Tuning Twelve Pitches

Debussy realized the 12-tone scale was doubly chromatic. What does
that mean?

Well a "diatonic" half-step goes from, say E to F on the white keys.
This is (4/3)/(5/4) in Just Intotation, that is, F/E = 16/15
A "chromatic" half-step goes from, say Eb to E natural, this is the
difference between minor and major. This is (5/4)/(6/5) in Just
Intonation, that is E/Eb = 25/24

Now lets look at what Debussy meant. Going from F to F# is chromatic,
but going from F to Gb is diatonic (Think of 6 flats, the Gb major
scale)

So (16/15)/(25/24)= 128/125. This is the "diesis", or how three major
thirds (5/4) map into the octave.

So, for example, start on Gb. One major third leads to Bb, another to
D, and a third to F#. F#/Gb is the "diesis"

This is at the root of all music theory. The two kinds of half steps
are one. It's also called "enharmonicity", Debussy said "doubly
chromatic" which is kind of true, he might have said "diatonic-
chromatic" or whatever. Of course, Gb is chromatic when going to G
for example.

So it's all pretty simple.

The root of ALL music theory? Just what kind of a perky statement is that?
Classical Western theory does not even begin to scratch the surface of maqam
intonation.

Oz.

----- Original Message -----
From: "Paul G Hjelmstad" <paul.hjelmstad@us.ing.com>
To: <tuning@yahoogroups.com>
Sent: 05 Haziran 2007 Sal� 1:15
Subject: [tuning] Tuning Twelve Pitches

> Debussy realized the 12-tone scale was doubly chromatic. What does
> that mean?
>
> Well a "diatonic" half-step goes from, say E to F on the white keys.
> This is (4/3)/(5/4) in Just Intotation, that is, F/E = 16/15
> A "chromatic" half-step goes from, say Eb to E natural, this is the
> difference between minor and major. This is (5/4)/(6/5) in Just
> Intonation, that is E/Eb = 25/24
>
> Now lets look at what Debussy meant. Going from F to F# is chromatic,
> but going from F to Gb is diatonic (Think of 6 flats, the Gb major
> scale)
>
> So (16/15)/(25/24)= 128/125. This is the "diesis", or how three major
> thirds (5/4) map into the octave.
>
> So, for example, start on Gb. One major third leads to Bb, another to
> D, and a third to F#. F#/Gb is the "diesis"
>
> This is at the root of all music theory. The two kinds of half steps
> are one. It's also called "enharmonicity", Debussy said "doubly
> chromatic" which is kind of true, he might have said "diatonic-
> chromatic" or whatever. Of course, Gb is chromatic when going to G
> for example.
>
> So it's all pretty simple.
>

Ozan Yarman wrote:

>The root of ALL music theory? Just what kind of a perky statement is that?
>

perky.

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

That explains a lot.

----- Original Message -----
From: "David Beardsley" <db@biink.com>
To: <tuning@yahoogroups.com>
Sent: 05 Haziran 2007 Sal� 4:17
Subject: Re: [tuning] Tuning Twelve Pitches

> Ozan Yarman wrote:
>
> >The root of ALL music theory? Just what kind of a perky statement is
that?
> >
>
>
> perky.
>
>
> --
> * David Beardsley
> * microtonal guitar
> * http://biink.com/db
> * http://biink.com/poole
>

Ozan Yarman wrote:

>That explains a lot.
>

I wasn't the one making the perky statement. I don't have to explain anything.

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

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> The root of ALL music theory? Just what kind of a perky statement is
that?
> Classical Western theory does not even begin to scratch the surface
of maqam
> intonation.

Paul Hjelmstad is a big fan of 12-et, but I have to say that tempering
out the diesis isn't even the root of all 5-limit music theory for 12-
et. To even derive 12, we should add that it also tempers out 81/80. If
you temper out both, you could claim that is the root of all 5-limit
music theory for 12, I suppose.

People wanting to temper out 128/125 but not stick with 12 can play
with 15, 24, or 27.

From: "Ozan Yarman" <ozanyarman@ozanyarman.com>
To: <tuning@yahoogroups.com>
Sent: Monday, June 04, 2007 8:11 PM
Subject: Re: [tuning] Tuning Twelve Pitches

> The root of ALL music theory? Just what kind of a perky statement is that?
> Classical Western theory does not even begin to scratch the surface of > maqam
> intonation.

He was talking about all of Western music theory in the common practice era; this is in reference to Debussy. Shame he didn't get outside of 12-tone; he did discover gamelan music and tried to emulate it in his compositions.

As a for-fun project, I thought of re-interpreting "Clair de lune" in meantone or possibly JI. In the middle part with the arpeggios, I thought of making F-flat and C-flat a diesis flat (or septimal), since they could also be thought of as E and B natural instead.

~D.

For sure.

----- Original Message -----
From: "David Beardsley" <db@biink.com>
To: <tuning@yahoogroups.com>
Sent: 05 Haziran 2007 Sal� 4:31
Subject: Re: [tuning] Tuning Twelve Pitches

> Ozan Yarman wrote:
>
> >That explains a lot.
> >
>
> I wasn't the one making the perky statement. I don't have to explain
> anything.
>
> --
> * David Beardsley
> * microtonal guitar
> * http://biink.com/db
> * http://biink.com/poole
>
>

He speaks as if Western theory is all there is, Danny.

Oz.

