Marc Jones EDOs

Now, here's something good:

http://www.ixpres.com/interval/dict/marc-edolist.htm

Is everybody here aware of the fact that Marc Jones used this many
different EDOs?

I think he deserves a special commendation, particularly, for his use
of 0-EDO and 1-EDO...

JP

--- In tuning@y..., "jpehrson2" <jpehrson@r...> wrote:
> Now, here's something good:
>
> http://www.ixpres.com/interval/dict/marc-edolist.htm
>
> Is everybody here aware of the fact that Marc Jones used this many
> different EDOs?
>
> I think he deserves a special commendation, particularly, for his
use
> of 0-EDO and 1-EDO...

some of the extremely-large-number temperaments have gotten quite a
bit of discussion on tuning-math . . . i wonder why marc doesn't post
much over there?

p.s. what's UHT stand for? is it yet another term synonymous with ET,
EQ, EDO, and ED2?

p.p.s. where can i hear your 152-equal music? as you may know, i
advocate 152-equal as a 'universal tuning' . . .

Marc,

Hmm, that just makes me want to hear some of these, especially all the
modified guitar stuff--I know, greedy, greedy, greedy!

take care,

--Dan Stearns

----- Original Message -----
From: "jpehrson2" <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Tuesday, February 19, 2002 9:00 AM
Subject: [tuning] Marc Jones EDOs

> Now, here's something good:
>
> http://www.ixpres.com/interval/dict/marc-edolist.htm
>
> Is everybody here aware of the fact that Marc Jones used this many
> different EDOs?
>
> I think he deserves a special commendation, particularly, for his
use
> of 0-EDO and 1-EDO...
>
> JP
>
>
>
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On 2/19/02 12:00 PM, "jpehrson2" <jpehrson@rcn.com> wrote:

> Now, here's something good:
>

Glad ya think so.

> http://www.ixpres.com/interval/dict/marc-edolist.htm
>
> Is everybody here aware of the fact that Marc Jones used this many
> different EDOs?
>

Joe, you know what, I can tell you the answer to that is a big NO. :(

Because - outside of having some consistent help in the early 1990s, my work
was pretty much off on my own for years, sort of regurgitating a manical
level of thought of music, math, physics and a lot of strange experiences
listening to music.

Johnny Reinhard didn't even know, because I lost touch with him for about 10
years as well. We only started talking again in early 2000.

I actually had to talk to Fred Freeburg, my old bass player, for a couple
hours the other night, to try to remember even all the guitars I built.
Anyone who would listen to me, I'd buy them a guitar and refret it in 19 for
them. I think I still missed a few.

* * * * *

"The Trance Who Played 323"

I remember when Ken first tried playing my 323 fretboard. He was having a
little trouble with it, and sort of gestured at me, what do I do. I said
"It's kind of like 94, only ... (I held my hands up measuring about a foot,
and jerked the distance to maybe 14 inches)" and within about 15 seconds, he
was soloing in sixteenth notes and such.

Thing is, at that point, I'd been playing the 323 a lot and sequencing a lot
in it, it was a current project so my sensitivity to it was very high. Put
it this way. The main fifth in 323 sounds just. 323 is 17 times 19. So
you go a step or two in either direction you hit the 17 or 19 fifth which
you could definitely hear with the guitar timbre. The note in between is
very close to 12. So you have:

"17", near just, near 12, "19".

That's a pretty recognizable arrangement. On a side note, this is how I was
able to distinguish a lot of higher temperaments, each having a unique
bouquet of useable fifths, so they sort of adopt little personality traits
of the proximities of each fifth. Anyway, I had learned over the week or so
to sense the different colorations. If anything each note is 4 cents apart
or so.

I was actually moved to see different colors when a note was off, honestly.
I suppose I could have tested that. Anyway, after a few seconds of
remembering the feel of 94, Ken took off and didn't come back for awhile.
Every note was right on the 229+94 scale, as he was able to visualize the
nested scale in the fretboard markings.

Ken's and Fred's free time were eventually destroyed by the same biological
virus, I think they called it "wife and two kids".

Actually it was Ken and his daughter who were supposed to be two of the
people playing the Mostly Electric String Quartet No. 1 who CANCELLED A WEEK
BEFORE THE SHOW... Leaving me spinning and exasperated which is what
motivated me to record the entire thing on my computer, play solo along with
my computer, and burn some CDs the night before the concert.

