Piano Tuning Schools

Jon writes:
>I'm willing to bet a guy named Ed Foote will chime in shortly; if he doesn't
we have to wake him up. He's an active (and advocative) piano tuner and will
be a good resource for you.<

Huh? Wha?? sumbody say sumpin?
Actually, I went to the North Bennett Street School, in Boston. I know of
no finer route to becoming a performance level technician in two years.
Living up there is pretty expensive now, but if you want to be a top-level
tuner, this is one way to give it your best shot.
There is also a living to be made away from the performance arena. If
that is beckoning, then Randy Potter's course will make a lot of sense.
There are also several university courses available around the country that
might fit your bill.
Otherwise, the traditional way of entering the trade is to find a busy
technician and pay to learn or offer to trade work for instruction. Large
rebuilding facilities often have shop work that you can learn quickly enough
to be of value. One thing that you really should do is find the nearest
chapter of the Piano Technician's Guild and join as an associate. There is a
lot of instruction going on in the Guild, (which may or may not be a good
thing for the established tuners out there), and you can avail yourself of
it.
Good luck,
Ed Foote RPT

Thanks for the comments, Ed, I was looking on the Web for a "home" course, and of all the things that I read, the Randy Potter stuff sounds like a good place to start. I would like to get some formal training, more so I can satisfy my own curiousity in exploring other tunings. I have two pianos of my own, and would like to use one to explore other NON equal tempered scales.

Thanks, I am going to call Randy Potter's school today...

Mike

a440a@aol.com wrote:
> Jon writes: > >>I'm willing to bet a guy named Ed Foote will chime in shortly; if he doesn't > > we have to wake him up. He's an active (and advocative) piano tuner and will > be a good resource for you.<
> > Huh? Wha?? sumbody say sumpin? > Actually, I went to the North Bennett Street School, in Boston. I know of > no finer route to becoming a performance level technician in two years. > Living up there is pretty expensive now, but if you want to be a top-level > tuner, this is one way to give it your best shot. > There is also a living to be made away from the performance arena. If > that is beckoning, then Randy Potter's course will make a lot of sense. > There are also several university courses available around the country that > might fit your bill. > Otherwise, the traditional way of entering the trade is to find a busy > technician and pay to learn or offer to trade work for instruction. Large > rebuilding facilities often have shop work that you can learn quickly enough > to be of value. One thing that you really should do is find the nearest > chapter of the Piano Technician's Guild and join as an associate. There is a > lot of instruction going on in the Guild, (which may or may not be a good > thing for the established tuners out there), and you can avail yourself of > it. > Good luck, > Ed Foote RPT > > > You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
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--- In tuning@y..., Michael J McGonagle <fndsnd@r...> wrote:
> Thanks for the comments, Ed, I was looking on the Web for a "home"
> course, and of all the things that I read, the Randy Potter stuff
sounds
> like a good place to start. I would like to get some formal
training,
> more so I can satisfy my own curiousity in exploring other tunings.
I
> have two pianos of my own, and would like to use one to explore
other
> NON equal tempered scales.
>
> Thanks, I am going to call Randy Potter's school today...
>
> Mike

i had absolutely no training as a piano tuner, got a tuning hammer,
and tuned my piano to 1/4-comma meantone (with the wolf, to my
roommate's dismay, between Eb and G#). it took me about a week, and
that was just a first approximation . . . but it can be done!

wallyesterpaulrus wrote:
> i had absolutely no training as a piano tuner, got a tuning hammer, > and tuned my piano to 1/4-comma meantone (with the wolf, to my > roommate's dismay, between Eb and G#). it took me about a week, and > that was just a first approximation . . . but it can be done!

I have been tuning for a while (primarily 12-tet), but I want to get some formal training and certification. I am not really sure how important having the "paper documentation" of your skills are in piano tuning, but I have been working with computers for the past 12 years, all without any kind of school. Now all of a sudden, I can't get a job because I don't have any "formal training".

While I don't have any illusions that tuning pianos will make me rich, I hope that it can help to put some food on the table.

Mike

--- In tuning@y..., Michael J McGonagle <fndsnd@r...> wrote:

> I have been tuning for a while (primarily 12-tet), but I want to
get
> some formal training and certification. I am not really sure how
> important having the "paper documentation" of your skills are in
piano
> tuning, but I have been working with computers for the past 12
years,
> all without any kind of school. Now all of a sudden, I can't get a
job
> because I don't have any "formal training".
>
> While I don't have any illusions that tuning pianos will make me
rich, I
> hope that it can help to put some food on the table.
>
> Mike

It sounds like you have two goals: 1) generate income and 2) learn
how to tune alternative tunings.

For alternative temperaments, it's mostly a matter of calculating the
frequencies for the central octave in order to find the beat rates
for the fifths and fourths. There is an excellent book on this
subject (complete with tuning routines) by Owen Jorgensen, _Tuning
the Historical Temperaments by Ear_ (The Northern Michigan University
Press, Marquette, 1977). This had a very limited printing (around
1000), so I don't know if you will be able to find it anywhere now.

The only "training" I had in piano tuning was a 3-hour "lesson" in
which I learned from a tuner (my piano teacher's husband) on one of
his jobs. One of the most important things I learned is that the
result you get by tuning the unisons and octaves for maximum
resonance by ear (a sound that almost "sparkles") is far superior to
that using an electronic tuning aid ("dead" by comparison).

--George

Hi George,

you said...
> There is an excellent book on this
> subject (complete with tuning routines) by Owen Jorgensen, _Tuning
> the Historical Temperaments by Ear_ (The Northern Michigan
University
> Press, Marquette, 1977). This had a very limited printing (around
> 1000), so I don't know if you will be able to find it anywhere now.
> --George

Do know a bookstore where I can go online that will sell me a print
of the Owen Jorgensen book? That is if they have it?

Thanks
Wally

In a message dated 10/3/02 12:13:09 PM Central Daylight Time,
gdsecor@yahoo.com writes:

> One of the most important things I learned is that the
> result you get by tuning the unisons and octaves for maximum
> resonance by ear (a sound that almost "sparkles") is far superior to
> that using an electronic tuning aid ("dead" by comparison).
>
> --George
>
In piano tuning (and some organs, so they can be played with pianos) the
upper octaves are stretched. This is done to make the harmonics of the notes
there agree more closely with those in the lower register where the steel
strings and soundboard are much longer, and the lowest strings wound with
copper wire.

In that regard, steel isn't the best metal to use to produce musical sound!
It emphasizes strongly the first eight harmonics, as a trumpet does, and the
rest can be what they may.

So for those wanting their pianos tuned to MT, WM, JT, or JI, I suggest you
get a fortepiano. It has three voicings in the strings--Bass, Alto,
Treble--similar as many organ stops do, which are strung at much less
tightness. This allows the player to retune cetain strings as needed for
certain compositions.

I saw it done at a fortepiano recital in Pasadena, CA, at the space school
after intermission just before the fortepianist was to play a piece by Mozart
which needed a # or b on a certain note in the keyboard middle. I'm sure he
didn't do it becasue the note was out of tune at that point. but, even it it
were, the same option holds true.

Pianos strung with steel strings were originally made such for concert halls
to get a louder sound. I see no musical advantage for such in homes or
average-size chruches, where the piano is shorter than a 9' grand..

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 a message dated 10/3/02 12:40:59 PM Central Daylight Time,
earth7@optonline.net writes:

> Do know a bookstore where I can go online that will sell me a print
> of the Owen Jorgensen book? That is if they have it?
>
> Thanks
> Wally
>
<A HREF="http://mmd.foxtail.com/Tech/jorgensen.html">Click here: Tuning by Owen Jorgensen</A>
http://mmd.foxtail.com/Tech/jorgensen.html

When you wnat something by a person, title, or website, just put it in the
Search box, and presto, you usualy find up front what you want.

Pauline

--- In tuning@y..., "electricwally77" <earth7@o...> wrote:
> Hi George,
>
> you said...
> > There is an excellent book on this
> > subject (complete with tuning routines) by Owen Jorgensen,
_Tuning
> > the Historical Temperaments by Ear_ (The Northern Michigan
> University
> > Press, Marquette, 1977). This had a very limited printing
(around
> > 1000), so I don't know if you will be able to find it anywhere
now.
> > --George
>
>
> Do know a bookstore where I can go online that will sell me a print
> of the Owen Jorgensen book? That is if they have it?
>
> Thanks
> Wally

I have no idea. I gave all of the pertinent information above.

Owen Jorgensen was the resident piano tuner at the University of
Michigan in Lansing and, I believe, a colleague of J. Murray Barbour
(author of _Tuning and Temperament_). Jorgensen had a lot of trouble
getting his book published -- UM-Lansing wouldn't do it. He had to
go to Northern Michigan University Press, and they only agreed to a
limited *numbered* edition. I bought my copy at the time it was
released, and I have no idea if it was ever reprinted. Perhaps you
could contact Northern Michigan University Press.

--George

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/3/02 12:40:59 PM Central Daylight Time,
> earth7@o... writes:
>
>
> > Do know a bookstore where I can go online that will sell me a
print
> > of the Owen Jorgensen book? That is if they have it?
> >
> > Thanks
> > Wally
> >
> <A HREF="http://mmd.foxtail.com/Tech/jorgensen.html">Click here:
Tuning by Owen Jorgensen</A>
> http://mmd.foxtail.com/Tech/jorgensen.html
>
> When you wnat something by a person, title, or website, just put it
in the
> Search box, and presto, you usualy find up front what you want.
>
> Pauline

Bravo!

Can someone explain why a piano centers (I think) on Middle C? How
many C's octaves are there below? above? Why only those many? Why
are they 8 notes apart and not 10? Why are they "harmonics" of each
other? How many C notes could you actually have on a piano that the
human ear could hear if the keyboard could be infinite? Why are there
not more?

Bill Arnold

Bill Arnold
billarnoldfla@yahoo.com
Independent Scholar
Independent Scholar, Modern Language Association
-------------------------------------------------------------------
"There is magic in the web" Shakespeare (Othello, Act 3, Scene 4)
-------------------------------------------------------------------

--- prophecyspirit@aol.com wrote:
> In a message dated 10/3/02 12:13:09 PM Central Daylight Time,
> gdsecor@yahoo.com writes:
>
>
> > One of the most important things I learned is that the
> > result you get by tuning the unisons and octaves for maximum
> > resonance by ear (a sound that almost "sparkles") is far superior
> to
> > that using an electronic tuning aid ("dead" by comparison).
> >
> > --George
> >
> In piano tuning (and some organs, so they can be played with
> pianos) the
> upper octaves are stretched. This is done to make the harmonics of
> the notes
> there agree more closely with those in the lower register where the
> steel
> strings and soundboard are much longer, and the lowest strings
> wound with
> copper wire.
>
> In that regard, steel isn't the best metal to use to produce
> musical sound!
> It emphasizes strongly the first eight harmonics, as a trumpet
> does, and the
> rest can be what they may.
>
> So for those wanting their pianos tuned to MT, WM, JT, or JI, I
> suggest you
> get a fortepiano. It has three voicings in the strings--Bass, Alto,
>
> Treble--similar as many organ stops do, which are strung at much
> less
> tightness. This allows the player to retune cetain strings as
> needed for
> certain compositions.
>
> I saw it done at a fortepiano recital in Pasadena, CA, at the space
> school
> after intermission just before the fortepianist was to play a piece
> by Mozart
> which needed a # or b on a certain note in the keyboard middle. I'm
> sure he
> didn't do it becasue the note was out of tune at that point. but,
> even it it
> were, the same option holds true.
>
> Pianos strung with steel strings were originally made such for
> concert halls
> to get a louder sound. I see no musical advantage for such in homes
> or
> average-size chruches, where the piano is shorter than a 9' grand..
>
> 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>
>

__________________________________________________
Do you Yahoo!?
New DSL Internet Access from SBC & Yahoo!
http://sbc.yahoo.com

In a message dated 10/3/02 5:07:08 PM Central Daylight Time,
billarnoldfla@yahoo.com writes:

> Can someone explain why a piano centers (I think) on Middle C? How
> many C's octaves are there below? above? Why only those many?

Bill, most pianos have 7 octaves, plus down to A below the lowest. The
Busendoffer (sp) has 8 octaves. The reasons for the extra notes beyond 7
octaves is that produces better bass notes due to the larger and longer
soundboard.

Why > are they 8 notes apart and not 10? Why are they "harmonics" of each
> other?

The 27th harmonic in the spectrum is A. That produces 7 white-key
notes--C-G-E-D-B-7F-A. Higher harmonics are #s or bs or white-key notes
slightly above or below the ones I listed. So by nature the octave has 7
diatonic notes. There are 5 chromatic notes becasue C7 is Bb, the others #s
to make major 3rds.

How many C notes could you actually have on a piano that the>
> human ear could hear if the keyboard could be infinite? Why are there
> not more?

The 8th Bass octave is in the 32' organ Pedal range which goes down near the
iinaudible level for most people. The highest C has strings so short the
sound is very weak. It would be impracticable to make higher notes. Most arms
couldn't reach them anyway.

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>

Hi Bill

> Can someone explain why a piano centers (I think) on Middle C? How
> many C's octaves are there below? above? Why only those many? Why
> are they 8 notes apart and not 10? Why are they "harmonics" of each
> other? How many C notes could you actually have on a piano that the
> human ear could hear if the keyboard could be infinite? Why are there
> not more?

For the number of notes to an octave, you should take a look at
Margo Schulter's article in the FAQ.

http://tunesmithy.netfirms.com/on_site_tree/margoschulter/Why_12_notes_as_one_attractive_arrangement.html

The question about why the scale starts at C rather than say A
was asked here a little while back - it is historical - that
the scale we happen to have settled on started from letter
C in a scale lettering system that did begin at A.