----- Original Message -----
From: "Danny Wier" <dawiertx@sbcglobal.net>
To: <tuning@yahoogroups.com>
Sent: 05 Haziran 2007 Sal� 6:54
Subject: Re: [tuning] Tuning Twelve Pitches

> From: "Ozan Yarman" <ozanyarman@ozanyarman.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, June 04, 2007 8:11 PM
> Subject: Re: [tuning] Tuning Twelve Pitches
>
>
> > The root of ALL music theory? Just what kind of a perky statement is
that?
> > Classical Western theory does not even begin to scratch the surface of
> > maqam
> > intonation.
>
> He was talking about all of Western music theory in the common practice
era;
> this is in reference to Debussy. Shame he didn't get outside of 12-tone;
he
> did discover gamelan music and tried to emulate it in his compositions.
>
> As a for-fun project, I thought of re-interpreting "Clair de lune" in
> meantone or possibly JI. In the middle part with the arpeggios, I thought
of
> making F-flat and C-flat a diesis flat (or septimal), since they could
also
> be thought of as E and B natural instead.
>
> ~D.
>

Debussy said he thought of 36 pitches in the octave
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> The root of ALL music theory? Just what kind of a perky statement
is that?
> Classical Western theory does not even begin to scratch the surface
of maqam
> intonation.
>
> Oz.

My bad. I meant European Classical music circa 1600-2000. With 12
pitches.

> ----- Original Message -----
> From: "Paul G Hjelmstad" <paul.hjelmstad@...>
> To: <tuning@yahoogroups.com>
> Sent: 05 Haziran 2007 Salý 1:15
> Subject: [tuning] Tuning Twelve Pitches
>
>
> > Debussy realized the 12-tone scale was doubly chromatic. What does
> > that mean?
> >
> > Well a "diatonic" half-step goes from, say E to F on the white
keys.
> > This is (4/3)/(5/4) in Just Intotation, that is, F/E = 16/15
> > A "chromatic" half-step goes from, say Eb to E natural, this is
the
> > difference between minor and major. This is (5/4)/(6/5) in Just
> > Intonation, that is E/Eb = 25/24
> >
> > Now lets look at what Debussy meant. Going from F to F# is
chromatic,
> > but going from F to Gb is diatonic (Think of 6 flats, the Gb major
> > scale)
> >
> > So (16/15)/(25/24)= 128/125. This is the "diesis", or how three
major
> > thirds (5/4) map into the octave.
> >
> > So, for example, start on Gb. One major third leads to Bb,
another to
> > D, and a third to F#. F#/Gb is the "diesis"
> >
> > This is at the root of all music theory. The two kinds of half
steps
> > are one. It's also called "enharmonicity", Debussy said "doubly
> > chromatic" which is kind of true, he might have said "diatonic-
> > chromatic" or whatever. Of course, Gb is chromatic when going to G
> > for example.
> >
> > So it's all pretty simple.
> >
>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@> wrote:
> >
> > The root of ALL music theory? Just what kind of a perky statement
is
> that?
> > Classical Western theory does not even begin to scratch the
surface
> of maqam
> > intonation.
>
> Paul Hjelmstad is a big fan of 12-et, but I have to say that
tempering
> out the diesis isn't even the root of all 5-limit music theory for
12-
> et. To even derive 12, we should add that it also tempers out
81/80. If
> you temper out both, you could claim that is the root of all 5-
limit
> music theory for 12, I suppose.
>
> People wanting to temper out 128/125 but not stick with 12 can play
> with 15, 24, or 27.
>
Yes, I meant to add in the syntonic comma. My statement related
to the fact that mode mixture, and what the main classical composers
did with accidentals, all revolve around this basic ingredient
for chromaticism.

A real easy peezy way to think about it:

Build a major triad on Bb (Bb, D, F) This is 4, 5, 6

Now work down from Bb to Gb (4/5)

Gb/F# is clearly 128/125

D-F#/D-F is 25/24

Gb-Bb/F-Bb is 15/16

PGH

Thank you for the correction, Paul.

Oz.

----- Original Message -----
From: "Paul G Hjelmstad" <paul.hjelmstad@us.ing.com>
To: <tuning@yahoogroups.com>
Sent: 05 Haziran 2007 Sal� 19:35
Subject: [tuning] Re: Tuning Twelve Pitches

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> The root of ALL music theory? Just what kind of a perky statement
is that?
> Classical Western theory does not even begin to scratch the surface
of maqam
> intonation.
>
> Oz.

My bad. I meant European Classical music circa 1600-2000. With 12
pitches.

Gene Ward Smith wrote:
> --- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>> The root of ALL music theory? Just what kind of a perky statement is > that?
>> Classical Western theory does not even begin to scratch the surface > of maqam
>> intonation.
> > Paul Hjelmstad is a big fan of 12-et, but I have to say that tempering > out the diesis isn't even the root of all 5-limit music theory for 12-
> et. To even derive 12, we should add that it also tempers out 81/80. If > you temper out both, you could claim that is the root of all 5-limit > music theory for 12, I suppose.
> > People wanting to temper out 128/125 but not stick with 12 can play > with 15, 24, or 27.

Or 21 for a slightly exotic sound. Or any multiple of 3 from 9-ET to 42-ET, really.

http://www.io.com/~hmiller/music/temp-augmented.html

It happens that the third movement of Beethoven's Moonlight Sonata doesn't require tempering out the 81/80 comma, which means it can be played using any augmented tuning (such as 15-ET).

http://www.io.com/~hmiller/midi/mlgt3-15.mid

But I imagine such music is probably less common than meantone-based music that tempers out 81/80 without tempering out 128/125.

<<< So (16/15)/(25/24)= 128/125. This is the "diesis", or how three major
thirds (5/4) map into the octave. >>>

Or as I like to call it, the 5-limit diminished second.

What is the technical definition of "diesis"? And when is something a diesis
and not a comma, or a limma? And does it rhyme with thesis?

Billy

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> My bad. I meant European Classical music circa 1600-2000. With 12
> pitches.

