Re: [tuning] Digest Number 1108

Joseph Pehrson wrote:

"I do have a question, though. Why does the "common" system of
enharmonic sharps and flats in notation end up working for 19??

I think it's just chance. There is no basis in the enharmonic system
for 19, is there... or is there...

Regardless. I, personally, feel such a notational system is poor,
since is goes against ALL musicianship "basic training." Yes, and I
mean 12-tET."

You've got your history of notation backwards. The staff notation and the
system of 7 nominals with the # and b modifications as one moves further out on
a series of fifths is pythagorean in origin, but has proven to work in the
successive meantone and 12tet eras as well. When the fifths are larger Just
intervals (or larger than 12tet), the sharps will be higher than the neighboring
flats, when the fifths are 12tet intervals, they will have the same size, and
when they are smaller than the 12tet intervals, like meantone, 19tet or 31 tet,
the sharps will be lower than the fifths.

A lot of confusion is due to the use of the term "enharmonic equivalence" in
musical training, which is an historically awful misnomer, and leaves the
ancient enharmonic genus without the independent dignity it deserves. Also, an
over investment in training 12tet equivalences makes it more difficult to learn
to play meantone repertoire, where equivalence is not assumed (take a look at
the hand horn chart in the New Grove, or at Berlioz's chart for the concertina
in his orchestration treatise for examples using meantone assumptions (i.e. #
lower than b)in standard repertoire).

One of the sweet features about using the pythagorean notation for 19tet, for
example, is that one can compose in 19tet using the seven nomimals and sharps
and flats, and then prepare a rehearsal score for players more comfortable with
12tet by just adding cent deviations from the same notation, but now reading it
as 12tet.

I.e

19tet score 12tet score
C C
C# C# -37
Db Db +26
D D -11
D# D# -47
Eb Eb +16
E E -21
E#/Fb E#-58 or Fb +42
F F +5
F# F# -32
Gb Gb +32
G G -5
G# G# -32
Ab Ab +21
A A -16
A# A# -53
Bb Bb +11
B B-26
B#/Cb B#-63 or Cb +37

Daniel Wolf

Daniel Wolf wrote:

> 19tet score 12tet score
> C C
> C# C# -37
> Db Db +26
> D D -11
> D# D# -47
> Eb Eb +16
> E E -21
> E#/Fb E#-58 or Fb +42
> F F +5
> F# F# -32
> Gb Gb +32
> G G -5
> G# G# -32
> Ab Ab +21
> A A -16
> A# A# -53
> Bb Bb +11
> B B-26
> B#/Cb B#-63 or Cb +37

G# should be -42. (That's much better than my error rate of 1 in 2.)

It's more symmetrical if you hold D constant instead of C. Let's see
if I can get that to work.

19= 12= +/- cents
-----------------------
D D
D# D#-37
Eb Eb+26
E E-11
E#/Fb E#-47 or Fb+53
F F+16
F# F#-21
Gb Gb+42
G G+5
G# G#-32
Ab Ab+32
A A-5
A# A#-42
Bb Bb+21
B B-16
B#/Cb Cb+47 or B#-53
C C+11
C# C#-26
Db Db+37
D D

Graham

--- In tuning@y..., "Daniel Wolf" <djwolf1@m...> wrote:

/tuning/topicId_18699.html#18699

> You've got your history of notation backwards.

Thanks, Daniel Wolf, for your commentary. Actually, I found your
post the most interesting of all, since it really put things in a
"larger picture!"

So basically, as I mentioned in my reply to Graham Breed, a system of
1/3 syntonic comma fifths at approximately 695 cents value each will
create a 19-tone scale... (??) If I'm getting this.

So, certainly, the enharmonics are part of the larger picture,
including the meantones. Wow. Why don't they teach these important
concepts in music school??

Regarding your "interpretation" of the 19-tET enharmonic notation
into 12-tET, the only problem I have is that it really seems to
"compound" matters by going from what I see as an unfamiliar notation
BACK into a familiar one with unfamiliar elements... like different
pitches for the enharmonics.

At this moment, it seems more direct for me to just use the ORIGINAL
12-tET (no enharmonics) with cents deviation values, but thank you so
much for the helpful, and rather astonishing...for me anyway...
overview!

_________ _____ _____ _
Joseph Pehrson

--- In tuning@y..., "Daniel Wolf" <djwolf1@m...> wrote:

/tuning/topicId_18699.html#18699

>
> I.e
>
> 19tet score 12tet score
> C C
> C# C# -37
> Db Db +26
> D D -11
> D# D# -47
> Eb Eb +16
> E E -21
> E#/Fb E#-58 or Fb +42
> F F +5
> F# F# -32
> Gb Gb +32
> G G -5
> G# G# -42
> Ab Ab +21
> A A -16
> A# A# -53
> Bb Bb +11
> B B-26
> B#/Cb B#-63 or Cb +37
>
> Daniel Wolf

Thanks again to Daniel Wolf and Graham Breed for helping me with the
19-tone notation situation and the understanding of the 1/3 comma
meantone background...