Maybe someone would liek to draft an FAQ entry on that??

In fact, all your questions seem good candidates for the FAQ.

Each octave is a doubling in pitch. The piano range almost covers
the range of notes that sound good musically - thunder is well
below the lowest note of the piano, and bird song can go above it,
also bat squeaks of course, but if you go much higher
you go beyond the range of human hearing.

Also, as one gets older, everyone (I believe) loses sensitivity
to the very highest pitches - first you stop hearing bats,
then eventually you will stop hearing the very
highest pitched notes of bird song too - some old bird watchers
can no longer hear some of the birds they see, the ones with
ultra high pitched notes. Children can hear bats best of all.

Very low notes are not so precisely heard in pitch - our sensitivity
to pitch gets less as you go down in pitch. YOu could play a melody
using thunder, but it mightn't be that recognisable.
Below that there comes a point where htey are felt rather than
heard, so there is no sudden cut off. (Evelyn Glenny the
percussionist is able to play percussion musically so well
because she can feel the musical sounds - she is the
famous percussionist who is profoundly deaf, but is an excellent
player nevertheless, gives many concerts, and plays
as soloists with orchestras).

High notes don't have much variety in timbre because the
timbre depends on the component frequencies of the note
- and if a note is high in pitch, the higher component frequencies
are too high to be audible.

Robert

In a message dated 10/4/02 12:46:05 AM Central Daylight Time,
robertwalker@ntlworld.com writes:

> High notes don't have much variety in timbre because the
> timbre depends on the component frequencies of the note
> - and if a note is high in pitch, the higher component frequencies
> are too high to be audible.
>
> Robert
>
Good post! Unfortunately, most analog electronic organs made their
high-pirched stops with hardly any harmonics. A big mistake. As the harmonics
not heard affect those that are, not only in a given stop, but for the rest
of the sound played together.

Pauline

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> Can someone explain why a piano centers (I think) on Middle C?

it's an arbitrary choice.

> How
> many C's octaves are there below? above?

a piano has 8 Cs altogether, but only 7 1/4 octaves of range.

> Why only those many?

more was not considered musically useful enough to justify the
expense.

> Why
> are they 8 notes apart and not 10?

they are 7 diatonic notes, or 12 chromatic notes, apart. but the
primary concern of this list is dividing the octave in other ways, or
abandoning the octave altogether. the octave is a 2:1 frequency
ratio, so the consecutive notes on the piano have a frequency ratio
of 2^(1/12).

> Why are they "harmonics" of each
> other?

because 2^n is always an integer, and harmonic occur at or near
integer multiples of the fundamental frequency. so if you start with
a low C, the 2nd, 4th, 8th, 16th, 32nd, . . . harmonics are all
higher Cs.

> How many C notes could you actually have on a piano that the
> human ear could hear if the keyboard could be infinite?

just a couple more.

> Why are there
> not more?

the ear is only sensitive to vibrations in the range of about 20 -
20,000 cycles per second. the ratio of 20,000 / 20 = 1000, and the
log base 2 of 1000 is about 10, so we can only hear 10 octaves of
pitch, never more.

My remarks will come at the end of the three recorded responses by
Pauline Phillips, Robert Walker and Wall Yester Paulrus: inasmuch as
I appreciate their thoughtful remarks and believe what they wrote is
a stepping stone [or note] to the next octave [hope I have punned
that correctly!]:

I, Bill Arnold, had written:

Can someone explain why a piano centers (I think) on Middle C? How
many C's octaves are there below? above? Why only those many? Why
are they 8 notes apart and not 10? Why are they "harmonics" of each
other? How many C notes could you actually have on a piano that the
human ear could hear if the keyboard could be infinite? Why are there
not more?

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

Pauline Phillips writes,

In a message dated 10/3/02 5:07:08 PM Central Daylight Time,
billarnoldfla@yahoo.com writes:

Can someone explain why a piano centers (I think) on Middle C? How
many C's octaves are there below? above? Why only those many?

Bill, most pianos have 7 octaves, plus down to A below the lowest.
The Busendoffer (sp) has 8 octaves. The reasons for the extra notes
beyond 7 octaves is that produces better bass notes due to the larger
and longer soundboard.

Why
are they 8 notes apart and not 10? Why are they "harmonics" of each
other?

The 27th harmonic in the spectrum is A. That produces 7 white-key
notes--C-G-E-D-B-7F-A. Higher harmonics are #s or bs or white-key
notes slightly above or below the ones I listed. So by nature the
octave has 7 diatonic notes. There are 5 chromatic notes becasue C7
is Bb, the others #s to make major 3rds.

How many C notes could you actually have on a piano that the

human ear could hear if the keyboard could be infinite? Why are there
not more?

The 8th Bass octave is in the 32' organ Pedal range which goes down
near the iinaudible level for most people. The highest C has strings
so short the sound is very weak. It would be impracticable to make
higher notes. Most arms couldn't reach them anyway.

Sincerely,
Pauline W. Phillips, Moderator, Johannus Organs eSchool
Johannus Orgelbouw, Holland, builds pipe, pipe-digital,
digital-sampled organs.
Moderator, Just Intonation Organ eSchool

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

"Robert Walker" <robertwalker@ntlworld.com> writes,

Hi Bill

> Can someone explain why a piano centers (I think) on Middle C? How
> many C's octaves are there below? above? Why only those many? Why
> are they 8 notes apart and not 10? Why are they "harmonics" of each
> other? How many C notes could you actually have on a piano that the
> human ear could hear if the keyboard could be infinite? Why are
there
> not more?

For the number of notes to an octave, you should take a look at
Margo Schulter's article in the FAQ.

http://tunesmithy.netfirms.com/on_site_tree/margoschulter/Why_12_notes_as_one_attractive_arrangement.html

The question about why the scale starts at C rather than say A
was asked here a little while back - it is historical - that
the scale we happen to have settled on started from letter
C in a scale lettering system that did begin at A.

Maybe someone would liek to draft an FAQ entry on that??

In fact, all your questions seem good candidates for the FAQ.

Each octave is a doubling in pitch. The piano range almost covers
the range of notes that sound good musically - thunder is well
below the lowest note of the piano, and bird song can go above it,
also bat squeaks of course, but if you go much higher
you go beyond the range of human hearing.

Also, as one gets older, everyone (I believe) loses sensitivity
to the very highest pitches - first you stop hearing bats,
then eventually you will stop hearing the very
highest pitched notes of bird song too - some old bird watchers
can no longer hear some of the birds they see, the ones with
ultra high pitched notes. Children can hear bats best of all.

Very low notes are not so precisely heard in pitch - our sensitivity
to pitch gets less as you go down in pitch. YOu could play a melody
using thunder, but it mightn't be that recognisable.
Below that there comes a point where htey are felt rather than
heard, so there is no sudden cut off. (Evelyn Glenny the
percussionist is able to play percussion musically so well
because she can feel the musical sounds - she is the
famous percussionist who is profoundly deaf, but is an excellent
player nevertheless, gives many concerts, and plays
as soloists with orchestras).

High notes don't have much variety in timbre because the
timbre depends on the component frequencies of the note
- and if a note is high in pitch, the higher component frequencies
are too high to be audible.

Robert

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

Wall Yester Paulrus writes,

--- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> Can someone explain why a piano centers (I think) on Middle C?

it's an arbitrary choice.

> How
> many C's octaves are there below? above?

a piano has 8 Cs altogether, but only 7 1/4 octaves of range.

> Why only those many?

more was not considered musically useful enough to justify the
expense.

> Why
> are they 8 notes apart and not 10?

they are 7 diatonic notes, or 12 chromatic notes, apart. but the
primary concern of this list is dividing the octave in other ways, or

abandoning the octave altogether. the octave is a 2:1 frequency
ratio, so the consecutive notes on the piano have a frequency ratio
of 2^(1/12).

> Why are they "harmonics" of each
> other?

because 2^n is always an integer, and harmonic occur at or near
integer multiples of the fundamental frequency. so if you start with
a low C, the 2nd, 4th, 8th, 16th, 32nd, . . . harmonics are all
higher Cs.

> How many C notes could you actually have on a piano that the
> human ear could hear if the keyboard could be infinite?

just a couple more.

> Why are there
> not more?

the ear is only sensitive to vibrations in the range of about 20 -
20,000 cycles per second. the ratio of 20,000 / 20 = 1000, and the
log base 2 of 1000 is about 10, so we can only hear 10 octaves of
pitch, never more.

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

OK: here is my comment in response to Pauline, Robert and Wall
Yester,
and it is, years ago my daughter took flute lessons, became first or
second flute in the orchestra, played a lot in the house, and would
sometime yell, "What do you want to hear"" and after several years, I
could say, "Play Bach," and she would tease my wife and I with
Schumann, and I would yell back "That's not Bach;" and still, I did
not know all the notes, and scales, and whatever. Then, a friend of
mine who is a professional singer, with fifteen albums to his credit,
with a perfect-pitch tenor voice asked my wife and I to manage his
horse farm in Nova Scotia while he cut an album for several months at
Warner Bros. in California. While there and the snows flew I played
with the piano, and taught myself chords and octaves and with both
hands could play music for an hour to the point that when he came
back, he sat down and listened for a half hour and praised my
"natural" ear, etc.

Question one: what is a "natural" ear? Why do I think I can tell
perfect pitch? Why do I say, as he does, that so-in-so cannot carry
a tune in a bucket, and their voice is flat? Does this all mean I am
born with something? Or did it develop when I listened to my
daughter during years taking formal training and playing it around
me?

Question two: what is "natural" sound in music? Why is it that there
are different scales for different folk around the world? Why is
something "natural" to us, not "natural" to them? Is there something
in a culture which predetermines our disposition toward certain
scales? Or should I ask, toward certain tuning? Or is it different
systems of music? Or, are these various systems merely offspring of
a system of sounds natural to Nature?

Question three: Why is "Do, Re, Me, Fa, So, La, Te, Do" taught to
really young music students? Why do they emphasize, three times,
"Me, Me, Me"? Is that Middle C? Is that the "tuning" center point
of our musical scale? Is that "tuning" center, the piano? Does a
piano get tuned first, then the Orchestra tune to that instrument?
And why? Or why not?

Question four: What is the starting point, I guess you all would say,
note on a piano? Either where it all began, or a tuner begins? Does
the scale or system begin at Middle C, or some other note? And if
so, does the system progress from some Zero point and progress
infinitely, technically, through the range of the human ear? Or does
the system start in the middle, at Middle C, and move down through
the lower notes, and move up through the upper notes, away from some
starting point in the middle?

Thank you, but as a student of music, these simple points have never
been laid out for me in anything I have ever read about music.

Lastly, down the road, I believe it will help me understand the
celestial music I think inherent in Nature. Maybe, musicians do not
agree that mathematics is the essence of nature and Nature as I do.
So, I think we can get there from here, and tuning seems to be the
key, at least to my way of think right now. Correct me, if you think
I am wrong. Thanks, again, so far.

Bill Arnold

Bill Arnold
billarnoldfla@yahoo.com
Independent Scholar
Independent Scholar, Modern Language Association
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>>Why only those many?
>
>more was not considered musically useful enough to justify the
>expense.

This is really just your interp. of historical facts. There was
no central top-down decision. Why is the QWERTY keyboard
standard? Why did it take 50 years for front-loading washing
machines to make it to the consumer market?

-Carl

Carl Lumma wrote:
> Why is the QWERTY keyboard standard?

Carl,

The reason that I heard was that the other Keyboard option (the Dvorak) allowed the opertor to type faster than the mechinism was able to operate at (the hammers would get tangled up in each other, as they were all trying to hit the same spot). Thus, they needed to provide a "slower" interface. Weather this true or not is really irrelevant with the advent of computers, because there are no moving parts to get all tangled up. (So, be the first one on your block to have a Dvorak Computer!!!).

I guess the point here is that a limitation of one age are either lessened or eliminated in the coming ages.

In regards to the number of octaves on a Piano, would it be practical to create a piano that has at least one octave more at the top? If the higher notes vibrate at about 4,000 CPS, this would put their first harmonic at about 8,000 CPS. Extending the keyboard one octave from this would place the first harmonic for the added octave at 16,000 CPS. While this is within the range of Human hearing, is this within the Piano's ability to "resonate" at that frequency?

When Bosendorfer created their "extended" piano (96 keys, I think), they only added notes to the lower end, was this because they thought it "unpractical" to go higher??? I seem to remember one comment about the added notes, they were meant to be "felt" and not heard.

I have often wondered why a keyboard has only 12 notes per octave, and I still think that it comes down to "practical" reasons. How much tention is generated by a set of strings on the frame of the piano? Is it possible to add another 7 notes per octave (this would come to a total of 21 strings per octave in the upper registers, adding approximately 115 strings to the piano). Also, what would it take for a "pianist" to relearn the new keyboard layout. It might be possible, today, to create a frame capabile of withstanding that pressure, but what about during the days of the advent of the piano? (Did not some instrument designer create a 19 note per octave piano sometime around 1600-1700???)

At the same time, the organ came first, so why did it only have 12 notes per octave, I would imagine the practical "excuse" was that 7 more pipes per octave was either not needed, or did it cost too much.

Or does the number 12 have some mystical/religious significance? There were 12 disciples, there are 12 zodiac signs, there are 12 cards in each suit in a deck of cards (which were derived from a Tarot deck). Was the development of the "scale" controlled (to some extend) by the church?

Just my opinion...

Mike

In a message dated 10/5/02 9:04:42 AM Central Daylight Time,
robertwalker@ntlworld.com writes:

> interesting that harmonics too high
> to be heard can still affect the quality of the note isn't it...