During much of that period the diesis was not being tempered out.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@>
> wrote:
>
> > My bad. I meant European Classical music circa 1600-2000. With 12
> > pitches.
>
> During much of that period the diesis was not being tempered out.

That seems rather ill-tempered, but it makes sense, if you want
Gb=/=F#

--- In tuning@yahoogroups.com, "Billy Gard" <billygard@...> wrote:
>
> <<< So (16/15)/(25/24)= 128/125. This is the "diesis", or how three
major
> thirds (5/4) map into the octave. >>>
>
> Or as I like to call it, the 5-limit diminished second.
>
> What is the technical definition of "diesis"?

Many different intervals have been called by the name "diesis", so
it's an interval class rather than a single interval. (The diesis
you describe above is the meantone diesis.)

> And when is something a diesis
> and not a comma, or a limma?

Unfortunately, these terms have been used rather loosely over the
centuries, so there are at present no generally accepted boundaries
between these (and kleisma, and schisma).

However, a systematic, non-arbitrary definition of these interval
classes was devised recently by Dave Keenan. See:
/tuning/topicId_56202.html#56261
and
/tuning/topicId_59383.html#59445

To view the tables, click on "Show Message Option" in the top part of
the gray area to the right of the message text, and then click
on "Use Fixed Width Font". (You may also need to click on "reply" to
fix the table properly in the 2nd link.)

> And does it rhyme with thesis?

I'm not sure. I pronounce it with 3 syllables, dee-EH-sis, but you
may prefer to put the emphasis on the first syllable.

--George

Hi Billy,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@...> wrote:
>
> --- In tuning@yahoogroups.com, "Billy Gard" <billygard@> wrote:
> >
> > <<< So (16/15)/(25/24)= 128/125. This is the "diesis",
> > or how three major thirds (5/4) map into the octave. >>>
> >
> > Or as I like to call it, the 5-limit diminished second.
> >
> > What is the technical definition of "diesis"?
>
> Many different intervals have been called by the name
> "diesis", so it's an interval class rather than a single
> interval. (The diesis you describe above is the meantone
> diesis.)

You can get a lot of additional information from my
Encyclopedia webpage:

http://tonalsoft.com/enc/d/diesis.aspx

> > And when is something a diesis
> > and not a comma, or a limma?
>
> Unfortunately, these terms have been used rather
> loosely over the centuries, so there are at present
> no generally accepted boundaries between these
> (and kleisma, and schisma).
>
> However, a systematic, non-arbitrary definition of
> these interval classes was devised recently by Dave Keenan.
> See:
> /tuning/topicId_56202.html#56261
> and
> /tuning/topicId_59383.html#59445

George is right on target here. You'd probably also
find my webpage on "comma" illuminating:

http://tonalsoft.com/enc/c/comma.aspx

Try looking up the individual entries on the other intervals
as well:

http://tonalsoft.com/enc/s/schisma.aspx
http://tonalsoft.com/enc/k/kleisma.aspx
http://tonalsoft.com/enc/p/pythagorean-comma.aspx
http://tonalsoft.com/enc/s/syntonic-comma.aspx
etc.

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

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@>
> > wrote:
> >
> > > My bad. I meant European Classical music circa 1600-2000. With 12
> > > pitches.
> >
> > During much of that period the diesis was not being tempered out.
>
> That seems rather ill-tempered, but it makes sense, if you want
> Gb=/=F#

Ill tempered? It's the only way to prevent the major third from taking
on the very sharp (average) value of 400 cents.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> > wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@>
> > > wrote:
> > >
> > > > My bad. I meant European Classical music circa 1600-2000.
With 12
> > > > pitches.
> > >
> > > During much of that period the diesis was not being tempered
out.
> >

> > That seems rather ill-tempered, but it makes sense, if you want
> > Gb=/=F#
>
> Ill tempered? It's the only way to prevent the major third from
taking
> on the very sharp (average) value of 400 cents.
>
It was a badly placed pun I guess. The main thing for choir directors
in terms of tuning is to get their choirs to sing the major third
real bright, 14c sharp of course, almost to 1.26. 126/125 is audible,
and by coincidence a fraction in the 7-limit. Does this wiggle
room come into play, with a capella singing, I wonder?

--- In tuning@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@...> wrote:
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@>
> wrote:
> >
> > --- In tuning@yahoogroups.com, "Paul G Hjelmstad"
<paul.hjelmstad@>
> > wrote:
> > >
> > > --- In tuning@yahoogroups.com, "Gene Ward Smith"
<genewardsmith@>
> > > wrote:
> > > >
> > > > --- In tuning@yahoogroups.com, "Paul G Hjelmstad"
> <paul.hjelmstad@>
> > > > wrote:
> > > >
> > > > > My bad. I meant European Classical music circa 1600-2000.
> With 12
> > > > > pitches.
> > > >
> > > > During much of that period the diesis was not being tempered
> out.
> > >
>
> > > That seems rather ill-tempered, but it makes sense, if you want
> > > Gb=/=F#
> >
> > Ill tempered? It's the only way to prevent the major third from
> taking
> > on the very sharp (average) value of 400 cents.
> >
> It was a badly placed pun I guess. The main thing for choir
directors
> in terms of tuning is to get their choirs to sing the major third
> real bright, 14c sharp of course, almost to 1.26. 126/125 is
audible,
> and by coincidence a fraction in the 7-limit. Does this wiggle
> room come into play, with a capella singing, I wonder?

Which gives me the opportunity to introduce "Hjelmstad's comma"

250,047/250,000 = 1.000188

It's merely (126/125 * 5/4)^3 / 2

Silly or useful?

PGH

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:
>
> The main thing for choir directors
> in terms of tuning is to get their choirs to sing the major third
> real bright, 14c sharp of course, almost to 1.26.