The joke had been "Ken has procrastinated working with me for so long that
he's produced a 12 year old daughter who plays violin." The "Mostly" slow
violin lines were tailored to her performance speed and volume capabilities
which I obtained by a rare phone interview in which I recorded her playing
and analyzed it later. It's something she could have handled. He said she
didn't have enough time and HE wasn't comfortable with it even though she
was.

The putz. Besides family, don't trust your friends. They're the first to
burn ya.

This time (No. 2, premiering 5/25/02) I'm playing it safe. Me and a laptop
and an open invite for people to work with me in the future...

* * * * *

"But how?"

In 1994, I wrote a program to retune midi files by splitting overlapping
voices in a midi track to avoid confusion and then calculating the
appropriate pitch bend for the note in the temperament I was working in.

My focus was eventually combinations of different fifths and major thirds.
After simply plugging in temperament data in the program every time I wanted
to run it, I found there are a few DOZEN midi controllers (14, 15, 46, etc)
that aren't in general use. So I used different combinations of those for
temperament, 100s digit of temperament, plus or minus syntonic commas and
pyuthagorean

I'm working on a book called "The Thresh Hold of Perception", which is going
to include a chronicling of my little journey of self-torture, hundreds of
hours spent pouring my entire brain into temperaments and finding as many
differences and similarities as I could. Also are my experiences with
volume and time tests and such.

* * * * *

"You heard WHAT?"

A few things I figured out was the ability to tell a temperament apart from
any other one depends on how big it is and how long you listen to it. One
sort of postulate I had was, if you listen to something in one temperament
and then listen to the same thing in a temperament four times as dense, it
will take you about four listens to readjust. So to evolve the sensitivity,
I found it easiest to always progress by doing slightly less than doubling.

In other words, to get from 118 to 559, instead of retuning 5 times and
forcing the progress, it's a lot easier on the brain to play 118, play 205
twice, play 323 twice, maybe play 441 twice, then 559 twice. Sort of the
difference between parachuting out of a crashing plane, and actually having
a soft landing.

One thing I'd like to explain though as it's one of the most incredible
things I list. Just to show it's possible... I had some randomly generated
many-voice chords which I was retuning to high temperaments. Ken was
working the knobs. I needed someone to test me on this one. I wanted to
make sure I wasn't tricking myself. But after AN HOUR of listening to the
same segment back and forth in 1171 and 1342, I swore I could tell the
difference. And a dozen or so tests confirmed it.

But it's elastic. I haven't heard over 100 in quite awhile. It would take
a little time to build back up an overall sensitivity.

Umm... And Angie just this minute scored us Who tickets for August. Talk
about hearing sensitivity? Umm think I should get some really good earplugs
:X

* * * * *

"But what have you RECORDED?"

I've been perfectionist style fussing over production specs and only tonight
I'm sitting down with the compromise that knowing things are never going to
be perfect, I have to burn some CDs.

A lot of non-music-theory people who heard my guitar quartet thing in 32
equal, said it didn't sound out of tune at all. I've done so much cross
referencing with two-digit temperaments, plus I have to say my fretboard
markings are really the key to it all. Very easy to find your way around
and learn quickly. One guy at the Microthon was taking a picture of my 32
fretboard, and I said hey you want one of my holding it, and he was like "no
that's ok."

What's actually done? Well not a lot. Some muddy multimicrotonal 4-track
stuff. Quite honestly, I've had some major mental problems in my life and
besides never being able to really start writing AT ALL until I was 22, it
wasn't until the concert in November 2000 where I'd ever been able to use my
real name, say that I did something, present it to people as my own, etc.

I think a lot of my current intensity is gotten from having pulled the
slingshot back further and further for a decade and a half. I'm so wound up
from not having really done anything that by the time I get around to doing
anything, I won't rest until it's gone through the whole filter of all I
want to do, pitch time volume and structure wise.

Sad that it's taken this long, I know, I apologize for depriving anyone, but
the good news is, the dam has started to break and I have a lot of equally
entertaining stuff ready to go.

I should have a few CD titles available by the time of the Roulette show in
May.

* * * * *

* * * * *

> I think he deserves a special commendation, particularly, for his use
> of 0-EDO and 1-EDO...
>

Philosophically I thought you might like the "infinity"-ET as well as I've
found occasionally looking to that idea reinforces the ET continuum.

Really, past a few thousand, I found quite a few temperaments with good
calcultor qualities. I'm not sure I even remember some. "Halloween 69" is
hard to forget. Actually since then I've gained a very good friend who was
born on that day!

