Yahoo Tuning Groups Ultimate Backup tuning 665-tone equal temperament?

I had to leave the list for a while (busy and/or lazy), came back.

Has anybody done any work on 665-tone (what I call Armageddon tuning, among
other things)? It approximates Pythagorean with extreme precision, and 5-
and 7-limit just works very well too. Some of the important small intervals
have the following sizes:

apotome (sharp/flat) = 63
limma = 50
comma = 12
Pythagorean comma = 13
diesis = 23
diaschisma = 11
septimal comma = 15
schisma = 1
Mercator's comma = 2

The undecimal comma is 29.5 steps of 665-edo, which breaks continuity for
11-limit, but what's half a schisma to the human ear anyway? I haven't
tested 13-limit and up yet, since I rarely use higher primes in my own
music. The only other interval I checked is the kleisma, which equals 4.5
steps.

Two more tiny intervals need to be considered: the Pythagorean equivalent of
the schisma is 3^306/2^485 (1.2267 cents; compare to schisma 1.3542 cents).
The 665-tone comma, 3^665/2^1054, equals 0.075575 cents. Neither of these
intervals have names as far as I know, like Mercator's comma.

I need to read more on Sauveur's work with 614-tone (or schisma equal
temperament) too.

🔗Justin Weaver <improvist@usa.net>

If you're going to go this precise, why not just have millioctave 1200edo? -Justin

--- In tuning@yahoogroups.com, "Danny Wier" <dawier@h...> wrote:
> I had to leave the list for a while (busy and/or lazy), came back.
>
> Has anybody done any work on 665-tone (what I call Armageddon tuning, among
> other things)? It approximates Pythagorean with extreme precision, and 5-
> and 7-limit just works very well too. Some of the important small intervals
> have the following sizes:
>
> apotome (sharp/flat) = 63
> limma = 50
> comma = 12
> Pythagorean comma = 13
> diesis = 23
> diaschisma = 11
> septimal comma = 15
> schisma = 1
> Mercator's comma = 2
>
> The undecimal comma is 29.5 steps of 665-edo, which breaks continuity for
> 11-limit, but what's half a schisma to the human ear anyway? I haven't
> tested 13-limit and up yet, since I rarely use higher primes in my own
> music. The only other interval I checked is the kleisma, which equals 4.5
> steps.
>
> Two more tiny intervals need to be considered: the Pythagorean equivalent of
> the schisma is 3^306/2^485 (1.2267 cents; compare to schisma 1.3542 cents).
> The 665-tone comma, 3^665/2^1054, equals 0.075575 cents. Neither of these
> intervals have names as far as I know, like Mercator's comma.
>
> I need to read more on Sauveur's work with 614-tone (or schisma equal
> temperament) too.

🔗monz@attglobal.net

hi Danny,

> From: Danny Wier [mailto:dawier@hotmail.com]
> Sent: Friday, August 01, 2003 10:05 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] 665-tone equal temperament?
>
>
> I had to leave the list for a while (busy and/or lazy), came back.

welcome back. vacations from the list are a
healthy thing ... i do it to from time to time.

> Has anybody done any work on 665-tone (what I call
> Armageddon tuning, among other things)?

Marc Jones. see:
http://sonic-arts.org/dict/marcdefs.htm#satanic

i've never played around with it, but i discovered
this independently myself before i knew Marc, and
have posted a few things about it to this list.
unfortunately, neither Google nor the search engine
at the Yahoo site turned up any of them. but see:

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

(near the bottom, under the last graphic)

> It approximates Pythagorean with extreme precision,
> and 5- and 7-limit just works very well too. Some
> of the important small intervals have the following
> sizes:
>
> apotome (sharp/flat) = 63
> limma = 50
> comma = 12
> Pythagorean comma = 13
> diesis = 23
> diaschisma = 11
> septimal comma = 15
> schisma = 1
> Mercator's comma = 2

here are some more accurate values:

apotome (sharp/flat) = 63.00044086
limma = 49.9996851
comma = 11.91806882
Pythagorean comma = 13.00075575
diesis = 22.7534507
diaschisma = 10.83538188
septimal comma = 15.10885087
schisma = 1.082686937
Mercator's comma = 2.003337917

665edo's representations of the diesis, diaschimsa,
and septimal comma are not as close as those of the
other intervals you list. but note how closely it
approximates all of the Pythagorean intervals:
apotome, limma, Pythagorean comma, and Mercator's comma
are all nearly identical to true Pythagorean tuning.

> The undecimal comma is 29.5 steps of 665-edo, which
> breaks continuity for 11-limit, but what's half a
> schisma to the human ear anyway? I haven't tested
> 13-limit and up yet, since I rarely use higher primes
> in my own music. The only other interval I checked
> is the kleisma, which equals 4.5 steps.
>
> Two more tiny intervals need to be considered: the
> Pythagorean equivalent of the schisma is 3^306/2^485
> (1.2267 cents; compare to schisma 1.3542 cents).

what schisma is 1.3542 cents? the interval usually
meant by "schisma" or "skhisma", [2 3 5]^[-15 8 1]
= 32805/32768 , is ~1.953720788 cents.