Is this a joke? ... What's the point of having a choir if you try to
make them do the acoustically impossible (and aesthetically repulsive)
and sing ET?

> 126/125 is audible,

Sure is, but I don't know why it should make choral music sound better.

> and by coincidence a fraction in the 7-limit. Does this wiggle
> room come into play, with a capella singing, I wonder?

No, but an entirely different wiggle room does: that between impure
melodic intervals and pure harmonic ones. Or if a pianner is in the
room, the wiggle room between an inharmonic decaying out-of-tune chord
and a harmonic sustained pure one.

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@>
> wrote:
> >
> > The main thing for choir directors
> > in terms of tuning is to get their choirs to sing the major third
> > real bright, 14c sharp of course, almost to 1.26.
>
> Is this a joke? ... What's the point of having a choir if you try to
> make them do the acoustically impossible (and aesthetically
repulsive)
> and sing ET?

But they do. If you are singing with a piano or organ, you have
to. If you are singing music with enharmonic relationships and
complex harmonies you have to, even if it is a capella.

If you run tests with oscilloscopes I'll bet you will find
most choirs sing 12-tET most of the time. I'd like to see some
tests. It's just the law of averages anyway, when you work
in vibrato and error and so forth.

>
> > 126/125 is audible,
>
> Sure is, but I don't know why it should make choral music sound
better.

That wasn't my point.
>
> > and by coincidence a fraction in the 7-limit. Does this wiggle
> > room come into play, with a capella singing, I wonder?
>
> No, but an entirely different wiggle room does: that between impure
> melodic intervals and pure harmonic ones. Or if a pianner is in the
> room, the wiggle room between an inharmonic decaying out-of-tune
chord
> and a harmonic sustained pure one.
>
> ~~~T~~~
>

Maybe. If you could get a choir to sing a 120-note scale, 10 cents
at a time, or even 20 cents at time, I would be real surprised.
Even to get a solo singer to do it. I just don't think there is
that kind of "continuity" but I am open minded.

> But they do. If you are singing with a piano or organ, you have
> to. If you are singing music with enharmonic relationships and
> complex harmonies you have to, even if it is a capella.

You don't *have* to. Your choices are drift, shift,
adaptive JI, adaptive temperament, and regular temperament.
Which one do you want me to explain to you first? :)

> If you run tests with oscilloscopes I'll bet you will find
> most choirs sing 12-tET most of the time.

How would an oscilloscope help?

> I'd like to see some
> tests. It's just the law of averages anyway, when you work
> in vibrato and error and so forth.

Have you ever listened to Barbershop quartets?

> Maybe. If you could get a choir to sing a 120-note scale, 10 cents
> at a time, or even 20 cents at time, I would be real surprised.
> Even to get a solo singer to do it. I just don't think there is
> that kind of "continuity" but I am open minded.

That's a very different kind of exercise than being able
to make 10-cent adjustments to bring chords into JI.

-Carl

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> Which gives me the opportunity to introduce "Hjelmstad's comma"
>
> 250,047/250,000 = 1.000188
>
> It's merely (126/125 * 5/4)^3 / 2
>
> Silly or useful?

Useful. That's the Landscape Comma, and is also (2401/2400)/(4375/4374),
and (126/125)^2/(64/63).

/tuning/topicId_58180.html#58217

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > But they do. If you are singing with a piano or organ, you have
> > to. If you are singing music with enharmonic relationships and
> > complex harmonies you have to, even if it is a capella.
>
> You don't *have* to. Your choices are drift, shift,
> adaptive JI, adaptive temperament, and regular temperament.
> Which one do you want me to explain to you first? :)

Let it be shown professor. I don't think it's ever far from 12t-ET.
>
> > If you run tests with oscilloscopes I'll bet you will find
> > most choirs sing 12-tET most of the time.
>
> How would an oscilloscope help?

Measurement of frequencies. I am sure there is some kind of
sophisticated technology in place that could run the tests I am
looking for. (Taking into account phase, timbre, etc)

> > I'd like to see some
> > tests. It's just the law of averages anyway, when you work
> > in vibrato and error and so forth.
>
> Have you ever listened to Barbershop quartets?

Yes I know, just-7 sevenths etc.
>
> > Maybe. If you could get a choir to sing a 120-note scale, 10 cents
> > at a time, or even 20 cents at time, I would be real surprised.
> > Even to get a solo singer to do it. I just don't think there is
> > that kind of "continuity" but I am open minded.
>
> That's a very different kind of exercise than being able
> to make 10-cent adjustments to bring chords into JI.
>
> -Carl
>
True. I "just" believe that church and classical choirs for one, are
trained to sing fat major thirds. 5/4 just sounds flat and nobody
likes to sound flat. That's what I think.

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> True. I "just" believe that church and classical choirs for one, are
> trained to sing fat major thirds. 5/4 just sounds flat and nobody
> likes to sound flat. That's what I think.

Have you listened to much a capella Renaissance music?

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@>
> wrote:
>
> > True. I "just" believe that church and classical choirs for one,
are
> > trained to sing fat major thirds. 5/4 just sounds flat and nobody
> > likes to sound flat. That's what I think.
>
> Have you listened to much a capella Renaissance music?

Yes although not lately. Also certain tribal music and even some folk
music is probably more like just intonation. Plus even Elvis sang
his thirds flatter. I am just saying is that just gets trained out of
a person, for better or for worse. It is interesting that blues thirds
go closer to neutral thirds and also just major and minor thirds are
indeed closer to the center, of course. In a way, temperament makes
them more distinctive but I am preaching to the choir. (Sorry
couldn't resist)
>

> > > But they do. If you are singing with a piano or organ, you have
> > > to. If you are singing music with enharmonic relationships and
> > > complex harmonies you have to, even if it is a capella.
> >
> > You don't *have* to. Your choices are drift, shift,
> > adaptive JI, adaptive temperament, and regular temperament.
> > Which one do you want me to explain to you first? :)
>
> Let it be shown professor. I don't think it's ever far from 12t-ET.

