how about this for a pattern

Howabout this for a pattern

http://www.grand-illusions.com/articles/tune_directory/

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> Howabout this for a pattern
>
> http://www.grand-illusions.com/articles/tune_directory/
>
> -Carl

Wow, Parsons's idea is really ingenious.

I have either the Barlow & Morgenstern book or one
exactly like it. I should find it and keep it handy,
for those times when i get an "earworm" (literal English
tranlation for the useful German term describing a tune
that gets stuck in your mind and won't go away) that i
can't identify. Used to use it a lot when i was a kid.

-monz
http://tonalsoft.com
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > Howabout this for a pattern
> >
> > http://www.grand-illusions.com/articles/tune_directory/
> >
> > -Carl
>
>
> Wow, Parsons's idea is really ingenious.
>
> I have either the Barlow & Morgenstern book or one
> exactly like it. I should find it and keep it handy,
> for those times when i get an "earworm" (literal English
> translation for the useful German term describing a tune
> that gets stuck in your mind and won't go away) that i
> can't identify. Used to use it a lot when i was a kid.
>
>
> -monz
>

... There is no book exactly like Barlow / Morgenstern except B / M
itself.

I remember reading an article about encoding music in searchable form.
Trouble is, some perfectly good music doesn't start with a readily
identifiable or notatable linear theme. And do you include ornaments
and grace notes...

The online equivalent is themefinder.org which offers pitch, interval,
degree, Parsons-style and other search modes.

And you never know how thorough they have been. If your melodic itch
comes from the middle of a movement you may be sunk.

Can anyone help with this Bach organ piece I heard in Dresden - I
notate it in A minor, but not sure of its actual key.

A G# A E A E B A c B c A c A d A etc.

~~~T~~~

> > > Howabout this for a pattern
> > >
> > > http://www.grand-illusions.com/articles/tune_directory/
> >
> > Wow, Parsons's idea is really ingenious.
> >
> > I have either the Barlow & Morgenstern book or one
> > exactly like it.
>
> ... There is no book exactly like Barlow / Morgenstern
> except B / M itself.
>
> I remember reading an article about encoding music in searchable
> form.

I was referring to:

"UU is the most popular opening, used in 23% of the time,
while *DR is the least popular, used in only 2% of themes.
And that this held true whether you looked at famous
classical composers, pop musicians, and even 240 Teton-Sioux
songs from North America fitted the pattern."

> The online equivalent is themefinder.org which offers pitch,
> interval, degree, Parsons-style and other search modes.

Good resource; thanks for the link. Interestingly, another
of their projects, which tests whether listeners can identify
a quartet movement as being written by either Mozart or
Haydn, shows that the following two movements are the most
'Mozart' in Mozart's output (about 70-75% recognized them
correctly)

k155-02.mid
k590-01.mid

And for Haydn

op76n3-02.mid
op33n3-02.mid

> Can anyone help with this Bach organ piece I heard in
> Dresden - I notate it in A minor, but not sure of its
> actual key.
>
> A G# A E A E B A c B c A c A d A etc.

How are you doing octaves here? And what does lowercase
mean?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
>
>
> > Can anyone help with this Bach organ piece I heard in
> > Dresden - I notate it in A minor, but not sure of its
> > actual key.
> >
> > A G# A E A E B A c B c A c A d A etc.
>
> How are you doing octaves here? And what does lowercase
> mean?
>
> -Carl
>

One question answers the other. Helmholtz notation. And a typo - it
should read

A G# A E A E B E c B c A c A d A

... if you haven't recognised it yet there's probably no hope.

~~~T~~~

> > > Can anyone help with this Bach organ piece I heard in
> > > Dresden - I notate it in A minor, but not sure of its
> > > actual key.
> > >
> > > A G# A E A E B A c B c A c A d A etc.
> >
> > How are you doing octaves here? And what does lowercase
> > mean?
>
> One question answers the other. Helmholtz notation. And a typo - it
> should read
>
> A G# A E A E B E c B c A c A d A

It doesn't answer whether G# is lower or higher than A.
One wonders if this Helmholtz fellow knew what he was doing.

-Carl

Carl Lumma wrote:

>> A G# A E A E B E c B c A c A d A
> > It doesn't answer whether G# is lower or higher than A.
> One wonders if this Helmholtz fellow knew what he was doing.

You know, it does seem strange that octaves traditionally start with C instead of A. I wonder how that got started? Logically it seems that A - G should be one octave and the break between octaves should go between G and A.

(In case anyone's still wondering, this is the "Dorian" Toccata and Fugue in D minor, transposed to A minor.)