> The 665-tone comma, 3^665/2^1054, equals 0.075575 cents.
> Neither of these intervals have names as far as
> I know, like Mercator's comma.

well, the 665-tone comma is the "satanic comma", as
i indicated above.

i mention 306edo on my "Pythagorean" page, but didn't
give the "comma" a name. use of 306edo to represent
Pythagorean tuning is a natural extension of recognizing
the 3^306/2^485 "comma".

> I need to read more on Sauveur's work with 614-tone
> (or schisma equal temperament) too.

i don't know anything about Sauveur's work on 614edo,
but around here we generally consider 612edo to be the
"temperament of schismas". Gene uses it as his analogue
of cents.

-monz

🔗monz@attglobal.net

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Justin Weaver <improvist@usa.net>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗kraig grady <kraiggrady@anaphoria.com>

665 is predicted by viggo brun's algorithm see
http://www.anaphoria.com/viggo.PDF
page 4

tuning@yahoogroups.com wrote:

>
> Message: 8
> Date: Fri, 1 Aug 2003 12:05:05 -0500
> From: "Danny Wier" <dawier@hotmail.com>
> Subject: 665-tone equal temperament?
>
> I had to leave the list for a while (busy and/or lazy), came back.
>
> Has anybody done any work on 665-tone (what I call Armageddon tuning, among
> other things)? It approximates Pythagorean with extreme precision, and 5-
> and 7-limit just works very well too. Some of the important small intervals
> have the following sizes:
>
>

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

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗kraig grady <kraiggrady@anaphoria.com>

of course you can hear this. especially if you start hearing whole pieces of music in it. I can hear the differance betweeen 6,144 and just. It is a
matter of feel maybe more thn hear. But what you feel is very very perceptable to all!

>
>
> Message: 3
> Date: Fri, 01 Aug 2003 19:45:20 -0000
> From: "Gene Ward Smith" <gwsmith@svpal.org>
> Subject: Re: 665-tone equal temperament?
>
> --- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...> wrote:
>
> > Can you hear that level of precision? (I'm guessing you can, but
> not at the conscious
> > level.) -Justin
>
> Of course not. No one can.
>
>

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

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Danny Wier <dawier@hotmail.com>

🔗kraig grady <kraiggrady@anaphoria.com>

Hello Gene!
I would suggest that you calulator knows nothing of such subltleties. We are not talking about a single interval or two, we are talking about playing
music on instruments of different resolutions. I have no interest in pulling a Johnny on you to prove how great my ears are, even though i am quite aware
of what he says he can do is true. I would suggest that most everyone on these list will hear the differance.

I would like to know when you have ever even heard music in Just intonatation if all you have available is 768 synths. And this i direct at all the
rest who accuse me of being a purist in this case. What other tuning increments have you heard? and listened to over some period of time. I am afraid
that somehow possibly i have had more experience than most people on this list in the 28 years i have been doing this

Secor has an organ that in certain keys can play JI in absolute precision. put that against you midi standard and the aural effect is drastically
different. I have written quite a bit of music on this organ (maybe more experiments) that when i have transposed to a synth of 6,144, the acoustical
results were lacking in more than one instance, or can i say "turned down". I am sure Secor can tell the differance from the music in these keys and
chord and your base midi standard. Now if i have a choice between the motorola scale a tron tuning or 6,144 ET , in some cases, i still prefer the scale
a tron because of the flavor it instills. I attribute this to differance tones and the way each system 'morphs" differance tones. I rthink though we
could live with 6,144 for a while. yet certain type of music would die in this context. La Montes for one or any drone based music

I have to play a show in two weeks with Robert Rich. I hope that he doesn't get wind of this since he was one of the people who lobby for the
standard. i do not foresee approaching the subject with him. when i last did a show with him maybe 17 years ago he was working with prophet 5 which i
know he preferred to the precision of what else was available. I am not even sure of what he tried to get compared to the final result Like yourself, it
"appeared" to be more than fine. I can use a calulator too. But like so much of this , our road is very difficult , and no matter how well you plan and
decipher, it isn't until you have the object right in front of you when you realize so much that happens that we just can predetermine (so far). So
things take a month to get a feel but once you get it , it just won't go away. I am sure that if you took a piece of yours in 768 and dropped in 6,144
you would hear it right away.
or put it on Secors organ.

>
> From: "Gene Ward Smith" <gwsmith@svpal.org>
> Subject: Re: 665-tone equal temperament?
>
> --- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> > >
> >
> > of course you can hear this.
>
> According to my handy-dandy hand-held calculator, we are talking
> about hearing a difference of 0.00011364 cents. I suggest you are
> talking through your hat, but would be interested to see a
> demonstration of your superhuman abilities if it could be arranged.
>

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

🔗Paul Erlich <perlich@aya.yale.edu>

as you can see on the first graph at

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

if you mouse-over "zoom 1000",

665-equal is a member of the "monzismic", "vavoom", and "enneadecal"
5-limit linear temperament families. so it's related, in different
ways, to 612-equal, 901-equal, and 171-equal, in terms of the scales
and chord progressions native to it (in the 5-limit at least) . . .