You can let the pitch standard _drift_ by a diesis every
time a _diesis pump_ (chord progression) is performed.
In other words, A will no longer be 440Hz. by the end of
the piece.

You can maintain the pitch standard but have tied or repeated
notes _shift_ (differ) by a diesis, melodically.

You can temper out the diesis, which can be done with 12-ET
among other _regular temperaments_.

You can temper the diesis over melodic intervals only, which
yields the _adaptive JI_ Tom mentioned. This makes the
note-note melodic shifts much smaller, maintains the pitch
standard, and keeps all vertical harmonies pure. It's
probably the best model we have for a capella vocal intonation
of common-practice music by expert-level singers. The
degree to which piano accompaniment changes this depends on
the rhythmic relationship of the piano part to the vocal
parts, the performance space, the rehearsal methods used,
etc. etc. But it's safe to say it's generally overstated.

> > > If you run tests with oscilloscopes I'll bet you will find
> > > most choirs sing 12-tET most of the time.
> >
> > How would an oscilloscope help?
>
> Measurement of frequencies.

There are an awful lot of frequencies to measure. You
need some way to filter the signal, and then to decide
which ones should be measured and which ignored.

> I am sure there is some kind of
> sophisticated technology in place that could run the tests
> I am looking for. (Taking into account phase, timbre, etc)

Phase actually isn't important, which is why FFT is
typically suggested for this. But there are limitations
on frequency resolution, sensitivity of noise, and still
the problem of how to decide how the frequencies in the
signal match up to the *pitches* in the score you're trying
to test the intonation of.

I've done some limited work with such analysis on recordings
of barbershop singing, and more recently, on a short bit
of Handel's Messiah.

The bottom line is, there is currently no known way to
do this kind of analysis efficiently and convincingly.

> True. I "just" believe that church and classical choirs
> for one, are trained to sing fat major thirds. 5/4 just
> sounds flat and nobody likes to sound flat. That's what
> I think.

Is that a troll or are you being sincere?

-Carl

> > > True. I "just" believe that church and classical choirs for
> > > one, are trained to sing fat major thirds. 5/4 just sounds
> > > flat and nobody likes to sound flat. That's what I think.
> >
> > Have you listened to much a capella Renaissance music?
>
> Yes although not lately.

What about brass quintets?

I've played in them, and sang in church choirs, and was
taught to 'flatten thirds for better intonation'.

-Carl

I wrote...
> > > You don't *have* to. Your choices are drift, shift,
> > > adaptive JI, adaptive temperament, and regular temperament.

I realized I forgot adaptive temperament, which is like
adaptive JI but also allows vertical sonorities to be
compromised somewhat (though not as much as in the
corresponding regular temperament solution) to reduce the
burden on the melodic intervals. John deLaubenfels'
BGE software used this approach.

One might also mix and match these techniques in different
sections of a piece.

There is also the idea of varying the pitch of a note while
it is sounding. Studies show the attack of a pitch conveys
most of its pitch-height information. Sustained chords
can be struck in a regular temperament and glissed to JI.
To my knowledge this was first suggested by Manuel op de Coul.

-Carl

> You can get a lot of additional information from my
> Encyclopedia webpage:
>
> http://tonalsoft.com/enc/d/diesis.aspx

There's a great wealth of information there. Thanks for pointing it out. I
know I've heard of tonalsoft. It may have come up in just intonation
searches. The "septimal diesis" (36/35) mentioned on your site particularly
interests me because it is the interval that separates a just minor 3rd
(6/5) from a sub-minor (septimal) third (7/6). I'm thinking of adding it to
my interval index. The septimal comma (64/63) immediately comes to mind
here, but it separates the pyth minor 3rd from the septimal one, and its
usefulness is in that it fixes the out-of-tune dominant 7th chord in the
just scale.

Billy

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > But they do. If you are singing with a piano or organ, you
have
> > > > to. If you are singing music with enharmonic relationships
and
> > > > complex harmonies you have to, even if it is a capella.
> > >
> > > You don't *have* to. Your choices are drift, shift,
> > > adaptive JI, adaptive temperament, and regular temperament.
> > > Which one do you want me to explain to you first? :)
> >
> > Let it be shown professor. I don't think it's ever far from 12t-
ET.
>
> You can let the pitch standard _drift_ by a diesis every
> time a _diesis pump_ (chord progression) is performed.
> In other words, A will no longer be 440Hz. by the end of
> the piece.
>
> You can maintain the pitch standard but have tied or repeated
> notes _shift_ (differ) by a diesis, melodically.
>
> You can temper out the diesis, which can be done with 12-ET
> among other _regular temperaments_.
>
> You can temper the diesis over melodic intervals only, which
> yields the _adaptive JI_ Tom mentioned. This makes the
> note-note melodic shifts much smaller, maintains the pitch
> standard, and keeps all vertical harmonies pure. It's
> probably the best model we have for a capella vocal intonation
> of common-practice music by expert-level singers. The
> degree to which piano accompaniment changes this depends on
> the rhythmic relationship of the piano part to the vocal
> parts, the performance space, the rehearsal methods used,
> etc. etc. But it's safe to say it's generally overstated.
>
> > > > If you run tests with oscilloscopes I'll bet you will find
> > > > most choirs sing 12-tET most of the time.
> > >
> > > How would an oscilloscope help?
> >
> > Measurement of frequencies.
>
> There are an awful lot of frequencies to measure. You
> need some way to filter the signal, and then to decide
> which ones should be measured and which ignored.
>
> > I am sure there is some kind of
> > sophisticated technology in place that could run the tests
> > I am looking for. (Taking into account phase, timbre, etc)
>
> Phase actually isn't important, which is why FFT is
> typically suggested for this. But there are limitations
> on frequency resolution, sensitivity of noise, and still
> the problem of how to decide how the frequencies in the
> signal match up to the *pitches* in the score you're trying
> to test the intonation of.
>
> I've done some limited work with such analysis on recordings
> of barbershop singing, and more recently, on a short bit
> of Handel's Messiah.
>
> The bottom line is, there is currently no known way to
> do this kind of analysis efficiently and convincingly.
>
> > True. I "just" believe that church and classical choirs
> > for one, are trained to sing fat major thirds. 5/4 just
> > sounds flat and nobody likes to sound flat. That's what
> > I think.
>
> Is that a troll or are you being sincere?
>
> -Carl