This does bring up an interesting question regarding extra nominals for microtonal scales. If you have a note between B and C that has its own name (as in my notation for blackwood, bug, kleismic, miracle, negri, and orwell temperaments among others), does it go in the same octave with the B below or the C above? Does it depend on whether the note is closer to B or closer to C?

It might make sense just to start the octave with C, but one way to notate the pitch between B and C is as a C with a half-flat symbol. This could cause all sorts of confusion if this note goes with the lower octave. So I'm thinking this note should go in the same octave with the C above.

> >> A G# A E A E B E c B c A c A d A
> >
> > It doesn't answer whether G# is lower or higher than A.
> > One wonders if this Helmholtz fellow knew what he was doing.
>
> You know, it does seem strange that octaves traditionally start

It seems like *you* know, but I still don't.

-Carl

hi Herman, Carl, et al,

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Carl Lumma wrote:
>
> >> A G# A E A E B E c B c A c A d A
> >
> > It doesn't answer whether G# is lower or higher than A.
> > One wonders if this Helmholtz fellow knew what he was doing.
>
> You know, it does seem strange that octaves traditionally
> start with C instead of A. I wonder how that got started?
> Logically it seems that A - G should be one octave and
> the break between octaves should go between G and A.

It *was* that way originally, and for a long time.

That should be rather obvious: in employing the natural
ordering of the alphabet to represent musical nominals,
the reference pitch would naturally be named "A" and
all the others follow until the octave-equivalence is
reached.

There was a standard set of pitches in European music-theory
ever since the time of the ancient Greeks (c.400 BC). The
entire set is known today as the "Perfect Immutable System"
(PIS):

http://tonalsoft.com/enc/p/pis.aspx

The PIS covers a 2-octave range, but was constructed on
the principle of tetrachordal similarity (i.e., "perfect-4th
equivalence"), and not on recognition of octave-equivalence.
This fact caused the note which we now call "Bb" to also
be a part of the system (... that's something i've discussed
in detail before and won't go into here). The important
point is that the entire PIS is based on one reference
pitch, which was called _mese_ {"middle") and which was
exactly in the middle of the pitch-range.

During the Greek and Roman era, the notes could be tuned
to a wide variety of different pitches, resulting in the
various different genera. After the German invasions (late
400s AD), use of the chromatic and enharmonic genera died
out, leaving only the diatonic.

http://tonalsoft.com/enc/d/diatonic-genus.aspx

Boethius (c.505) had used Roman letters to represent
pitches in many of his diagrams, but he did not recognize
any kind of pitch-equivalence in his naming schemes, and
often used the entire alphabet and then continued from
the beginning using double letters. But he used the Roman
letters mainly to designate points on his diagrams, in a
geometric sense, and so the order of the letters generally
does not even reflect pitch order.

It was during the time of Charlemagne (c.800) that our
modern music-theory originated. The Frankish theorists
did not read Greek, and struggled to find ways to represent
musical pitches in writing, utilizing what they knew of the
ancient PIS (diatonic genus only). Also, at this point,
the only standard tuning in European theory became 3-limit
"pythagorean" tuning.

In the late 900s, the pseudo-Odo _Dialogus_ was the first
treatise to use the Roman alphabet to represent pitches
in pitch order. The ascending order was chosen, even tho
the ancient Greeks actually reckoned their scales in
descending order, and the reference pitch _mese_ obviously
became "A". I discuss some of this in a post from last year:

/tuning/topicId_62290.html#62442

Thus, the entire PIS was written:

A B C D E F G a b c d e f g aa

_mese_ was "a", and the "b" above it was either a semitone
or whole-tone above "a" (i.e., either a B or Bb), depending
on the tetrachord employed. And it stayed this way for
about 600 years.

Now, about the shift to C ...

It was during the centuries from about 1300 to 1500 that
shift ocurred. In part, it was because of the increasing
use of keyboard instruments, and ultimately, it was because
of the recognition of prime-factor 5 as an element in the
ratios of musical harmony, i.e., "5-limit JI".

The standard 7-white/5-black keyboard appeared in this
form for the first time in the Halberstadt organ in 1361.
From that time on, it became fairly common for musicians
to describe as "A" the note we now know as "C". This is
obviously because, with the ascending orientation, the
scale which we today call C-major, where the "do re mi fa
sol la ti" appears on the white keys, was felt to be the
most natural one, thus its tonic was often called "A".
But the older nomenclature persisted, and is the one
which ultimately survived as the one we still use today.

