Most of you
probably never heard scales like these before.

-monz
http://www.ixpres.com/interval/monzo/homepage.html

> Even a scale with 90-cent steps would have almost nothing in common with
> 12-tET, as regards its musical properties. Think of Gary Morrison's 88-¢et
> scale. Think of 13-tET.

I definitely agree. I find that 88CET music is very difficult to confuse with 12TET, both
melodically and harmonically. That despite the somewhat similar step size, or in a sense
because of the similar step size.

With a larger number of steps per octave's span, you have a stronger chance of having
recognizable approximations to familiar intervals. 88CET's closest approximations to a major
third for example, are not very close to 5:4, and are clearly recognizable as approximations
to 11:9 and 9:7. If you double that, to 44CET, you gain a couple intervals that are clearly
perceptable as appoximations to 6:5 and 5:4.

So, by keeping the step size large, it's easier to stay away from anything traditional.

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

http://www.egroups.com/message/tuning/13712

> Joseph wrote,
>
> >Actually, I would also maintain that you *OWN* choice of 22-tET,
> >particularly when you divided it up into TWO 12 note scales (well,
OK you left out the E or whatever) was due to the fact that you wanted
> >to emulate 12-tET to a degree in PRACTICE, while retaining all the
> >xenharmonic benefits of the sonorities of 22...
>
> Please enlighten me.
>
> >That's just my cursory "take..."
>
> Do you find "fifths" and "fourths" in McLaren's scales? Major and
minor triads? What about them reminds you of 12-tET? Playing them
chromatically? I hope that's not what 12-tET is to you -- the
chromatic scale.

I'm not being so specific... and, actually, I am not trying to
compare things specifically! I'm just talking about step sizes, and
the fact that I find the Bohlen Pierce scale to be particularly
"weird" because the step sizes are "roughly" (well compared with
31t-ET or something) around the size of 12-tET but don't repeat in
octave equivalence! That's all there is to it. Nothing more
quantitative.

ALSO, I haven't "tuned up" the McLaren scales yet, so I have really
no "audible" comments...
_____________ ___ ___ _
Joseph Pehrson

--- In tuning@egroups.com, Gary Morrison <MR88CET@T...> wrote:

http://www.egroups.com/message/tuning/13720

> > Even a scale with 90-cent steps would have almost nothing in
common with 12-tET, as regards its musical properties. Think of Gary
Morrison's 88-¢et scale. Think of 13-tET.
>
> I definitely agree. I find that 88CET music is very difficult to
confuse with 12TET, both melodically and harmonically. That despite
the somewhat similar step size, or in a sense because of the similar
step size.
>
> With a larger number of steps per octave's span, you have a
stronger chance of having recognizable approximations to familiar
intervals. 88CET's closest approximations to a major third for
example, are not very close to 5:4, and are clearly recognizable as
approximations to 11:9 and 9:7. If you double that, to 44CET, you
gain a couple intervals that are clearly perceptable as appoximations
to 6:5 and 5:4.
>
> So, by keeping the step size large, it's easier to stay away from
anything traditional.

Hmmm. This is very interesting and, perhaps, is a "solution" to the
little discussion (one never says "argument" with Paul :)) regarding
my perception of the Bohlen Pierce scale!

My *initial* reaction was that the scale seemed so "weird" because
the step size was "similar but different" to 12-tET. Now, however,
after your explanation, I'm beginning to wonder.

Maybe what's happening is that I'm not hearing any INTERVALS that are
similar to what I'm "used" to...

In any case, the "reaction" is the same... these larger interval
scales are "stranger" than some with smaller step sizes.

I like 'em. (Now *that's* really quantified!)
______________ ___ __ _ _
Joseph Pehrson

Gary Morrison wrote,

> I find that 88CET music is very difficult to confuse with 12TET,
both melodically and harmonically.

For those of you who may not know, Gary's excellent "New Awakening" in
88-cET tuning is up at John Starrett's Tuning Punk site. Though I'd
only heard this piece a couple of times well over a year ago now, upon
thinking of it I was somewhat surprised to see that I could easily
remember the opening theme and the first fast ("tambourine") section,
and pretty much retain the character of those pitches as well. Nice
piece, nice tuning.

--Dan Stearns

"D.Stearns" wrote:

> For those of you who may not know, Gary's excellent "New Awakening" in
> 88-cET tuning is up at John Starrett's Tuning Punk site. Though I'd
> only heard this piece a couple of times well over a year ago now, upon
> thinking of it I was somewhat surprised to see that I could easily
> remember the opening theme and the first fast ("tambourine") section,
> and pretty much retain the character of those pitches as well.

Another musician coworker friend (a saxophonist with a big-band jazz background if that
matters - probably not) had a somewhat similar impression from hearing 88CET music. He said
that he expected it to be unlistenably bizarre and freaky-sounding, but was surprised to find
that it has an alien but definite musical meaningfulness to it.

>
>
> Nice piece, nice tuning.

Thanks. Gladja enjoyed it!

Gary Morrison wrote,

> Another musician coworker friend (a saxophonist with a big-band jazz
background if that matters - probably not) had a somewhat similar
impression from hearing 88CET music. He said that he expected it to
be unlistenably bizarre and freaky-sounding, but was surprised to find
that it has an alien but definite musical meaningfulness to it.

I'm a firm believer in the idea that good music = good tunings (as
well as a firm disbeliever in the opposite; good tunings = good
music). I really think that tunings, no matter how "bizarre" or
removed from what most folks know (or even like), are easier to retain
(and acquire "meaning") if they are tethered to some memorable (or
striking) music.

--Dan Stearns