All pitches in the natural harmonic spectrum create Difference (below the
note played) and Sumational (above the note played) Combinational tones. When
they get to high to be heard, the Sumational tones won't be heard either, but
the Difference tones below the note played may be. These tones ad richness to
the tones played individually and when played together.

Pauline

In a message dated 10/5/02 2:31:36 PM Central Daylight Time,
fndsnd@rcnchicago.com writes:

> , the organ came first, so why did it only have 12 notes
> per octave, I would imagine the practical "excuse" was that 7 more pipes
> per octave was either not needed, or did it cost too much.
>
Some organ had a few split digitals per octave for added ntoes. But organists
didn't like them. As they were offset about halfway to the right or left of
the regular black keys. Thus rather than split the digitals physically, they
need to be layered to be in the same postiion as the regualr keys. That's the
way my organ is.

Pauline

prophecyspirit@aol.com wrote:
> In a message dated 10/5/02 2:31:36 PM Central Daylight Time, > fndsnd@rcnchicago.com writes:
> > >> , the organ came first, so why did it only have 12 notes
>> per octave, I would imagine the practical "excuse" was that 7 more pipes
>> per octave was either not needed, or did it cost too much.
> > > Some organ had a few split digitals per octave for added ntoes. But > organists didn't like them. As they were offset about halfway to the > right or left of the regular black keys. Thus rather than split the > digitals physically, they need to be layered to be in the same postiion > as the regualr keys. That's the way my organ is.

Pauline,

When you use the word "digitals", are you using that as a synonym for "key" (the lever-thingy that is used to play the pitch???)?

I am not completely sure about this, but I think there was an organ designed that had 19 tones per octave. It (kinda-sorta) sounds like what you describe above. It was arranged such that for every black key, there were two keys, and the spots with two adjacent white keys, there is an addition key.

Is this something similar to what you are describing? Is the organ keyboard something you built? Do you know of a picture on the web?

Thanks,

Mike

Michael J McGonagle wrote:

>Carl Lumma wrote:
>>Why is the QWERTY keyboard standard?
>
> Carl,
>
>The reason that I heard was that the other Keyboard option (the
>Dvorak) allowed the opertor to type faster than the mechinism was
>able to operate at (the hammers would get tangled up in each
>other, as they were all trying to hit the same spot). Thus, they
>needed to provide a "slower" interface. Weather this true or not
>is really irrelevant with the advent of computers, because there
>are no moving parts to get all tangled up. (So, be the first one
>on your block to have a Dvorak Computer!!!).

By the time the Dvorak layout was invented, QWERTY was already
entrenched and any issues with keys jamming on early machines
had already been solved. In fact, if you look into it (the best
I could do, anyway, reading some patents and such), nobody really
knows why or how the QWERTY layout was chosen.

The maximum speed of human typists doesn't seem to be limited by
the QWERTY layout, though on average Dvorak may be faster. It's
certainly easier for beginners to learn, and results in less hand
strain.

Both the MacOS and Windows have supported Dvorak for a long time.
Linux, too. I switched two years ago, and I'm very glad I did.
I read that I'd loose my QWERTY ability, but I was shocked when it
actually happened. :(

>I guess the point here is that a limitation of one age are either
>lessened or eliminated in the coming ages.

The point is that sometimes, things happen for _no reason_.
Shocking but true.

>In regards to the number of octaves on a Piano, would it be
>practical to create a piano that has at least one octave more
>at the top? If the higher notes vibrate at about 4,000 CPS, this
>would put their first harmonic at about 8,000 CPS. Extending the
>keyboard one octave from this would place the first harmonic for
>the added octave at 16,000 CPS. While this is within the range of
>Human hearing, is this within the Piano's ability to "resonate"
>at that frequency?

Don't know. I doubt there's much musical use for such notes, in
the conventional sense, as the precise sense of pitch drops out
of human perception somewhere in this range.

>When Bosendorfer created their "extended" piano (96 keys, I think),
>they only added notes to the lower end, was this because they
>thought it "unpractical" to go higher???

Don't know. I have it that the lower strings are for resonance
only, and that they are the most frequently broken strings by
tuners. The B. technician recommends against even trying to tune
them!

>I have often wondered why a keyboard has only 12 notes per octave,
>and I still think that it comes down to "practical" reasons. How
>much tention is generated by a set of strings on the frame of the
>piano?

Lots. The exact figure is on Steinway's site, in tons.

>Is it possible to add another 7 notes per octave (this would come
>to a total of 21 strings per octave in the upper registers, adding
>approximately 115 strings to the piano).

Yes, it is possible.

>Also, what would it take for a "pianist" to relearn the new
>keyboard layout.

Lots and lots of work. So hard, that it's nearly impossible for
an individual working in a vacuum. The support of a community
really helps. Unfortunately, very few on this list have any
interest in it!

>It might be possible, today, to create a frame capabile of
>withstanding that pressure,

It is.

>but what about during the days of the advent of the piano?
>(Did not some instrument designer create a 19 note per octave
>piano sometime around 1600-1700???)

Early pianos, today called fortepianos, were strung with much less
tension than modern instruments. Legend has it that B. invented
the first iron-frame piano for Liszt, so he could not break the
frame during his famed improvisation-concerts!

>At the same time, the organ came first, so why did it only have
>12 notes per octave, I would imagine the practical "excuse" was
>that 7 more pipes per octave was either not needed, or did it
>cost too much.

That might have made experimentation difficult, but keep in mind
that organs already have many pipes per pitch. Organ builders
could have easily reduced the number of stops a bit in favor of a
microtonal scale. The real answer is that the 12-tone system was
already very entrenched before anybody thought to ask where it
came from. It happens a lot in bottom-up evolution.

-Carl

My remarks will come at the end of the thoughtful response of Joe
Monz:

I, Bill Arnold, had written:

Can someone explain why a piano centers (I think) on Middle C? How
many C's octaves are there below? above? Why only those many? Why
are they 8 notes apart and not 10? Why are they "harmonics" of each
other? How many C notes could you actually have on a piano that the
human ear could hear if the keyboard could be infinite? Why are there
not more?

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

From monz Sat Oct 5 01:08:09 2002
X-Sender: monz@attglobal.net
X-Apparently-To: tuning@yahoogroups.com and
celestial-tuning@yahoogroups.com
X-Yahoo-Profile: joemonz
Subject: [tuning] questions about those C's (was: Piano Tuning
Schools)
hi Bill,

> From: "Bill Arnold" <billarnoldfla@yahoo.com>
> To: <tuning@yahoogroups.com>; <celestial-tuning@yahoogroups.com>
> Sent: Thursday, October 03, 2002 3:04 PM
> Subject: Re: [tuning] Re: Piano Tuning Schools
>
>
> Can someone explain why a piano centers (I think) on Middle C? How
> many C's octaves are there below? above? Why only those many? Why
> are they 8 notes apart and not 10? Why are they "harmonics" of
each
> other? How many C notes could you actually have on a piano that
the
> human ear could hear if the keyboard could be infinite? Why are
there
> not more?

i'm perhaps not really answering any of your specific questions
here, but you'll probably find this useful:

in the original paper i put online about my tuning theories
(<http://makeashorterlink.com/?M6C022302> -- wait a moment
for the redirected link to work), there's a section discussing
a "reference pitch", which i call "C n^0" and suggest as
referring to either 1 Hz or 256 (= 2^8) Hz.

since my notation is based on prime-factoring, this makes
"middle-C" either 2^8 in the former case or n^0 in the latter.

i also state here: "The approximate range of human hearing is
from 20 to 20,000 Hz. Described as powers of 2, this is roughly
2^4 (=16) to 2^14 (= 16,384) Hz." if "middle C" at 256 Hz is
C n^0, this range is described as 2^(-4...+6).

they are "harmonics" of each other because they are all
powers of 2, and by definition, the interval which most
scales set up as the "interval of equivalence" is one whose
bounding pitches have the frequency ratio of 2:1.

this ratio usually goes by the more familiar musical name
of "octave" (abbreviated "8ve"), which is Latin for "eighth".

during the medieval period, the standard scale in use was the
heptatonic diatonic scale -- that is, 7 different pitches
("heptatonic" = "7-tone") within one "8ve", assumed to repeat
exactly in all other "8ves", and which have a mixture of both
"half-steps" and "whole-steps" as the intervals between the
degrees of the scale.

("diatonic" is Greek for "thru tones", because of the three
basic _genera_ in ancient Greek theory, this was the one
which had 2 tones in each "tetrachord"; the other two _genera_
had an interval which was bigger and two which were smaller.
see my "Tutorial on ancient Greek tetrachord-theory"
<http://makeashorterlink.com/?X65121302> for more info.)

when listening to a scale such as this, one is immediately
struck by how similar the 8th note (doesn't matter if it's
the 8th note below or the 8th note above the starting pitch)
sounds like the starting note.

thus, the "8ve" became the most basic interval involved in
scale construction as well as harmonic usage and analysis.

i suggest you peruse the following definitions from my
Tuning Dictionary:

/tuning/files/dict/harm.htm
/tuning/files/dict/harmser.htm
/tuning/files/dict/equivalenceinterval.htm
/tuning/files/dict/octave.htm
/tuning/files/dict/diatonic.htm
/tuning/files/dict/tetrachd.htm
/tuning/files/dict/semi.htm
/tuning/files/dict/wholetone.htm
/tuning/files/dict/degree.htm

later (c. 1200s to 1300s), mainly thru the process of "mutation",
the scale resources expanded to include what we would now call
the "flats" and "sharps", eventually leading to the "chromatic"
scale.

during the early development of Western music, from its origins
in the Frankish kingdom c. 700 up to the recognition of "3rds"
and "6ths" as "consonances" c. 1500, the "Pythagorean" (3-limit)
scale was the basic tuning.

after 1500, 5-limit "just-intonation" became a theoretical
paradigm but proved difficult to achieve in practice, leading
to the idea of "temperament". in roughly chronological order,
the leading families of temperaments have been "meantone",
"well-temperament", and then "equal-temperament".

for a long time it has been recognized that 12 different pitches
could form a nearly-closed circle, and by tempering, it could
become an actual closed circle. thus during the 1900s the
tuning standard became "12-tone equal-temperament", so that
the 2:1 ratio or "8ve" now contained 12 different notes, each
one spaced the same distance from those adjacent to it.

more definitions:

/tuning/files/dict/mutation.htm
/tuning/files/dict/chromati.htm
/tuning/files/dict/major3rd.htm
/tuning/files/dict/minor3rd.htm
/tuning/files/dict/consonance.htm
/tuning/files/dict/pythag.htm
/tuning/files/dict/limit.htm
/tuning/files/dict/just.htm
/tuning/files/dict/temp.htm
/tuning/files/dict/meantone.htm
/tuning/files/dict/well.htm
/tuning/files/dict/eqtemp.htm

the real question about the range of the piano keyboard
(a real piano has 88 keys, or a range of about 7&1/2 "8ves")
is not "why aren't there more notes?", but rather "why are
there that many?". the notes at either end of the keyboard
are so low or high that their pitch can barely be discerned,
and they're usually used only in combination with like notes
an "8ve" apart, to give and effect of increased depth or
brilliance respectively.

for an illustration and explanation of a keyboard that was
designed to use the 24-tone equal-temperament, commonly known
as the "quarter-tone scale", see my newly updated web version
(with Klaus Schmirler's English translation) of Willi
M�llendorff's _Musik mit Viertelt�nen_ (Music With
Quarter Tones) at <http://makeashorterlink.com/?L67124302>.

the diagram of the keyboard is here:
<http://makeashorterlink.com/?C1A123302>.

-monz (this group's list-mom)
"all roads lead to n^0"

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

OK: here is my comment in response to Joe Monz:

and it is, years ago my daughter took flute lessons, became first or
second flute in the orchestra, played a lot in the house, and would
sometime yell, "What do you want to hear"" and after several years, I
could say, "Play Bach," and she would tease my wife and I with
Schumann, and I would yell back "That's not Bach;" and still, I did
not know all the notes, and scales, and whatever. Then, a friend of
mine who is a professional singer, with fifteen albums to his credit,
with a perfect-pitch tenor voice asked my wife and I to manage his
horse farm in Nova Scotia while he cut an album for several months at
Warner Bros. in California. While there and the snows flew I played
with the piano, and taught myself chords and octaves and with both
hands could play music for an hour to the point that when he came
back, he sat down and listened for a half hour and praised my
"natural" ear, etc.

Question one: what is a "natural" ear? Why do I think I can tell
perfect pitch? Why do I say, as he does, that so-in-so cannot carry
a tune in a bucket, and their voice is flat? Does this all mean I am
born with something? Or did it develop when I listened to my
daughter during years taking formal training and playing it around
me?

Question two: what is "natural" sound in music? Why is it that there
are different scales for different folk around the world? Why is
something "natural" to us, not "natural" to them? Is there something
in a culture which predetermines our disposition toward certain
scales? Or should I ask, toward certain tuning? Or is it different
systems of music? Or, are these various systems merely offspring of
a system of sounds natural to Nature?

Question three: Why is "Do, Re, Me, Fa, So, La, Te, Do" taught to
really young music students? Why do they emphasize, three times,
"Me, Me, Me"? Is that Middle C? Is that the "tuning" center point
of our musical scale? Is that "tuning" center, the piano? Does a
piano get tuned first, then the Orchestra tune to that instrument?
And why? Or why not?

Question four: What is the starting point, I guess you all would say,
note on a piano? Either where it all began, or a tuner begins? Does
the scale or system begin at Middle C, or some other note? And if
so, does the system progress from some Zero point and progress
infinitely, technically, through the range of the human ear? Or does
the system start in the middle, at Middle C, and move down through
the lower notes, and move up through the upper notes, away from some
starting point in the middle?