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning@yahoogroups.com, <monz@a...> wrote:

> > It approximates Pythagorean with extreme precision,
> > and 5- and 7-limit just works very well too. Some
> > of the important small intervals have the following
> > sizes:
> >
> > apotome (sharp/flat) = 63
> > limma = 50
> > comma = 12
> > Pythagorean comma = 13
> > diesis = 23
> > diaschisma = 11
> > septimal comma = 15
> > schisma = 1
> > Mercator's comma = 2
>
>
>
> here are some more accurate values:
>
>
> apotome (sharp/flat) = 63.00044086
> limma = 49.9996851
> comma = 11.91806882
> Pythagorean comma = 13.00075575
> diesis = 22.7534507
> diaschisma = 10.83538188
> septimal comma = 15.10885087
> schisma = 1.082686937
> Mercator's comma = 2.003337917

monz and danny, to my mind, all the values should really be integers,
since they're constructed from an integer number of the consonant
intervals of the tuning, just like the tables you have on your
http://sonic-arts.org/dict/eqtemp-gallery.htm page, for example

31edo prime interval
degrees vector ratio name
3 5

-1 [ 8 1] 32805:32768 skhisma
1 [-4 -2] 2048:2025 diaschisma
0 [ 4 -1] 81:80 syntonic comma
1 [ 0 -3] 128:125 diesis
2 [-1 2] 25:24 JI chromatic semitone
2 [ 3 1] 135:128 Ellis larger limma, Rameau mean
semitone
3 [-5 0] 256:243 limma

etc.

🔗monz@attglobal.net

hi paul,

> From: Paul Erlich [mailto:perlich@aya.yale.edu]
> Sent: Saturday, August 02, 2003 11:14 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: 665-tone equal temperament?
>
>
> --- In tuning@yahoogroups.com, <monz@a...> wrote:
>
> > > It approximates Pythagorean with extreme precision,
> > > and 5- and 7-limit just works very well too. Some
> > > of the important small intervals have the following
> > > sizes:
> > >
> > > apotome (sharp/flat) = 63
> > > limma = 50
> > > comma = 12
> > > Pythagorean comma = 13
> > > diesis = 23
> > > diaschisma = 11
> > > septimal comma = 15
> > > schisma = 1
> > > Mercator's comma = 2
> >
> >
> >
> > here are some more accurate values:
> >
> >
> > apotome (sharp/flat) = 63.00044086
> > limma = 49.9996851
> > comma = 11.91806882
> > Pythagorean comma = 13.00075575
> > diesis = 22.7534507
> > diaschisma = 10.83538188
> > septimal comma = 15.10885087
> > schisma = 1.082686937
> > Mercator's comma = 2.003337917
>
>
> monz and danny, to my mind, all the values should really be integers,
> since they're constructed from an integer number of the consonant
> intervals of the tuning, just like the tables you have on your
> http://sonic-arts.org/dict/eqtemp-gallery.htm page, for example
>
>
> 31edo prime interval
> degrees vector ratio name
> 3 5
>
> -1 [ 8 1] 32805:32768 skhisma
> 1 [-4 -2] 2048:2025 diaschisma
> 0 [ 4 -1] 81:80 syntonic comma
> 1 [ 0 -3] 128:125 diesis
> 2 [-1 2] 25:24 JI chromatic semitone
> 2 [ 3 1] 135:128 Ellis larger limma, Rameau mean semitone
> 3 [-5 0] 256:243 limma
>
> etc.

yes, that's true. i simply wanted to show exactly
which intervals are "extremely close" and which are
merely "very close".

by using the decimal places, it's easy to see that
*all* of the best approximations are Pythagorean,
and the 5- and 7-limit intervals, while approximated
very well, are represented quite a bit less well
than the 3-limit ones.

this points to 665edo as being a very good
"Pythagorean" tuning.

... altho, of course, Kraig has some reservations about it.
and to an extent i agree with him.

in my own listening experiments, and also when listening
to La Monte Young's music live at the Dream House, i often
swear that i can hear differences in tuning that i'm
theoretically "not supposed" to be able to hear because
the tiny differences in pitch are so small.

i speculate that perhaps this is attributable to my
being able to *feel* the difference in vibrations
rather than perceive them audibly via the ear/brain.
but more research is needed to follow-up on that,

and that's fine, because i means that i'm required
to listen to more microtonal music! ;-)

-monz

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Graham Breed <graham@microtonal.co.uk>

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning@yahoogroups.com, <monz@a...> wrote:

> yes, that's true. i simply wanted to show exactly
> which intervals are "extremely close" and which are
> merely "very close".
>
> by using the decimal places, it's easy to see that
> *all* of the best approximations are Pythagorean,
> and the 5- and 7-limit intervals, while approximated
> very well, are represented quite a bit less well
> than the 3-limit ones.
>
> this points to 665edo as being a very good
> "Pythagorean" tuning.

yes, but you could have gleaned this information from just looking at
how 665-equal approximates the basic consonances. going through the
process for these various "commas" is redundant at best.