* * * * *

"The Talking Octave - in 1-ET."

I never transcribed, I could probably rewrite from scratch, I think I should
- This was something I thought of when off in some of my first microtonal
thoughts, listening to cassettes.

I had recently listened to King Crimson's "Larks Tongues in Aspic" album, so
the tune "The Talking Drum" was still menacing and repeating through my
brain. This was about a 140bpm jazz rock improv for guitar and violin, with
the bass clearly volleying back and forth between D and Ab for over seven
minutes.

The Warner/Electra/Atlantic conglomerate put this somewhat annoying series
of 1/2 second long tones (I think 250 Hz, 500 Hz, 1000 Hz, 2000 Hz), I think
so you could calibrate an equalizer, a series of short sine-wave tones an
octave apart. I had the headphones on louder than I thought and being a bit
out of reach of the volume knob, I was a little tangled in the cord and was
trying desperately to rip the headphones off before the 4000 or 8000 Hz
tones punctured my ears. Made the few seconds seem like a streetfighting
eternity.

So a little inspired and a little annoyed, I wrote a couple minute long
somewhat communicative poking and peeking of what little could actually be
done with octave-only melodies and harmonies. I'll give you a hint, it's
mostly time and volume based. Lots of polyrhythms. You got me humming it
again. It's turning into a good night.

(Boo BEEP. Bee BOOP...)

Marc

On 2/19/02 8:02 PM, "paulerlich" <paul@stretch-music.com> wrote:

> some of the extremely-large-number temperaments have gotten quite a bit of
> discussion on tuning-math . . . i wonder why marc doesn't post much over
> there?
>

I just got back on the ATL really. I lost touch after my trip to L A last
August, then the Sept 11 thing then a pretty tough winter, well. I have
over 8000 tuning posts to catch up on. Over 2000 in tuning math alone.

> p.s. what's UHT stand for? is it yet another term synonymous with ET, EQ, EDO,
> and ED2?
>

Ultra high temperament. My sort of disclaimer siphon to sanction off
four-digit temperaments for "calculation use only".

Look here:
http://www.ixpres.com/interval/dict/marcdefs.htm

As I said in my reply to Joe Pehrson, my work was very isolated for almost
15 years, and I had to come up with my own terminology for things. Which is
why when I showed up on the tuning list, I had no idea what the status quo
was as far as who "else" thought of what when, what was coined, what was
foreign, what was beaten half to death etc.

In recent negotiations of bringing my work forward by way of Monzo's
dictionary, I figured the easiest means to an end was to just talk about my
work in the way I always have, and every time I hit a word I knew as my own,
I add it to the Marc definition page.

Notice the disclaimer AT THE BEGINNING, that I'd like to know if any of what
I came up with IS IN current circulation, that my motive is not to supercede
but to adapt. Basically if it's out there what do YOU GUYS call it, and if
it's not out there, then it's something new so chekkit owt.

But to further answer your question, why haven't I posted much to tuning
math. Beyond so many posts, I'm still trying to catch up with the rest of
Monzo's dictionary. The only thing I've ever "read" microtonally is
Mandelbaum's 1961 dissertation on temperament, focused on 19-tone. In other
words, I haven't posted because I don't really know how to speak the
conventional tuning language although in purely mathematical terms, I can
express myself even if it is long-winded.

> p.p.s. where can i hear your 152-equal music? as you may know, i advocate
> 152-equal as a 'universal tuning' . . .
>

Yes I remember. Well you can hear "half" of it soon :) The third Acoustic
String Quartet is to be in 76, and is to be dedicated to you in lieu of our
conversation of 11NOV00.

Otherwise, ALL of those 3 digit boards are long gone :( Well I know where
they might be if I can track people down but I'm pretty sure my storage
allowance has expired. More than anything in Partch's music, what little
I've heard, what I can relate to is the "homeless" element, as I've until
recently moved around a lot and sometimes out to nowhere. I heard some
stuff from his hobo-ing days and of anything I heard said yeah I was out
there too.

Actually (so soon we forget?) I rebuilt my first 19-tone guitar while
homeless in NYC, on the F-train, waiting for the train to stop so I could
continue working. At one point I looked up since we'd been stopped awhile,
the conductor was watching me. I said hey what's going on, he said don't
worry we're ahead of schedule, go ahead.

The 28th Piano Sonata will be in 152. I might attack the middle ones soon
(24-40) just to get them out of the way. In case anything happens to me.
No need to do them in order. You know, planes crashing into things two
miles away and such. My work could be rendered forever undone in the wink
of an EGR*O&#O#UGBH@B*&*(U#JBOijlkl.d./vm......