Question five: If Middle C is 256 Hz
[you wrote: "there's a section discussing
a "reference pitch", which i call "C n^0" and suggest as
referring to either 1 Hz or 256 (= 2^8) Hz."
Can you tell me how many zeros that is after the 256?]

Also, now, I do know that 256 is:
2X1=2 [is this the first octave?of the base note? is that note below
the range of the human ear? is it a vibration like thunder?]

2x2=4 [is this the second octave?]
4X2=8 [is this the third octave?]
8X2=16 [is this the fourth octave?]
16X2=32 [is this the five octave?]
32X2=64 [is this the sixth octave?]
64X2=128 [is this the seventh octave?]
128X2=256 [is this the eighth octave? And is it Middle C?
is that why it is called 2^8 and "the eighth"?
Are we now on the same page, mentally in agreement?]

Thank you, but as a student of music, these simple points have never
been laid out for me in anything I have ever read about music.

Lastly, down the road, I believe it will help me understand the
celestial music I think inherent in Nature. Maybe, musicians do not
agree that mathematics is the essence of nature and Nature as I do.
So, I think we can get there from here, and tuning seems to be the
key, at least to my way of think right now. Correct me, if you think
I am wrong. Thanks, again, so far.

Bill Arnold

Bill Arnold
billarnoldfla@yahoo.com
Independent Scholar
Independent Scholar, Modern Language Association
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In a message dated 10/6/02 12:00:52 AM Central Daylight Time,
clumma@yahoo.com writes:

> keep in mind
> that organs already have many pipes per pitch. Organ builders
> could have easily reduced the number of stops a bit in favor of a
> microtonal scale.

But trained organists usually want more stops to work with, not less. A
cathedral in Spain had 14 organs in it. I suspect some at least were tuned to
different keys or different tunings.

Pauline

In a message dated 10/6/02 11:36:05 AM Central Daylight Time,
billarnoldfla@yahoo.com writes:

> 2x2=4 [is this the second octave?]
> 4X2=8 [is this the third octave?]
> 8X2=16 [is this the fourth octave?]
> 16X2=32 [is this the five octave?]
> 32X2=64 [is this the sixth octave?]
> 64X2=128 [is this the seventh octave?]
> 128X2=256 [is this the eighth octave?

In betwen these are odd harmonics that are undivisible. They are multiplied
by 2 also in octaves. And multipied with other numbers. Thus G is 3 x C1, D 3
x G, A 3 x D, B 3 x E, F# 3 x B, C# 3 X F# and so forth.

Psuline

>>keep in mind that organs already have many pipes per pitch.
>>Organ builders could have easily reduced the number of stops
>>a bit in favor of a microtonal scale.
>
>But trained organists usually want more stops to work with,
>not less. A cathedral in Spain had 14 organs in it. I suspect
>some at least were tuned to different keys or different
>tunings.

Glenn Gould wasn't a trained organist, but he did want fewer
stops, and got world-class results. Some of my favorite organs
have been continuo organs, though I'm not a trained organist
either, and I'm a bit of a nut for small things in general.

My point was just that there was no reason that organs could
not have been microtonal. They were already spending plenty of
money on them.

-C.

In a message dated 10/6/02 12:44:05 PM Central Daylight Time,
clumma@yahoo.com writes:

> My point was just that there was no reason that organs could
> not have been microtonal.

I agree. Btu I show in my JI discussion in my JI forum that this could've
been done without sacrificing stops nor pipe ranks. As everything needed to
create JI organs was techonology already known very long since. The real
problem was, no one had invented a practical all-key scale that would
faithfully play music written for tempered scales based on the 12-note
octave. But I did invent such a scale, and posted its C scale here.

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:

/tuning/topicId_39189.html#39225

> In a message dated 10/3/02 12:40:59 PM Central Daylight Time,
> earth7@o... writes:
>
>
> > Do know a bookstore where I can go online that will sell me a
print
> > of the Owen Jorgensen book? That is if they have it?
> >
> > Thanks
> > Wally
> >
> <A HREF="http://mmd.foxtail.com/Tech/jorgensen.html">Click here:
Tuning by Owen Jorgensen</A>
> http://mmd.foxtail.com/Tech/jorgensen.html
>
> When you wnat something by a person, title, or website, just put it
in the
> Search box, and presto, you usualy find up front what you want.
>
> Pauline

***Dunno. That link doesn't seem to work for *me...* Anybody else
have any trouble with it? I also was under the impression that this
book was long out of print...

Joseph Pehrson

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

/tuning/topicId_39189.html#39239

wrote:
> --- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
> > Can someone explain why a piano centers (I think) on Middle C?
>
> it's an arbitrary choice.
>
> > How
> > many C's octaves are there below? above?
>
> a piano has 8 Cs altogether, but only 7 1/4 octaves of range.
>
> > Why only those many?
>
> more was not considered musically useful enough to justify the
> expense.
>
> > Why
> > are they 8 notes apart and not 10?
>
> they are 7 diatonic notes, or 12 chromatic notes, apart. but the
> primary concern of this list is dividing the octave in other ways,
or
> abandoning the octave altogether. the octave is a 2:1 frequency
> ratio, so the consecutive notes on the piano have a frequency ratio
> of 2^(1/12).
>
> > Why are they "harmonics" of each
> > other?
>
> because 2^n is always an integer, and harmonic occur at or near
> integer multiples of the fundamental frequency. so if you start
with
> a low C, the 2nd, 4th, 8th, 16th, 32nd, . . . harmonics are all
> higher Cs.
>
> > How many C notes could you actually have on a piano that the
> > human ear could hear if the keyboard could be infinite?
>
> just a couple more.
>
> > Why are there
> > not more?
>
> the ear is only sensitive to vibrations in the range of about 20 -
> 20,000 cycles per second. the ratio of 20,000 / 20 = 1000, and the
> log base 2 of 1000 is about 10, so we can only hear 10 octaves of
> pitch, never more.

***Don't forget, too, that if you start with the lowest C on the
piano and make a circle of fifths, the circle closes exactly the time
you reach the very *highest* C on the piano! Surely, that can't be
just coincidence!

Joseph Pehrson

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

/tuning/topicId_39189.html#39248

> My remarks will come at the end of the three recorded responses by
> Pauline Phillips, Robert Walker and Wall Yester Paulrus: inasmuch as
> I appreciate their thoughtful remarks and believe what they wrote is
> a stepping stone [or note] to the next octave [hope I have punned
> that correctly!]:
>

**Actually, Bill, you can included LINKS in your messages as I just
did above. Just *copy* the text in your browser and *paste* into the
body of the messages. That way we don't have to use bandwidth
repeating the same messages in text over and over!

>
> Question one: what is a "natural" ear? Why do I think I can tell
> perfect pitch? Why do I say, as he does, that so-in-so cannot carry
> a tune in a bucket, and their voice is flat? Does this all mean I
am
> born with something? Or did it develop when I listened to my
> daughter during years taking formal training and playing it around
> me?
>

***Well, quite simply certain people have "perfect pitch"
or "absolute pitch" and others develop a fine sense of "relative
pitch" through practice. "Perfect pitch" is a special gift that lets
one recognize a certain frequency with a specific name. However,
it's not necessarily a *musical* gift. Some people who are not
musicians at all have that ability, and some *musicians* who have it
regard it as a curse... particularly if they want to study "alternate
tunings!"

> Question two: what is "natural" sound in music? Why is it that
there are different scales for different folk around the world? Why
is something "natural" to us, not "natural" to them? Is there
something
> in a culture which predetermines our disposition toward certain
> scales? Or should I ask, toward certain tuning? Or is it different
> systems of music? Or, are these various systems merely offspring of
> a system of sounds natural to Nature?
>

***Well, this has been discussed a *lot* on this forum, and you can
find more in the archives. Paul Erlich has pointed to a lot of
studies that show the preeminence of the OCTAVE or 2:1 ratio as
a "special recognition." Terhardt:

http://www.mmk.ei.tum.de/persons/ter.html

The fifth 3:2 is not far behind in terms of "special significance"
since it is the *next* overtone after the 2:1 in the vibrational
series.

So, in that sense, the 2:1 and 3:2 are "natural" builders or
foundations of music. Reconciling these two ratios in music has
*much* to do with the *entire* study of tuning and temperament!!!

If you string 5 ratios of 3:2 together in a chain you get a
PENTATONIC scale, a basic scale that is seen all over in the world.
So, in that sense, there are certain "natural" scalar developments.

[Sorry to bore the "ole time tuners" with this basic stuff...]

> Question three: Why is "Do, Re, Me, Fa, So, La, Te, Do" taught to
> really young music students?

***This solfege system was invented by Guido d'Arezzo and was a
method to teach singing by showing the syllables on a person's hand!
It was called the "Guidonian Hand..." (seriously...)

http://www.stevenestrella.com/composers/composerfiles/guido1050.html

Why do they emphasize, three times,
> "Me, Me, Me"? Is that Middle C? Is that the "tuning" center point
> of our musical scale? Is that "tuning" center, the piano?

***Well, that's not necessarily true. Certainly the "Me" was not
emphasized so much in Medieval music, in fact, it was carefully
avoided! Only later have some done this. Also, you should be aware
of the fact that many traditional piano tuners start on the "A" below
Middle C. That's how I was taught piano tuning at the University of
Michigan. It was called the "old German method," presumably invented
by "old Germans..."

Does a
> piano get tuned first, then the Orchestra tune to that instrument?
> And why? Or why not?
>

***Pas de tout. Not at all, not a toot! The "tooter" is the OBOE,
which has a VERY STABILIZED pitch. Next time you go to the orchestra
(have you been lately?? :) you will see the OBOE giving the tuning
pitch...

> Question four: What is the starting point, I guess you all would
say, note on a piano? Either where it all began, or a tuner begins?

***See above. Some start on A, some start on C. As I have mentioned
previously, if you start on the LOWERMOST C on the piano and play
fifths, you traverse ONLY ONE circle of fifths upon reaching the
highest C. Surely that's not just coincidence in the construction of
the instrument.

Does
> the scale or system begin at Middle C, or some other note? And if
> so, does the system progress from some Zero point and progress
> infinitely, technically, through the range of the human ear? Or
does
> the system start in the middle, at Middle C, and move down through
> the lower notes, and move up through the upper notes, away from some
> starting point in the middle?
>

***I wouldn't obsess so about a "starting note" if I were you.
Probably music all started with some "singable" note, and I believe
there have been *various* starting pitches since the very earliest
times. Usually they correspond to the primary notes of various
CLEFS... so that would be *G* for the treble clef, and *F* for the
bass clef.

Medieval scholars on this list may here show me wrong, but I believe
*F* and *G* were just as important as starting pitches as *C* in the
very earliest music...

> Thank you, but as a student of music, these simple points have never
> been laid out for me in anything I have ever read about music.
>

***Simple points are *never* laid out in music teaching, certainly
not in the music schools. Why would somebody keep paying more and
more money, if it were all shown clearly at the start??? :)

> Lastly, down the road, I believe it will help me understand the
> celestial music I think inherent in Nature. Maybe, musicians do not
> agree that mathematics is the essence of nature and Nature as I do.
> So, I think we can get there from here, and tuning seems to be the
> key, at least to my way of think right now. Correct me, if you
think I am wrong. Thanks, again, so far.
>

***Monz is your man-iac :) and his website devoted to this. He made
the most GLORIOUS solar system chord that, quite frankly, was one of
the greatest art-internet happenings/art projects, that I have *ever*
experienced. If you haven't heard his chord, already, I would make
haste to do so. Of course, the resemblance to a major triad makes
things particularly pleasing! :)

I would suggest just posting your FINDINGS on this topic on *this*
particular list. Don't hesitate to make liberal use of *LINKS*
rather than writing text or off topic topics over and over.

best,

Joseph Pehrson

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

/tuning/topicId_39189.html#39263

>>
> That might have made experimentation difficult, but keep in mind
> that organs already have many pipes per pitch. Organ builders
> could have easily reduced the number of stops a bit in favor of a
> microtonal scale. The real answer is that the 12-tone system was
> already very entrenched before anybody thought to ask where it
> came from. It happens a lot in bottom-up evolution.
>
> -Carl

***I just wanted to add that I went to the Metropolitan Museum of Art
a few years ago and studied a keyboard from 500 years ago that had
*exactly* the same physical layout as our present-day one. I think
there are examples that go back further than that. So this
Halberstadt layout has really been with us for a long time. It's
really striking seeing it on something as old as that...

J. Pehrson

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

/tuning/topicId_39189.html#39271

> In a message dated 10/6/02 12:00:52 AM Central Daylight Time,
> clumma@y... writes:
>
>
> > keep in mind
> > that organs already have many pipes per pitch. Organ builders
> > could have easily reduced the number of stops a bit in favor of a
> > microtonal scale.
>
> But trained organists usually want more stops to work with, not
less. A
> cathedral in Spain had 14 organs in it. I suspect some at least
were tuned to
> different keys or different tunings.
>
> Pauline

***The thing about *stops* is crucial, since it really is the basic
way an organist changes *dynamics* in a piece! (Character, of
course, too...) I know, since I just recently finished an organ
piece...

J. Pehrson

>>My point was just that there was no reason that organs could
>>not have been microtonal.
>
>I agree. Btu I show in my JI discussion in my JI forum that this
>could've been done without sacrificing stops nor pipe ranks. As
>everything needed to create JI organs was techonology already
>known very long since. The real problem was, no one had invented
>a practical all-key scale that would faithfully play music written
>for tempered scales based on the 12-note octave. But I did invent
>such a scale, and posted its C scale here.