🔗monz@attglobal.net

> -----Original Message-----
> From: Paul Erlich [mailto:perlich@aya.yale.edu]
> Sent: Saturday, August 02, 2003 12:11 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: 665-tone equal temperament?
>
>
> --- In tuning@yahoogroups.com, <monz@a...> wrote:
>
> > yes, that's true. i simply wanted to show exactly
> > which intervals are "extremely close" and which are
> > merely "very close".
> >
> > by using the decimal places, it's easy to see that
> > *all* of the best approximations are Pythagorean,
> > and the 5- and 7-limit intervals, while approximated
> > very well, are represented quite a bit less well
> > than the 3-limit ones.
> >
> > this points to 665edo as being a very good
> > "Pythagorean" tuning.
>
>
> yes, but you could have gleaned this information
> from just looking at how 665-equal approximates
> the basic consonances.

can't argue with you there.

> going through the process for these various
> "commas" is redundant at best.

yeah, i know ... but i believe in redundancy.
i think it helps the learning process.

... besides, i think it's easier to really get a
feel for a tuning mentally when you can comprehend
a lot of different intervals and how they compare
to other tuning with which you're already familiar.

i've created whole sets of tables showing how various
interval sizes compare, i.e., how many 72edo-moria
there are in a syntonic comma, Pythagorean comma,
kleisma, skhisma, etc., how many 43edo-merides there
are in a syntonic comma, Pythagrean comma, ... etc.
as i create webpages for particular tunings, those
tables go into them.

-monz

🔗Mark Rankin <markrankin95511@yahoo.com>

--- Danny Wier <dawier@hotmail.com> wrote:
> From: Justin Weaver
>
> > If you're going to go this precise, why not just
> have millioctave
> 1200edo? -Justin
>
> Wouldn't that be 12,000,000-edo? Anyway, 665 is not
> an arbitrary division;
> it's based on a very long spiral of Pythagorean
> fifths. Same reason the
> Turks use 53-tone.
>
> And by the way, 665-edo is proposed for measurement
> only. I don't have the
> desire to design a 665-tone keyboard..>

I first heard of 665-ET in 1975 from Jacques Dudon who
had worked it out by himself and used it for
measurement. He showed it to Alain Danielou, who
proceeded to publish it without even mentioning
Jacques' name. I later found it in Barbour.

Let's be clear about Millioctaves, which were used for
measurement in Germany and Scandinavia, and which are
the same thing as 1000-ET. "Millioctave 1200-ET" would
be 1,200,000-ET, not 12,000,000-ET. But it looks as
if you were really trying to say either Millioctave
(1000-ET), or 1200-ET, rather than both of them
together as "millioctave 1200edo".

The first mention of 1200-ET that I know about was in
an article called 'Making Sense of Cents' (or some
such) which I had published in Jonathan Glasier's
"Interval" magazine in the late 1970's or early
1980's.

As mentioned by others, 665-ET is from 3-limit
Pythagorean, an approximation of a massive circle of
665 3/2 Fifths. 612-ET is an approximation of 5-limit
J.I. (3/2, 5/4, and 6/5), and was found by Isaac
Newton in the 1660's (see Penelope Gouk's article in
the book called 'Let Newton Be!').

-- Mark Rankin

__________________________________
Do you Yahoo!?
Yahoo! SiteBuilder - Free, easy-to-use web site design software
http://sitebuilder.yahoo.com

🔗kraig grady <kraiggrady@anaphoria.com>

Basically i now know how Galileo felt when he said there was moons around Jupiter.

I know the limits of the calulator while so many here worship it far more than i worship JI. I am appauled by this group attitude against first hand
knowledge with real sound in real time. You all know how the human eye can pick up even a single photon under optimium conditions. Why you have trouble
accepting that small increments have very noticable musical consequences especially as the ear gets more and more cues in actual music. So much happens in
even the simpliest music that will expose the underlining framework on which it stands

I want to know who has had experience here hearing pure JI
6,144 ?
1200?
768?

care to step up to the telescope and look?

The credibility of the methods employed here are, for what i can see, are at this point highly questionable. the castles built upon such structures are
doomed to collapse.

> From: Graham Breed <graham@microtonal.co.uk>
> Subject: Re: 665-tone equal temperament?
>
> Carl Lumma wrote:
>
> > I think you and Gene are talking about different things. You are
> > talking about the diff. between 1200-et and 665-et. Gene's talking
> > about something else (the diff. between 665-et and JI?).
>
> Gene must be talking about the difference between 665-et and Pythagorean
> intonation to get the 0.11 millicent error. Kraig talks about
> everything from 768-et (0.4 cent error) to 6144-et and the MIDI tuning
> standard, both of which have the same fifth with an error of 1.9
> millicents. As he doesn't believe in calculators, obviously orders of
> magnitude don't bother him.
>
> Graham
>
> ________________________________________________________________________
>

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

🔗Carl Lumma <ekin@lumma.org>

Kraig wrote...
>I am appauled by this group attitude against first hand
>knowledge with real sound in real time.