On 2/20/02 12:06 AM, "D.Stearns" <STEARNS@CAPECOD.NET> wrote:

> Marc,
>
> Hmm, that just makes me want to hear some of these, especially all the
> modified guitar stuff--I know, greedy, greedy, greedy!
>

Yes I knew YOU would. Heh heh heh.

Well that's what this phase is all about. I've got a small repuation and
I'm working off the interest of fellow micro indulgers to get things DONE.

I'm also going to start making fretboards again for the first time in a
couple years. It's going to be nice now that I have, for the first time
since actually have plans on EXACTLY what ones I want to make, in what
order, and not just that, what I want to do with them.

Plus I just upgraded to Digital Performer... So I have unlimited audio
tracks now... 1GB ram... A 60GB FireWire drive... Stirring the paint here,
working up the inspiration and then who knows what I'll do this time around.

I'm going to rerecord all the old pop stuff too sometime and outside of my
pseudo-jazz-rock-classical fusion efforts, I should be making those
available as well. Plus some of the stuff in the late 80s early 90s I was
producing for a few underground types. I did some midi sequencing for a few
people. I lost SO MUCH more than equipment when I first got robbed :(
Which is part of why I had my first heart attack at age 29.

I did make a promise to certain people that I'd make sure their music got
out if both of these things were true: that I never heard from them again,
and that I was able to finish fully producing it. Which now they are.
Sigh.

Marc

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> > p.p.s. where can i hear your 152-equal music? as you may know, i
advocate
> > 152-equal as a 'universal tuning' . . .
> >
>
> Yes I remember. Well you can hear "half" of it soon :) The third
Acoustic
> String Quartet is to be in 76, and is to be dedicated to you in
lieu of our
> conversation of 11NOV00.

wow thank you. but why "in lieu"? i'd rather have both :)

> The 28th Piano Sonata will be in 152. I might attack the middle
ones soon
> (24-40) just to get them out of the way.

can't wait!

p.s. about 103169-equal -- on tuning-math we looked at the graph
of "7-limit goodness", and noticed a "wave". the wave's first peak
was at 1-equal and the 62nd peak was at 103169-equal. this implied
a "periodicity" of

(103169 - 1)/62 = 1664 exactly!!!

this was pretty mind-blowing to some of us at the time. then i
noticed that the 7-limit interval 2401:2400 fits within an octave
about 1663.998 times. the explanation was that you tend to find
better 7-limit ets if 2400:2401 is nearly an integer number of steps
than if it's nearly a half-integer number of steps. makes sense if
you think about it -- lower-limit example abound. but why don't we
see a wave corresponding to 4375:4374??? mystery of mysteries . . .

On 2/20/02 12:06 AM, "D.Stearns" <STEARNS@CAPECOD.NET> wrote:

> Marc,
>
> Hmm, that just makes me want to hear some of these, especially all the
> modified guitar stuff--I know, greedy, greedy, greedy!
>

Dan -

Actually I just wondered, have you seen the update on my definitions page?

http://www.ixpres.com/interval/dict/marcdefs.htm

I listed all of my techniques for layering more than one temperament.
Thought you might be interested in some of the new additions, as I scratch
the top of my head to see what used to be there. (nice metaphor eh)

I never realized that it's a little matrix in itself; of the four
techniques, two are inducive while two are conducive, and two are convergent
while two are divergent. By con/di/vergent, I mean moving toward or away
from a target frequency. By in/con/ducive, I think that's a little more
self apparent, either pushing a sound through or making room for it first.

Marc

On 2/19/02 9:31 PM, "paulerlich" <paul@stretch-music.com> wrote:

> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
>
>>> p.p.s. where can i hear your 152-equal music? as you may know, i advocate
>>> 152-equal as a 'universal tuning' . . .
>>>
>>
>> Yes I remember. Well you can hear "half" of it soon :) The third Acoustic
>> String Quartet is to be in 76, and is to be dedicated to you in lieu of our
>> conversation of 11NOV00.
>>
> wow thank you. but why "in lieu"? i'd rather have both :)
>

You know I still confuse (e.g.) with (i.e.) ... I meant apropos of our
conversation, or no, in LIGHT of... Well I meant as a result of, not in
place of.

>> The 28th Piano Sonata will be in 152. I might attack the middle ones soon
>> (24-40) just to get them out of the way.
>>
> can't wait!
>

Well you have to. HAA. Not for long though I hope.