The earliest mention of 5-limit ratios in post-classical
theory are from Theinred of Dover (1100s) and Walter
Odington (1300s), both in England. The first theorist to
give measurements for a monochord which form a true
5-limit basis for a musical tuning was Ramos:

http://tonalsoft.com/monzo/ramos/ramos.htm

(and even at this late date we can see Ramos using letters
to represent geometric points on his diagrams, just as with
Boethius -- this time recognizing pitch order but still
not recognizing octave-equivalence.)

Within about 70 years, this led to Zarlino's 1558 treatise
_Le institutione harmoniche_, which laid the foundation
for modern music-theory:

http://www.sonic-arts.org/monzo/zarlino/1558/zarlino1558-2.htm

By this time, the practice of calling the "do" of the
major scale "A" had pretty much died out, and so it was
established as "C".

Zarlino stated that all consonances are based on the
_senario_, ratios using only the numbers 1,2,3,4,5,6.
He defined the PIS (diatonic genus only) in 5-limit terms
as illustrated on the following lattice:

(horizontal axis = powers of 3, vertical axis = powers of 5;
to view correctly on the Yahoo web interface, click on
"Option" under the date at the right of this message, then
click "Use Fixed Width Font".)

.....| -1 ..... 0 ...... 1 ..... 2 ..... 3
-----|--------------------------------------
.. 0 |. d' .. A,a,aa .. E,e ... B,h
|
. -1 |. b .... F,f .... C,c ... G,g ... D,d

In ascending pitch order:
A, B, C, D, E, F, G, a, b, h, c, d, d', e, f, g, aa

(I use "d'" to distinguish that note from "d", but
Zarlino didn't -- the proper tuning would be evident
from the context of which tetrachord the note appeared in.
Also note the "b" for Bb and "h" for B-natural.)

Note that Zarlino is using "A" as his 1/1!

Within this limited pitch universe, Zarlino posited the
C-major scale as the "natural" one, and the lattice
demonstrates that its three main chords, which we today
would call I, IV, and V, are all triads with 4:5:6
proportions, the most consonant possible in the 5-limit.

Zarlino's theory was tremendously influential, and formed
the basis for the subsequent use of "C" as the reference
pitch.

Glearean came shortly after Zarlino and actually rearranged
the system of modes so that C was made the reference note.
But largely due to Zarlino's theory, the whole system of
modes had by 1700 morphed into the "common-practice"
major/minor system of keys.

In my book _JustMusic: A New Harmony_:

http://tonalsoft.com/monzo/book/book.htm

i put forth the thesis that it is the duality of possible
rational interpretations of JI tuning systems which led
to the transformation of the old modal system into the
major/minor key system.

For example, on the lattice above which shows Zarlino's
system, the major-7th chord C-E-G-h could be interpreted
either as the otonal proportions 8:10:12:15 or as the
utonal proportions 1/(15:12:10:8). Because the numbers
here are exactly the same in either interpretation, i
would posit that either interpretation is equally valid.

However, for the simpler triads which were the basis of
both Zarlino's theory and the whole era of classical music,
the C-major triad would be otonal 4:5:6 and utonal 1/(15:12:10);
conversely, the E-minor triad would be otonal 10:12:15 and
utonal 1/(6:5:4). Obviously, the otonal interpretation is
better for major triads, and utonal is better for minor.

This led to the simplification of classification, so that
the number of modes was reduced to only two: major or minor.

Anyway, the major scale was felt to be the overriding
basis of musical pitch resources, and because the C-major
scale is the one which has no accidentals and appears in
straightforward fashion on the white keys of the keyboard,
the entire gamut of pitches was standardized so that its
nomenclature defines octaves ascending as C D E F G A B.

-monz
http://tonalsoft.com
Tonescape microtonal music software

This is an excellent summary on the music theory of European Dark Ages that
I would like to copy-paste directly into my thesis (with proper references
of course), if it is alright with you dear monz.

Cordially,
Oz.