What's the message # of that post? Or could you reproduce the
scale in this thread?

-Carl

In a message dated 10/6/02 5:44:34 PM Central Daylight Time, jpehrson@rcn.com
writes:

> ***The thing about *stops* is crucial, since it really is the basic
> way an organist changes *dynamics* in a piece! (Character, of
> course, too...) I know, since I just recently finished an organ
> piece...
>
> J. Pehrson
>
Exactly. Whether the organist is playing on a Principal/Diapason, Flute,
String or Reed stop, more stops of a similar character need to be available
to increase the loudness. This is best done in most cases by adding
higher-pitched stops. So an organ with merely 5 or 10 stops just won't do it
for most organists!

Pauline

>***I just wanted to add that I went to the Metropolitan Museum of
>Art a few years ago and studied a keyboard from 500 years ago that
>had *exactly* the same physical layout as our present-day one. I
>think there are examples that go back further than that. So this
>Halberstadt layout has really been with us for a long time. It's
>really striking seeing it on something as old as that...

Yup. I think you're right about it going back further, too.
Grove's has an entry on it, a copy of which I have around here
somewhere...

...Ah yes. *puff* Under, "Keyboard", "2. Layout", a woodcut from
Praetorius's 'Syntagma musicum' is shown, depicting the Halberstadt
organ itsbadself, from 1361. Later, it says that the earliest
examples of printed keyboard music are from the early 14th century,
but that instruments and players are know to have existed "long
before".

-Carl

Joseph Pehrson writes, "***Don't forget, too, that if you start with
the lowest C on the piano and make a circle of fifths, the circle
closes exactly the time you reach the very *highest* C on the piano!
Surely, that can't be just coincidence!"

It seems to me, from all I read, that music is mathematical, and
therefore I would have to agree it "can't be just coincidence!"

Thus, precisely, what is the "lowest C on the piano" and what is "the
very *highest* C on the piano"? Can you also give their mathematical
equivalencies? Is not Middle C at 256 Hz? By the way, no one has
told me yet how many zeroes are after the 256?

How many C's make up what you call "a circle of fifths"?

And, as a novice, I really would like to know why you call it "a
circle" of notes, and not a sphere or a linear series or a triangle
or some other "gon"--say a hexagon or other?

I am not trying to be facetious, but really wondering why music uses
the term "circle"? As a mathematician I would tell you that is
injecting the concept of pi, or 3.14etc. into the series of notes.
The reason this is of interest to me, is that Einstein said that all
space was curved, i.e., partakes of pi, and therefore music must too?
Agreed? And if all space is curved and all music is curved, then it
seems that the argument for the Music of the Spheres gains from the
parallel curved structure, does it not?

Obviously, if the Music of the Spheres is real, which I believe it is
as I see the numbers, then this discussion might help me understand
my subject better and allow me to explain it better to others. I did
explain this somewhat in my earlier paper "Bode's Law Explained,"
published in Cycles Bulletin, Vol. XXX, No. 4, 1979, pp. 82-92, which
I have shared some of it with this group already in my earliest
posts. I will share more as warranted, as I do not believe the
earlier cycles bulletins are online yet.
Bill Arnold

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 10/6/02 8:54:26 PM Central Daylight Time,
billarnoldfla@yahoo.com writes:

> I really would like to know why you call it "a
> circle" of notes,

A notes circle is created by tempering the notes theoretical values via the
Equal Temperament 00 series: C-G-D-A-E-B-Gb-Dd-Ab-Eb-Bb-F.

If you start at E 386.316 and make a cycle of 6 just 701.955 fifths, you
arrive at F 500! Which is really E#. Its actual value is 499.999 cents.

Pauline

Yes, I suppose one should really call the 12 equal circle of fifths
a dodecagon - or maybe a star dodecagon. (star polygon = one with
intersecting edges - and if you draw the circle as an octave,
place th epoints on it and join them up then the 12 equal tempered
fifths will form a regular star dodecagon)

Then similarly the 17 19, 31 or whatever fifths of other equal
temperaments could be drawn as star polygons with vertices
on a circle.

So circle of fifths seems reasonably appropriate to me.

Or - star polygon of fifths with arbitrarily many vertices.

Robert

In a message dated 10/6/02 8:54:41 PM Central Daylight Time,
billarnoldfla@yahoo.com writes:

> And, as a novice, I really would like to know why you call it "a
> circle" of notes, and not a sphere or a linear series or a triangle
> or some other "gon"--say a hexagon or other?
>
> I am not trying to be facetious, but really wondering why music uses
> the term "circle"? As a mathematician I would tell you that is
> injecting the concept of pi, or 3.14etc. into the series of notes.
> The reason this is of interest to me, is that Einstein said that all
> space was curved, i.e., partakes of pi, and therefore music must too?
> Agreed? And if all space is curved and all music is curved, then it
> seems that the argument for the Music of the Spheres gains from the
> parallel curved structure, does it not?
>

See my website. There, you will find a lot of answers to a lot of questions
but unfortunately, you'll have even more questions after that. But that's OK.
It's a never ending circle.

Bill Bremmer RPT
Madison, Wisconsin
www.Billbremmer.com

Ed Foote writes, "Braid-White gives the lowest ET C a freq. of
32.703 Hz and the highest C = 4186.009 Hz. Middle C is listed as
261.626 Hz. These numbers are only approx. The tuner that uses less
stretch will have different figures for the extremes. The piano
scales that produce higher inharmonicity will also "expand" these
figures. I also believe that it makes no sense to associate the
pianos range with C's, since the earlier keyboards didn't necessarily
begin and end with C,(today's don't either, they ususally have A as
the lowest note). Indeed, before the 1880's, pianos usually only went
to A7 with the 85 note keyboards. The Romantic era of music, and
perhaps marketing, caused a shift upwards to finalize the scale at C.
The top note is C because of several reasons. One is that it
approaches the human limits of hearing and physical arm length.
Another is that it add a C# as a final note, since musically, C#
didn't usually represent an oft-used tonic and ending on a raised key
would have been mechanically awkward). Another is the point of
diminishing returns, the string length for C8 is approx. 1 7/8" on
ALL pianos, be they concert grands or spinets, and it becomes
physically difficult to create a shorter scale and still leave room
for soundboard under it as well as finding a way for the hammer to
contact it. The bottom of the keyboard reached A0 and ended there
because we can't really hear much under 27 Hz. The extended
Bosendorfer scales are intended to add tension beyond the last
playable note (A0) in order to improve the response of that string.
(the last string on a bridge often suffers tonal deficincies due to
mechanical reasons)."

Wonderful explanation. Thank you. Now, am I correct in this summary
chart? Of course, I accept that my chart is an IDEAL chart of the
frequencies of C OFF AND on the piano, agreed?
IDEAL WAVES OF C NOTES
Also, now, I do know that 256 is arrived at, by extension:
2X1=2 [is this the first octave, of the base C note? OFF PIANO
2x2=4 [is this the second octave?] OFF PIANO
4X2=8 [is this the third octave?] OFF PIANO
8X2=16 [is this the fourth octave?] OFF PIANO
16X2=32 [is this the five octave?] On the piano
32X2=64 [is this the sixth octave?] On the piano
64X2=128 [is this the seventh octave?] On the piano
128X2=256 [is this the eighth octave? Middle C! On the piano
is that why it is called 2^8 and "the eighth"?
Are we now on the same page, mentally in agreement?]

From what you write, I cannot hear 1, 2, 4 and 8 in the chart,
agreed? The lowest C note on the piano is 16X2=32, agreed? Is it
correct to say that the lowest or base C note [not on the piano, but
THEORETICALLY in ideal existence] is 2X1=2 Hz?

Bill Arnold

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:

/tuning/topicId_39189.html#39292

> Joseph Pehrson writes, "***Don't forget, too, that if you start with
> the lowest C on the piano and make a circle of fifths, the circle
> closes exactly the time you reach the very *highest* C on the
piano!
> Surely, that can't be just coincidence!"
>
> It seems to me, from all I read, that music is mathematical, and
> therefore I would have to agree it "can't be just coincidence!"
>

***Well, music *can* be mathematical, but not necessarily in all
cases. Even music *theory* can SOMETIMES be mathematical, but not in
all cases. I guess you can't avoid mathematics much in the science
of *acoustics...*

> Thus, precisely, what is the "lowest C on the piano" and what
is "the very *highest* C on the piano"? Can you also give their
mathematical equivalencies? Is not Middle C at 256 Hz? By the way,
no one has told me yet how many zeroes are after the 256?

***The lowest C is just that: the lowest C. Similarly for the
highest. If you mean *frequency* equivalents in Hertz, look at any
acoustics book like Backus, _Fundamentals of Acoustics_ and they have
the Hertz breakdown for every note of the piano. I don't have my
copy with me at the moment...

>
> How many C's make up what you call "a circle of fifths"?

***Really only *one!* The *next* "C" that one would reach is really
B#! The difference between these two is the famous "Pythagorean
Comma..." I suggest you go to Joe Monzo's informative dictionary if
you want more information on this, Bill:

/tuning/files/dict/pythcom.htm

Actually, I think the chart of fifths could have been a little
clearer. Just start at the lowest C on the piano and keep playing
fifths until you get to the top of the piano. Ummm, first of all, do
you *have* a piano?? That might help.

However, the very *top* "C" you reach is a B#, a Pythagorean comma
HIGHER from the "octave C" created by repeated multiplication of the
fundamental C frequency by 2x.

This is why the fifths must be *tempered* by 1/12 of this comma each
time in the circle.

(Sorry to again bore the ole' tuning readers with this...)

>
> And, as a novice, I really would like to know why you call it "a
> circle" of notes, and not a sphere or a linear series or a triangle
> or some other "gon"--say a hexagon or other?
>

***Probably this term came about because the pitches come back around
to the same place, i.e. 7 octaves equals 12 fifths, provided, that
is, the fifths are *tempered.*

The octave naming scheme is just a *convention*... i.e. C and octave
C are both called "C", D and octave D are called "D" etc. This
testifies to the significance of octave equivalence as a perceptual
identifier... As Gertrude Stein would say: a D is a D is a D.

> I am not trying to be facetious, but really wondering why music uses
> the term "circle"? As a mathematician I would tell you that is
> injecting the concept of pi, or 3.14etc. into the series of notes.
> The reason this is of interest to me, is that Einstein said that all
> space was curved, i.e., partakes of pi, and therefore music must
too?
> Agreed? And if all space is curved and all music is curved, then it
> seems that the argument for the Music of the Spheres gains from the
> parallel curved structure, does it not?
>

***I don't believe the people who coined the term "circle" for the
fifths had pi in mind... sorry to disappoint you... :)

Good luck with your investigations. Maybe Kyle Gann's history of
tuning would help:

http://home.earthlink.net/~kgann/histune.html

I'm sure you can find some other links on musical acoustics from John
Starrett's site:

http://www-math.cudenver.edu/~jstarret/microtone.html

I think Joe Monzo could be a great resource, too, if he's interested,
since he seems to share the same interests.

Good luck!

Joseph Pehrson

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

/tuning/topicId_39189.html#39304

> 128X2=256 [is this the eighth octave? Middle C! On the piano
> is that why it is called 2^8 and "the eighth"?
> Are we now on the same page, mentally in agreement?]
>

***I may be wrong, but I don't think 256 as "Middle C" has anything
to do with the multiplication process you cite... (??)

J. Pehrson

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> Michael J McGonagle wrote:
>
> >Carl Lumma wrote:
> >>Why is the QWERTY keyboard standard?
> >
> > Carl,
> >
> >The reason that I heard was that the other Keyboard option (the
> >Dvorak) allowed the opertor to type faster than the mechinism was
> >able to operate at (the hammers would get tangled up in each
> >other, as they were all trying to hit the same spot). Thus, they
> >needed to provide a "slower" interface. Weather this true or not
> >is really irrelevant with the advent of computers, because there
> >are no moving parts to get all tangled up. (So, be the first one
> >on your block to have a Dvorak Computer!!!).
>
> By the time the Dvorak layout was invented, QWERTY was already
> entrenched and any issues with keys jamming on early machines
> had already been solved. In fact, if you look into it (the best
> I could do, anyway, reading some patents and such), nobody really
> knows why or how the QWERTY layout was chosen.
>
> The maximum speed of human typists doesn't seem to be limited by
> the QWERTY layout, though on average Dvorak may be faster. It's
> certainly easier for beginners to learn, and results in less hand
> strain.

I don't have (or remember) the source of this information, but I once
read that the inventor of the typewriter was responsible for the
QWERTY layout, and it was indeed to slow down the user so the
mechanism wouldn't be as likely to jam. This particular key
arrangement was chosen because it was among the most inefficient
possible -- either an alphabetical order or a random arrangement
would have been more efficient. (It made me a little angry to read
something like this!)

--George

Joseph Pehrson writes, "***Monz is your man-iac :) and his website
devoted to this. He made the most GLORIOUS solar system chord that,
quite frankly, was one of the greatest art-internet happenings/art
projects, that I have *ever* experienced. If you haven't heard his
chord, already, I would make haste to do so. Of course, the
resemblance to a major triad makes things particularly pleasing! :)
I would suggest just posting your FINDINGS on this topic on *this*
particular list. Don't hesitate to make liberal use of *LINKS*
rather than writing text or off topic topics over and over."

I assume you mean Monz's "most GLORIOUS solar system chord" is a
musical rendition?

I have been to Monz's website and am reading there, as well. I have
not found an entry for "most GLORIOUS solar system chord."

I am interested in understanding the chord, mathematically, however.
Thus, do you know if his "most GLORIOUS solar system chord" has been
expressed in notation, so that I could look at it, as well as hear
it?
Has it been expressed as a set of frequency numbers, with the names
of the notes which make up the chord?