Kraig dude, don't make a simple misunderstanding into a
holy war! Do you, or do you not claim:

() To be able to hear the difference between a 665-et
3:2 and a pure 3:2?

() To have an instrument that would even allow you to
test such a thing?

>You all know how
>the human eye can pick up even a single photon under
>optimium conditions.

I didn't know that, but I understand that the ear can
detect a single hydrogen atom on the ear drum under
optimum conditions. Not sure what it has to do with
with the price of tea in china, though.

>The credibility of the methods employed here are, for
>what i can see, are at this point highly questionable.
>the castles built upon such structures are doomed to
>collapse.

Kraig, what on Earth are you talking about? All of us
involved in this thread have experience listening to and
work with various tunings and mistunings on JI on highly
accurate equipment.

-Carl

🔗Danny Wier <dawier@hotmail.com>

I can't hear the difference between a Pythagorean comma and a syntonic comma
myself; or even a syntonic and septimal comma for that matter. Plus it's
hard to play exact just intervals on a fretless bass in a dark 6th St. club
with the guitarist and drummer playing deafeningly loud.

I probably think more in terms of cents (or fractions of a semitone really)
myself, since I have lighter-colored lines in 12-tet. I used a maple-colored
wood filling when I took the frets out of my Ibanez six-string bass which
has a rosewood fingerboard.

614- and 665-tet

----- Original Message -----
From: Gene Ward Smith
To: tuning@yahoogroups.com
Sent: Saturday, August 02, 2003 1:10 AM
Subject: [tuning] Re: 665-tone equal temperament?

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> >
>
> of course you can hear this.

According to my handy-dandy hand-held calculator, we are talking
about hearing a difference of 0.00011364 cents. I suggest you are
talking through your hat, but would be interested to see a
demonstration of your superhuman abilities if it could be arranged.

🔗Danny Wier <dawier@hotmail.com>

1,200-tet is right. I got "milli" confused with "micro".

----- Original Message -----
From: Danny Wier
To: tuning@yahoogroups.com
Sent: Saturday, August 02, 2003 5:55 AM
Subject: Re: [tuning] Re: 665-tone equal temperament?

From: Justin Weaver

> If you're going to go this precise, why not just have millioctave
1200edo? -Justin

Wouldn't that be 12,000,000-edo? Anyway, 665 is not an arbitrary division;
it's based on a very long spiral of Pythagorean fifths. Same reason the
Turks use 53-tone.

And by the way, 665-edo is proposed for measurement only. I don't have the
desire to design a 665-tone keyboard....

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🔗Justin Weaver <improvist@usa.net>

I actually agree with this-- I think you can feel any change in air movement, of which
sound is a measurement, no matter how small. Plus, if you tune A one millionth of a
cent above A440, it might not rain in China six years later! -Justin

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> >
>
> of course you can hear this. especially if you start hearing whole pieces of music in
it. I can hear the differance betweeen 6,144 and just. It is a
> matter of feel maybe more thn hear. But what you feel is very very perceptable to
all!
>
> >
> >
> > Message: 3
> > Date: Fri, 01 Aug 2003 19:45:20 -0000
> > From: "Gene Ward Smith" <gwsmith@s...>
> > Subject: Re: 665-tone equal temperament?
> >
> > --- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...> wrote:
> >
> > > Can you hear that level of precision? (I'm guessing you can, but
> > not at the conscious
> > > level.) -Justin
> >
> > Of course not. No one can.
> >
> >
>
> -- -Kraig Grady
> North American Embassy of Anaphoria Island
> http://www.anaphoria.com
> The Wandering Medicine Show
> KXLU 88.9 FM WED 8-9PM PST

🔗Justin Weaver <improvist@usa.net>

Are the harmonics on Secor's organ perfectly harmonic? -Justin

>
> Secor has an organ that in certain keys can play JI in absolute precision. put that
against you midi standard and the aural effect is drastically
> different. I have written quite a bit of music on this organ (maybe more
experiments) that when i have transposed to a synth of 6,144, the acoustical
> results were lacking in more than one instance, or can i say "turned down". I am
sure Secor can tell the differance from the music in these keys and
> chord and your base midi standard. Now if i have a choice between the motorola
scale a tron tuning or 6,144 ET , in some cases, i still prefer the scale
> a tron because of the flavor it instills. I attribute this to differance tones and the
way each system 'morphs" differance tones. I rthink though we
> could live with 6,144 for a while. yet certain type of music would die in this
context. La Montes for one or any drone based music
>

🔗Justin Weaver <improvist@usa.net>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, kraig grady <kraiggrady@a...> wrote:
> >
>
> Hello Gene!
> I would suggest that you calulator knows nothing of such
subltleties.

If you have no clue what you are talking about, the best course is
silence.

We are not talking about a single interval or two, we are talking
about playing
> music on instruments of different resolutions.