> p.s. about 103169-equal -- on tuning-math we looked at the graph of "7-limit
> goodness", and noticed a "wave". the wave's first peak was at 1-equal and the
> 62nd peak was at 103169-equal. this implied a "periodicity" of
>
> (103169 - 1)/62 = 1664 exactly!!!
>
> this was pretty mind-blowing to some of us at the time. then i noticed that
> the 7-limit interval 2401:2400 fits within an octave about 1663.998 times. the
> explanation was that you tend to find better 7-limit ets if 2400:2401 is
> nearly an integer number of steps than if it's nearly a half-integer number of
> steps. makes sense if you think about it -- lower-limit example abound. but
> why don't we see a wave corresponding to 4375:4374??? mystery of mysteries . .
> .

Oh interesting. I didn't know you got into higher math stuff over there.

Otherwise :::thumbing through monz.com::: ... "Hah?" LOL seriously I have
to brush up on all these terms. Either way it's going to be "oh is THAT
what you're talking about", but it's probably better that the one says that
to the many. I'll study.

Marc

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> As I said in my reply to Joe Pehrson, my work was very isolated for almost
> 15 years, and I had to come up with my own terminology for things. Which is
> why when I showed up on the tuning list, I had no idea what the status quo
> was as far as who "else" thought of what when, what was coined, what was
> foreign, what was beaten half to death etc.

Welcome to the club--I was in this position when I showed up last year, and George Secor, though discussed often in these parts, was in something of the same position also.

--- In tuning@y..., "paulerlich" <paul@s...> wrote:

the explanation was that you tend to find
> better 7-limit ets if 2400:2401 is nearly an integer number of steps
> than if it's nearly a half-integer number of steps. makes sense if
> you think about it -- lower-limit example abound. but why don't we
> see a wave corresponding to 4375:4374??? mystery of mysteries . . .

2401/2400 has a fourth power in the numerator, which I think explains some of it.

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> http://www.ixpres.com/interval/dict/marcdefs.htm

whoa . . . a lot of these observations look like the sorts of things
that gene and maybe graham could say a whole hell of a lot about.
gene could do it with proofs, too :)

On 2/19/02 11:54 PM, "genewardsmith" <genewardsmith@juno.com> wrote:

> Welcome to the club--I was in this position when I showed up last year, and
> George Secor, though discussed often in these parts, was in something of the
> same position also.

Hey I was in this position last year too! Sort of why I stopped posting.
BAAAAAAA

Hi Gene - I've heard of you recently, I hear you showed up around the time I
got fat and divorced the internet for awhile.

Down almost 30 pounds thanks to Tiger Schulmann's Karate www.tsk.com

Marc

--- In tuning@y..., "genewardsmith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "paulerlich" <paul@s...> wrote:
>
> the explanation was that you tend to find
> > better 7-limit ets if 2400:2401 is nearly an integer number of
steps
> > than if it's nearly a half-integer number of steps. makes sense
if
> > you think about it -- lower-limit example abound. but why don't
we
> > see a wave corresponding to 4375:4374??? mystery of
mysteries . . .
>
> 2401/2400 has a fourth power in the numerator, which I think
>explains some of it.

why is that? you can reply on tuning-math, though i'm sure your
explanation is already there somewhere . . . but my eyes tend to
glaze over in incomprehension at the way you initially explain
certain things . . .

On 2/20/02 12:05 AM, "paulerlich" <paul@stretch-music.com> wrote:

> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
>
>> http://www.ixpres.com/interval/dict/marcdefs.htm
>>
> whoa . . .
>

LOL I get a WHOA huh? :)

> a lot of these observations look like the sorts of things that gene and maybe
> graham could say a whole hell of a lot about. gene could do it with proofs,
> too :)
>

Yeah I never bothered to get to the actual geometry style proofs. Just some
stuff I've been using for myself.

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, February 19, 2002 9:05 PM
> Subject: [tuning] Re: (Stearns 2) Marc Jones EDOs
>
>
> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
>
> > http://www.ixpres.com/interval/dict/marcdefs.htm
>
> whoa . . . a lot of these observations look like the sorts of things
> that gene and maybe graham could say a whole hell of a lot about.
> gene could do it with proofs, too :)

see that, Marc? that's exactly what i wrote to you last week,
and why i asked you for your definitions.

