Re: [tuning-math] [tuning] Re: Everyone Concerned

--- wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:
> --- In tuning-math@y..., Bill Arnold <billarnoldfla@y...> wrote:
>
> > Also, if you play a C octave as "the most perfect harmonic
> structure" as you say
> > "of just intonation," at least in that scale, would adding an F
> note in that octave,
> > as you play it, form for you, a consonant or dissonant chord?
>
> it would be consonant, but the root would now be F.
>
> > And what do you call the F
> > note relative to the C octave, as described? Would you call it a
> >harmonic chord?
>
> it could still be seen as a harmonic chord, with proportions 3:4:6
> over a fundamental _F_ two octaves lower. it could also be seen as a
> subharmonic chord, with proportions (1/4):(1/3):(1/2) under a common
> overtone c' an octave above the higher c in the chord. since 4, 3,
> and 2 are simpler numbers than 3, 4, 6, the chord C-F-c has been
> considered as a "subharmonic" or "undertonal" trine, while C-G-c
> would the the "harmonic" or "overtonal" trine, with the proportions
> exactly reversed.
>
>
Thank you for that response.

Why is it not a C chord, with two C notes in C-F-c?

Also, what if F # or Fb were substituted for the F note:

in other words, C-F#-c?

and: C-Fb-c?

Are the more harmonic chords?

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> Why is it not a C chord, with two C notes in C-F-c?
>
> Also, what if F # or Fb were substituted for the F note:
>
> in other words, C-F#-c?
>
> and: C-Fb-c?
>
> Are the more harmonic chords?

Bill, the questions you are asking involve very elementary (Western) music harmony principles. The standard Western triad involves three notes: a root, a perfect fifth above it, and a note in between that forms the third of the chord. The terms root, third, and fifth derive from their sequence in the scale. The chord is either major or minor depending on whether it has a third that is, respectively, two whole steps or one whole step and one half step. This, again, is all relating to standard 12tet Western harmony. You should also note that the root, major third and perfect fifth form the first triad that appears in the natural harmonic overtone series.

So if the root is C, the third is either E or E-flat, and the fifth is G. If you were to have C and F, they form a perfect fourth. If you were to have those as two components of a triad, it would be F on the bottom and C as the fifth, and then either A or A-flat as the third.

You might want to check out an elementary (Western) music theory book from a library, as all of this, including inversions, 7th chords, etc. would be explained.

Jon

--- Jon Szanto <JSZANTO@ADNC.COM> wrote:
> --- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> > Why is it not a C chord, with two C notes in C-F-c?
> >
> > Also, what if F # or Fb were substituted for the F note:
> >
> > in other words, C-F#-c?
> >
> > and: C-Fb-c?
> >
> > Are the more harmonic chords?
>
> Bill, the questions you are asking involve very elementary (Western) music harmony
> principles. The standard Western triad involves three notes: a root, a perfect fifth
> above it, and a note in between that forms the third of the chord. The terms root,
> third, and fifth derive from their sequence in the scale. The chord is either major or
> minor depending on whether it has a third that is, respectively, two whole steps or one
> whole step and one half step. This, again, is all relating to standard 12tet Western
> harmony. You should also note that the root, major third and perfect fifth form the
> first triad that appears in the natural harmonic overtone series.
>
> So if the root is C, the third is either E or E-flat, and the fifth is G. If you were
> to have C and F, they form a perfect fourth. If you were to have those as two
> components of a triad, it would be F on the bottom and C as the fifth, and then either
> A or A-flat as the third.
>
> You might want to check out an elementary (Western) music theory book from a library,
> as all of this, including inversions, 7th chords, etc. would be explained.
>
> Jon
>
>

Hi, Jon. Why thank you very much for your lucid explanation. It makes perfect sense to
me now, although I will have other questions as I go along in my research. Charles Lucy
has put his URL on, and I went to :

http://www.lucytune.com/colour_and_mapping/clock_face.html

I note he has two distinct clock faces: his first clock face is 12 Tone Equal Temperment,
which I guess is what you are referring to above as Western music theory? Is that
correct?

His second clock face is what he calls: Lucy Tuning Intervals or Naturals?

In what sense are the latter "Naturals" and the "Western" are not natural?

I thank you for your suggestion that I read an elementary book. However, I am not after
an elementary understanding. I look at Charles Lucy's Charts, and they are not
elementary nor do I find any of this elementary, but complex. Not that that scares
me from investigating it.

I guess what I am after now: can you explain to me if there IS such a thing as
"Natural" scales? And "Natural" chords? Or, are they, like words, the creation
of the mind? You know, as pointed out by many authors such as Guy Murchie in Music of
the Spheres, that there are "Natural" shapes in Nature: six-sided hexagonal gems like
emeralds and eight-sided pyramidal gems like diamonds. So: are their such "Natural"
shapes in scales and chords in Nature? Or, are they creatings of minds?

Thanks in advance.

Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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There, I'm dating myself.

And, yes, there have been times where dating myself would have helped out at dances, or something...

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> It makes perfect sense to me now, although I will have other
> questions as I go along in my research.

Why does that not surprise me? :)

> Charles Lucy ... I note he has two distinct clock faces: his
> first clock face is 12 Tone Equal Temperment, which I guess
> is what you are referring to above as Western music theory?
> Is that correct?

Without going back to his site to check, I'd reservedly say yes.

> His second clock face is what he calls: Lucy Tuning Intervals or
> Naturals? In what sense are the latter "Naturals" and the
> "Western" are not natural?

Before we go too much further, note the following:

1. For explanations of LucyTuning (and related materials, with Galaxy-wide Copyrights or whatever) you should ask Mr. Lucy himself. They are his theories.

2. The term "natural", in all uses but especially (for us) in music, is layered with many meanings. I *think* I know what you are asking, but using the term "natural" will lead you into a *lot* of confusion.

I will defer to the many more knowledgeable people on the tuning list, but I'll try to at least point you in the right direction.

> I thank you for your suggestion that I read an elementary book.
> However, I am not after an elementary understanding.

I am not meaning for you to have _only_ an elementary understanding, but if you are confused over the most basic elements of Western music, and then going out from there, you will need to instruct yourself in those basics. I, myself, may one day want to understand, deeply, quantum physics. If so, I better learn the mathematical and physical tenets and basics of those disciplines (or other suitable ones) before simply casting myself in the deep end.

> I guess what I am after now: can you explain to me if there IS
> such a thing as "Natural" scales? And "Natural" chords?

I am going to stop you right there and give what I *think* is what you are after: I _believe_ you are looking to the natural frequency vibrations of the harmonic series, sometimes (frequently) referred to as the harmonic series. These are the frequencies that start with a root, produce an octave above that, then the perfect fifth, another octave, a major third, etc. These frequencies vibrate in a relationship to each other: 2/1, 3/2, 4/3, etc.

Again, there are physio-acoustic wizards here on the list (Paul Erlich, to name one) who can explain this not only more correctly and exactly but also with proper terminology.

That said, there is one branch of music/tuning that is a direct outgrowth of the natural harmonic series. This one large branch is known as Just Intonation, and it is practiced - by composers and performers - in a number of different ways. An introduction to this subject (indeed, the first chapter from the "Just Intonation Primer", by David Doty) can be found here:

http://www.dnai.com/~jinetwk/primer2.html

> You know, as pointed out by many authors such as Guy Murchie in
> Music of the Spheres, that there are "Natural" shapes in Nature:
> six-sided hexagonal gems like emeralds and eight-sided pyramidal
> gems like diamonds. So: are their such "Natural"
> shapes in scales and chords in Nature? Or, are they creatings of
> minds?

Yes. And no.

Cheers,
Jon

First, a generic comment to all.
I am cross-posting this message to just two groups,
tuning and tuning-math,
because some of the answers come back to me
from tuning,
and some come back from
tuning-math.

So: I am trying explain myself to both
groups. Although some in both groups want me to send
to only ONE group, I have yet to figure out why. I
have gotten answers from both groups. The DELETE button
is on my computer and gets used on messages that do not
speak to me. But some insist on emailing me off-list
and asking me to cease. OK: I get the message.

To ALL: if my sig file is clicked, it can be seen that
I was a professor of world literature classics over three
decades, among other unrelated odd jobs, including
being a motion picture projectionist for 23 years, mostly
summers. I have not been idle, as apparently have none
of you. I am also an author, and am working on another
book, ON THE GENERAL THEORY OF ORDER. It might be also
subtitled Music of the Spheres. I am not sure yet. Time
will tell.

Two decades ago, I published
a couple science papers on the broad topics: MUSIC OF THE SPHERES,
BODE'S LAW EXPLAINED,
ON THE SPECIAL THEORY OF ORDER [in contradistiction to Einstein's
"relativity theory": I consider his theory a statistical theory
within the larger GENERAL THEORY OF ORDER. I do not wish to go
into details, on these music theory lists, which may surprise and
also please some.] A few members and I have an off-list correspondence.
I hope to have my papers online for those so interested, as someone
who you all know has them now. I believe the content will interest
musicologists with theoretic minds.

After my initial papers two decades ago, Guy Murchie called me, and
asked to write a paper about me for The Old Farmer's Almanac. As a
prerequisite, he invited me to his house in New Hampshire to conduct
a symposium on the subject. To my surprise, when I got there, there
were two dozen mathematicians, scientists, mostly astrophysicists,
physicists, and musicologists. Murchie was a Harvardian, which was
right down the road in Boston. I was stunned to lecture to those pure
science minds, as I was a THEORIST, but it went well, and the rest
is history. At this point: I am working on a last paper entitled
ON THE GENERAL THEORY OF ORDER. That is the reason for my questions
to trained musicologists. I apologize to those who found me a distraction,
or boring, or whatever. Unbeknownst to all, a few have emailed me off-list,
and some have become communicators and others wished to take me to task.
It makes sense to me that members should answer questions if they wish,
rather than lecture members and create ad hominems which only tend to
shut down communication.

I wish to thank Pauline, Joe S and Joe M. I am not disappearing,
but I am to become a lurker. I have NOT gotten ALL my answers from you all,
but you all have been for the most part kind and gracious, and I thank
you. To those who were annoyed, so be it. I did not mean to be that,
figuring musicologists were interested in music theory. I guess I was
wrong. If I was not, those who care need to speak up. Otherwise, I will
lurk.

As said above: I KNEW Guy Murchie, have devoured his book
MUSIC OF THE SPHERES. Please understand, I have a vast library, and
have read many many many many many many many books on the subjects I
am putting forth. If you wonder why 7 manys, you might enjoy
Hemingway's HILLS LIKE WHITE ELEPHANTS

I know Pythagoras, et al., as anyone
who has read my papers will know. I have read more books than
I care to delineate.

As I stated in my papers
ALL sciences are based on MATHEMATICS. Anyone who does not
agree with me on that is in DISAGREEMENT with me. So be it.
As I said in my BODE'S LAW EXPLAINED paper, and what impressed
Murchie was just THAT. I argued that MATH is the basis of
MUSIC OF THE SPHERES. It take PHYSICS to EXPLAIN the relationships
of the ENTITIES observed by their mathematical trails, regardless
of the DISCIPLINE. I believe the (a) MATH and (b) PHYSICS relationship
as I stated in this paragraph, implicitly.

Because you all have ADVANCED TUNING and TUNING-MATH beyond that
of Murchie and others of two decades ago, things have changed.
I had hoped that some of you could assist me. In fact, I did
open up a few discussions which Pauline and others added to re:
Organs. But it was a MEMBER who asked me NOT to take my thoughts
off list.

Now, I am NOT so sure. No, I do not have all my answers, and will
lurk and at some point ask a question, down the road, and answer those
who query me about my ideas re: Music of the Spheres.

It is the minds of musicologists which can assist the topic. Do not
forget that Pythagoras, et al., developed these theses millenniums ago,
and it can take another couple millenniums to resolve the questions.
For those NOT interest in the subject, I apologize for bring it up.

In conclusion: if someone KNOWS of a message board which WELCOMES a
discussion of MUSIC OF THE SPHERES and the MATH and PHYSICS thereof,
let me know. I will take my question THERE.

Thanks in advance.

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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> ALL sciences are based on MATHEMATICS.

Bill,

Fine. But I think those interested in tuning have the cart before the horse
(music rack before the music) when they use math to create an arbitarary just
scale, then write music to fit it. My approach as a trained musician
(organist, composer, arranger, transcriber) was to take music that had
already been composed for tempered scales and determine what theoretical just
scale would permit one to accurately play such music. And new music as well.

And I found the answer--a scale based on the harmonic-partials spectrum
rather than arbitararily chosen just intervals. As the notes in a chord need
to be in agreement with their counterparts in the harmonic spectrum. Just as
organ mutation stops with fractional footages need to be tuned to jsut
intonation. And thus why ET isn't the best tuning for organs. The result was
the 0 #/b 19-limit (in C) Phillips Just Scale I posted here.

Once the best theoretical just scale was determined, it had to be made
practical. As it has more notes per octave in the wrong places than a
practical keyboard will permit. A practical keyboard simply cannot have a #
and b at the same digital location. As one interval will be smaller in reach
than normaal, and the other larger. Such not only creates awkwardness, but
prohibits the player from playing without looking at the keys. As any
proffessional musican is supposed to be able to do. Such digitals were never
popular when used on organs historically.

A proper scale and keyboard can't be just for experimenters. They needs to be
useful to trained musicians willing to use them.