Go ahead and play both 665 and JI Pythagorean and report back. The
first part of your report should detail how you managed to produce
tones so precisely that 3-limit 665 and JI were distinguishable at
all.

> I would like to know when you have ever even heard music in
Just intonatation if all you have available is 768 synths.

I have no idea where you get your weird notions, but this, of course,
is not true. I have nothing to do with such things.

🔗Carl Lumma <ekin@lumma.org>

🔗Paul Erlich <perlich@aya.yale.edu>

--- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...> wrote:
> Are the harmonics on Secor's organ perfectly harmonic? -Justin

yes, that's the easy part. the clever part is that the *harmonies*
are perfectly harmonic too. the misunderstanding is that this thread
(or the set of claims made here by those with "calculators") is not
about 6144-equal vs. ji in general, it's about 665-equal vs. 3-limit
ji. a far smaller difference.

>
>
> >
> > Secor has an organ that in certain keys can play JI in
absolute precision. put that
> against you midi standard and the aural effect is drastically
> > different. I have written quite a bit of music on this organ
(maybe more
> experiments) that when i have transposed to a synth of 6,144, the
acoustical
> > results were lacking in more than one instance, or can i
say "turned down". I am
> sure Secor can tell the differance from the music in these keys and
> > chord and your base midi standard. Now if i have a choice between
the motorola
> scale a tron tuning or 6,144 ET , in some cases, i still prefer the
scale
> > a tron because of the flavor it instills. I attribute this to
differance tones and the
> way each system 'morphs" differance tones. I rthink though we
> > could live with 6,144 for a while. yet certain type of music
would die in this
> context. La Montes for one or any drone based music
> >

🔗Paul Erlich <perlich@aya.yale.edu>

🔗Justin Weaver <improvist@usa.net>

Somewhere in the Just Intonation network. It struck me as odd, but the way these
divisions are used in describing bytes is weird too. -Justin

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> justin, milli- means 1/1000. lindley and other authors who have used
> the term "millioctave" meant 1/1000 of an octave. where did you see
> it defined as 1/1200 octave?
>
> --- In tuning@yahoogroups.com, "Justin Weaver" <improvist@u...> wrote:
> > I've seen millioctave defined as 1 cent. -Justin
> >
> > --- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> > > --- In tuning@yahoogroups.com, "Danny Wier" <dawier@h...> wrote:
> > > > From: Justin Weaver
> > > >
> > > > > If you're going to go this precise, why not just have
> millioctave
> > > > 1200edo? -Justin
> > > >
> > > > Wouldn't that be 12,000,000-edo?
> > >
> > > i think justin left out an "or" -- millioctaves are 1000-equal,
> and
> > > cents are 1200-equal.

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > >Are the harmonics on Secor's organ perfectly harmonic?
> >
> > If we're talking about the generalized-keyboard scalatron,
> > they almost certainly are. But the tuning precision is
> > not that good, if, as I suspect, it uses the same tone
> > generation hardware as the normal scalatron.

That's correct.

> it doesn't. george has explained this exhaustively here before. the
> tones are all generated by frequency dividers from a
single "master"
> tone. so everything is completely phase-locked, and completely ji.
no
> 1024 or any other equal division.

The 1024 pitches per octave are unequal -- subharmonics 1025 through
2048 of a master oscillator, just like all other Scalatrons, making
the steps range from ~0.8 to 1.6 cents.

The "phase-locked" JI tuning (described in message #38014) was
achieved by choosing a particular subharmonic for 1/1, such that the
entire 20-tone set would be a subset of that subharmonic sequence.
Otherwise, a Scalatron tuning is only an approximation.

At the time that the generalized keyboard was introduced, an
improvement was made by changing the pitch of the master oscillator
from 3579545 to 3581600 hz, which resulted in significantly less
overall error in the approximation of some ET's (including 12-ET).

--George

🔗Kurt Bigler <kkb@breathsense.com>

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, <monz@a...> wrote:

/tuning/topicId_46045.html#46105

> ... altho, of course, Kraig has some reservations about it.
> and to an extent i agree with him.
>
> in my own listening experiments, and also when listening
> to La Monte Young's music live at the Dream House, i often
> swear that i can hear differences in tuning that i'm
> theoretically "not supposed" to be able to hear because
> the tiny differences in pitch are so small.
>
> i speculate that perhaps this is attributable to my
> being able to *feel* the difference in vibrations
> rather than perceive them audibly via the ear/brain.
> but more research is needed to follow-up on that,
>
> and that's fine, because i means that i'm required
> to listen to more microtonal music! ;-)
>
>
>
> -monz

***Just to be a devilish devil's disciple: is it possible that in
music there is a "placibo" effect. Or, in other words, one's
*psychology* makes one *believe* one is hearing something, or hearing
a difference that is mostly just in the imagination??