-monz

_________________________________________________________
Do You Yahoo!?
Get your free @yahoo.com address at http://mail.yahoo.com

In-Reply-To: <a4vaqr+2tcl@eGroups.com>
paulerlich wrote:

> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
>
> > http://www.ixpres.com/interval/dict/marcdefs.htm
>
> whoa . . . a lot of these observations look like the sorts of things
> that gene and maybe graham could say a whole hell of a lot about.
> gene could do it with proofs, too :)

Oh, yes, some of that's quite interesting. I would like to hear some of
the music behind this.

The "Diatonic Aperture" is similar to one of Easley Blackwood's measures,
is it "R"? I'm not sure if it's exactly R, but some ratio of tempered
intervals.

"The ALL Temperament" is usually referred to as "the pitch continuum" or
simply "the continuum".

Graham

On 2/20/02 7:19 AM, "monz" <joemonz@yahoo.com> wrote:

>> --- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:
>>
>>> http://www.ixpres.com/interval/dict/marcdefs.htm
>>
>> whoa . . . a lot of these observations look like the sorts of things
>> that gene and maybe graham could say a whole hell of a lot about.
>> gene could do it with proofs, too :)
>
>
> see that, Marc? that's exactly what i wrote to you last week,
> and why i asked you for your definitions.
>
>
> -monz
>

Yes I suppose you would know, having been active here. Like any computer
from the 1970s, my brain could use a Post Execution Memory Dump.

Marc

On 2/20/02 8:00 AM, "graham@microtonal.co.uk" <graham@microtonal.co.uk>
wrote:

> paulerlich wrote:
>>> http://www.ixpres.com/interval/dict/marcdefs.htm
>>
>> whoa . . . a lot of these observations look like the sorts of things
>> that gene and maybe graham could say a whole hell of a lot about.
>> gene could do it with proofs, too :)
>
> Oh, yes, some of that's quite interesting. I would like to hear some of
> the music behind this.
>

Hi Graham. Thanks for writing.

Give me a couple weeks or so I'll have CDs ready.

> The "Diatonic Aperture" is similar to one of Easley Blackwood's measures,
> is it "R"? I'm not sure if it's exactly R, but some ratio of tempered
> intervals.
>

There was an "r" I've heard of that I think was the difference between 12 of
a certain fifth minus an octave. But yeah, it seems common enough an idea.
Borrowed from camera terminology, I just called it an aperture because it
describes the "opening" of the minor second.

Ironically enough it was Fred Freeburg's facetiousness, immediately saying
"well what about shutter speed", that started my micro-studies of musical
time (absolute note duration, pitch and tempo integration etc).

> "The ALL Temperament" is usually referred to as "the pitch continuum" or
> simply "the continuum".
>

Yeah I usually call it some kind of continuum as well. Gives you a slightly
different mental twitch of perspective if you think of it as an actual
temperament, even when you're playing or writing. Sort of goes back to when
I first discovered infinity. Calling the number line a continuum kind of
deromanticizes the mystery of infinity.

About calling it a pitch continuum, what do you usually measure pitch in? I
would think Hertz. Intervals maybe you measure in cents, but only relative.
There's no real system of measuring "middle C minus 12 cents" as an absolute
pitch reference. Or its duration other than seconds.

The idea was to visualize not so much a geometric pitch but also geometric
duration, in that an octave up doubles the frequency but halves the
duration, while an octave down doubles the duration and halves the
frequency. And intermittent are geometric intervals which, approaching
infinity made a smooth geometric frequency *and* duration scale:

1. arithmetic Time (harmonic inverse time) - the "seconds" continuum
2. arithmetic Inverse Time (harmonic time) - the "Hertz" continuum
3. geometric time (also geometric inverse time) - the continuum of equal
temperament.

...which as I said, I use the flip side, duration, in calculating continuum
type tempo changes and note lengths. And as I also said, I use the Cesium
tick to anchor and relate both.

Also the All temperament goes hand in hand with the Null temperament. Ehh I
forgot to add the defs of the silences, empty (0 Hz) and full (inf Hz)...
It's all sort of Zen after awhile.

Marc

--- In tuning@y..., "Orphon Soul, Inc." <tuning@o...> wrote:

> > The "Diatonic Aperture" is similar to one of Easley Blackwood's
measures,
> > is it "R"? I'm not sure if it's exactly R,

blackwood's "R" is actually the inverse of marc's "diatonic
aperture". blackwood gives 12-equal an R of 2, 17-equal an R of 3,
and 19-equal an R of 1.5, IIRC.