I can certainly see how, from a theoretical standpoint, illustrating
the meantone with non-equivalent "enharmonics" makes a lot of sense...

It also would seem to be the easiest way to notate 19, tET or
otherwise, on an instrument with a set fingering... such as guitar,
for example... which is probably why Neil Haverstick likes this kind
of notation so much.

I still remain unconvinced, however, that it works well for a
"continuous pitch" instrument. Learning a completely new set of
notational symbols with non-equivalent enharmonics and "unadorned"
pitches that are not the "usual" 12-tET seems more difficult for a
performer to learn than, let's say, a system of "regular" 12-tET with
alterations by, for example, quartertones and cents deviation...

It seems that way right now to me, but I'll try to keep an open mind
about it....

Thanks again!

__________ _____ ____
Joseph Pehrson

Joseph wrote,

>I still remain unconvinced, however, that it works well for a
>"continuous pitch" instrument. Learning a completely new set of
>notational symbols with non-equivalent enharmonics and "unadorned"
>pitches that are not the "usual" 12-tET seems more difficult for a
>performer to learn than, let's say, a system of "regular" 12-tET with
>alterations by, for example, quartertones and cents deviation...

Perhaps you missed the point, Joseph, which was that if you use the correct
notation _and_ cents deviations from 12-tET, the score will work _both ways
simultaneously_! Did you miss that?

--- In tuning@y..., "Paul H. Erlich" <PERLICH@A...> wrote:
> Joseph wrote,
>
> >I still remain unconvinced, however, that it works well for a
> >"continuous pitch" instrument. Learning a completely new set of
> >notational symbols with non-equivalent enharmonics and "unadorned"
> >pitches that are not the "usual" 12-tET seems more difficult for a
> >performer to learn than, let's say, a system of "regular" 12-tET
with alterations by, for example, quartertones and cents deviation...
>
> Perhaps you missed the point, Joseph, which was that if you use the
correct notation _and_ cents deviations from 12-tET, the score will
work _both ways simultaneously_! Did you miss that?

Yes, I *did* study what Daniel Wolf said. However, in the following
chart that he posted:

19tet score 12tet score
C C
C# C# -37
Db Db +26
D D -11
D# D# -47
Eb Eb +16
E E -21
E#/Fb E#-58 or Fb +42
F F +5
F# F# -32
Gb Gb +32
G G -5
G# G# -42
Ab Ab +21
A A -16
A# A# -53
Bb Bb +11
B B-26
B#/Cb B#-63 or Cb +37

the actual "letter names" that would appear on the staff would have
to be "adjusted" in order to get 12-tET. Although undoubtedly
historically accurate, it seems "counterintuitive" to the "common
practice" that is so ingrained in so many musicians...

Rather than adjusting *19-tET* so that it comes out correctly in 12,
wouldn't it be more intuitive to use the 12-tET pitches and adjust in
cents values and quartertones from there?? Besides, the concept of
non-equivalent enharmonics is rather foreign to most players, is it
not?? (Well maybe not to string players playing pythagorean and other
exceptions...)

I'm just finding that when I look at the staff and see a scale with a
C followed by a C#, my traditional training wants me to be hearing a
100 cent difference FROM THE NOTATED pitch, not after "adjustments."

So, for example, I would rather have the second note of the 19-tone
scale be a C quarter-tone sharp with a +13 added, to get the 63 cents
of 19-tET that way.

That seems, right now, to be more "grounded" to me. However, I do
understand from the discussions on this list, that it is not as
"historically accurate."

Do you agree that that method is more immediately comprehensible to a
12-tET trained musician??

My mind is open and the jury is still out. I just hope they will
come back in time for the trial...

_________ ______ ______ _
Joseph Pehrson

--- In tuning@y..., jpehrson@r... wrote:
>
> Yes, I *did* study what Daniel Wolf said. However, in the
following
> chart that he posted:
>
>
> 19tet score 12tet score
> C C
> C# C# -37
> Db Db +26
> D D -11
> D# D# -47
> Eb Eb +16
> E E -21
> E#/Fb E#-58 or Fb +42
> F F +5
> F# F# -32
> Gb Gb +32
> G G -5
> G# G# -42
> Ab Ab +21
> A A -16
> A# A# -53
> Bb Bb +11
> B B-26
> B#/Cb B#-63 or Cb +37
>
>
> the actual "letter names" that would appear on the staff would have
> to be "adjusted" in order to get 12-tET.

What do you mean??? The letter names in the right column are _exactly
the same_ as the letter names in the left column!
>
> I'm just finding that when I look at the staff and see a scale with
a
> C followed by a C#, my traditional training wants me to be hearing
a
> 100 cent difference FROM THE NOTATED pitch, not after "adjustments."
>
> So, for example, I would rather have the second note of the 19-tone
> scale be a C quarter-tone sharp with a +13 added, to get the 63
cents
> of 19-tET that way.

Oh. But what's wrong with C# with a -37 added? Even Johnny Reinhard
said that he'd rather notate the 7th harmonic of C as Bb with a -31
added, rather than as A quarter-tone sharp with a +19 added . . .