troll? like in fishing? I'm sincere. 99% of the time you fight
against being flat. The times you are sharp - that's just weird.
Often you are just really flat on the neighboring tone above.
>

Hi Billy,

--- In tuning@yahoogroups.com, "Billy Gard" <billygard@...> wrote:
>
> > You can get a lot of additional information from my
> > Encyclopedia webpage:
> >
> > http://tonalsoft.com/enc/d/diesis.aspx
>
> There's a great wealth of information there. Thanks for
> pointing it out. I know I've heard of tonalsoft.

Thanks. If your OS is Windows XP, you can download
Tonescape for free and hopefully it will work for you.
Check out our homepage.

Unfortunately the Encyclopedia temporarily (going on
three years now) doesn't have all the internal links
that it used to have. Upon reading the diesis page,
i thought you might want to read about my suggestion
for the "super-tripental diesis" etc. names:

http://sonic-arts.org/td/monzo/o483-26new5limitnames.htm

As i say in that webpage, i was never really crazy
about those names, but they do convey more information
about the 5-limit intervals than the more whimsical
names like "magic comma".

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

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

> Unfortunately the Encyclopedia temporarily (going on
> three years now) doesn't have all the internal links
> that it used to have. Upon reading the diesis page,
> i thought you might want to read about my suggestion
> for the "super-tripental diesis" etc. names:
>
> http://sonic-arts.org/td/monzo/o483-26new5limitnames.htm
>
> As i say in that webpage, i was never really crazy
> about those names, but they do convey more information
> about the 5-limit intervals than the more whimsical
> names like "magic comma".
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

From the page you posted above: "Each interval is qualified by a
pseudo-Graeco-Latin term indicating the exponent of 5 and
its 'tivity', positive or negative. (Is there a real mathematical
term for that?) "

Isn't that "sign"?

-Cameron Bobro

Hi Cameron,

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:

> > http://sonic-arts.org/td/monzo/o483-26new5limitnames.htm
>
> From the page you posted above: "Each interval is
> qualified by a pseudo-Graeco-Latin term indicating
> the exponent of 5 and its 'tivity', positive or negative.
> (Is there a real mathematical term for that?) "
>
> Isn't that "sign"?

Duh ... yes. Thanks for noticing that. I should have
fixed it a *long* time ago. Will do so as soon as i can.

That webpage is adapted from a post i sent to this list,
and my brain just temporarily went blank at the moment
i was writing the post, and i couldn't remember 'sign'.
The correction was pointed out to me way back then.
Thanks for picking it up.

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

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

> As i say in that webpage, i was never really crazy
> about those names, but they do convey more information
> about the 5-limit intervals than the more whimsical
> names like "magic comma".

No they don't. "Magic comma" conveys the significant information that
tempering it out gives 5-limit magic--in other words, it is the
defining 5-limit comma of magic, in the sense of being the first comma
of the Hermite comma list for magic, etc. "super-pentapental small
diesis" is a repulsive name which tells me mostly that you've got a
naming scheme which promotes the overuse of aleady overloaded terms
such as "limma" and "diesis". If I know what this sceme is, I can guess
the size, but that is not the most interesting thing about a comma.

I hate this system.

Here is an article by Duffin that was discussed some time ago here:

http://mto.societymusictheory.org/issues/mto.06.12.3/mto.06.12.3.duffin.html

... while I don't endorse everything in it (his concept of JI seems
unnecessarily strict for unaccompanied vocal performance), it does
have an audio example of the Hilliard Ensemble singing some Tallis, in
which the thirds seem to be pretty near pure.

Maybe some singers and choirs do have a problem with going flat ...
most of the time this is due to a lack of sense of pitch, in other
words not really listening to the sounds they are making. People who
have learnt how to sing in tune with themselves and each other don't
have chronic problems of drifting flat, except possibly in passages
which are truly puzzling within JI, ie comma pumps.

Good singers, by definition, don't just go flat for no reason.

Anyhow, the historical evidence for the use of pure thirds at
musically convenient and effective moments is so overwhelming that it
would be extremely tedious to go into more than a tiny fraction. I
borrowed recently an article by Max Planck, the well-known physicist,
which discussed intonation problems in choral music, giving an example
of a Berlin choral society singing a piece by Schuetz. The problem was
precisely the comma drift of a passage in which the mediant of a major
chord (eg A in F-A-C) was held on its own and then became the tonic of
the next (A-C#-E), with a subsequent progression in the subdominant
direction. If all intervals are sung as pure as possible, Planck found
that the end is two commas below the beginning.

The crucial point is that Planck actually listened to the choir
singing the passage slowly with pure intonation and, by comparing to
their piano, verified that the comma drift did take place.

Planck, Max. "Die natürliche Stimmung in der modernen Vokalmusik",
Vierteljahrsschrift Musikwissenschaft vol. 9, 1893, p. 418.