----- Original Message -----
From: "monz" <monz@tonalsoft.com>
To: <tuning@yahoogroups.com>
Sent: 05 Temmuz 2006 �ar�amba 12:11
Subject: [tuning] how the reference pitch changed from A to C (was: how
about this for a pattern)

> hi Herman, Carl, et al,
>
> --- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> >
> > Carl Lumma wrote:
> >
> > >> A G# A E A E B E c B c A c A d A
> > >
> > > It doesn't answer whether G# is lower or higher than A.
> > > One wonders if this Helmholtz fellow knew what he was doing.
> >
> > You know, it does seem strange that octaves traditionally
> > start with C instead of A. I wonder how that got started?
> > Logically it seems that A - G should be one octave and
> > the break between octaves should go between G and A.
>
>
> It *was* that way originally, and for a long time.
>
> That should be rather obvious: in employing the natural
> ordering of the alphabet to represent musical nominals,
> the reference pitch would naturally be named "A" and
> all the others follow until the octave-equivalence is
> reached.
>
> There was a standard set of pitches in European music-theory
> ever since the time of the ancient Greeks (c.400 BC). The
> entire set is known today as the "Perfect Immutable System"
> (PIS):
>
> http://tonalsoft.com/enc/p/pis.aspx
>
> The PIS covers a 2-octave range, but was constructed on
> the principle of tetrachordal similarity (i.e., "perfect-4th
> equivalence"), and not on recognition of octave-equivalence.
> This fact caused the note which we now call "Bb" to also
> be a part of the system (... that's something i've discussed
> in detail before and won't go into here). The important
> point is that the entire PIS is based on one reference
> pitch, which was called _mese_ {"middle") and which was
> exactly in the middle of the pitch-range.
>
> During the Greek and Roman era, the notes could be tuned
> to a wide variety of different pitches, resulting in the
> various different genera. After the German invasions (late
> 400s AD), use of the chromatic and enharmonic genera died
> out, leaving only the diatonic.
>
> http://tonalsoft.com/enc/d/diatonic-genus.aspx
>
> Boethius (c.505) had used Roman letters to represent
> pitches in many of his diagrams, but he did not recognize
> any kind of pitch-equivalence in his naming schemes, and
> often used the entire alphabet and then continued from
> the beginning using double letters. But he used the Roman
> letters mainly to designate points on his diagrams, in a
> geometric sense, and so the order of the letters generally
> does not even reflect pitch order.
>
> It was during the time of Charlemagne (c.800) that our
> modern music-theory originated. The Frankish theorists
> did not read Greek, and struggled to find ways to represent
> musical pitches in writing, utilizing what they knew of the
> ancient PIS (diatonic genus only). Also, at this point,
> the only standard tuning in European theory became 3-limit
> "pythagorean" tuning.
>
> In the late 900s, the pseudo-Odo _Dialogus_ was the first
> treatise to use the Roman alphabet to represent pitches
> in pitch order. The ascending order was chosen, even tho
> the ancient Greeks actually reckoned their scales in
> descending order, and the reference pitch _mese_ obviously
> became "A". I discuss some of this in a post from last year:
>
> /tuning/topicId_62290.html#62442
>
> Thus, the entire PIS was written:
>
> A B C D E F G a b c d e f g aa
>
> _mese_ was "a", and the "b" above it was either a semitone
> or whole-tone above "a" (i.e., either a B or Bb), depending
> on the tetrachord employed. And it stayed this way for
> about 600 years.
>
> Now, about the shift to C ...
>
> It was during the centuries from about 1300 to 1500 that
> shift ocurred. In part, it was because of the increasing
> use of keyboard instruments, and ultimately, it was because
> of the recognition of prime-factor 5 as an element in the
> ratios of musical harmony, i.e., "5-limit JI".
>
> The standard 7-white/5-black keyboard appeared in this
> form for the first time in the Halberstadt organ in 1361.
> >From that time on, it became fairly common for musicians
> to describe as "A" the note we now know as "C". This is
> obviously because, with the ascending orientation, the
> scale which we today call C-major, where the "do re mi fa
> sol la ti" appears on the white keys, was felt to be the
> most natural one, thus its tonic was often called "A".
> But the older nomenclature persisted, and is the one
> which ultimately survived as the one we still use today.
>
>
> The earliest mention of 5-limit ratios in post-classical
> theory are from Theinred of Dover (1100s) and Walter
> Odington (1300s), both in England. The first theorist to
> give measurements for a monochord which form a true
> 5-limit basis for a musical tuning was Ramos:
>
> http://tonalsoft.com/monzo/ramos/ramos.htm
>
> (and even at this late date we can see Ramos using letters
> to represent geometric points on his diagrams, just as with
> Boethius -- this time recognizing pitch order but still
> not recognizing octave-equivalence.)
>
> Within about 70 years, this led to Zarlino's 1558 treatise
> _Le institutione harmoniche_, which laid the foundation
> for modern music-theory:
>
> http://www.sonic-arts.org/monzo/zarlino/1558/zarlino1558-2.htm
>
> By this time, the practice of calling the "do" of the
> major scale "A" had pretty much died out, and so it was
> established as "C".
>
> Zarlino stated that all consonances are based on the
> _senario_, ratios using only the numbers 1,2,3,4,5,6.
> He defined the PIS (diatonic genus only) in 5-limit terms
> as illustrated on the following lattice:
>
> (horizontal axis = powers of 3, vertical axis = powers of 5;
> to view correctly on the Yahoo web interface, click on
> "Option" under the date at the right of this message, then
> click "Use Fixed Width Font".)
>
> .....| -1 ..... 0 ...... 1 ..... 2 ..... 3
> -----|--------------------------------------
> .. 0 |. d' .. A,a,aa .. E,e ... B,h
> |
> . -1 |. b .... F,f .... C,c ... G,g ... D,d
>
> In ascending pitch order:
> A, B, C, D, E, F, G, a, b, h, c, d, d', e, f, g, aa
>
> (I use "d'" to distinguish that note from "d", but
> Zarlino didn't -- the proper tuning would be evident
> from the context of which tetrachord the note appeared in.
> Also note the "b" for Bb and "h" for B-natural.)
>
> Note that Zarlino is using "A" as his 1/1!
>
> Within this limited pitch universe, Zarlino posited the
> C-major scale as the "natural" one, and the lattice
> demonstrates that its three main chords, which we today
> would call I, IV, and V, are all triads with 4:5:6
> proportions, the most consonant possible in the 5-limit.
>
> Zarlino's theory was tremendously influential, and formed
> the basis for the subsequent use of "C" as the reference
> pitch.
>
> Glearean came shortly after Zarlino and actually rearranged
> the system of modes so that C was made the reference note.
> But largely due to Zarlino's theory, the whole system of
> modes had by 1700 morphed into the "common-practice"
> major/minor system of keys.
>
>
> In my book _JustMusic: A New Harmony_:
>
> http://tonalsoft.com/monzo/book/book.htm
>
> i put forth the thesis that it is the duality of possible
> rational interpretations of JI tuning systems which led
> to the transformation of the old modal system into the
> major/minor key system.
>
> For example, on the lattice above which shows Zarlino's
> system, the major-7th chord C-E-G-h could be interpreted
> either as the otonal proportions 8:10:12:15 or as the
> utonal proportions 1/(15:12:10:8). Because the numbers
> here are exactly the same in either interpretation, i
> would posit that either interpretation is equally valid.
>
> However, for the simpler triads which were the basis of
> both Zarlino's theory and the whole era of classical music,
> the C-major triad would be otonal 4:5:6 and utonal 1/(15:12:10);
> conversely, the E-minor triad would be otonal 10:12:15 and
> utonal 1/(6:5:4). Obviously, the otonal interpretation is
> better for major triads, and utonal is better for minor.
>
> This led to the simplification of classification, so that
> the number of modes was reduced to only two: major or minor.
>
> Anyway, the major scale was felt to be the overriding
> basis of musical pitch resources, and because the C-major
> scale is the one which has no accidentals and appears in
> straightforward fashion on the white keys of the keyboard,
> the entire gamut of pitches was standardized so that its
> nomenclature defines octaves ascending as C D E F G A B.
>
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>
>