J. Pehrson

🔗monz@attglobal.net

hi Joe (and David Beardsley),

> From: Joseph Pehrson [mailto:jpehrson@rcn.com]
> Sent: Tuesday, August 19, 2003 8:23 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: 665-tone equal temperament?
>
>
> --- In tuning@yahoogroups.com, <monz@a...> wrote:
>
> /tuning/topicId_46045.html#46105
>
> > ... altho, of course, Kraig has some reservations about it.
> > and to an extent i agree with him.
> >
> > in my own listening experiments, and also when listening
> > to La Monte Young's music live at the Dream House, i often
> > swear that i can hear differences in tuning that i'm
> > theoretically "not supposed" to be able to hear because
> > the tiny differences in pitch are so small.
> >
> > i speculate that perhaps this is attributable to my
> > being able to *feel* the difference in vibrations
> > rather than perceive them audibly via the ear/brain.
> > but more research is needed to follow-up on that,
> >
> > and that's fine, because i means that i'm required
> > to listen to more microtonal music! ;-)
> >
> >
> >
> > -monz
>
>
> ***Just to be a devilish devil's disciple: is it
> possible that in music there is a "placibo" effect.
> Or, in other words, one's *psychology* makes one
> *believe* one is hearing something, or hearing
> a difference that is mostly just in the imagination??

well, sure, i'm certain that that's *possible*.

but i also know that i've learned to trust my ears
more than any of my other four (regular) senses.

most humans who are not blind typically experience
about 80% of their sensory input thru vision. but
i know for certain that that's not true with me. i'd
say that my hearing and vision each account for
between 40% and 50%.

anyway ... La Monte Young knows that this kind of
thing happens when people hear his music, and he
deliberately plays around with it.

one piece in particular ... i think it was
_4th Dream of China_ (Dave, was that the name of it?
the one with the four cellos) ... had an amazing
interplay of "phantom" high harmonics floating above
the notes that the cellos were actually playing.

this is the result of combination tones, due to
the strong consonance and low-integer-ratios of
the notes which are actually being played.
La Monte certainly did it on purpose.

i've also heard this kind of thing in some parts
of _The Well-Tuned Piano_ CD, particularly during
the "Bose Brontosaurus Boogie" section. so anyone
who has access to the CDs can check it out.

(and Joe, since you live in NYC, you should be on
the lookout for any special Dream House events where
you can hear this stuff.)

BTW, this is another one of those great effects that
occur in JI but are much more difficult to achieve
(if it's possible at all) in a typical temperament.

(yes, i know, one can find a microtemperament that gets
arbitrarily close to JI ... that's why i said "typical".)

Ezra Sims has also written that this is the basic
procedure that he uses to determine his "JI"
chord progressions, which he notates in 72edo.

-monz

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗monz@attglobal.net

hi Joe,

> From: Joseph Pehrson [mailto:jpehrson@rcn.com]
> Sent: Friday, August 22, 2003 9:05 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: phantom microtones (was: 665-tone equal
> temperament?)
>
>
> --- In tuning@yahoogroups.com, <monz@a...> wrote:
>
> /tuning/topicId_46045.html#46458
> >>
> > (and Joe, since you live in NYC, you should be on
> > the lookout for any special Dream House events where
> > you can hear this stuff.)
> >
> ***Oh, sure... I go there from time to time.
> I haven't been aware, though, of any special
> exhibition other than the usual long-running
> piece. Maybe David B. can keep us updated on this....

yes, in fact, i believe David put together the "tape concert"
which i attended largely for my own benefit. (it's nice to
have good connections! ... thanks, Dave.) perhaps a
repeat can be arranged?

-monz

🔗David Beardsley <db@biink.com>

monz@attglobal.net wrote:

>hi Joe,
>
>From: Joseph Pehrson [mailto:jpehrson@rcn.com]
>
>--- In tuning@yahoogroups.com, <monz@a...> wrote:
>
>/tuning/topicId_46045.html#46458
> >
>>>(and Joe, since you live in NYC, you should be on
>>>the lookout for any special Dream House events where
>>>you can hear this stuff.)
>>>
>>> >>>
>>***Oh, sure... I go there from time to time.
>>I haven't been aware, though, of any special >>exhibition other than the usual long-running >>piece. Maybe David B. can keep us updated on this....
>> >>
>yes, in fact, i believe David put together the "tape concert"
>which i attended largely for my own benefit. (it's nice to
>have good connections! ... thanks, Dave.) perhaps a >repeat can be arranged?
> >
I never put together any tape concert. What were
we listening to?

http://melafoundation.org

and an email list:

/melafoundation/?yguid=70544219

I don't know what kind of plans they have for the future, but I
know that La Monte sang raga twice this year (June & August)
in the Dream House. For a few weeks last Spring, Jung He Choi
had an instalation running every Friday.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

🔗harmonics7111317 <db@biink.com>

--- In tuning@yahoogroups.com, <monz@a...> wrote:
> hi Joe (and David Beardsley),

> anyway ... La Monte Young knows that this kind of
> thing happens when people hear his music, and he
> deliberately plays around with it.
>
> one piece in particular ... i think it was
> _4th Dream of China_ (Dave, was that the name of it?
> the one with the four cellos) ... had an amazing
> interplay of "phantom" high harmonics floating above
> the notes that the cellos were actually playing.