Bill Arnold

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:

/tuning/topicId_39189.html#39316

>
> I assume you mean Monz's "most GLORIOUS solar system chord" is a
> musical rendition?
>

***Oh yes, Bill. It's a chord of such cosmic resonance that one is
tempted not to want to ever hear any more music after listening to
it...

> I have been to Monz's website and am reading there, as well. I have
> not found an entry for "most GLORIOUS solar system chord."
>
> I am interested in understanding the chord, mathematically, however.
> Thus, do you know if his "most GLORIOUS solar system chord" has been
> expressed in notation, so that I could look at it, as well as hear
> it?
> Has it been expressed as a set of frequency numbers, with the names
> of the notes which make up the chord?
>

***I believe the data for this chord is right here on our very list!:

/tuning/topicId_11922.html#11923

And the chord itself is right here in our file (solar) system!:

/tuning/files/monz/solarsystem/

***Enjoy, but be careful... it's very potent...

J. Pehrson

>I don't have (or remember) the source of this information, but I
>once read that the inventor of the typewriter was responsible for
>the QWERTY layout, and it was indeed to slow down the user so the
>mechanism wouldn't be as likely to jam. This particular key
>arrangement was chosen because it was among the most inefficient
>possible -- either an alphabetical order or a random arrangement
>would have been more efficient. (It made me a little angry to read
>something like this!)

Heya, George!

Like I say, I believe this is an urban legend:

() I was unable to find evidence for this in the patents.
() Folks on the usenet were unable to find evidence for this.
() QWERTY dosen't seem that much slower, if at all, in the
limit, at least on ditigal keyboards with easy-pushing keys.

You're right that it's worse than alphabetical or random, so that
does require an explanation. One thread on the usenet concerned
itself with jamming caused by adjacent hammers firing sequentially.
I forget the conclusion reached, if any.

-Carl

hi mike,

keyboards with split keys, and sometimes complete systems of 19 and
even 31 notes per octave, were not altogether rare in the 16th and
17th centuries. meantone tuning was standard then, and meantone
tunings can "close the circle" after 19 or 31 notes. here's a picture
of a 31 note keyboard from the 16th century:

http://www.infosys.it/pamparato/ima/ma/ma81/tastiere.html

i've seen plenty of 19 note keyboards on the web, maybe someone else
can find a link for you.

i don't think the church had anything to do with the ultimate
decision to go with 12 note closed systems. composers were hotly
debating this early in the 18th century -- by the end of the 18th
century, european musical culture had pretty much abandoned the idea
of using instruments or fixed tuning systems with more than 12 notes
per octave, the main driving forces being the convenience factor, and
the great music of composers such as bach and beethoven which assumed
a closed system of 12 pitches.

----- Original Message -----
From: "Joseph Pehrson" <jpehrson@rcn.com>

> ***I believe the data for this chord is right here on our very list!:
>
> /tuning/topicId_11922.html#11923
>
>
> And the chord itself is right here in our file (solar) system!:
>
> /tuning/files/monz/solarsystem/
>
> ***Enjoy, but be careful... it's very potent...

So what's the tuning - in ratios? I might have missed it in those links,
but what is it?

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

In a message dated 10/7/02 1:34:10 PM Central Daylight Time,
gdsecor@yahoo.com writes:

> This particular key
> arrangement was chosen because it was among the most inefficient
> possible -- either an alphabetical order or a random arrangement
> would have been more efficient. (It made me a little angry to read
> something like this!)
>
> --George
>
Typewriter keys are arranged in the order the letters on them are used in
print. And the letter rows likewise.The top row is 1, then 2, then 3. Note
that of the 6 vowels 5 are on the top row--e, y, u, i, o.

Pauline

Jay here,
First, what in blazes this hasta do with pianos, tunings, or tuning schools
is quite beyond my ken, but anyway, there's also the explanation that the
qwerty keyboard was devised so that typewriter-challenged salespeople of
the day could write the word "typewriter" without changing rows.
At 06:31 PM 10/7/02 -0000, you wrote:
>--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
>> Michael J McGonagle wrote:
>>
>> >Carl Lumma wrote:
>> >>Why is the QWERTY keyboard standard?
>> >
>> > Carl,
>> >
>> >The reason that I heard was that the other Keyboard option (the
>> >Dvorak) allowed the opertor to type faster than the mechinism was
>> >able to operate at (the hammers would get tangled up in each
>> >other, as they were all trying to hit the same spot). Thus, they
>> >needed to provide a "slower" interface. Weather this true or not
>> >is really irrelevant with the advent of computers, because there
>> >are no moving parts to get all tangled up. (So, be the first one
>> >on your block to have a Dvorak Computer!!!).
>>
>> By the time the Dvorak layout was invented, QWERTY was already
>> entrenched and any issues with keys jamming on early machines
>> had already been solved. In fact, if you look into it (the best
>> I could do, anyway, reading some patents and such), nobody really
>> knows why or how the QWERTY layout was chosen.
>>
>> The maximum speed of human typists doesn't seem to be limited by
>> the QWERTY layout, though on average Dvorak may be faster. It's
>> certainly easier for beginners to learn, and results in less hand
>> strain.
>
>I don't have (or remember) the source of this information, but I once
>read that the inventor of the typewriter was responsible for the
>QWERTY layout, and it was indeed to slow down the user so the
>mechanism wouldn't be as likely to jam. This particular key
>arrangement was chosen because it was among the most inefficient
>possible -- either an alphabetical order or a random arrangement
>would have been more efficient. (It made me a little angry to read
>something like this!)
>
>--George
>
>
>
>
>You do not need web access to participate. You may subscribe through
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>
>
>
>

hi Joe, Bill, and Dave,

----- Original Message -----
From: "Joseph Pehrson" <jpehrson@rcn.com>
To: <tuning@yahoogroups.com>
Sent: Monday, October 07, 2002 1:47 PM
Subject: [tuning] Monz solar system chord

> --- In tuning@y..., Bill Arnold <billarnoldfla@y...> wrote:
>
> /tuning/topicId_39189.html#39316
>
> >
> > I assume you mean Monz's "most GLORIOUS solar system chord" is a
> > musical rendition?
> >
>
> ***Oh yes, Bill. It's a chord of such cosmic resonance that one is
> tempted not to want to ever hear any more music after listening to
> it...
>
>
> > I have been to Monz's website and am reading there, as well. I have
> > not found an entry for "most GLORIOUS solar system chord."
> >
> > I am interested in understanding the chord, mathematically, however.
> > Thus, do you know if his "most GLORIOUS solar system chord" has been
> > expressed in notation, so that I could look at it, as well as hear
> > it?
> > Has it been expressed as a set of frequency numbers, with the names
> > of the notes which make up the chord?
> >
>
> ***I believe the data for this chord is right here on our very list!:
>
> /tuning/topicId_11922.html#11923
>
>
> And the chord itself is right here in our file (solar) system!:
>
> /tuning/files/monz/solarsystem/
>
> ***Enjoy, but be careful... it's very potent...

thanks for posting a link to the old tuning list message, Joe,
but because it has ASCII-formatted tables, it should be viewed
from this link instead, to look correct:
/tuning/topicId_11922.html#11923?expand=1

this message at celestial-tuning gives links to the most
relevant tuning list posts concerning this project:
/celestial-tuning/message/5

also, if you wait long enough, the celestial-tuning group
homepage should open with an mp3 of the Solar System chord.
/celestial-tuning/

-monz
"all roads lead to n^0"

>First, what in blazes this hasta do with pianos, tunings, or
>tuning schools is quite beyond my ken,

My assertion is that it has everything to do with why the piano
keyboard looks the way it does. Think about it.

>but anyway, there's also the explanation that the qwerty keyboard
>was devised so that typewriter-challenged salespeople of the day
>could write the word "typewriter" without changing rows.

How plausible does that explanation sound to you?

-Carl

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

/tuning/topicId_39189.html#39340

> >First, what in blazes this hasta do with pianos, tunings, or
> >tuning schools is quite beyond my ken,
>
> My assertion is that it has everything to do with why the piano
> keyboard looks the way it does. Think about it.
>

***Well, yes, and there are many, many examples in music, I believe,
of various "conventions" that make no real sense. Such customs,
though (take the 5-line staff, for instance) should not be
contraverted, in *my* opinion, since there are more important things
to worry about, and musicians are *accustomed* to the conventions
through years of practice.

BLATANT AD:

That's why 72-tET is such a great scale... :)

Joseph Pehrson

In a message dated 10/8/02 3:32:52 AM Central Daylight Time, clumma@yahoo.com
writes:

> My assertion is that it has everything to do with why the piano
> keyboard looks the way it does. Think about it.
>

In a message dated 10/8/02 3:32:52 AM Central Daylight Time, clumma@yahoo.com
writes:

> My assertion is that it has everything to do with why the piano
> keyboard looks the way it does. Think about it.
>
The reason the organ/harpsichord/piano and other keyboard instruments
lkeyboars ooks the way they do is because Meantone temperament allowed
playing in 5 major keys--0-2#/b with simpler harmony that was later used. it
has nothing to do with typewriters which came centures later.

Pauline

Monz wrote, "<MONZ@J...>
Date: Fri Aug 25, 2000 7:18 pm

http://www.egroups.com/message/tuning/11867

Subject: visualizing harmony, and 'music of the spheres'
Going back to the stuff about Bode's Law: there are indeed
some interesting ratios embedded in the motions of the planets,
but they have to do not with distance but with orbital period.
Hmmm... where Bode's Law was an attempt to portray the 'grand
design' of the whole solar-system, this comparision of orbital
periods *only of adjacent planets* is similar to Paul Erlich's
comparison of *dyadic* harmonic entropy among members of a larger
set (such as a chord or scale).
-monz
http://www.ixpres.com/interval/monzo/homepage.html"

At the suggestion of others, I, Bill Arnold, have gone back and
read messages about Monz's solar system chord, and note that tuning
did, indeed, discuss "Bode's Law" in tuning in 2000.

I have some thoughts I wish to share with all about "Bode's Law,"
and note again that I published in Cycles Bulletin, Vol. XXX, No. 4,
1979, page 82 to 92, "BODE'S LAW EXPLAINED: On the Definitive Directions,
Dimensions and Proportions of Our Solar-Planetary System."

Therefore, the statement above: "...there are indeed
some interesting ratios embedded in the motions of the planets,
but they have to do not with distance but with orbital period,"
is not, accordingly, correct, as I see it inasmuch as the solar-system
planetary distances from the sun, and the orbital periods round the sun,
are in fact proportional, and therefore the distances are equally
related mathematically, and I offered the data in my paper. I
can elaborate if necessary.

I believe this is of interest to musicians and others in related
disciplines, including physics and math, because I do see methematical
relationships between the planets similar to music, and hopefully we
can achive a clear statement on these message boards, mathematically,
and musically, of what is meant by "The Music of the Spheres."

Bill Arnold

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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John Kuefel <kuefel@yahoo.com> writes,

"Date: Mon, 7 Oct 2002 14:34:38 -0700 (PDT)
Subject: Re: [cyclesi] Re: Piano Tuning
Greetings All,
I went down this road about twenty five years ago. The
lowest note on a standard (full keyboard) piano is an
"A" that vibrates at 440 cycles per second. The
stantard full key board has 88 keys (11 octaves). A
"spinnet" has 66 keys. There is one exception: The
Bosendorfer (brand) full grand has an extra octave on
the low end. All of the extra keys are black. On the
Bosendorfer, the low A sounds at 220 cycles per
second.

Working up from the 440 cps "A", each octave
represents a doubling of the frequency of the previous
"A". The eight keys of each octive are divided into
half, quarter, and eighths of that octave. (IN
THEORY!)

I decided to use a clip-on pick-up, a frequency meter,
and o-scope to do a more perfect (according to
Pythagoras) tuning than some piano tuner could
possably do by ear. When I was done, each key sounded
at precisely the right (theoretical) frequency, but
the piano sounded awfull. Here is the trick. There are
micro harmonics that produce the discordant sounds I
obtained. I called the piano tuner. He tuned each key
(other than the botton A) SLIGHTLY sharper (higher)
than the theoretical frequency. The start of the
second octave was about a half cycle higher. of course
this effect produces a high "C" that is several cycles
higher than the theoretical frequency. He explaned
that it had something to do with "fifths" that don't
come out even.

After he tweeked the piano - all was good. The
standard three note chords sounded right.

I hope this experience is usefull.

John Kuefel"

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

Hi, I find this of interest, in the comparison of musical note scales
to the solar-planetary system because there is a shift in the solar-planetary
system as John Kuefel points out in "tuning" a piano. And therefore,
Nature has its own rationale in different systems for why the IDEAL
does not work out in REALITY. As we note that DNA would make people
come out certain ways, mutations in DNA makes the REALITY other than
the IDEAL. That seems to be the nature of reality based upon the ideal!

Today, the press is filled with the story of a new so-called planet
outside the orbit of Pluto, yet it intersects the orbit of Pluto, as
does Pluto's orbit intersect Neptune's. The REALITY of the orbits is
different than the IDEAL. It is the IDEAL data which is the basis from
which we all as practitioners in our disciplines make our choices. And
tuning a piano seems similar to the tuning I see in the solar-planetary
system. I hope we can achieve an understanding via language and math.

Bill Arnold

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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>>My assertion is that it has everything to do with why the piano
>>keyboard looks the way it does. Think about it.
>
>The reason the organ/harpsichord/piano and other keyboard
>instruments lkeyboars ooks the way they do is because Meantone
>temperament allowed playing in 5 major keys--0-2#/b with simpler
>harmony that was later used. it has nothing to do with
>typewriters which came centures later.