The solution was to slightly temper (- 2 cents) the just 5th in the scale to
the ET 5th. This caused the 7Eb and D# to virtually merge in pitch, and the
7Ab and G# likewise. Tempering the just major 3rds 1-2 cents merged them
completely. But then, since the harmonic minor 7ths are also used as D# and
G# they had to be raised or lowered 1 cent to make a perfect match. The
result was the 0 #/b 19-limit (in C) Phillips Just-Temperament Scale I posted
here. (The 19th limit is Eb--298 cents 19/16. While C doesn't use it in its
chromatic scale, it does use flatted chords occasionally.)

A practical just-temperament keyboard has to have split digitals for
rarely-used notes. But they must be in the same general location for a given
diatonic key signature as the regular digitals. Thus, since C uses no #s nor
bs, all the split digitals for that key are white ones. Septimal c and
tertian e, using the same scale and tuning, do use bs and #s, but the regular
black keys are used for them with my tuning and keyboard layout. The same
basic principles apply to all other key signatures commonly used.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

Pauline,

--- In tuning@y..., prophecyspirit@a... wrote:
> Fine. But I think those interested in tuning have the cart before
> the horse (music rack before the music) when they use math to
> create an arbitarary just scale, then write music to fit it.
> My approach ...

Um, *exactly*. It is *your* approach. That doesn't necessarily mean that people who craft their tunings another way and then create a music to work in that tuning are somehow not valid, does it?

Well, I don't think so, even if it doesn't happen to be my particular modus operandi.

Cheers,
Jon

In a message dated 10/20/02 12:58:52 PM Central Daylight Time,
JSZANTO@ADNC.COM writes:

> That doesn't necessarily mean that people who craft their tunings another
> way and then create a music to work in that tuning are somehow not valid,
> does it?
>
Such a scale can only be used by its creator unless someone else learns it,
how to use it,and considrable notation marks. Mine can be used by anyone once
it's installed in an organ. And needs no notation marks except for the few
notes on split digitals.

Pauline

what wrong with everybody using their own tuning system? As many tuning
systems as musicians!

Dante
-----Original Message-----
From: prophecyspirit@aol.com [mailto:prophecyspirit@aol.com]
Sent: Sunday, October 20, 2002 6:17 PM
To: tuning@yahoogroups.com
Subject: Re: [tuning] Re: MUSIC OF THE SPHERES

In a message dated 10/20/02 12:58:52 PM Central Daylight Time,
JSZANTO@ADNC.COM writes:

That doesn't necessarily mean that people who craft their tunings
another way and then create a music to work in that tuning are somehow not
valid, does it?

Such a scale can only be used by its creator unless someone else learns
it, how to use it,and considrable notation marks. Mine can be used by anyone
once it's installed in an organ. And needs no notation marks except for the
few notes on split digitals.

Pauline

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In a message dated 10/20/02 5:24:03 PM Central Daylight Time,
dante.interport@rcn.com writes:

> what wrong with everybody using their own tuning system? As many tuning
> systems as musicians!
>
> Dante
>
All the just tuning systems I read about besides mine have very limited
usage, and that to modern music. My scale will play virtually any Western
World music.

Pauline

OK: My remarks will be between the
+++++++++++++++++++++++++++++++++ lines
my remarks: some more follow, between
comments by others; I have deleted tuning-math
from my replies at the request of 2 members, and
if others there who are not on tuning and
celestial-tuning care about it, they can
join tuning or celestial-tuning; I looked
at the membership lists and assume the
celestial-tuning members are all lurkers
who await the ENLIGHTENMENT OF THE WORLD,
and I will try NOT to disappoint them:
I know Joe Monz has ENLIGHTENED them,
already, so
the MUSICOLOGISTS on tuning can tune in
the MATH sides of their brains, as they choose,
on tuning. The tuning-math board will NOT hear
from me, per requests of a couple of your members.
+++++++++++++++++++++++++++++++++++lines

> From: prophecyspirit@a...
> Date: Sun Oct 20, 2002 8:17am
> Subject: Re: MUSIC OF THE SPHERES
>
>
>
>
> ALL sciences are based on MATHEMATICS.
>
>
> Bill,
>
> Fine. But I think those interested in tuning have the cart before the horse (music rack
> before the
> music) when they use math to create an arbitarary just scale, then write music to fit
> it. My
> approach as a trained musician (organist, composer, arranger, transcriber) was to take
> music that
> had already been composed for tempered scales and determine what theoretical just scale
> would
> permit one to accurately play such music. And new music as well.
>
>

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Pauline: please do not misunderstand me. I agree with you, and with your statement here;
all I MEANT by that was: All sciences are BASED on mathematics. That means, that one
must
USE the system of basic MATH somewhere, somplace, in the manipulation of the science
discipline the scientist is working in: in other words, I see musicologists as
scientists,
and they USE MATH at times to EXPLAIN things. The danger has been that in the attempt
to understand THE MUSIC OF THE SPHERES concept, astronomers who rule the roost in thAT
discipline have violated basic MATH principles when they measure the solar-planetary
system. As I wrote in BODE'S LAW EXPLAINED, they use the a.u., the measure between
Sun-Earth distance as the ruler of the system, and I say that is WRONG, that the
measuring stick should be the Sun-Mercury distance, then all the MEAN data numbers become
a "natural series of numbers" as expressed by Margo, below, about MUSIC and I have
applied the same logic to the SPHERES. But it took MATH to get ALL to be ENLIGHTENED.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
>
> From: prophecyspirit@a...
> Date: Sun Oct 20, 2002 9:47am
> Subject: in phase v. out of phase
>
>
>
> in phase : in a synchronized or correlated manner
>
> -out of phase : in an unsynchronized manner : not in correlation
>
> Merriam Webster Internet Dictionary. The 1996 printed version says the same.
>
> The above is how I use the terms "in phase" and "out of phase." in relation to
> theoretical exact
> just intonation intervals or chords v. the same just temperamed +/- 2 cents. JI is in
> phase when
> done electonically, and JT is out of phase when done electroncially or acoustically.
>
> Pauline
> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Pauline: I absolutely agree with your definition, as it is a standard definition
in PHYSICS: the discipline that attemtps to EXPLAIN how things works, regardless
of the DISCIPLINE. In cycle science, in or out of phase is a major concept.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> From: monz <monz@a...>
> Date: Sun Oct 20, 2002 3:41pm
> Subject: Re: [tuning-math] Re: MUSIC OF THE SPHERES
>
>
> hello Bill,
>
>
> > From: "Gene Ward Smith" <genewardsmith@j...>
> > To: <tuning-math@yahoogroups.com>
> > Sent: Sunday, October 20, 2002 9:07 AM
> > Subject: [tuning-math] Re: MUSIC OF THE SPHERES
>
>
> > --- In tuning-math@y..., Bill Arnold <billarnoldfla@y...> wrote:
> >
> > > In conclusion: if someone KNOWS of a message board which WELCOMES a
> > > discussion of MUSIC OF THE SPHERES and the MATH and PHYSICS thereof,
> > > let me know. I will take my question THERE.
> >
> > I thought someone had made a list for that very topic.
>
>
> /celestial-tuning/
>
>
> i know you already subscribe, and i also know that
> your questions have gone unanswered by members of the
> celestial-tuning list, but if you're going to lurk on
> tuning and tuning-math, i encourage you to keep posting
> there on celestial-tunings as your work is entirely
> relevant to the subject matter of that group.
>
> (and this time *i'll* aplogize for the cross-post)
>
>
> -monz
>
>
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Joe and Gene: I see Joe's point, and will lurk on 11 science lists, but post to
only tuning and celestial-tuning with cross-posts, in as much as those on
CELESTIAL-TUNING wish to be ENLIGHTENED/or they can teach/but so far none have
responded to anything I put there, and it IS a small membership, and most of the
musicologists are on TUNING, and therefore cross-posting those two should not
upset those easily upset. I am surprised that THE MATH HEADS on tuning-math
cannot find their delete button [it looks like D :) and when it is struck, it
will delete messages; hey, but THE MATH HEADS know that. And Gene, you said
"most" members are subscribed to BOTH tuning-math and tuning, and as a MATH HEAD
I am sure you know you are saying not all, and therefore you deny me my right to
reach ALL with your zealousness to avoid your D button, but you shall rule the
day. I hope it makes you FEEL better :) God knows, we want everyone to not feel
upset over message board messages.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

From: "M. Schulter" <MSCHULTER@V...>
Date: Sun Oct 20, 2002 2:12 am
Subject: Re: [tuning math] Re: everyone concerned

Hello, there, everyone, and how one analyzes 3:4:6 depends a great
deal upon what period or style of Western European or other theory one
is focusing on.

To me, 3:4:6 is a variation on the more conclusive 2:3:4, with the
latter arrangement (outer 2:4 octave, 2:3 fifth below, 3:4 fourth
above) as a complete stable sonority in 13th-14th century music of
Western Europe.

As one theorist around 1300 explains, in 2:3:4 the intervals follow a
"natural series" of numbers 2-3-4, with the 2:3 fifth "preceding" the
more complex 3:4 fourth.

Interestingly, this passage was written about three centuries before
the discovery of the harmonic series, or of the way a vibrating string
in effect subdivides itself to produce partials such as the 2:1 octave
and 3:1 twelfth (fifth plus octave).

In the era around 1300, a theorist named Johannes de Grocheio
describes a complete 2:3:4 sonority as manifesting _trina harmoniae
perfectio_, the "threefold perfection of harmony," since it includes
all three simple stable consonances: the 2:1 octave, 3:2 fifth, and
4:3 fourth.

This phrase leads to the modern English term "trine" for a complete
2:3:4 sonority; in Gothic and neo-medieval styles, it defines the
standard of full stable harmony, and the ideal resolution for unstable
sonorities.

Theorists around 1300 also note that 2:3:4 is smoother than 3:4:6,
with the 3:4 fourth below the 4:6 or 2:3 fourth. Either is regarded by
Jacobus of Liege (c. 1325) as perfectly concordant, but with the first
form generally preferable.

This preference, however, may vary: around 1030, Guido d'Arezzo in his
_Micrologus_ prefers the 3:4 fourth to the 2:3 fifth as a basic
interval, and advocates the placement of the fourth below the fifth in
a technique of three-voice singing which involves a series of 3:4:6
sonorities.

If we want a name for the 3:4:6 reflecting later stylistic trends
around the 13th century, we could call it a "converse trine," since
the intervals are said to be arranged "conversely" (_e converso_) from
the more conclusive 2:3:4 sonority with the fifth below the fourth.

A standard Gothic Pythagorean tuning, generally assumed in medieval
European theory (with a few interesting variations), makes both the
2:3:4 and its "conversity" of 3:4:6 pure.

In neo-medieval music, however, the fifths are often tuned somewhat
wider than pure, and the fourths somewhat narrower, with about 2 cents
of tempering standard.

It should be noted that in the 18th-19th century styles discussed by
Jon Szanto, a complete 2:3:4 or 3:4:6 trine of medieval or
neo-medieval styles would be considered some kind of incomplete
sonority, for example a portion of a 4:5:6 triad. Similarly, in the
21st-century decatonic harmony of Paul Erlich based on a complete
4:5:6:7 tetrad, the complete 4:5:6 triad of 18th-century music would
be considered an incomplete portion of a tetrad.

Most appreciatively,

Margo Schulter
mschulter@v...
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Margo: your message was on tuning but SEEMS in response to tuning-math: but I am glad
it is on tuning. Margo, I have always seen what you express above as basic to MATH
and I guess it speaks directly to musicologists: your wrote,
"To me, 3:4:6 is a variation on the more conclusive 2:3:4, with the
latter arrangement (outer 2:4 octave, 2:3 fifth below, 3:4 fourth
above) as a complete stable sonority in 13th-14th century music of
Western Europe."

In my quest to understand MUSIC OF THE SPHERES, I observed the MEAN data of the orbitals
of the planets from the center out toward the perimeter as, Sun 0, Mercury 1, Venus 2,
Earth 3, Mars 4, Ceres 8^*, Jupiter 15, Saturn 30, Uranus 60, Neptune 90, and Pluto at
120, or in reverse, from out toward the center, Pluto 4/4, Neptune 3/4, Uranus 1/2,
Saturn 1/4, Jupiter 1/8, Ceres 1/15, Mars 1/30, earth 1/40, Venus 1/60, Mercury 1/120,
and Sun at 0. It seems to me that your basic statement about Western music describes the
solar-planetary system MEAN oribital data quite well: "As one theorist around 1300
explains, in 2:3:4 the intervals follow a "natural series" of numbers 2-3-4, with the 2:3
fifth "preceding" the more complex 3:4 fourth."

^* I explained in my papers, that the solar-planetary system is REAL, and not an
arbitrary structure such as DIFFERENT music systems, and therefore the Ceres orbital
at 8 and the next at 15-16^* are points of discussion. In attempts to EXPLAIN something
observed in MATH the observers has to seek the IDEAL just as Margo, I think, is pointing
out in her fuller statement.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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In a message dated 10/20/02 6:38:39 PM Eastern Daylight Time,
prophecyspirit@aol.com writes:

> All the just tuning systems I read about besides mine have very limited
> usage, and that to modern music. My scale will play virtually any Western
> World music.
>
>

Dear Pauline, this appears to be a bit of self-prophesizing to me. I
regularly compose in different tunings for different combinations of
musicians and instruments. It's great that you have a facility with the
organ, because that is about the most difficult for me to use in a concert in
a tuning a would like.

best, Johnny Reinhard

In a message dated 10/20/02 8:39:35 PM Central Daylight Time, Afmmjr@aol.com
writes:

> It's great that you have a facility with the organ, because that is about
> the most difficult for me to use in a concert in a tuning a would like.
>
> best, Johnny Reinhard
>

My scale won't play regular music requiring the 11th harmonic. A close
approximation of it at 555 cents is availabie in certain keys. But not in the
normal key signature one would be using. However an approximation of the 13th
harmonic at 855 cents is available for every key signature. As that's the
harmonic minor 7th for the subtonic VII.