Ah! You were at one of the Charles Cutis arranged
tape concerts.

What I remember about the pieces with just cellos,
is hearing a phrase start slightly out of tune,
then they'd lock in.

There are:
The Melodic Versions (1984) of The Four Dreams of China (1962),
tunable, sustaining
instruments of like timbre, in multiples of 4, including
The First Dream of China,
The First Blossom of Spring,
The First Dream of The High-Tension Line Stepdown Transformer,
The Second Dream of The High-Tension Line Stepdown Transformer,

and also:
The Melodic Versions (1984) of The Twelve Subsequent Dreams of China,
(1980), tunable, sustaining instruments of like timbre, in multiples
of 10, including
The High-Tension Line Stepdown Transformer's Second Dream of The First
Blossom of Spring

I don't remember which piece we heard because there
were a string of these semi-private taped concerts
for about a year or so while Charles was living in
NYC.

* David Beardsley
* microtonal guitar
* http://biink.com/db

🔗monz@attglobal.net

hi Dave,

> From: harmonics7111317 [mailto:db@biink.com]
> Sent: Saturday, August 23, 2003 7:48 AM
> To: tuning@yahoogroups.com
> Subject: [tuning] Re: phantom microtones (was: 665-tone equal
> temperament?)
>
>
> --- In tuning@yahoogroups.com, <monz@a...> wrote:
> > hi Joe (and David Beardsley),
>
> > anyway ... La Monte Young knows that this kind of
> > thing happens when people hear his music, and he
> > deliberately plays around with it.
> >
> > one piece in particular ... i think it was
> > _4th Dream of China_ (Dave, was that the name of it?
> > the one with the four cellos) ... had an amazing
> > interplay of "phantom" high harmonics floating above
> > the notes that the cellos were actually playing.
>
> Ah! You were at one of the Charles Cutis arranged
> tape concerts.
>
> What I remember about the pieces with just cellos,
> is hearing a phrase start slightly out of tune,
> then they'd lock in.
>
> There are:
> The Melodic Versions (1984) of The Four Dreams of China (1962),
> tunable, sustaining
> instruments of like timbre, in multiples of 4, including
> The First Dream of China,
> The First Blossom of Spring,
> The First Dream of The High-Tension Line Stepdown Transformer,
> The Second Dream of The High-Tension Line Stepdown Transformer,
>
> and also:
> The Melodic Versions (1984) of The Twelve Subsequent Dreams of China,
> (1980), tunable, sustaining instruments of like timbre, in multiples
> of 10, including
> The High-Tension Line Stepdown Transformer's Second Dream of The First
> Blossom of Spring
>
> I don't remember which piece we heard because there
> were a string of these semi-private taped concerts
> for about a year or so while Charles was living in
> NYC.

the one i attended included the piece that was a
recording of tables and chairs being scraped across
a concrete floor. that was where i took an intermission
and left the building for a couple of hours.

(for those who don't know ... the entire concert was
about 9 hours long.) but i loved everything else
i heard.

-monz

🔗David Beardsley <db@biink.com>

monz@attglobal.net wrote:

>>I don't remember which piece we heard because there
>>were a string of these semi-private taped concerts
>>for about a year or so while Charles was living in
>>NYC.
>> >>
>
>
>
>the one i attended included the piece that was a
>recording of tables and chairs being scraped across
>a concrete floor. that was where i took an intermission
>and left the building for a couple of hours.
>
>(for those who don't know ... the entire concert was
>about 9 hours long.) but i loved everything else
>i heard.
>
>
>
>-monz
>
> >

/Poem for Chairs, Tables, Benches, etc./ (1960), chairs, tables, benches and unspecified sound sources;

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

🔗Afmmjr@aol.com

🔗David Beardsley <db@biink.com>

🔗monz@attglobal.net

hi Dave and Johnny,

> From: David Beardsley [mailto:db@biink.com]
> Sent: Sunday, August 24, 2003 5:25 AM
> To: tuning@yahoogroups.com
> Subject: Re: [tuning] Re: phantom microtones (was: 665-tone equal
> temperament?)
>
>
> David Beardsley wrote:
> >>
> >>
> > > Poem for Chairs, Tables, Benches, etc./ (1960),
> > > chairs, tables, benches and unspecified sound sources;
> >
> > I think it was 2/96, Hamburg, Germany.
> >
> Because this series was presented by Charles Curtis who
> was concert master for this performance.

thanks for the full reference, Dave. and thanks for
inviting me to that tape concert.

i believe that the full title of the piece that
really blew me away is:

The Four Dreams of China (The Harmonic Versions) (1962) including
The First Dream of China
The First Blossom of Spring
The First Dream of The High-Tension Line Stepdown Transformer
The Second Dream of The High-Tension Line Stepdown Transformer
tunable sustaining instruments of like timbre in multiples of 4

(... and you're also reminding me that i ought to get together
with Charles Curtis, who's here in San Diego and with whom i'm
on pretty friendly terms. i haven't seen him in quite a while.)

-monz