The clear implications are that:
1) A good choir did not use ET, far from it, chords were tuned as pure
as possible in context
2) A good choir could hold its pitch and sing pure intervals to the
extent that a drift of two commas was found to be unusual and
significantly problematic.

In the end Planck suggested that the drift may even have been an
intentional part of the composition, since the words were something
like 'I will lay down and rest'...

He didn't, though, consider the possibility that Schuetz might have
had the piece accompanied by a meantone-tuned organ.

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> Here is an article by Duffin that was discussed some time ago here:
>
>
http://mto.societymusictheory.org/issues/mto.06.12.3/mto.06.12.3.duffi
n.html
>
> ... while I don't endorse everything in it (his concept of JI seems
> unnecessarily strict for unaccompanied vocal performance), it does
> have an audio example of the Hilliard Ensemble singing some Tallis,
in
> which the thirds seem to be pretty near pure.
>
> Maybe some singers and choirs do have a problem with going flat ...
> most of the time this is due to a lack of sense of pitch, in other
> words not really listening to the sounds they are making. People who
> have learnt how to sing in tune with themselves and each other don't
> have chronic problems of drifting flat, except possibly in passages
> which are truly puzzling within JI, ie comma pumps.
>
> Good singers, by definition, don't just go flat for no reason.
>
> Anyhow, the historical evidence for the use of pure thirds at
> musically convenient and effective moments is so overwhelming that
it
> would be extremely tedious to go into more than a tiny fraction. I
> borrowed recently an article by Max Planck, the well-known
physicist,
> which discussed intonation problems in choral music, giving an
example
> of a Berlin choral society singing a piece by Schuetz. The problem
was
> precisely the comma drift of a passage in which the mediant of a
major
> chord (eg A in F-A-C) was held on its own and then became the tonic
of
> the next (A-C#-E), with a subsequent progression in the subdominant
> direction. If all intervals are sung as pure as possible, Planck
found
> that the end is two commas below the beginning.
>
> The crucial point is that Planck actually listened to the choir
> singing the passage slowly with pure intonation and, by comparing to
> their piano, verified that the comma drift did take place.
>
> Planck, Max. "Die natürliche Stimmung in der modernen Vokalmusik",
> Vierteljahrsschrift Musikwissenschaft vol. 9, 1893, p. 418.
>
> The clear implications are that:
> 1) A good choir did not use ET, far from it, chords were tuned as
pure
> as possible in context
> 2) A good choir could hold its pitch and sing pure intervals to the
> extent that a drift of two commas was found to be unusual and
> significantly problematic.
>
> In the end Planck suggested that the drift may even have been an
> intentional part of the composition, since the words were something
> like 'I will lay down and rest'...
>
> He didn't, though, consider the possibility that Schuetz might have
> had the piece accompanied by a meantone-tuned organ.
>
> ~~~T~~~
>
Well, I'm not going to argue with Max Planck, but you still missed me
point. I never said singers just go flat. (I am in a very good choir).
I am just saying that we are trained to sing tempered major thirds,
and that singing them just would cause many directors to want to
fix that. I still think that, at least in the choir I am in, we are
conditioned to sing major thirds a little bright and minor thirds
a little "dark". With organ accompaniment, you would have to lock
into 12-tET. A capella, the jury is still out, let me study the
"literature" you are referring to.

"I don't believe it"

PGH

> Well, I'm not going to argue with Max Planck, but you still missed me
> point. I never said singers just go flat. (I am in a very good choir).
> I am just saying that we are trained to sing tempered major thirds,
> and that singing them just would cause many directors to want to
> fix that. I still think that, at least in the choir I am in, we are
> conditioned to sing major thirds a little bright and minor thirds
> a little "dark". With organ accompaniment, you would have to lock
> into 12-tET. A capella, the jury is still out, let me study the
> "literature" you are referring to.

Of course it depends what you're singing. What kind of music
does your choir sing? In what way are you trained to sing in
12-tET? Do you rehearse with a piano?

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Well, I'm not going to argue with Max Planck, but you still
missed me
> > point. I never said singers just go flat. (I am in a very good
choir).
> > I am just saying that we are trained to sing tempered major
thirds,
> > and that singing them just would cause many directors to want to
> > fix that. I still think that, at least in the choir I am in, we
are
> > conditioned to sing major thirds a little bright and minor thirds
> > a little "dark". With organ accompaniment, you would have to lock
> > into 12-tET. A capella, the jury is still out, let me study the
> > "literature" you are referring to.
>
> Of course it depends what you're singing. What kind of music
> does your choir sing? In what way are you trained to sing in
> 12-tET? Do you rehearse with a piano?
>
> -Carl
>
Yes, we rehearse with a piano, and do more difficult British
music for the most part, mostly 1800-2000. (Howells, Stanford,
Ireland, etc.) But I don't think people just switch into "JI"
or "Adaptive JI". I think pretty much everyone in the USA does music
that is essentially 12t-ET. Think of a symphony orchestra. Sure,
the strings have the flexibility of tuning intervals pure. But then
it would just clash with the winds, the brass, etc. (Okay, not
trombones!) I just don't think it is that cerebral. I am almost
inclined to believe that if anything, choral singing is close to
Pythagorean tuning, where whole steps are essentially 9/8 and half
steps their square root.

Otherwise, music with augmented chords and arpeggios (Howells comes
to mind here) would have the diesis all over the place and that just
doesn't happen, C'mon, octaves off by 42 cents? That's ridiculous!

Tribal music of Africa probably is just. But those major (natural)
thirds sound strange to our ears. I am not saying the artificiality
of temperament/the modern world is always an improvement, it's just
a fact. We adjust to our environment. I have chemicals in my system
(due to pollution, HGH, etc) that people didn't have 500 years ago.
Things change.