Personally though, I haven't seen any need for either the 11th or 13
harmonic. As they don't belong to any regular chord. A practical keyboard
can't provide for every theoretical possiblity. So I settled for what is
commonly used in classical and sacred music. And thus most other Western
music.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/20/02 12:58:52 PM Central Daylight Time,
> JSZANTO@A... writes:
>
>
> > That doesn't necessarily mean that people who craft their tunings another
> > way and then create a music to work in that tuning are somehow not valid,
> > does it?

> Such a scale can only be used by its creator unless someone else learns it,
> how to use it,and considrable notation marks.

I've used many different scales and tuning systems; my computer has yet to complain of it.

I have up on mp3.com music using scales and/or tuning involving Orwell, 171-et, 126/125-planar, 64/63-planar, {3,7}-subgroup 36-et, 72-et, and pure 11-limit JI. I've just uploaded something in (175-et)Blackjack, for that matter. The question of how to manage such things in live performance is an important one, but of course it can always be done, if in no other way, by means of electronic surrogates.

I asked my teacher Daniel Wolf about the Music of the Sphere thread,
and he emailed to me:

"I think that there is some misunderstanding about the use of the
word "music" here. The classical and medieval art of "music" (in the
quadrivium with arithmetic, geometry, and astronomy) was essentially
the theoretical study of proportions, with the acoustic realisation
of those proportions (on the monochord or canon) a secondary or even
incidental aspect. The proportions could be expressed as well in
architectural forms or in apparent distances between heavenly bodies.
From these origins, the west has had a long tradition of talking
about architecture or celestial mechanics in terms of "harmony". The
actual practice of music was never a central subject of this
discipline, although there were isolated attempts to identify
particular configurations with real scales. (A beautiful example of
the use of classical _geometry_, on the other hand, to describe a
musical performance is to be found in Jon Barlow's _Xemharmonikon_
article on Euclid's proofs as monochord examples).

I think that "music", in this quadrivial sense, remains useful for
talking about the basic _local_ pitch structures in music, both
melodic and harmonic, and is often delightfully useful in discussing
architectural forms or forms found in visual arts. The application
of whole number of proportions to natural systems, however, is more
problematic. The arrangement of planets around a sun at any given
point in time, for example, is the result of the historical
interaction of masses, distances, gravitation and probably a lot of
accidents along the way. Classical theorists knew precious little
about this, with their earth-centered and circular models, and we
still don't know enough. This is notoriously complex (tried solving
the three-body problem lately?) and all the interest really lies -
for met, at least - in the details. A "Harmony of the Spheres" model,
based upon static, whole number proportions is going to be a gross
simplification of a single moment in a dynamic system -- but how do
you choose the moment? Pluto's not always the furthest out. How do
you express the masses musically? The masses are as essential as the
distances, aren't they?"

"That said, there have been interesting attempts to turn "harmony of
the spheres" models into real music. Laurie Spiegel did a dynamic
version of Kepler, with continuously sliding tones. Another
intersting piece is Charles Dodge's _Earth's Magnetic Field_,
directing translating one index of the effect of solar radiation on
the earth's magnetic field into audible sounds. In both of these
cases, however, we are not dealing with a actual, sounding, harmony
made by a natural phenomenon but rather with a mapping into a
parallel experience that retains some proportional relationships. I
think that distinction is a subtle one and may often be lost."

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

> I have up on mp3.com music using scales and/or tuning involving Orwell, 171-et, 126/125-planar, 64/63-planar, {3,7}-subgroup 36-et, 72-et, and pure 11-limit JI. I've just uploaded something in (175-et)Blackjack, for that matter. The question of how to manage such things in live performance is an important one, but of course it can always be done, if in no other way, by means of electronic surrogates.

I forgot Magic--can't forget Magic, though my somber Magic piece may be missing its inner cheer.

My remarks, are below between the +++++++++++++lines
as such
++++++++++++++++++++++++++++++++++++++++++++++++++++
39818 From: alternativetuning <alternativetuning@y...>
Date: Mon Oct 21, 2002 5:00am
Subject: Re: MUSIC OF THE SPHERES

I asked my teacher Daniel Wolf about the Music of the Sphere thread,
and he emailed to me:

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Hey: thanks for your post, and I do not know WHO you are, so I guess
I will respond to Daniel Wolf, your teacher:
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Daniel writes:
"I think that there is some misunderstanding about the use of the
word "music" here. The classical and medieval art of "music" (in the
quadrivium with arithmetic, geometry, and astronomy) was essentially
the theoretical study of proportions,

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Exactly: Daniel Wolf, a member of these lists have my early papers of
two decades ago with permission to put them online for scholarship
and educational purposes, gratis, and if they are you will SEE my
long and involved discussion of PROPORTIONS: you are ABSOLUTELY right
on, in THIS PART of your statement.

In fact, Pythagoras, according to Guy Murchie, in MUSIC OF THE SPHERES,
circa 400 BC, wrote:

"There is geometry in the humming of the strings.
There is music in the spacings of the spheres."

Daniel, so far, we are on the same page!
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Daniel writes:
with the acoustic realisation
of those proportions (on the monochord or canon) a secondary or even
incidental aspect. The proportions could be expressed as well in
architectural forms or in apparent distances between heavenly bodies.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Here IS the ARCHITECTURE, as seen in the data:

I, Bill Arnold would add, here, that in my paper published in Cycles Bulletin,
Vol. XXX, No. 4, 1979, I pointed out that any "cycle" is a IDEAL linear phenomenon
created by a mathematician based upon a REAL observed phenomenon of an oscillating
nature which inherently is "circular," hence the mathematical expression thereof
contains the value of pi [3.14etc]. More anon.

I published Arnold's Law in 1979, as follows:
however, note I have added the Harmonic C Note [bodies]

C Notes_____Bodies_Proportion___Degreed Arcs___Fraction___Ideal Mean**
Octaves Or Perimeter
Or Harmonics

0***________Sun__________0___________0________0____________0
1___________Mercury______1___________3_____1/120______3.14 X10(7th)miles
2___________Venus________2___________6______1/60______6.28
?___________Earth________3___________9______1/40______9.42
4.09________Mars_________4__________12______1/30_____12.56
8.18________Ceres*_______8__________24______1/15_____25.13
16.4________Jupiter_____15__________45______1/8______47.12
32.7________Saturn______30__________90______1/4______94.24
65.4________Uranus______60_________180______1/2_____188.49
?___________Neptune_____90_________270______3/4_____282.74
130.8_______Pluto______120_________360______4/4_____376.99

*Ceres: prime representative of so-called "asteroids"

**means: adjusted for diameters of both bodies, sun and planet

***the NO SOUND point, from which the C Scale originates in the 1 C Note,
expressed at a perimeter of pi [3.14] when it so oscillates and sounds,
audibly to perception, however perceived: [to me, a scale is really a
series of concentric spheres of sound, with each higher note created
by another sphere surrounding the inner spheres in the same way the
Music of the Spheres appears to us, visually and mathematically, with
the planetary orbitals as means of their distances, expressed as spheres.]

So, Daniel, what do you think about the IDEAL PROPORTIONS discovered in
the MUSIC OF THE SPHERES or spacings of the planets?

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Daniel writes: The application
of whole number of proportions to natural systems, however, is more
problematic. The arrangement of planets around a sun at any given
point in time, for example, is the result of the historical
interaction of masses, distances, gravitation and probably a lot of
accidents along the way.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
No doubt, Daniel, in the "relativity" of the system, individual orbitals
the way astronomers look at them are unique. But I have postulated the
STATISTICAL MEAN or the AVERAGE distance DATA as relevant, over long
periods of time. Mankind has viewed the planetary data for millennium
and the planets are where predicted. H.'s Uncertainty Principle argues
that if a scientists seeks the particle, then wave data cannot be determined,
and vice versa. If the wave data is sought, the particle cannot be
determined. I covered this in my papers.

Musicologists KNOW that if only one bar of music is heard, one might not
hear ALL notes. But if lots and lots and LOTS of music is heard, one
might be able to ascertain ALL notes, yes, there will errant F# notes
that were meant to be F by the score sheet. But, on average, over many
notes looked at, something could be said about the IDEAL MUSICAL TUNING
of the particular system being analyzed.

Think of it this way: suppose someone lives in the New York area, and over
a year uses a cell phone and is TRACKED by the police. One day, or one
orbital will not NECESSARILY show where that person lives, resides, works.
But IF all calls are TRACKED for a year, then a SPHERE of data will show
the ORBITAL RANGE of positions of the CALLER.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Daniel writes:
Classical theorists knew precious little
about this, with their earth-centered and circular models, and we
still don't know enough.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
No, Daniel, I do not agree. Two decades ago I published my BODE'S LAW
EXPLAINED and it proves that the solar-planetary system DATA over long
periods of time carves out CIRCULAR ORBITALS similar to DIFFRACTION PATTERNS
OF ATOMS. I made that point then, and reiterate it now. Those PATTERNS
of the ORBITALS have MEANS just as INTENDED F notes of an orchestra over
a long period of RECORDED time would show a MEAN OF F NOTES. We all know
what it means [pun intended :)] to SING off-pitch, and for some of us
our ears hurt when notes are thrown too high and dropped too low. But still,
the PURE IDEAL NOTE SCALE or the SCORE SHEET exists, and can be ascertained;
in other words, the Bach piece EXISTS IDEALLY ON PAPER even though the
orchestra does not PLAY it PERFECTLY ON PITCH EACH AND EVERY TIME.
The SCORE SHEET is the IDEAL and I have given in Arnold's Law the IDEAL.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Daniel writes:
This is notoriously complex (tried solving
the three-body problem lately?) and all the interest really lies -
for met, at least - in the details. A "Harmony of the Spheres" model,
based upon static, whole number proportions is going to be a gross
simplification of a single moment in a dynamic system -- but how do
you choose the moment? Pluto's not always the furthest out.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
But Daniel, I THINK NOW you understand that Pluto has a MEAN which is,
indeed, OUTSIDE the orbital of Neptune. My paper covered all that.
There is, as you express above: A HARMONY OF THE SPHERES MODEL, and you
can SEE it in the DATA above. It is AWESOMELY BEAUTIFUL like a crystal
emerald with hexagonal six-sides or a diamond with pyramidal eight-sides.
Musicologists can PROBABLY now RELATE to the NUMBERS???????????????

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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My remarks, are below between the +++++++++++++lines
as such
++++++++++++++++++++++++++++++++++++++++++++++++++++
Message 39821
From: "Mark Gould" <mark.gould@a...>
Date: Mon Oct 21, 2002 9:57 am
Subject: Music of the Spheres
Comments here and there (with no implied accuracy than casual reading of
astronomy books)

1. Planets travel in elliptical orbits perturbed by each other
gravitationally. So no nice circles with nice 'harmonic' relationships.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Hi, Mark Gould. If you read my prior message to this list,

/tuning/topicId_39746.html#39825

you will NOW
UNDERSTAND that Plato spoke of the IDEAL and how REALITY shadows or mirrors
the IDEAL. Musicologists KNOW that an IDEAL F note exists and try to play
it, and like your referred to "elliptical orbits" do NOT always make it.
BTW: members should know that astrophysics explains the individual
"ellipitcal orbits" very nicely as a DANCE of the two centers of the Sun
and the individual planet, and yes, there are other perturbations. But
as Pauline points out, the same thing happens in REALITY when she plays
her organ and individual pipes INTERFER with each other, or the organist
mis-hits a key, or the pedal was held too-o-o-o-o long, or whatever. But
the IDEAL Bach piece on the SOCRE SHEET that Pauline looks at, is IDEAL.

Thus, Mark, there ARE NICE CIRCLES WITH NICE HARMONIC relationships on
paper in the STATISTICAL DATA. That is ALL Pythagoras or I have said.
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Actually, 'harmonic' ratios of orbital periods are I think unstable as they
are 'resonant'. So planets in this configuration probably won't remain that
way for the long term.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Are you talking about entropy from an IDEAL state? This is a LIST about TUNING,
and WHO knows WHO keeps the solar-planetary system TUNED [pun intended :) ]
Actually, Mark, PHYSICS explains ENTROPY as a decaying state over TIME from
an IDEAL state which existed, at some prior point.

But, can YOU now SEE the IDEAL state in the IDEAL data? This is NOT a
PHYSICS list, so I will not go into the relationship of the IDEAL solar-planetary
system to TIME, as that is a matter for another day and place. But Pauline could
tell you much about ENTROPY of pipes TUNED at a certain point in TIME and probably
predict when CERTAIN pipes need to be TUNED anew. I don't have a clue :)

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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Hey,

--- In tuning@y..., "alternativetuning" <alternativetuning@y...> wrote:
> I asked my teacher Daniel Wolf about the Music of the Sphere
> thread, and he emailed to me:

...and his message. Thanks so much for getting Daniel's input and forwarding it here. As usual, it is valued information, and I'll thank DW personally in another place on the net...