As recently discussed, the Halberstadt keyboard predates the
wide-spread use of meantone temperament by something like 200
years.

My assertion is that both share the same evolutionary story; that
the same fundamental forces shaped both the piano keyboard and
the typewriter keyboard.

() To learn either typing or piano playing a human individual
must make an investment of energy.

() In choosing a particular layout in either case the individual
will consider the choice of the layout that was made by
neighboring individuals.

It has been shown that these two ingredients alone are enough to
explain what we see: Neither layout was engineered for the
purpose for which it is currently employed.

In fact, given enough time this setup can destroy all information
about the original purpose of the layout. We just saw how tough
it was to track down the origin of QWERTY (and we still don't
have good references), and Halberstadt would prove a much harder
nut to crack.

-Carl

[I wrote...]
> It has been shown that these two ingredients alone are enough to
> explain what we see:
/.../
> In fact, given enough time this setup can destroy all information

Technical note: The above situation is only one possibility for
such systems, depending on details. Some systems preserve
information about about their initial conditions in an obvious way.
Others are reversible but can be traced back to initial conditions
no faster than by brute force.

-Carl

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> >>My assertion is that it has everything to do with why the piano
> >>keyboard looks the way it does. Think about it.
> >
> >The reason the organ/harpsichord/piano and other keyboard
> >instruments lkeyboars ooks the way they do is because Meantone
> >temperament allowed playing in 5 major keys--0-2#/b with simpler
> >harmony that was later used. it has nothing to do with
> >typewriters which came centures later.
>
> As recently discussed, the Halberstadt keyboard predates the
> wide-spread use of meantone temperament by something like 200
> years.
>
> My assertion is that both share the same evolutionary story; that
> the same fundamental forces shaped both the piano keyboard and
> the typewriter keyboard.
>
> () To learn either typing or piano playing a human individual
> must make an investment of energy.
>
> () In choosing a particular layout in either case the individual
> will consider the choice of the layout that was made by
> neighboring individuals.
>
> It has been shown that these two ingredients alone are enough to
> explain what we see: Neither layout was engineered for the
> purpose for which it is currently employed.
>
> In fact, given enough time this setup can destroy all information
> about the original purpose of the layout. We just saw how tough
> it was to track down the origin of QWERTY (and we still don't
> have good references), and Halberstadt would prove a much harder
> nut to crack.
>
> -Carl

where's my nutcracker . . .

the halberstadt is arranged according to the MOSs of the chain of
fifths.

how'd i do?

>>In fact, given enough time this setup can destroy all information
>>about the original purpose of the layout. We just saw how tough
>>it was to track down the origin of QWERTY (and we still don't
>>have good references), and Halberstadt would prove a much harder
>>nut to crack.
>
>where's my nutcracker . . .
>
>the halberstadt is arranged according to the MOSs of the chain
>of fifths.
>
>how'd i do?

Pretty well. But what does "arranged according to" mean? Of
the 36 keys of 5-, 7-, and 12-tone MOS available, two are made
to stand out visually, at the expense of the others, and none
are transpositionally invariant by mode. I have suggested that
things can be explained in terms of a compromise between key
and mode trans. invariance, but haven't taken a systematic look
at it. I think Dave Keenan has a keyboard-finding spreadsheet
somewhere...

-Carl

I, Bill Arnold, will put my remarks at the end of these inserts,
used here for scholarship and educational purposes, only,
from sources online, separated by double-lines, as follows:
==============================================================================
==============================================================================

Mark Kesti wrote,
"This table assumes A = 440 and equal temperment. The ratio of adjacent notes
is the 12th root of 2, or about 1.05946.

NOTE FREQUENCIES (Hz)
+----------------------------------------------------------------------+
| OCTAVE |
+-----+----------------------------------------------------------------------+
|NOTE | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+-----+----------------------------------------------------------------------+
| A |13.7|27.5| 55.0|110.0|220.0|440.0| 880.0|1760.0|3520.0| 7040.0|14080.0|
|A#/Bb|14.6|29.1| 58.3|116.5|233.1|466.2| 932.4|1864.7|3729.4| 7458.9|14917.8|
| B |15.4|30.9| 61.7|123.5|247.0|493.9| 987.8|1975.7|3951.3| 7902.7|15805.3|
| C |16.4|32.7| 65.4|130.8|261.6|523.3|1046.6|2093.2|4186.5| 8372.9|16745.8|
|C#/Db|17.3|34.6| 69.3|138.6|277.2|554.4|1108.8|2217.7|4435.5| 8871.1|17742.1|
| D |18.4|36.7| 73.4|146.8|293.7|587.4|1174.8|2349.7|4699.5| 9398.9|18797.8|
|D#/Eb|19.4|38.9| 77.8|155.6|311.2|622.4|1244.8|2489.5|4979.1| 9958.1|19161.3|
| E |20.6|41.2| 82.4|164.9|329.7|659.4|1318.8|2637.7|5275.3|10550.6|21101.3|
| F |21.8|43.7| 87.3|174.7|349.3|698.7|1397.3|2794.6|5589.2|11178.4|22356.8|
|F#/Gb|23.1|46.2| 92.5|185.1|370.1|740.2|1480.4|2960.8|5921.8|11843.5|23687.1|
| G |24.4|49.0| 98.0|196.1|392.1|784.3|1568.2|3137.1|6274.1|12548.2|25096.4|
|G#/Ab|26.0|51.9|103.9|207.7|415.5|830.9|1661.9|3323.7|6647.4|13294.8|29589.7|
+-----+----------------------------------------------------------------------+

+----------------------------------------------------------------------+
| OCTAVE |
+-----+----------------------------------------------------------------------+
|NOTE | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+-----+----------------------------------------------------------------------+
| C |16.4|32.7| 65.4|130.8|261.6|523.3|1046.6|2093.2|4186.5| 8372.9|16745.8|
|+-----+----------------------------------------------------------------------+"

http://oyt.oulu.fi/notfreq.html
Michael Kesti Grass Valley Group, Inc. |
mrk@gvgspd.GVG.TEK.COM |
!tektronix!gvgpsa!gvgspd!mrk |
================================================================================
================================================================================

http://www.phy.mtu.edu/~suits/notefreqs.html

Frequencies for equal-tempered scale
A4 = 440 Hz
Speed of sound = 345 m/s
("Middle C" is C4 )

Note Frequency (Hz) Wavelength (cm)

C0 16.35 2100.

C1 32.70 1050.

C2 65.41 527.

C3 130.81 264.

C4 261.63 132.

C5 523.25 65.9

C6 1046.50 33.0

C7 2093.00 16.5

C8 4186.01 8.2

http://www.phy.mtu.edu/~suits/notefreqs.html
===============================================================================
===============================================================================

Frequencies and Ranges
Note Frequency (Hz) Comments Lowest note for: Highest note* for:
C-2
4.09
128'C: C""; CCCCC
Gregg Bailey's 64' PVC subcontrabass clarinet

C-1 8.18 64' C: C'''; CCCC; MIDI#0; lowest organ note Hill organ, Sydney Town Hall,
Sydney AU
C#-1/ Db-1 8.66 C#'''; DDDDb; MIDI#1
D-1 9.18 D'''; DDDD; MIDI#2
D#-1/ Eb-1 9.73 D#'''; EEEEb; MIDI#3
E-1 10.30 E'''; EEEE; MIDI#4
F-1 10.92 F'''; FFFF; MIDI#5
F#-1/ Gb-1 11.56 F#'''; GGGGb; MIDI#6
G-1 12.25 G'''; GGGG; MIDI#7
G#-1/ Ab-1 12.98 G#'''; AAAAb; MIDI#8
A-1 13.75 A'''; AAAA; MIDI#9
Bb-1 14.57 A#'''; BBBBb; MIDI#10 BBBb octocontrabass clarinet
B-1 15.44 B'''; BBBB; MIDI#11
C0 16.35 32' C; C"; CCC; MIDI#12; lowest note written for tuba ("Encounters II" by
William Kraft) large pipe organs, B�sendorfer Imperial Grand Piano
C#0/ Db0 17.32 C#"; DDDb; MIDI#13 Lowest bass guitar strings made
D0 18.35 D"; DDD; MIDI#14
D#0/ Eb0 19.45 D#"; EEEb; MIDI#15 EEEb octocontralto clarinet , slide reed subcontrabass

E0 20.60 E"; EEE; MIDI#16
F0 21.83 F"; FFF; MIDI#17 B�sendorfer Grand Pianos
F#0/ Gb0 23.12 F#"; GGGb; MIDI#18 7/8/9-string bass guitars (additional link)
G0 24.50 G"; GGG; MIDI#19 BBb tuba* , contrabass trombone
G#0/ Ab0 25.95 G#"; AAAb; MIDI#20 BBb contrabass sarrusophone
A0 27.50 A"; AAA; MIDI#21; lowest A on piano piano, extended contrabassoon , Wolfe contra
forte , string octocontrabass
A#0/ Bb0 29.14 A#"; BBBb; MIDI#22 contrabassoon , extended Bb contrabass clarinet , C
contrabass sarrusophone
B0 30.87 B"; BBB; MIDI#23 double-contrabass flute , 5 & 6 string bass
C1 32.70 C'; CC; MIDI#24; 16' C contrabass rackett , string bass with extension, Chapman
Stick� (standard tuning), contrabassophone
C#1/ Db1 34.65 C#'; DDb; MIDI#25 Bb contrabass clarinet (not extended) , Eb contrabass
saxophone , Eb contrabass sarrusophone , tubax
D1 36.71 D'; DD; MIDI#26 reed contrabass , Eb contrabass ophicleide
D#1/ Eb1 38.89 D#'; EEb; MIDI#27 extended Eb contralto clarinet slide reed
subcontrabass
E1 41.20 E'; EE; MIDI#28 string bass, bass guitar, bass harmonica , F contrabass
ophicleide
F1 43.65 F'; FF; MIDI#29 F sub-subcontrabass recorder , harpsichord
F#1/ Gb1 46.25 F#'; GGb; MIDI#30 Eb contralto clarinet (not extended)
G1 49.00 G'; GG; MIDI#31 Great Bass Sordune , Great Bass Shawm
G#1/ Ab1 51.91 G#'; AAb; MIDI#32 Bb bass saxophone, Bb bass sarrusophone
A1 55.00 A'; AA; MIDI#33 Bb bass Ophicleide
A#1/ Bb1 58.27 A#'; BBb; MIDI#34 bassoon, extended Bb bass clarinet
B1 61.74 B'; BB; MIDI#35 contrabass flute , contrabass oboe , C bass ophicleide
C2 65.41 C; MIDI#36; 8' C cello, mandocello, bass shawm (extended), baritone sax (with
low A), alto/tenor rackett , C subcontrabass recorder
C#2/ Db2 69.30 C#; MIDI#37 Bb bass clarinet (not extended), A bass clarinet, baritone
sax (with low Bb), baritone sarrusophone
D2 73.42 D; MIDI#38 F contrabass trumpet *
D#2/ Eb2 77.78 D#; MIDI#39
E2 82.41 E; MIDI#40 Guitar (standard tuning)
F2 87.31 F; MIDI#41 F basset horn, bass crumhorn, F contrabass recorder
F#2/ Gb2 92.50 F#; MIDI#42 Eb alto clarinet
G2 98.00 G; MIDI#43; lowest line of bass clef octave mandolin, euphonium * , bass trumpet
* , tenor shawm (extended range), bass octavin
Gb2/ Ab2 103.83 G#: MIDI#44 Bb tenor sax, Bb tenor sarrusophone, F alto clarinet
A2 110.00 A; MIDI#45; lowest space of bass clef Heckelphone
A#2/ Bb2 116.54 A#; MIDI#46
B2 123.47 B; MIDI#47 bass oboe, bass flute (with low B)
C3 130.81 c; MIDI#48; 4' C viola, mandola, bass flute , tenor crumhorn, tenor shawm
(without extension), great bass recorder , Eb alto sax with low A (rare)
C#3/ Db3 138.59 c#; MIDI#49 Eb alto saxophone, Eb alto sarrusophone
D3 146.83 d; MIDI#50 Bb soprano clarinet, Eb alto horn * , F mezzo Conn-O-Sax,
Heckel-Clarinet
D#3/ Eb3 155.56 d#; MIDI#51 F mezzo-soprano saxophone, English horn (with low Bb) Bb
contrabass sarrusophone*
E3 164.81 e; MIDI#52 English horn, C soprano clarinet bass harmonica
F3 174.61 f; MIDI#53 bass recorder, alto crumhorn, alto shawm
F#3/ Gb3 185.00 f#; MIDI#54 D soprano clarinet
G3 196.00 g; MIDI#55; top space of bass clef violin, alto flute, Eb soprano clarinet, Bb
trumpet, flugelhorn, cornet, mandolin C contrabass sarrusophone*
G#3/ Ab3 207.65 g#; MIDI#56 Bb soprano saxophone, Bb soprano sarrusophone, oboe d'amore,
octavin Eb contrabass saxophone * , tubax
A3 220.00 a; MIDI#57; top line of bass clef flute d'amore in A, oboe (with A extension),
Bb Heckel-clarina
A#3/ Bb3 233.88 a#; MIDI#58 oboe, Bb flute d'amore Eb contrabass sarrusophone *
B3 246.94 b; MIDI#59 C flute (with B foot)
C4 261.63 middle C, 2' C; c'; MIDI#60 C flute (with C foot), Ab sopranino clarinet, tenor
recorder, soprano crumhorn, soprano shawm
C#4/ Db4 277.18 c#'; MIDI#61 Eb sopranino saxophone, Eb sopranino sarrusophone
D4 293.66 d'; MIDI#62 Eb oboe musette, Eb piccolo Heckel-clarina
D#4/ Eb4 311.13 d#'; MIDI#63 Eb soprano flute bass saxophone *
E4 329.63 bottom line of treble clef; e'; MIDI#64 F piccolo heckelphone
F4 349.23 bottom space of treble clef, f', MIDI#65 F treble flute, alto (treble) recorder
bass sarrusophone *
F#4/ Gb4 369.99 f#', MIDI#66
G4 392.00 g', MIDI#67 G treble flute
G#4/ Ab4 415.30 g#', MIDI#68 Bb sopranissimo saxophone Baritone saxophone *
A4 440.00 a', MIDI#69, "tuning A"
A#4/ Bb4 466.16 a#'; MIDI#70 Ab piccolo flute baritone sarrusophone *
B4 493.88 b'; MIDI#71
C5 523.25 1' C; c"; MIDI#72 soprano (descant) recorder
C#5/ Db5 554.36 c#"; MIDI#73
D5 587.32 d"; MIDI#74 C piccolo flute
D#5/ Eb5 622.26 d#"; MIDI#75 Db piccolo flute Tenor Saxophone*
E5 659.26 e"; MIDI#76; top space of treble clef
F5 698.46 f"; MIDI#77; top line of treble clef sopranino recorder Tenor Sarrusophone*
F#5/ Gb5 739.99 f#"; MIDI#78
G5 783.99 g"; MIDI#79
G#5/ Ab5 830.61 g#"; MIDI#80 Alto Saxophone*
A5 880.00 a"; MIDI#81
http://www.contrabass.com/pages/frequency.html

A#5/ Bb5 932.33 a#"; MIDI#82 Alto Sarrusophone*
B5 987.77 b"; MIDI#83
C6 1046.50 c'''; MIDI#84 garklein recorder

* "Nominal range - the range commonly written. Skilled players frequently exceed this
range.