--- In tuning@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> Carl Lumma wrote:
>
> >> A G# A E A E B E c B c A c A d A
> >
> > It doesn't answer whether G# is lower or higher than A.
> > One wonders if this Helmholtz fellow knew what he was doing.
>
> You know, it does seem strange that octaves traditionally start with C
> instead of A. I wonder how that got started? Logically it seems that
A -
> G should be one octave and the break between octaves should go
between G
> and A.
>
> (In case anyone's still wondering, this is the "Dorian" Toccata and
> Fugue in D minor, transposed to A minor.)

Yes, I was still wondering! Also wondering whether I would have to
start teaching Helmholtz notation to a member of this group... so thanks!

Are there any themes starting with skips of a major seventh up and down??

~~~T~~~

Tom Dent wrote:

> Yes, I was still wondering! Also wondering whether I would have to
> start teaching Helmholtz notation to a member of this group... so thanks!

Perhaps a note about the source of that name would be in order.

klaus

Hi Oz,

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> This is an excellent summary on the music theory of
> European Dark Ages that I would like to copy-paste
> directly into my thesis (with proper references
> of course), if it is alright with you dear monz.

Of course -- paste away!

-monz
http://tonalsoft.com
Tonescape microtonal music software

> Yes, I was still wondering! Also wondering whether I would have to
> start teaching Helmholtz notation to a member of this group... so
> thanks!

Ok, I'll look it up. And I'll remember your attitude the next
time you ask some misguided question about tuning theory.

-Carl