Much appreciated,
Jon

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/20/02 5:24:03 PM Central Daylight Time,
> dante.interport@r... writes:
>
>
> > what wrong with everybody using their own tuning system? As many
tuning
> > systems as musicians!
> >
> > Dante
> >
> All the just tuning systems I read about besides mine have very
limited
> usage, and that to modern music. My scale will play virtually any
Western
> World music.
>
> Pauline

pauline -- aren't you forgeting about helmholtz's 24-note system and
groven's 36-tone system, both of which were designed to play
virtually any Western World music, but with much smaller deviations
from just intonation in chords than in your system? i explained them
at length after you started posting here -- it might be worth your
time to go back and read those posts.

also, i find the comma shifts in your system, as well as those in
above systems, problematic for both the performer and for the
listener. from the latter point of view, for Western music before
beethoven, i far prefer vicentino's second tuning of 1555, in which
the triads are perfectly just.

In a message dated 10/21/02 2:30:06 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> aren't you forgeting about helmholtz's 24-note system and
> groven's 36-tone system, both of which were designed to play
> virtually any Western World music, but with much smaller deviations
> from just intonation in chords than in your system?

A just-tempermanet scale only needs 19 notes per key signature octave to play
classical music As that provies a harmonic 7th and 9th chord for each
diatonic note..
There ae six of these to a major scale. In C thats C, D, E, G , A and B. F
has its own scale, as there's no low-order harmonic-partial ratio for it in
C.. Thus more than one scale and keyboard has to be used at a time to play
most compositions. As music is composed in key-signature prhases, not whole
composition key signatures as such. Very simple music modulates frequently.

>
> also, i find the comma shifts in your system, as well as those in
> above systems, problematic for both the performer and for the
> listener. from the latter point of view, for Western music before
> beethoven, i far prefer vicentino's second tuning of 1555, in which
> the triads are perfectly just.
>
I made no comma shifts as such. I simply deutune very slightly the just
intervals. There's no problem in playing. I've played hundreds of short
pieces to test it. The reason many have problems with scales is they try to
use too few notes per oectave, or cram too many in a keyboard.

The solution is to use more than one keyboard, each tuned to a different
scale. Three are needed. One for the tonic, another for the subdominant, And
the third for the dominant, or a flatted-chord scale. For example, one short
piece in C I play uses the IV scale, I scale, and IIb scale to provide a VIb
phrase.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:

> Those PATTERNS
> of the ORBITALS have MEANS just as INTENDED F notes of an orchestra
over
> a long period of RECORDED time would show a MEAN OF F NOTES. We
all know
> what it means [pun intended :)] to SING off-pitch, and for some of
us
> our ears hurt when notes are thrown too high and dropped too low.
But still,
> the PURE IDEAL NOTE SCALE or the SCORE SHEET exists, and can be
ascertained;
> in other words, the Bach piece EXISTS IDEALLY ON PAPER even though
the
> orchestra does not PLAY it PERFECTLY ON PITCH EACH AND EVERY TIME.
> The SCORE SHEET is the IDEAL and I have given in Arnold's Law the
IDEAL.

first of all, the musical pitch standard has risen dramatically over
time and varied from location to location. it's completely arbitrary
what letter name is assigned to what frequency, but it helps to have
a standard, and today in the united states it's C-264, A-440, etc.,
but this could change again in the future, and i believe it's higher
in europe. secondly, bach's ideal tuning was almost certainly
something resembing Werckmeister III or Kellner's Bach tuning -- but
this is only defined up to the *relative* proportions of the notes,
not their absolute frequencies. hope this helps.

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/21/02 2:30:06 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > aren't you forgeting about helmholtz's 24-note system and
> > groven's 36-tone system, both of which were designed to play
> > virtually any Western World music, but with much smaller
deviations
> > from just intonation in chords than in your system?
>
> A just-tempermanet scale only needs 19 notes per key signature
octave to play
> classical music

helmholtz's and groven's systems already play in *all 12 key
signatures*.

> As that provies a harmonic 7th and 9th chord for each
> diatonic note..
> There ae six of these to a major scale. In C thats C, D, E, G , A
and B. F
> has its own scale, as there's no low-order harmonic-partial ratio
for it in
> C.. Thus more than one scale and keyboard has to be used at a time
to play
> most compositions.

sounds complex. but it certainly seems your statement about your
system being the *only* such-and-such was not correct.

> > also, i find the comma shifts in your system, as well as those in
> > above systems, problematic for both the performer and for the
> > listener. from the latter point of view, for Western music before
> > beethoven, i far prefer vicentino's second tuning of 1555, in
which
> > the triads are perfectly just.
> >
> I made no comma shifts as such.

in the last example you provided, wasn't the note e moving up by a
comma from the c-major chord to the a-minor chord?

> I simply deutune very slightly the just
> intervals. There's no problem in playing. I've played hundreds of
short
> pieces to test it. The reason many have problems with scales is
they try to
> use too few notes per oectave,

can you give some examples of who "they" are?

> or cram too many in a keyboard.
>
> The solution is to use more than one keyboard, each tuned to a
different
> scale. Three are needed. One for the tonic, another for the
subdominant, And
> the third for the dominant, or a flatted-chord scale. For example,
one short
> piece in C I play uses the IV scale, I scale, and IIb scale to
provide a VIb
> phrase.

how many pitches in all three keyboards put together?

In a message dated 10/21/02 6:22:39 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> in the last example you provided, wasn't the note e moving up by a
> comma from the c-major chord to the a-minor chord?

E 408 as the 81st harmonic is simply a perfect 5th above A 906. It's just a
second E. E 386 is still there for C. I've read explanations of JI and JT
here that could be explained much simpler, without so much jargon. If music
and scoring terms were used more, more musicians could understand what is
being discussed better.

> can you give some examples of who "they" are?

"They" were even back in Baroque days who struggled to make MT and WM fit
into 12 notes, or tried to add extra notes in an awkward manner keyboardists
didn't like. And I've read about new keyboards here I know most musicians
wouldn't want. As revised keyboards have been proposed from time to time, and
rejected.

The 12-tone regular keyboard is here to stay. All one can do for the majority
is to add split digitals that aren't part of the regular keyboard, and don't
interfere with playing the regular keyboard. My layout accomplishs that.

> how many pitches in all three keyboards put together?
>
Most are duplicated between F, C and G. Scales a 5th apart add 3 new notes,
and retain 9 of the prior one. So when the above 3 scales are selected at
once via the key-signature stops, 6 new notes are added that say C doesn't
have.

The split digitals 7 per key signature are distributed similarly. In their
case two sets of 7 notes an augmented 4th apart, sharing the same tuning, use
2 same notes. Thus two key signatures for them will fit onto 12 split
digitals.

For example, the split digitals for Gb and C use the same tuning, and work
for either of the two keyboard key signatures. The layout is quite simple,
which I described before.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/21/02 6:22:39 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > in the last example you provided, wasn't the note e moving up by
a
> > comma from the c-major chord to the a-minor chord?
>
> E 408 as the 81st harmonic is simply a perfect 5th above A 906.

right . . .

> It's just a
> second E. E 386 is still there for C. I've read explanations of JI
and JT
> here that could be explained much simpler, without so much jargon.
If music
> and scoring terms were used more, more musicians could understand
what is
> being discussed better.

well it still moves up a comma, right?

> > how many pitches in all three keyboards put together?
> >
> Most are duplicated between F, C and G. Scales a 5th apart add 3
new notes,
> and retain 9 of the prior one. So when the above 3 scales are
selected at
> once via the key-signature stops, 6 new notes are added that say C
doesn't
> have.
>
> The split digitals 7 per key signature are distributed similarly.
In their
> case two sets of 7 notes an augmented 4th apart, sharing the same
tuning, use
> 2 same notes. Thus two key signatures for them will fit onto 12
split
> digitals.
>
> For example, the split digitals for Gb and C use the same tuning,
and work
> for either of the two keyboard key signatures. The layout is quite
simple,
> which I described before.

so, how many pitches in all three keyboards put together? how many do
you need if you have to play music in all 12 keys?

--- In tuning@y..., "Jon Szanto" <JSZANTO@A...> wrote:

/tuning/topicId_39746.html#39828

> Hey,
>
> --- In tuning@y..., "alternativetuning" <alternativetuning@y...>
wrote:
> > I asked my teacher Daniel Wolf about the Music of the Sphere
> > thread, and he emailed to me:
>
> ...and his message. Thanks so much for getting Daniel's input and
forwarding it here. As usual, it is valued information, and I'll
thank DW personally in another place on the net...
>
> Much appreciated,
> Jon

***Where does he "hang out" these days...? Just nosey...

JP

In a message dated 10/21/02 7:17:15 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> how many pitches in all three keyboards put together? how many do
> you need if you have to play music in all 12 keys?
>
In my just all-key scale there are 4 pitches per keyboard digital-taken from
C 0, E 386, 7Bb 969, 7D 155 cents for white-key key signatures C-B. That's 48
per octave. The just scale uses four cycles of 5ths. In the just-temperament
verious the 4 cycles become circles.

The black-key flat key signatures are laid out the same, except the just flat
cycle begins with Db 105 cents. Eb is 298 cents, and Gb is 610 cents. Ab and
Bb are 5ths above Db at 807 and above Eb at 999 cents. Gb is the harmonic
minor 7th above the 13th harmonic.

The necessary notes are greatly reduced by the JT version where the
key-signature roots for all major keys use the ET 0-series pitches. Off my
head I can't give the exact number of notes for the JI version, but have a
chart listing them somehwere.

Since the JT version uses the ET note values, the flat key signatures use the
same notes as the white-key signatures--48 in all for the 12 major keys. The
minor keys use these as well, but in lesser numbers generally..

Both the JI and JT scales will play in the 12 major keys, 12 septimal minor
keys, and 12 tertian (relative) minor keys.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

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

> also, i find the comma shifts in your system, as well as those in
> above systems, problematic for both the performer and for the
> listener.

Pauline's 225/224-planar is an excellent temperament, giving about the amount of error Pauline seems to prefer, though I wonder if she has ever tried 72-et. As for its ability to play meantone, well...

Has anyone posted the cents value for Pauline's scale? It would be nice to have it as a Scala file, and sic Scala on it.

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

> so, how many pitches in all three keyboards put together?

What are the pitch values in cents of of these pitches?

My remarks are between+++++++++++++++lines
as such below
+++++++++++++++++++++++++++++++++++++++++

From: Jon Szanto <JSZANTO@A...>
Message: 39828
Date: Mon Oct 21, 2002 2:16pm
Subject: Re: MUSIC OF THE SPHERES

Hey,

--- In tuning@y..., "alternativetuning" <alternativetuning@y...> wrote:
> I asked my teacher Daniel Wolf about the Music of the Sphere
> thread, and he emailed to me:

...and his message. Thanks so much for getting Daniel's input and forwarding it here. As
usual, it is valued information, and I'll thank DW personally in another place on the
net...

Much appreciated,
Jon
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Hi, Jon: so where is this Daniel "in another place on the net" ? Is he a public
person on the net? Is he a member of TUNING? If it is a privacy issue, ignore
my query.

Thanks in advance,
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
-------------------------------------------------------------------
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My remarks are between+++++++++++++++lines
as such below
+++++++++++++++++++++++++++++++++++++++++
From: wallyesterpaulrus <wallyesterpaulrus@y...>
Message: 39845
Date: Mon Oct 21, 2002 6:05pm
Subject: Re: MUSIC OF THE SPHERES

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:

> Those PATTERNS
> of the ORBITALS have MEANS just as INTENDED F notes of an orchestra
over
> a long period of RECORDED time would show a MEAN OF F NOTES. We
all know
> what it means [pun intended :)] to SING off-pitch, and for some of
us
> our ears hurt when notes are thrown too high and dropped too low.
But still,
> the PURE IDEAL NOTE SCALE or the SCORE SHEET exists, and can be
ascertained;
> in other words, the Bach piece EXISTS IDEALLY ON PAPER even though
the
> orchestra does not PLAY it PERFECTLY ON PITCH EACH AND EVERY TIME.
> The SCORE SHEET is the IDEAL and I have given in Arnold's Law the
IDEAL.

first of all, the musical pitch standard has risen dramatically over
time and varied from location to location. it's completely arbitrary
what letter name is assigned to what frequency, but it helps to have
a standard, and today in the united states it's C-264, A-440, etc.,
but this could change again in the future, and i believe it's higher
in europe. secondly, bach's ideal tuning was almost certainly
something resembing Werckmeister III or Kellner's Bach tuning -- but
this is only defined up to the *relative* proportions of the notes,
not their absolute frequencies. hope this helps.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
I thank you kindly for the response. It would help me more if you
would give me the NAME of the IDEAL note halfway between two C NOTES
in an IDEAL OCTAVE? And you can give me the FREQUENCY value if you wish,
and make the assessment based on one or more tuning systems. I hope you know
I agree with you that I am seeking RELATIVE PROPORTION and yet if you wish
to assign which tuning system you mean it in, and give me also those FREQUENCY
VALUES, that is fine by me.