Copyright � 2000-2002 by Grant Green
Last Modified: 10/02/2002 19:39:06
=================================================================================
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
=================================================================================

Here begins my, Bill Arnold's, remarks:

I published Arnold's Law in 1979, as follows:

Bodies_Proportion___Degreed Arcs___Fraction___Ideal Mean**
Or Perimeter

Sun__________0___________0________0____________0
Mercury______1___________3_____1/120______3.14 X10(7th)miles
Venus________2___________6______1/60______6.28
Earth________3___________9______1/40______9.42
Mars_________4__________12______1/30_____12.56
Ceres*_______8__________24______1/15_____25.13
Jupiter_____15__________45______1/8______47.12
Saturn______30__________90______1/4______94.24
Uranus______60_________180______1/2_____188.49
Neptune_____90_________270______3/4_____282.74
Pluto______120_________360______4/4_____376.99

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

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

We can supplement my solar-system planetary data with the C scale note data
from the sources above, accordingly, adding:

Frequencies and Ranges
Note Frequency (Hz) Comments Lowest note for: Highest note* for:
C-2
4.09
128'C: C""; CCCCC
Gregg Bailey's 64' PVC subcontrabass clarinet

C-1 8.18 64' C: C'''; CCCC; MIDI#0; lowest organ note Hill organ, Sydney Town Hall,
Sydney AU

*Source:
Copyright � 2000-2002 by Grant Green
Last Modified: 10/02/2002 19:39:06
=================================================================================
=================================================================================

+----------------------------------------------------------------------+
| OCTAVE |
+-----+----------------------------------------------------------------------+
|NOTE | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
+-----+----------------------------------------------------------------------+
| C |16.4|32.7| 65.4|130.8|261.6|523.3|1046.6|2093.2|4186.5| 8372.9|16745.8|
|+-----+----------------------------------------------------------------------+"

*Source:
http://oyt.oulu.fi/notfreq.html
Michael Kesti Grass Valley Group, Inc. |
mrk@gvgspd.GVG.TEK.COM |
!tektronix!gvgpsa!gvgspd!mrk |
================================================================================
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
================================================================================

Hertz [Hz], according to The American Heritage Dictionary of the English
Language: "symbol Hz, a unit of frequency equal to one cycle per second"

and

Hertzian Wave, same source, "former name for a radio wave"

and

Hertz, same source, "worked on 'electromagnetic phenomena'"
=================================================================================
=================================================================================

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.]

Thus, I, Bill Arnold, seek assistance from musicians who can explain
why the solar-planetary system music is basically octaval, and in the
C Note Scale, except the system IS bodies in curved space, in a perceived
vacuum, and WHAT are Earth at circa 3 and Neptune circa 90, musically expressed
as notes? They are at "fretted" midpoints between their respective-adjacent
bodies, in a planetary sense, and I wonder what they would be, musically
expressed in the C Scale? And, any guess, WHY they are there, musically?
They make perfect physical [in the sense of physics, as expressed mathematically]
sense to me, as I see them: physically and mathematically, and I expressed
in ON THE SPECIAL THEORY OF ORDER.
Bill Arnold

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..., "Carl Lumma" <clumma@y...> wrote:
> >>In fact, given enough time this setup can destroy all information
> >>about the original purpose of the layout. We just saw how tough
> >>it was to track down the origin of QWERTY (and we still don't
> >>have good references), and Halberstadt would prove a much harder
> >>nut to crack.
> >
> >where's my nutcracker . . .
> >
> >the halberstadt is arranged according to the MOSs of the chain
> >of fifths.
> >
> >how'd i do?
>
> Pretty well. But what does "arranged according to" mean? Of
> the 36 keys of 5-, 7-, and 12-tone MOS available, two are made
> to stand out visually, at the expense of the others,

yes, there's a "crystallized favoritism" for the ancient, unaltered
diatonic scale, and as a result, for its complement. it's nice for
beginners to be able to play any diatonic music using only the white
keys. as an unfortunate result, guitarists like me still struggle to
play the piano in keys like B major and G# minor. i would definitely
support a "generalized revolution" . . .

> I think Dave Keenan has a keyboard-finding spreadsheet
> somewhere...

he sure does, but it comes up with a Wilson/Bosanquet-type
arrangement, though of course generalized to cases they probably
would never have thought of. unfortunately, it doesn't seem to be
listed here:

http://www.uq.net.au/~zzdkeena/Music/

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...> wrote:
> --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> > I think Dave Keenan has a keyboard-finding spreadsheet
> > somewhere...
>
> he sure does, but it comes up with a Wilson/Bosanquet-type
> arrangement, though of course generalized to cases they probably
> would never have thought of. unfortunately, it doesn't seem to be
> listed here:
>
> http://www.uq.net.au/~zzdkeena/Music/

Sorry about that. The spreadshete file was there, but no link from the
index page. Fixed now. See the second last link on the above page. You
may need to hit the reload button on your browser. I'm not here.

--- In tuning@y..., "Dave Keenan" <d.keenan@u...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> > --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> > > I think Dave Keenan has a keyboard-finding spreadsheet
> > > somewhere...
> >
> > he sure does, but it comes up with a Wilson/Bosanquet-type
> > arrangement, though of course generalized to cases they probably
> > would never have thought of. unfortunately, it doesn't seem to be
> > listed here:
> >
> > http://www.uq.net.au/~zzdkeena/Music/
>
> Sorry about that. The spreadshete file was there, but no link from
the
> index page. Fixed now. See the second last link on the above page.
You
> may need to hit the reload button on your browser. I'm not here.

thanks to the non-existent man for this. i will reference this
message in a private e-mail to george secor about his paper, when i
get a chance, in which it will figure in point #5 of 5 . . .

> I am an electronics engineer by profession, an amateur pianist and a
> self-taught piano tuner (my own piano and those of a few close friends,
> definitely not commercially). It is in connection with the latter activity
> that I have a question.
>
> With the help of a metronome to adjust the required beats I use a series
> of fourths and fifths to determine the pitches of the centre octave. I
> also refer back to the starting note to confirm whether I have perhaps
> made a mistake along the way. The problem with the finished product is
> that the one and a quarter octave intervals in the middle register do not
> sound very nice. E.g. the F below middle C played with the A(440) above
> middle C. (This inteval can probably be described as a Major 12th). My
> calculations show that these two notes should beat against each other at a
> rate of 7 beats per second, which sounds a bit out of tune to the human
> ear. So it seems my tuning is accurate and the problem lies with the equal
> tempered scale, which is at best a compromise. As one proceeds up the
> scale it becomes worse until the harmonic which causes the dissonance (the
> fifth harmonic of the lower note) becomes too weak to hear. I can "solve"
> the problem by raising the pitch of the lower note very slightly, but this
> has the effect that the octaves in the bass do not sound very pure because
> they are stretched slightly.
>
> The question is, can I "detune" something in order to lessen the effect,
> or do I have to learn to live with the phenomenon?
>
> Andre du Plessis
>
>
DISCLAIMER:
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hi Andre,

--- In tuning@yahoogroups.com, Du Plessis Andre <duPlessisA@d...>
wrote:

> With the help of a metronome to adjust the required beats
> I use a series of fourths and fifths to determine the pitches
> of the centre octave. I also refer back to the starting note
> to confirm whether I have perhaps made a mistake along the
> way. The problem with the finished product is that the
> one and a quarter octave intervals in the middle register
> do not sound very nice. E.g. the F below middle C played
> with the A(440) above middle C. (This inteval can probably
> be described as a Major 12th). My calculations show that
> these two notes should beat against each other at a rate
> of 7 beats per second, which sounds a bit out of tune to
> the human ear. So it seems my tuning is accurate and the
> problem lies with the equal tempered scale, which is at
> best a compromise. As one proceeds up the scale it becomes
> worse until the harmonic which causes the dissonance (the
> fifth harmonic of the lower note) becomes too weak to hear.
> I can "solve" the problem by raising the pitch of the
> lower note very slightly, but this has the effect that the
> octaves in the bass do not sound very pure because they
> are stretched slightly.
>
> The question is, can I "detune" something in order to
> lessen the effect, or do I have to learn to live with
> the phenomenon?

it is standard practice in piano tuning to stretch the
tuning a bit, because the extreme tension of piano strings
causes them to have harmonics which are slightly higher
in pitch than those of most other acoustic instruments.

however, this stretching works the opposite of the way
you suggested: the higher notes are tuned sharper, and
the lower notes are tuned flatter.

i made of graph of this which is here:
/tuning/files/monz/rhodes.jpg

when i originally posted that to this list, Allan Myhara
used calculus to find a formula for it. you can read
the final correct formula here:
/tuning/topicId_13830.html#13879

and go backwards ("Up Thread") to trace the whole discussion.

of course, you're always free to use tunings other than
12-tone equal-temperament (which we abbreviate 12-et
around here). good possibilities would be a form of
meantone or a 12-tone well-temperament.

there's endless discussion of these things on this list.

there's also list-member and pro piano-tuner Ed Foote,
who will probably answer you much better than i have.

-monz

Hi Andre and Monz,

Andre, I think you are referring to the major third, e.g.
from F to A, rather than stretched octaves.

Major thirds on an equal tempered piano are a bit rough
sounding and that's just the way it is, it is a compromise
to allow unlimited modulation and have the tuning the same
in all keys. You need to lower the A by 15 cents or so
(a twelfth tone approximately) to get it in tune.

But then that puts other notes out of tune, for instance
if you try and get F A C# in tune as F A, A C# both
pure major thirds, then the C# F interval will be
way out of tune (it's out of tune
by a diesis - the ratio of frequencies
for a pure major third is 5/4, and you can calculate that
the diesis is 125/128, or 41.059, cents - nearly half a
semitone)

There is nothing one can do about that
if you want the other major thirds pure (i.e. unbeating).

The C G interval of course is impure too, and if you wanted
that pure you would tune it so that it doesn't beat
at all, and then you have the Pythagorean tuning,
which is fairly close to equal temperament, with
all the fifths pure, and the thirds even sharper than
they are in twelve equal.

Quarter comma meantone is a system in which two in every
three major thirds is pure, which is the most possible
and the major thirds in the most commonly used keys are pure
- but it has a fifth flatter than the pure one and one
wolf fifth which is so sharp that it makes its key
unplayable for normal diatonic music.

I'm sure others will say more about practicalities
of piano tuning and suitable temperaments
to try, and I don't know anything about that
but perhaps this background info on a couple of newbie
tuning concepts will be helpful to have.

Robert

Monz: it is standard practice in piano tuning to stretch the
tuning a bit, because the extreme tension of piano strings
causes them to have harmonics which are slightly higher
in pitch than those of most other acoustic instruments.

however, this stretching works the opposite of the way
you suggested: the higher notes are tuned sharper, and
the lower notes are tuned flatter.

Andre: I think the stretching (of the octaves) occurs naturally when tuning
by ear. The problem I have is with the Maj 10th (Sorry, I referred to it as
a Maj 12th in the previous post) which is already a stretched interval, to
such an extent that it has quite a fast beat. I can raise the pitch of the
lower note (In this example the F) slightly, but then there is the danger of
distorting the temperament.

Robert: Andre, I think you are referring to the major third, e.g.
from F to A, rather than stretched octaves.

Major thirds on an equal tempered piano are a bit rough
sounding and that's just the way it is, it is a compromise
to allow unlimited modulation and have the tuning the same
in all keys. You need to lower the A by 15 cents or so
(a twelfth tone approximately) to get it in tune.

Andre: I do not have a problem with the roughness of the maj 3rds, as a
matter of fact, I use that feature to confirm the accuracy of my tuning. The
interval under discussion is the maj 10th, mostly in tne middle register.

Andre

DISCLAIMER:
This message and any attachments are confidential and intended solely for
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liability whatsoever for any loss, whether it be direct, indirect or
consequential, arising from this e-mail, nor for any consequence of its use
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