Thanks in advance,
meant kindly,
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
-------------------------------------------------------------------
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-------------------------------------------------------------------

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--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/21/02 7:17:15 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > how many pitches in all three keyboards put together? how many do
> > you need if you have to play music in all 12 keys?
> >
> In my just all-key scale there are 4 pitches per keyboard digital-
taken from
> C 0, E 386, 7Bb 969, 7D 155 cents for white-key key signatures C-B.
That's 48
> per octave.
>
> The just scale uses four cycles of 5ths. In the just-temperament
> verious the 4 cycles become circles.
>
> The black-key flat key signatures are laid out the same, except the
just flat
> cycle begins with Db 105 cents. Eb is 298 cents, and Gb is 610
cents. Ab and
> Bb are 5ths above Db at 807 and above Eb at 999 cents. Gb is the
harmonic
> minor 7th above the 13th harmonic.
>
> The necessary notes are greatly reduced by the JT version where the
> key-signature roots for all major keys use the ET 0-series pitches.
Off my
> head I can't give the exact number of notes for the JI version, but
have a
> chart listing them somehwere.
>
> Since the JT version uses the ET note values, the flat key
signatures use the
> same notes as the white-key signatures--48 in all for the 12 major
keys. The
> minor keys use these as well, but in lesser numbers generally..
>
> Both the JI and JT scales will play in the 12 major keys, 12
septimal minor
> keys, and 12 tertian (relative) minor keys.

thanks pauline!

In a message dated 10/22/02 1:43:55 AM Central Daylight Time,
genewardsmith@juno.com writes:

> Pauline's 225/224-planar is an excellent temperament, giving about the
> amount of error Pauline seems to prefer, though I wonder if she has ever
> tried 72-et. As for its ability to play meantone, well...

I want to play music composed for MT, WM or ET in just tempermanet, the way
many in the music world say the compoer heard in his mind--that is, in just
intonation.

> Has anyone posted the cents value for Pauline's scale? It would be nice to
> have it as a Scala file, and sic Scala on it.
>
I posted my JI scale and JT version of it here. And labeled the latter as my
Phillips scale. I gave the root pitches for each of the 12 major scales, and
included the cents and ratios for the C scale.

Pauline

In a message dated 10/22/02 2:42:07 AM Central Daylight Time,
genewardsmith@juno.com writes:

> What are the pitch values in cents of of these pitches?
>
I explaiend this in a prior post. I even relabel some posts. If people only
read here and there without at least opening a post, it's not my fault.

Pauline

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
++++++++++++
> I thank you kindly for the response. It would help me more if you
> would give me the NAME of the IDEAL note halfway between two C NOTES
> in an IDEAL OCTAVE?

it depends on what you mean by halfway. if you mean halfway in
frequency, it's G. if you mean halfway in wavelength or period, it's
F. if you mean halfway in terms of how we hear pitch-height, or
geometrically, it's the equal-tempered F#/Gb.

relative to a two C notes an octave apart, assigned the relative
*frequency* numbers 1 and 2, these various means would come out to
3/2, 4/3, and sqrt(2), respectively.

> And you can give me the FREQUENCY value if you wish,

of course not, since frequency standards are arbitrary. you can
multiply all the numbers above by 264 to get the frequencies relative
to the modern american tuning for C.

--- In tuning@y..., prophecyspirit@a... wrote:

> I posted my JI scale and JT version of it here. And labeled the latter as my
> Phillips scale. I gave the root pitches for each of the 12 major scales, and
> included the cents and ratios for the C scale.

What I saw ambled all over the screen, and it wasn't clear to me it was intended to be a scale. I'll go find it and sort it out.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., prophecyspirit@a... wrote:
>
> > I posted my JI scale and JT version of it here. And labeled the
latter as my
> > Phillips scale. I gave the root pitches for each of the 12 major
scales, and
> > included the cents and ratios for the C scale.
>
> What I saw ambled all over the screen,

in general, the solution to this problem is to click on "message
index" and then on "expand messages".

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

> I'll go find it and sort it out.

If I've sorted it out, this is it:

! phillips.scl
!
Phillips C scale
22
!
92.
155.
204.
269.
274.
386.
408.
471.
500.
590.
675.
702.
768.
772.
857.
906.
969.
976.
1088.
1110.
1173.
2/1

This does not seem to be a very good 225/224 planar scale, and the ets
130, 171, 224, 311 or 364 seem to be more to the point than 72. Linear temperaments which might be considered in connection are
[4,-32,-15,55,35,-60] with commas {2401/2400, 32805/32768} and
[22,-5,3,21,57,-59] with commas {2401/2400, 65625/65536}. The et which tempers out all three is 171.

Of course all of this involves far more tuning accuracy than Pauline seems to want. Either I am missing something, or she would do well to adjust these values further. Where do the 225/224 approximations come in?

In a message dated 10/22/02 5:16:02 PM Central Daylight Time,
genewardsmith@juno.com writes:

> This does not seem to be a very good 225/224 planar scale,

It isn't. It's a theoretical just scale taken straight from the harmonic
spectrum theoretical values. I temper it by making all 5ths 700 cents, the
major 3rds 384 cents, and the harmonic minor 7th 968 cents. this merges the
#s and bs that are very close together in pitch.

> Of course all of this involves far more tuning accuracy than Pauline seems
> to want. Either I am missing something, or she would do well to adjust
> these values further. Where do the 225/224 approximations come in?
>
As esplained above.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/22/02 5:16:02 PM Central Daylight Time,
> genewardsmith@j... writes:

> > This does not seem to be a very good 225/224 planar scale,
>
> It isn't. It's a theoretical just scale taken straight from the harmonic
> spectrum theoretical values.

What I was most interested in was any scale you proposed actually building an organ for. In case anyone wants to know, this particular scale fits pretty well into a 59 out of 171 scale with generator
71/171; or anything with a [1,-8,39,113,-59,-15] linear temperament.

From what you have said, a good match to what you want might be an organ built for Canasta, a 31-tone "Miracle" scale. This could play all kinds of things.

>What I was most interested in was any scale you proposed actually
>building an organ for. In case anyone wants to know, this
>particular scale fits pretty well into a 59 out of 171 scale with
>generator 71/171; or anything with a [1,-8,39,113,-59,-15] linear
>temperament.
>
>From what you have said, a good match to what you want might be an
>organ built for Canasta, a 31-tone "Miracle" scale. This could play
>all kinds of things.

Pauline,

Sorry if I missed something, but does your scale have 19 or 22
notes?

Gene,

Recommending something with 31 notes over something with 19 or 22?
Have you no decent scales in the artist's size? You must know more
about Pauline's intended musical approach than I to make so brazen
a suggestion...

-Carl

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:

> Recommending something with 31 notes over something with 19 or 22?

Well, she's pretty interested in getting the tuning right--close, but not too close. I was actually thinking if Canasta wasn't quite good enough, the same 31 notes tuned to hemiwuerschmidt (a very good 7-limit temperament despite the fact that little attention has been paid to it) might be the ticket. However, it has the same problem that Blackjack or the orwell 22 note MOS or 26 note 2MOS would have; not enough circle of fifths.

Of course if she really wants to play meantone, 19 tones tuned to meantone is a painfully obvious suggestion.

> Have you no decent scales in the artist's size?

How much tuning leeway do we get? Besides meantone, the other obvious choice is schismic, which has a 24 note 2MOS to bring a smile to the face of Helmholtz. In its 53-et incarnation, it is

[3,1,3,1,4,1,3,1,3,1,4,1,3,1,3,1,4,1,3,1,4,1,3,1,4,1]

Helmholtz's reasons for thinking this is a good way to adapt common practice music still apply.

On the other hand, Canasta allows for five consecutive fifths, excellent if we plan on adapting diatonic music to this scale.

You must know more
> about Pauline's intended musical approach than I to make so brazen
> a suggestion...

Naah; I raise the flag to see if she salutes; that way I might learn what she really wants.

My remarks are between+++++++++++++++lines
as such below
+++++++++++++++++++++++++++++++++++++++++
From: wallyesterpaulrus <wallyesterpaulrus@y...>
Message: 39898
Date: Tue Oct 22, 2002 3:30pm
Subject: Re: MUSIC OF THE SPHERES

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> I thank you kindly for the response. It would help me more if you
> would give me the NAME of the IDEAL note halfway between two C NOTES
> in an IDEAL OCTAVE?

it depends on what you mean by halfway. if you mean halfway in
frequency, it's G. if you mean halfway in wavelength or period, it's
F. if you mean halfway in terms of how we hear pitch-height, or
geometrically, it's the equal-tempered F#/Gb.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Again: thank you very very much, this time as you have ABSOLUTELY
answered my quest, and my question.

Someone off-list wrote me that
my question resulted into two separate SCALES: one harmonic [I assume
the C Scale] and the other subharmonic [I assume the F, or F#/Gb.]
Is my assumption correct?

And from your point of view, as a musicologist,
would such harmonic/subharmonic fit all THREE of your answers? Or
only one, or two of them? And which one or two, if not all three?
In other words, does HARMONIC/SUBHARMONIC in music theory fit
halfway in frequency, or G? Or halfway in wavelength or period,
or F? Or halfway in pitch-height, or geometrically, the equal-tempered
F#/Gb?

[by the way: I mean the AVERAGE physical distance between them or the MEAN,
mathematically: NOT the period, and NOT the pitch-height]

[by the way: you are stating that in music theory frequency does NOT equate
with wavelength, agreed? And, also, you are stating that wavelength is
equal to period, again in music theory, agreed?]

Daniel Wolf was correct, from my assessment[if I am to understand what
he said]: that only harmonic/proportions
can fit the relationships between mean planetary distances
and musical notes
if a comparison is to be made, and I wonder if you see the words
PROPORTIONS
and HARMONIC/SUBHARMONIC so related?

Thanks in advance,
meant kindly,

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
-------------------------------------------------------------------
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-------------------------------------------------------------------
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

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In a message dated 10/23/02 3:11:26 AM Central Daylight Time,
clumma@yahoo.com writes:

> Recommending something with 31 notes over something with 19 or 22?
> You must know more
> about Pauline's intended musical approach than I to make so brazen
> a suggestion...
>
> -Carl
>
Carl,

I get the impression that some think a scale with very many notes is the
thing. Whereas jsut the reverse is true. My C Tonic I JT scale has 19 notes
per octave. And when used with the F Subdominent IV scal with its 19 notes,
and occasionally the Dominent V scale iwth its 19 notes, or more rarely a
flatted scale with its 19 notes, htat all that's needed to play a compoisiton
written for MT, WM or ET.

Pauline

gene, here you've quoted pauline's JI scale, not her JT scale, which
was the one which tempers out 225/224. the 22 notes of the scale
below reduce to 19 when 225/224 is tempered out, i believe.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
>
> > I'll go find it and sort it out.
>
> If I've sorted it out, this is it:
>
> ! phillips.scl
> !
> Phillips C scale
> 22
> !
> 92.
> 155.
> 204.
> 269.
> 274.
> 386.
> 408.
> 471.
> 500.
> 590.
> 675.
> 702.
> 768.
> 772.
> 857.
> 906.
> 969.
> 976.
> 1088.
> 1110.
> 1173.
> 2/1
>
> This does not seem to be a very good 225/224 planar scale, and the
ets
> 130, 171, 224, 311 or 364 seem to be more to the point than 72.
Linear temperaments which might be considered in connection are
> [4,-32,-15,55,35,-60] with commas {2401/2400, 32805/32768} and
> [22,-5,3,21,57,-59] with commas {2401/2400, 65625/65536}. The et
which tempers out all three is 171.
>
> Of course all of this involves far more tuning accuracy than
Pauline seems to want. Either I am missing something, or she would do
well to adjust these values further. Where do the 225/224
approximations come in?

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:

> Gene,
>
> Recommending something with 31 notes over something with 19 or 22?
> Have you no decent scales in the artist's size? You must know more
> about Pauline's intended musical approach than I to make so brazen
> a suggestion...

pauline said she would require 48 pitches to play in all 12 keys --
clearly a necessity for her stated goal of rendering all Western
World music . . .

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> My remarks are between+++++++++++++++lines
> as such below
> +++++++++++++++++++++++++++++++++++++++++
> From: wallyesterpaulrus <wallyesterpaulrus@y...>
> Message: 39898
> Date: Tue Oct 22, 2002 3:30pm
> Subject: Re: MUSIC OF THE SPHERES
>
>
> --- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> > I thank you kindly for the response. It would help me more if you
> > would give me the NAME of the IDEAL note halfway between two C
NOTES
> > in an IDEAL OCTAVE?
>
> it depends on what you mean by halfway. if you mean halfway in
> frequency, it's G. if you mean halfway in wavelength or period,
it's
> F. if you mean halfway in terms of how we hear pitch-height, or
> geometrically, it's the equal-tempered F#/Gb.
> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> Again: thank you very very much, this time as you have ABSOLUTELY
> answered my quest, and my question.
>
> Someone off-list wrote me that
> my question resulted into two separate SCALES: one harmonic [I
assume
> the C Scale] and the other subharmonic [I assume the F, or F#/Gb.]
> Is my assumption correct?

i have no idea what you mean.

> And from your point of view, as a musicologist,
> would such harmonic/subharmonic fit all THREE of your answers? Or
> only one, or two of them? And which one or two, if not all three?
> In other words, does HARMONIC/SUBHARMONIC in music theory fit
> halfway in frequency, or G? Or halfway in wavelength or period,
> or F? Or halfway in pitch-height, or geometrically, the equal-
tempered
> F#/Gb?

HARMONIC fits halfway in frequency, so a root C-c octave would
acquire a G. SUBHARMONIC fits halfway in wavelength and period, so
a "root" (or common overtone) C-c octave would acquire an F.

> [by the way: I mean the AVERAGE physical distance between them or
the MEAN,
> mathematically: NOT the period, and NOT the pitch-height]

how do you measure the physical distance between musical pitches?

> [by the way: you are stating that in music theory frequency does
NOT equate
> with wavelength, agreed?

right, frequency is inversely proportional to wavelength.

> And, also, you are stating that wavelength is
> equal to period, again in music theory, agreed?]

wavelength is *proportional* to period.

> Daniel Wolf was correct, from my assessment[if I am to understand
what
> he said]: that only harmonic/proportions
> can fit the relationships between mean planetary distances
> and musical notes
> if a comparison is to be made,

i don't think he said that . . .

> and I wonder if you see the words
> PROPORTIONS
> and HARMONIC/SUBHARMONIC so related?

they are related. in the old days, before the physical harmonic
series was known (a natural phenomenon in which any tone tends to be
accompanied by tones with integer multiples of its FREQUENCY), string
lengths on monochords were used to compare pitches, and many
theorists demanded simple proportions in those string lengths. string
length is approximately inversely proportional to frequency. if these
string-length proportions were ARITHMETIC (that is, in proportions
belonging to the series 1, 2, 3, 4, 5 . . .), the result was what is
today known as SUBHARMONIC. if these proportions were HARMONIC (that
is, in proportions belonging to the series 1/1, 1/2, 1/3, 1/4,
1/5 . . .), the result was what is today still known as HARMONIC
(though typically expressed today as a set of ARITHMETIC proportions
in FREQUENCY).

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/23/02 3:11:26 AM Central Daylight Time,
> clumma@y... writes:
>
>
> > Recommending something with 31 notes over something with 19 or 22?
> > You must know more
> > about Pauline's intended musical approach than I to make so brazen
> > a suggestion...
> >
> > -Carl
> >
> Carl,
>
> I get the impression that some think a scale with very many notes
is the
> thing. Whereas jsut the reverse is true. My C Tonic I JT scale has
19 notes
> per octave. And when used with the F Subdominent IV scal with its
19 notes,
> and occasionally the Dominent V scale iwth its 19 notes, or more
rarely a
> flatted scale with its 19 notes, htat all that's needed to play a
compoisiton
> written for MT, WM or ET.
>
> Pauline

how can that be? i thought you needed 48 pitches for a piece that
travels through all 12 key signatures. and there are several such
pieces written for WT or ET.

In a message dated 10/23/02 1:06:36 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> pauline said she would require 48 pitches to play in all 12 keys --
> clearly a necessity for her stated goal of rendering all Western
> World music . . .
>
This can be reduced to 36 by using the C harmonic 7th circle of 5ths for the
E 384 cents circle of 5ths, based on the 30/17 ratio worth 983 cents, rather
than its own harmonic 7th. But that's an arbitrary selected-interval
compromise, that reduces the number of tone generators needed. I'm using that
at the monent, but hope later to add more tone generators to avoid any
harmonic-partial ratios compromises.

Pauline

In a message dated 10/23/02 1:28:56 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> i thought you needed 48 pitches for a piece that
> travels through all 12 key signatures.

That is correct. Most notes in a given key signature are repeated in the next
one a 5th apart, and so on. But to use my scales one needs a three-keyboard
instrument. As all three scales needed for a given compostion need to be
instantly available from phrase to phrase. In the most complex music that
goes at a rapid pace, an assistant might be needed to change key-signature
stops. But that's a performance matter, not a construction one. And recital
organists commonly use someone to turn pages, and sometimes change stops at
an awkward place.

Pauline

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
> --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
>
> > Gene,
> >
> > Recommending something with 31 notes over something with 19 or 22?
> > Have you no decent scales in the artist's size? You must know more
> > about Pauline's intended musical approach than I to make so brazen
> > a suggestion...
>
> pauline said she would require 48 pitches to play in all 12 keys --
> clearly a necessity for her stated goal of rendering all Western
> World music . . .

By the way, could someone please simply post Pauline's scale? I'm tired of playing guessing games and guessing wrong.

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> > --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> >
> > > Gene,
> > >
> > > Recommending something with 31 notes over something with 19 or
22?
> > > Have you no decent scales in the artist's size? You must know
more
> > > about Pauline's intended musical approach than I to make so
brazen
> > > a suggestion...
> >
> > pauline said she would require 48 pitches to play in all 12 keys -
-
> > clearly a necessity for her stated goal of rendering all Western
> > World music . . .
>
> By the way, could someone please simply post Pauline's scale? I'm
>tired of playing guessing games and guessing wrong.

the 19-tone scale she posted was for playing basically in *one* key.
i was merely replying to carl, saying that pauline could have plenty
of reasons for looking at scales with ~31 notes.

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

> the 19-tone scale she posted was for playing basically in *one* key.

Fine. What are the notes?

My remarks are between+++++++++++++++lines
as such below
+++++++++++++++++++++++++++++++++++++++++
From: wallyesterpaulrus <wallyesterpaulrus@y...>
Message: 39926
Date: Wed Oct 23, 2002 2:16 pm
Subject: Re: MUSIC OF THE SPHERES

> And from your point of view, as a musicologist,
> would such harmonic/subharmonic fit all THREE of your answers? Or
> only one, or two of them? And which one or two, if not all three?
> In other words, does HARMONIC/SUBHARMONIC in music theory fit
> halfway in frequency, or G? Or halfway in wavelength or period,
> or F? Or halfway in pitch-height, or geometrically, the equal-
tempered
> F#/Gb?

HARMONIC fits halfway in frequency, so a root C-c octave would
acquire a G. SUBHARMONIC fits halfway in wavelength and period, so
a "root" (or common overtone) C-c octave would acquire an F.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
my remarks: the above is where I think the confusion has arisen
by astrophysicists who deal with planetary distances and periods
and have tried to make themselves understood to musicologists.
I hope I can get us on the same page of understanding. I want to
thank you for your kindness is trying to make me understand this.
I hope you would read through my remarks, which is really exploratory,
since I am not sure what astrophysicists NEED from musicologists
to make sense of this COMPARISON of planetary DISTANCES to
musical HARMONY of the spheres.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

> [by the way: you are stating that in music theory frequency does
NOT equate
> with wavelength, agreed?

right, frequency is inversely proportional to wavelength.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
my remarks, inverse proportion takes a formula: what is it?
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

> And, also, you are stating that wavelength is
> equal to period, again in music theory, agreed?]

wavelength is *proportional* to period.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
my remarks: I think why astrophysicists [my catch-all word for
cycle scientists, astronomers, et al., who have tried to come to
grips with the MATH of the solar-planetary system, and its
so-called Titius-BODE'S LAW, which I claim to have simplified
as Arnold's Law, mainly OF PROPORTIONS] have been unable to make
the leap to MUSIC is that they have been confused by these very
points we are dealing with. So please bear with me, if you are
willing.

I agree wavelength is PROPORTIONAL to period. My papers, which
hopefully will be put online by a member of TUNING, covers my
take on that. The trouble is that the distances between the planets
and the Sun were expressed in fractions of a.u., the distance from
the Sun to the Earth. Technically, it is a Radian of a Circle.
The Perimeter of the Circle that the Earth travels round the Sun
is Equal to 2 Pi Radians. That 2 in the mix confused those who
would try to relate all this to MUSIC which in octaval terms
has a 2X factor built into its system, as well. Thus PERIOD in
planetary terms gets confused with DISTANCE between planets,
whereas they are different terms, inasmuch as PERIOD is a
PERIMETER descriptive term and DISTANCE is either a RADIAN term
or a DIAMETER term. In my heart of hearts I believe the same is
true in MUSIC but I leave that for MATH minds in music to deal with.
The point is: that in order for planetary DISTANCES or PERIODS to
be related to MUSICAL terms, we must be assured which terms we are
using. I hope I am being understood. I know to some this is really
abstruse stuff, but I hope those who don't care will hit the D button,
and those that do will help out. I know you CARE and apparently
can relate. And maybe we can get to a common ground of understanding.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

> and I wonder if you see the words
> PROPORTIONS
> and HARMONIC/SUBHARMONIC so related?

they are related. in the old days, before the physical harmonic
series was known (a natural phenomenon in which any tone tends to be
accompanied by tones with integer multiples of its FREQUENCY), string
lengths on monochords were used to compare pitches, and many
theorists demanded simple proportions in those string lengths. string
length is approximately inversely proportional to frequency.

++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
my remarks: I think this is where non-musicians in planetary science
have stumbled in attempts to relate the harmonics of the spheres
with planetary distances as I said above. Let us move on to the
NEW musicology of ALTERNATE TUNING knowledge which seems to have
advanced knowledge since to good ole days. I am guessing that what
Guy Murchie wrote in MUSIC OF THE SPHERES has been advanced enough
that a NEW take on these matters would improve the understanding.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
if these
string-length proportions were ARITHMETIC (that is, in proportions
belonging to the series 1, 2, 3, 4, 5 . . .), the result was what is
today known as SUBHARMONIC.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
my remarks: I do not think that HARMONIC and SUBHARMONIC as you are
using them are used the same way by cycle-scientists, astrophysicists,
and the like. Thus, I hope you would make me understand what you mean,
as you seem to make absolute sense to me. But so many musicologists use
these two terms so differently.
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
if these proportions were HARMONIC (that
is, in proportions belonging to the series 1/1, 1/2, 1/3, 1/4,
1/5 . . .), the result was what is today still known as HARMONIC
(though typically expressed today as a set of ARITHMETIC proportions
in FREQUENCY).

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
my remarks: the fact that "today" it is "still known as HARMONIC"
but is "typically expressed...as a set of ARITHMETIC proportions in
FREQUENCY" is what I think confuses the astrophysicsts [my umbrella-word
meaning, of course] who wish to talk to musicologists. For some reason,
I always lumped words like frequency, harmonic and the like into one
nebulous basket. And so do many outside the realm of music. I know
that is NOT proper, inasmuch as you are using MATH as a basis of transference
between TERMS and I must understand what you mean. So, I hope you bear
with me. In the IDEAL state of the solar-planetary system, there is
an ARITHMETIC series of NUMBERS which represents the planetary RADIANS:
Sun 0, Mercury 1, Venus 2, Earth 3, Mars 4, Ceres 8, Jupiter 15,
Saturn 30, Uranus 60, Neptune 90, and Pluto 120.

If we express the same
in DIAMETERS,
obviously the ARITHMETIC series of NUMBERS doubles.

If we express the
same in PERIMETERS,
obviously the ARITHMETIC series of NUMBERS is only
increased PORPORTIONALLY by the value of PI: 3.14+....

Thus, I ask
of you: Is this an ARITHMETIC series as I suggest? If so, is IT a
HARMONIC series? Or SUBHARMONIC? And what does IT mean in music
terms?

I grant that two items, Earth and Neptune, are HALFWAY
between their respective NUMBERS. And that IS in terms of ARITHMETICS.

So, I am understanding from your statements, that the PRIMARY series of
ARITHMETIC NUMBERS is OCTAVAL. And I am understanding that the OTHER
two ARITHMETIC NUMBERS is halfway between them. We are really talking
about DISTANCES between these NUMBERS, even if we EXPAND the numbers by
2X and again by PI at 3.14+.... Does this help you in telling me which
NOTE I am seeking?

Can I make the MAGICAL leap to MUSIC with your help? Please understand,
that because there is a different DEFINITION from one group of scientists
[astrophysicists] to the other [musicologists], there appears to me to
be confusion. And I am not imply you or I or either group is confused.
On the contrary, I think we need to find the common language, the precise
TERMS and the precise DEFINITIONS. I hope I haven't asked for too much?

Thanks in advance,
meant kindly,

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
-------------------------------------------------------------------
"There is magic in the web" Shakespeare (Othello, Act 3, Scene 4)
-------------------------------------------------------------------
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

__________________________________________________
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--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:

> > [by the way: you are stating that in music theory frequency does
> NOT equate
> > with wavelength, agreed?
>
> right, frequency is inversely proportional to wavelength.
>
>
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> my remarks, inverse proportion takes a formula: what is it?
> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

frequency equals the speed of sound divided by the wavelength.

wavelength equals the speed of sound divided by the frequency.

> wavelength is *proportional* to period.

in case you're interested:

wavelength equals period times the speed of sound.

period equals wavelength divided by the speed of sound.

>
> Thus, I ask
> of you: Is this an ARITHMETIC series as I suggest?

i suppose, since you gave a set of integers, this can be viewed as an
incomplete arithmetic series.

> If so, is IT a
> HARMONIC series? Or SUBHARMONIC?

musically, it's neither, since you have distances (in units of
legnth) instead of frequencies or periods (in units of inverse time
or time, respectively -- your series does not pertain to those
quantities, correct?) -- though you could convert distance to
wavelength, you would need the speed of sound in the relevant medium.
since the medium of empty space

> And what does IT mean in music
> terms?

see above.

> So, I am understanding from your statements, that the PRIMARY
series of
> ARITHMETIC NUMBERS is OCTAVAL.

hmm . . . i don't think so. the "octaval" series would be 1, 2, 4,
8 . . . just the powers of 2 . . . if 1 is C, then 2, 4, 8 . . . are
also Cs, just in different octave.s

> And I am understanding that the OTHER
> two ARITHMETIC NUMBERS is halfway between them. We are really
talking
> about DISTANCES between these NUMBERS, even if we EXPAND the
numbers by
> 2X and again by PI at 3.14+.... Does this help you in telling me
which
> NOTE I am seeking?

no, what note *are* you seeking?

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> though you could convert distance to
> wavelength, you would need the speed of sound in the relevant
medium.
> since the medium of empty space

. . . does not transmit sound, such a conversion would be
impossible/meaningless in the context of the solar system, i'd
think . . .

In a message dated 10/23/02 2:04:46 PM Central Daylight Time,
genewardsmith@juno.com writes:

> , could someone please simply post Pauline's scale? I'm tired of playing
> guessing games and guessing wrong.
>
I've posted my Phillips scales several times since the beginning of the
month. I don't want to have to do it again.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/23/02 2:04:46 PM Central Daylight Time,
> genewardsmith@j... writes:

> I've posted my Phillips scales several times since the beginning of the
> month. I don't want to have to do it again.

So far as I recall, you've never simply given 19 notes in succession.

These are the scales that I managed to distill from
Pauline's posts. Please correct where wrong. Maybe
someone can post a 225/224 tempered version? What's the
19-note scale?

Manuel

! phillips.scl
!
Pauline Phillips, organ manual scale, TL 7-10-2002
12
!
84.00000
200.00000
268.00000
384.00000
468.00000
584.00000
700.00000
768.00000
900.00000
968.00000
1084.00000
2/1

! phillips_22.scl
!
All-key 19-limit JI scale (2002), TL 21-10-2002
22
!
135/128
35/32
9/8
76545/65536
75/64
5/4
81/64
21/16
10935/8192
45/32
3/2
399/256
25/16
51/32
105/64
27/16
7/4
225/128
15/8
243/128
63/32
2/1

! phillips_ji.scl
!
Pauline Phillips, JI 0 #/b "C" scale (2002), TL 8-10-2002
21
!
135/128
35/32
9/8
76545/65536
75/64
5/4
81/64
10935/8192
45/32
189/128
3/2
399/256
25/16
105/64
27/16
7/4
225/128
15/8
243/128
63/32
2/1

In a message dated 10/24/02 5:21:32 AM Central Daylight Time,
genewardsmith@juno.com writes:

> you've never simply given 19 notes in succession

I did so, even yesterday again as the Phillips scale. The title was in the
subject line.

Pauline

In a message dated 10/24/02 6:56:04 AM Central Daylight Time,
manuel.op.de.coul@eon-benelux.com writes:

> These are the scales that I managed to distill from
> Pauline's posts. Please correct where wrong. Maybe
> someone can post a 225/224 tempered version? What's the
> 19-note scale?
>
> Manuel
>
Besides the 12 notes of the Phillips scale you gave in your 10/24/02 post,
there's 155, 400, 500, 668, 855, 1100 and 1168. These notes are on split
digtials. As every diatonic note needs a harmonic 7th and harmonic 9th.

Pauline

Ah, so that was the 19-note scale, thanks.
I'll have the three scales added to the archive.

Manuel

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/24/02 6:56:04 AM Central Daylight Time,
> manuel.op.de.coul@e... writes:
>
>
> > These are the scales that I managed to distill from
> > Pauline's posts. Please correct where wrong. Maybe
> > someone can post a 225/224 tempered version? What's the
> > 19-note scale?

Putting together this with Pauline's latest, we get

! phillips19.scl
!
Pauline Phillips, 19 note organ manual scale
19
!
84.00000
155.00000
200.00000
268.00000
384.00000
400.00000
468.00000
500.00000
584.00000
668.00000
700.00000
768.00000
855.00000
900.00000
968.00000
1084.00000
1100.00000
1168.00000
2/1

I would strongly urge that anyone who wishes to present a scale do so in any manner that they see fit, so long as they *also* present a clearly labled scale given as an increasing sequence of pitches.

In a message dated 10/24/02 3:07:53 PM Central Daylight Time,
genewardsmith@juno.com writes:

> I would strongly urge that anyone who wishes to present a scale do so in any
> manner that they see fit, so long as they *also* present a clearly labled
> scale given as an increasing sequence of pitches.
>
I did that, except I did so horizontally, so there were two lines.

Pauline

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:

You can cram this scale into a scale of 43 succesive secors without being too awfully abusive; for thise following tuning-math that would be a 4MOS.

My remarks today are between$$$$$$$$$$$$$$$lines
as such below: I admit up front that I include
the totality of both wallyesterpaulrus messages
without deletions...for the sake of the thread,
I apologize but thought it important to do that.
$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
From: wallyesterpaulrus <wallyesterpaulrus@y...>
Message 39951 of 40100
From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
Date: Wed Oct 23, 2002 8:51 pm
Subject: Re: MUSIC OF THE SPHERES

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:

> > [by the way: you are stating that in music theory frequency does
> NOT equate
> > with wavelength, agreed?
>
> right, frequency is inversely proportional to wavelength.
>
>
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
> my remarks, inverse proportion takes a formula: what is it?
> ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

frequency equals the speed of sound divided by the wavelength.

wavelength equals the speed of sound divided by the frequency.

> wavelength is *proportional* to period.

in case you're interested:

wavelength equals period times the speed of sound.

period equals wavelength divided by the speed of sound.

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$
my remarks: in this post I intend, after a few days thinking about
the Q & A we have been through, to make a broader THEORETICAL point
as sort of groundwork for future SPECIFIC and DETAILED comments.

my remarks: I have known these formulas in the past. Of course,
most of my science research was three decades ago. Although, I
have not given up on it. More anon. But let me say at this point,
although I am not cross-posting these remarks to tuning-math, I
am reading the archives on yahoogroups and I do note that there
is disagreement over definition of terms, say lattice from one
discipline to another. I would also say, that within one discipline,
such as astrophysics, or cycle science, even math itself, certain
knowledgable disciplinarians in those groups use terms differently,
or interchangeably without knowing it at the time. In other words,
I believe a lot of us could be of assistance to each other in other
disciplines if we could come to a commonality of terms. Not that
that will happen, or should. But it is a confusion to science,
whether musicology or astrophysics or cycle-science and even math,
if disciplinarians are not aware that they are not using the same
transference terms to express ideas, and sometimes they are using
the same transference terms but defining terms differently. Accepting
this: we can proceed.

I will not take it up in detail now, but at some point my BODE'S LAW
EXPLAIN paper should be online, in the near future, and we could go
into detail as warranted. But I would say, as a disciplinarian in
disciplines outside music, that PERIOD and PERIODICITY contain TIME
within the expression. Briefly: the PERIODS of planets round the
Sun are not the same, as the DISTANCES between them might be PROPORTIONAL
but the PERIODS contain different RATES OF SPEED, if my memory serves me
correctly. Perhaps, in music, the PERIODS of NOTES might NOT find
different expression because they are NOT related to each other differently.
Am I to assume that the RATES OF SPEED of NOTES are the SAME in ALL
cases? Perhaps, you understand my point? This pertains to your remarks
below about the MEDIUM OF SOUND.

Indeed, supposedly, outer SPACE is supposedly CURVED, according
to Einstein's Theory of Relativity, and IF SPHERICAL contains PI at
3.14+ ad infinitum, and OBJECTS in outer SPACE appear SPHERICAL, that
IS the SHELL MEDIUM according to modern astronomy, then we have MEDIUMS
placed within a supposed-VACUUM.

However, musicologists know better than I what would happen IF a TUNING
fork placed in MEDIUM and VIBRATED, separated by a VACUUM--whether or
not it could be PERCEIVED in an ADJACENT MEDIUM. Tough question: and not
one I am sure has been scientifically tested. Maybe there would be NO
transmission of SOUND, but might there be a transmission of VIBRATIONS.
And what is LIGHT but vibrations, measured in cycles per TIME?

Thus, what I am saying in a convoluted way IS that the formulas you bring
forward still are relevant, although they may NOT be applicable to the
situation. In other words, if the relationships between FREQUENCY and
PERIOD and DISTANCE are fixed, which I accept are, then the CONCEPTS ought
to make sense INTELLECTUALLY and we ought to be able to related MUSIC to
ASTRONOMY in MATHEMATICAL and PHYSICS terms. I do not know: you tell me!

What I see as a barrier to understanding is that MUSIC is NOTES and the
FREQUENCY and DISTANCE relationships are the SIZES of ATOMS. Whereas,
the analogy might be the same, but ASTRONOMY/ASTROPHYSICS is LARGER BODIES
called STARS/SUN and PLANETS and the FREQUENCY and DISTANCE relationships are
the SIZES of SOLAR-PLANETARY SYSTEMS, and LARGER still, GALAXIES, and larger
still, UNIVERSES [pun intended, making that plural :) ].

Still I ask: would the INORDINATE SIZE OF DISTANCE at the level of solar-planetary
systems make as difference in comparison with MUSICAL NOTES IN SCALES?

Is it possible, that in MUSIC the lattices and notes and other items you all
are relating, by math, by structure in a physic[cal] sense, et al., that they
are easier to INTER-RELATE because they are the SIZES of ATOMS. In other words,
they are SMALL and the DISTANCE relationships are equally SMALL and problems
of MAGNIFICATION of NUMBERS does NOT play into the discussion?

But is it also possible, that in MUSIC that NOTES might not be related to each
other in SPIRAL lattices, but GEOMETRIC shapes: whether HEXAGONAL or the more
sophisticated SPHERICAL? Might it be that the root NOTE in a chord or a series
is ENCASED by other NOTES as opposed to SEPARATE MEDIUMS separated by empty
SPACE between them akin to VACUUMS if the outer SPACE analogy is brought into
the equation [pun intended]?

Finally: I did EQUATE two formulas as you do above. I believe that the
CIRCUMFERENCE OR PERIMETER or PI DISTANCE a planet travels round the Sun
is equal to PI times DIAMETER or 2 RADIANS of that planet
[the old C = PI D formula].

I also believe that the PI DISTANCE a planet travels round the Sun is also
equal to the RATE OF SPEED of the planet in question times the TIME it takes for
the planet to complete one TRIP around
[the old D = tr formula].

By EQUATING these two commonly known formulas, wherein the PI DISTANCE around
the sun that a planet travels are common to both: PI time DIAMETER equals
TIME of the trip around times RATE OF SPEED of the planet during its trip.

Thus: whether ATOMS or SOLAR-PLANETARY SYSTEMS, the PARTICLE moving round
the CENTER, shares these relationships. Or PARTICLES.

I wonder if the latter formula has APPLICATION to MUSIC?

Could it be that NOTES are ATOMIC in structure?
Do they have PARTICLES going around a CENTER?
What do musicologists mean when they say a NOTE VIBRATES?
Do NOTES have SHELL structure?
Has anyone done DIFFRACTION PATTERNS of NOTES aka ATOMIC STRUCTURE?

[By the way: these remarks above are meant to be exploratory for musicologists,
and other disciplines, and I took them out of my memory without attempts at
this point to related them to the MUSIC formulas given above. I mean all
this input as kindly intended to open up dialogue and not be contrary and
argumentative with a discipline, musicology, I admit I have much to learn
about.

$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$

>
> Thus, I ask
> of you: Is this an ARITHMETIC series as I suggest?

i suppose, since you gave a set of integers, this can be viewed as an
incomplete arithmetic series.

> If so, is IT a
> HARMONIC series? Or SUBHARMONIC?

musically, it's neither, since you have distances (in units of
legnth) instead of frequencies or periods (in units of inverse time
or time, respectively -- your series does not pertain to those
quantities, correct?) -- though you could convert distance to
wavelength, you would need the speed of sound in the relevant medium.
since the medium of empty space

> And what does IT mean in music
> terms?

see above.

> So, I am understanding from your statements, that the PRIMARY
series of
> ARITHMETIC NUMBERS is OCTAVAL.

hmm . . . i don't think so. the "octaval" series would be 1, 2, 4,
8 . . . just the powers of 2 . . . if 1 is C, then 2, 4, 8 . . . are
also Cs, just in different octave.s

> And I am understanding that the OTHER
> two ARITHMETIC NUMBERS is halfway between them. We are really
talking
> about DISTANCES between these NUMBERS, even if we EXPAND the
numbers by
> 2X and again by PI at 3.14+.... Does this help you in telling me
which
> NOTE I am seeking?

no, what note *are* you seeking?

================================================================================
================================================================================
===============================================================================
Message 39954 of 40100 From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
Date: Wed Oct 23, 2002 8:57 pm
Subject: Re: MUSIC OF THE SPHERES

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> though you could convert distance to
> wavelength, you would need the speed of sound in the relevant
medium.
> since the medium of empty space

. . . does not transmit sound, such a conversion would be
impossible/meaningless in the context of the solar system, i'd
think . . .

===============================================================================
==============================================================================
=============================================================================

Thanks in advance,
meant kindly,

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
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--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:

> But it is a confusion to science,
> whether musicology or astrophysics or cycle-science and even math,
> if disciplinarians are not aware that they are not using the same

yikes! i'm very frightened of disciplinarians . . .

> PERIOD and PERIODICITY contain TIME
> within the expression.

good!

> Briefly: the PERIODS of planets round the
> Sun are not the same, as the DISTANCES between them might be
PROPORTIONAL
> but the PERIODS contain different RATES OF SPEED, if my memory
serves me
> correctly.

well, the period of the earth is one year, for example . . .

> Perhaps, in music, the PERIODS of NOTES might NOT find
> different expression because they are NOT related to each other
>differently.

i have no idea what that statement means.

> Am I to assume that the RATES OF SPEED of NOTES are the SAME in ALL
> cases?

notes don't move. sound moves, usually around 750 mph or something in
average-temperature, average humidity air.

> However, musicologists know better than I what would happen IF a
TUNING
> fork placed in MEDIUM and VIBRATED, separated by a VACUUM--whether
or
> not it could be PERCEIVED in an ADJACENT MEDIUM.

no!

> Tough question: and not
> one I am sure has been scientifically tested.

this is a standard high-school physics class demonstration, usually
involving a loud bell and a vacuum pump.

> Maybe there would be NO
> transmission of SOUND, but might there be a transmission of
VIBRATIONS.
> And what is LIGHT but vibrations, measured in cycles per TIME?

right -- different *colors* correspond to different rates of
vibration of the electromagnetic field.

> Thus, what I am saying in a convoluted way IS that the formulas you
bring
> forward still are relevant, although they may NOT be applicable to
the
> situation. In other words, if the relationships between FREQUENCY
and
> PERIOD and DISTANCE are fixed, which I accept are,

they're not fixed because the medium varies.

> Still I ask: would the INORDINATE SIZE OF DISTANCE at the level of
solar-planetary
> systems make as difference in comparison with MUSICAL NOTES IN
SCALES?

i have no idea what this question means.

> Is it possible, that in MUSIC the lattices and notes and other
items you all
> are relating, by math, by structure in a physic[cal] sense, et al.,
that they
> are easier to INTER-RELATE because they are the SIZES of ATOMS.

the sizes of atoms? i don't see what they have to do with that.

> In other words,
> they are SMALL and the DISTANCE relationships are equally SMALL and
problems
> of MAGNIFICATION of NUMBERS does NOT play into the discussion?

????

> But is it also possible, that in MUSIC that NOTES might not be
related to each
> other in SPIRAL lattices,

we've constructed such spiral lattices, indeed -- joe monzo has a few
kinda laid out on some of his webpages . . .

> but GEOMETRIC shapes: whether HEXAGONAL or the more
> sophisticated SPHERICAL? Might it be that the root NOTE in a chord
or a series
> is ENCASED by other NOTES as opposed to SEPARATE MEDIUMS separated
by empty
> SPACE between them akin to VACUUMS if the outer SPACE analogy is
brought into
> the equation [pun intended]?

sounds imaginative. like a dream.

I, Bill Arnold, wrote, "PERIOD and PERIODICITY contain TIME within
the expression."
/tuning/topicId_39746.html#40105

wallyesterpaulrus wrote, "good!"
/tuning/topicId_39746.html#40137

I, Bill Arnold, ask: what is the formula for PERIOD and PERIODICITY which contains
TIME within it for which TUNING musicologists agree fits their MUSIC MATH?
Am I correct that it is a mere translation of Hz into cps: CYLES PER SECOND?
If so: am I also correct in my assumption that we are talking about MUSIC
which is perceived as SOUND in our AIR MEDIUM here on Earth but can also be
viewed as RADIO WAVES as described by Hertz and in the case of a TUNING FORK
created to OSCILLATE above or below the RANGE OF HUMAN HEARING would still be
perceived in PHYSICS with the proper equipment, i.e., an oscilloscope?

I, Bill Arnold wrote: "Briefly: the PERIODS of planets round the Sun are not
the same, as the DISTANCES between them might be PROPORTIONAL but the PERIODS
contain different RATES OF SPEED, if my memory serves me correctly."
/tuning/topicId_39746.html#40105

wallyesterpaulrus wrote, "well, the period of the earth is one year, for
example . . ."
/tuning/topicId_39746.html#40137

I, Bill Arnold, write: well, yes, and the period the planet Jupiter round
the Sun is approximately 11.86 years. But have you considered what the
PROPORTIONAL PERIODS are for ALL the planets as expressed by the ARITHMETICAL
SERIES OF NUMBERS we are dealing with? That is: Sun 0, Mercury 1, Venus 2,
Earth 3, Mars 4, etc.

In other words: Mercury is 88 Earth days. Thus, in the series above, we find
that the PERIODS do not show the SAME PROPORTIONALITY as the DISTANCES or RADIANS
from the Sun because in the formula, the RATES OF SPEEDS of the planets VARY and
are NOT PROPORTIONAL in the same ways the the DISTANCES. At least such is my
understanding but I am willing to be corrected in my current assessment.

What I am suggesting IS that perhaps musicologists ought to INVESTIGATE the
MATH and PHYSICS of NOTES, their FREQUENCY, their PERIOD, their PERIODICITY,
and yes, in my way of SEEING it, whether or not, it is dreamlike as you suggest,
thus: in their DISTANCES or RADIANS from their respective CENTERS and their
respective VIBRATION ORBITALS. It is my firm belief, based on MATH and PHYSICS
that the reason Pythagoras SAW what he did IS because there IS such a SIMILARITY
between the DISTANCES between the planets as there are between the NOTES in
the C Octave as I have suggested on this message board. We will get to that
understanding, of verification or denial of it, only by investigation.

I, Bill Arnold, wrote: "Am I to assume that the RATES OF SPEED of NOTES are the
SAME in ALL cases?"
/tuning/topicId_39746.html#40105

wallyesterpaulrus wrote, "notes don't move. sound moves, usually around 750 mph
or something in average-temperature, average humidity air."
/tuning/topicId_39746.html#40137

I, Bill Arnold, write: I believe that perhaps this is worthy of some discussion.
By calculations, atoms are shown to have SIZE: they have a CENTER or NUCLEUS and
ORBITALS or PARTICLES moving round in an ENCLOSED SPACE. I SEE the SAME in the
solar-planetary system and I SEE the SAME in DIFFRACTION PATTERNS of atoms as put
forth years ago by Rutherford. It seems reasonable to me, because the MATH and
PHYSICS of music is quantified, termed and defined, that a similarity probably
EXISTS, theoretically, in music and awaits amplification. By this I suggest that
musical NOTES can be put in LATTICES like PERIODIC ELEMENT tables because they ARE
IN FACT comparable. It is up to the musicologists to do this, as you ALL apparently
are working on it on TUNING and TUNING-MATH and elsewhere. I do NOT conclude that
NOTES have NECESSARILY a CENTER and ORIBTALS, but WHY NOT? Why should they defy
the LAWS OF MATH and the LAWS OF PHYSICS and not have SIZE? Pauline pointed out
that an OCTAVE creates LOUDNESS in the HIGHER REGISTER NOTE when BOTH are struck
together on an organ. Is that NOT because of VOLUME concepts, and are NOT the
HIGHER NOTES encompassing MORE VOLUME than the LOWER NOTES in the SAME SCALE?

I, Bill Arnold, wrote: "but GEOMETRIC shapes: whether HEXAGONAL or the more
sophisticated SPHERICAL? Might it be that the root NOTE in a chord
or a series is ENCASED by other NOTES as opposed to SEPARATE MEDIUMS separated
by empty SPACE between them akin to VACUUMS if the outer SPACE analogy is
brought into the equation [pun intended]?"
/tuning/topicId_39746.html#40105

wallyesterpaulrus wrote, "sounds imaginative. like a dream."
/tuning/topicId_39746.html#40137

I, Bill Arnold, write: Pythagoras and Kepler said as much. As I pointed out in
my BODE'S LAW EXPLAINED paper, the ancient Greeks had a very sophisticated and
quite accurate MODEL of the solar-planetary system which was displaced by
Ptolemy. Copernicus only revived what was already accepted millennium ago: a
HELIOCENTRIC solar-planetary system. The history is well document, from which
I summarize the details in my cited paper. Kepler, in fact, argued that they
were six-sided HEXAGONAL SHELLS, and what are musicologists' LATTICES but attempts
to get at the SAME arrangements. What I am suggesting, however, is that BOTH
the HEXAGON and the CIRCLE or the DODECAHEDRON and the SPHERE are relevant. My
Arnold's law has both series: the hexagonal Sun 0, Mercury 3, Venus 6, etc., and
the circle Sun 0, Mercury 3.14+, Venus 6.28+, etc. In my mind, it seems REASONABLE
that SOUNDS [that is to say: NOTES] are CENTERED and RADIATE OUT in an ever INCREASING
SPHERE ad infinitum until the ENERGY dissipates or meets resistance. That is the
nature of the MATH and PHYSICS of SOUND and hence, MUSIC. Therefore, those SIZE
attributes of NOTES ought to be able to be quantified and would redefinte what
I believe I hear musicologists referring to as PERIOD and PERIODICITY. Hey: this
is THEORY and what is wrong with MUSIC THEORY being considered?

I, Bill Arnold wrote, "However, musicologists know better than I what would
happen IF a TUNING fork placed in MEDIUM and VIBRATED, separated by a VACUUM--
whether or not it could be PERCEIVED in an ADJACENT MEDIUM. Tough question:
and not one I am sure has been scientifically tested."
/tuning/topicId_39746.html#40105

wallyesterpaulrus wrote, "no! this is a standard high-school physics class
demonstration, usually involving a loud bell and a vacuum pump."
/tuning/topicId_39746.html#40137

I, Bill Arnold, write: "Agreed. However, I suggested a TUNING FORK with a
specific reason in mind. The Sun IS similar to a TUNING FORK in this sense.
It is sending OUT from the CENTER of the solar-planetary system a continuous
stream of so-called RADIO WAVES, some perceived at LIGHT, and some perceived as
SOUND. They even have a name in astrophysics for the latter. Thus, the so-called
INTERSTELLAR MEDIUM is NOT a complete VACUUM and this has been confirmed
by astrophysics. In fact, astrophysicists of the last several decades have
demonstrated that the INTERGALACTIC MEDIUM is also NOT a complete VACUUM.

Thus, in my conclusion, Joe Monzo is correct in his DESIRE
to express the SOUND of the MUSIC OF THE SPHERES as a CHORD.

It is my intent to understand that MATH and PHYSICS so that an
accurate description of both can be so interrelated.

Thanks in advance,
meant kindly,

Bill Arnold
billarnoldfla@yahoo.com
http://www.cwru.edu/affil/edis/scholars/arnold.htm
Independent Scholar
Independent Scholar, Modern Language Association
-------------------------------------------------------------------
"There is magic in the web" Shakespeare (Othello, Act 3, Scene 4)
-------------------------------------------------------------------

__________________________________________________
Do you Yahoo!?
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--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> I, Bill Arnold, wrote, "PERIOD and PERIODICITY contain TIME
within
> the expression."
> /tuning/topicId_39746.html#40105
>
> wallyesterpaulrus wrote, "good!"
> /tuning/topicId_39746.html#40137
>
> I, Bill Arnold, ask: what is the formula for PERIOD and
PERIODICITY which contains
> TIME within it for which TUNING musicologists agree fits their
MUSIC MATH?
> Am I correct that it is a mere translation of Hz into cps: CYLES
PER SECOND?

no -- that's frequency.

period is the inverse -- seconds per cycle.

> If so: am I also correct in my assumption that we are talking
about MUSIC
> which is perceived as SOUND in our AIR MEDIUM here on
Earth but can also be
> viewed as RADIO WAVES as described by Hertz

a carrier radio wave is an electromagnetic oscillation with
frequency in the millions or billions of cycles per second, but is
*modulated* by frequencies in the audible range, representing
the signal to be heard . . .

> and in the case of a TUNING FORK
> created to OSCILLATE above or below the RANGE OF HUMAN
HEARING would still be
> perceived in PHYSICS with the proper equipment, i.e., an
oscilloscope?

you'd need a special microphone to hook up to that
oscilloscope, but yes . . .

> What I am suggesting IS that perhaps musicologists ought to
INVESTIGATE the
> MATH and PHYSICS of NOTES, their FREQUENCY, their
PERIOD, their PERIODICITY,
> and yes, in my way of SEEING it, whether or not, it is dreamlike
as you suggest,
> thus: in their DISTANCES or RADIANS from their respective
CENTERS and their
> respective VIBRATION ORBITALS.

i have no idea what that could mean.
>
> Pauline pointed out
> that an OCTAVE creates LOUDNESS in the HIGHER
REGISTER NOTE when BOTH are struck
> together on an organ. Is that NOT because of VOLUME
concepts, and are NOT the
> HIGHER NOTES encompassing MORE VOLUME than the
LOWER NOTES in the SAME SCALE?

pauline was confused about the difference between in vs. out of
phase, and phase-locked vs. non-phase locked. it is just as
easy to create destructive interference as it is to create
constructive interference (the loudness increase mentioned)
with phase-locked pitches.

> The Sun IS similar to a TUNING FORK in this sense.
> It is sending OUT from the CENTER of the solar-planetary
system a continuous
> stream of so-called RADIO WAVES, some perceived at LIGHT,
and some perceived as
> SOUND. They even have a name in astrophysics for the latter.

please fill us in about this electromagnetic radiation perceived by
the eardrum!

> Thus, the so-called
> INTERSTELLAR MEDIUM is NOT a complete VACUUM and
this has been confirmed
> by astrophysics. In fact, astrophysicists of the last several
decades have
> demonstrated that the INTERGALACTIC MEDIUM is also NOT
a complete VACUUM.

true -- but do you have any idea what the speed of sound is in the
intergalactic medium? there are ways of calculating this!

> Thus, in my conclusion, Joe Monzo is correct in his DESIRE
> to express the SOUND of the MUSIC OF THE SPHERES as a
CHORD.

and it seems he did so in an appropriate way, multiplying the
frequencies of the planets' orbit by enough powers of 2 to get
them into an audible octave . . . the distances only come into it
through one of kepler's laws, the one which relates period to
distance . . .