Anyway, in summary, sure comma pumps happen in a capella singing.
(I don't think the perfect fifth is an issue, 2 cents is really
really close, so whole steps are essentially perfect, and 81/64
major thirds reasonable.) But I am open to changing my mind. I know
how hard it is the sing "O sacrum convivium", (Messaien) so I am
willing to admit I may be wrong. I just cannot imagine an orchestra
playing "Rite of Spring" in anything but 12t-ET. So the same would
apply for choirs singing choral music of the 19th and 20th centuries.

Having AP, I think I would know if I was singing 14 cents flat. So
maybe they should get rid of singers with AP, but I've never been
accused of singing sharp. Or singing minor thirds flat. I think
Occam's razor applies: It's just plain 12t-ET. Sorry to rain on
anyone's parade.

> Yes, we rehearse with a piano, and do more difficult British
> music for the most part, mostly 1800-2000. (Howells, Stanford,
> Ireland, etc.) But I don't think people just switch into "JI"
> or "Adaptive JI". I think pretty much everyone in the USA does
> music that is essentially 12t-ET. Think of a symphony orchestra.
> Sure, the strings have the flexibility of tuning intervals pure.

...as do all of the instruments.

> But then it would just clash with the winds, the brass, etc.
> (Okay, not trombones!)

Actually brass ensembles intone the most accurate 5-limit JI
I've heard in the instrumental world. Have you ever listened
to a good brass quintet?

Saying orchestras intone in 12-tET is accurate at some level
of abstraction. The actual intonation of the ensemble depends
on the orchestra and the music. Then there is sectional
intonation, and finally the intonation of the individual
instruments.

Instrument intonation can be viewed as sectional intonation
with small, random perturbations. And not so small if you're
most violin sections. :)

Brass, wind, and string sections will intone differently if
playing alone. Mahler's symphonies are good demonstrations
of this. When playing together, one may assume they come
togogether somewhat, but not entirely. Check out your local
orchestra sometime, try to focus on interval qualities instead
of pitch height, and try to hear out the different sections.
You may be surprised at what's going on.

Some orchestras can play in adaptive JI. I have a modern
Firebird on Deutsche Grammaphone that comes to mind. And
no orchestras play accurately enough in 12 that the
characteristic beat rates of the intervals can be heard, as
they can in MIDI music.

And that's a very good comparison. Check out your local
orchestra, then come home and download some MIDI versions
of what you just heard. Or use recordings in your library.
The difference you hear is in large part due to the
deviations from 12-tET in the intonation of the real
orchestra.

> I am almost inclined to believe that if anything, choral
> singing is close to Pythagorean tuning, where whole steps are
> essentially 9/8 and half steps their square root.

There's no square root of anything in Pythagorean intonation.

> Otherwise, music with augmented chords and arpeggios (Howells
> comes to mind here) would have the diesis all over the place
> and that just doesn't happen, C'mon, octaves off by 42 cents?
> That's ridiculous!

Melodic intonation can be different from harmonic intonation.

> Tribal music of Africa probably is just.

Why do you say that? Have you listened to much tribal music
from Africa? I have. It's mostly percussion and chanting.
Perhaps you're thinking of Mbube singing? That's not tribal
music...

> But those major (natural) thirds sound strange to our ears.

I frankly don't think you would recognize one, or you wouldn't
be complaining of their paucity. It's actually not uncommon
for APers to have relatively poor relative pitch like this.

> I just cannot imagine an orchestra
> playing "Rite of Spring" in anything but 12-tET.

The UC Berkeley orchestra did it in 2003 with no 12-tET
intervals audible. The Firebird I mention above is Boulez,
Chicago '93, Deutsche Grammophon 437-850-2.

> So the same would apply for choirs singing choral music of
> the 19th and 20th centuries.

Why would the same thing be true of choirs as is of orchestras??
They're completely different domains.

> Having AP, I think I would know if I was singing 14 cents flat.

Maybe you aren't. Is your AP sensitive to the thirds played
by brass quintets?

> So maybe they should get rid of singers with AP, but I've never
> been accused of singing sharp. Or singing minor thirds flat. I
> think Occam's razor applies: It's just plain 12t-ET. Sorry to
> rain on anyone's parade.

Unfortunately intonation is not something that is understood
by musicians.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Yes, we rehearse with a piano, and do more difficult British
> > music for the most part, mostly 1800-2000. (Howells, Stanford,
> > Ireland, etc.) But I don't think people just switch into "JI"
> > or "Adaptive JI". I think pretty much everyone in the USA does
> > music that is essentially 12t-ET. Think of a symphony orchestra.
> > Sure, the strings have the flexibility of tuning intervals pure.
>
> ...as do all of the instruments.

Some, with the lip as they say.

> > But then it would just clash with the winds, the brass, etc.
> > (Okay, not trombones!)
>
> Actually brass ensembles intone the most accurate 5-limit JI
> I've heard in the instrumental world. Have you ever listened
> to a good brass quintet?

Okay, valuable!

> Saying orchestras intone in 12-tET is accurate at some level
> of abstraction. The actual intonation of the ensemble depends
> on the orchestra and the music. Then there is sectional
> intonation, and finally the intonation of the individual
> instruments.
>
> Instrument intonation can be viewed as sectional intonation
> with small, random perturbations. And not so small if you're
> most violin sections. :)

??? So you mean string ensembles tune closer to just?

>
> Brass, wind, and string sections will intone differently if
> playing alone. Mahler's symphonies are good demonstrations
> of this. When playing together, one may assume they come
> togogether somewhat, but not entirely. Check out your local
> orchestra sometime, try to focus on interval qualities instead
> of pitch height, and try to hear out the different sections.
> You may be surprised at what's going on.
>
> Some orchestras can play in adaptive JI. I have a modern
> Firebird on Deutsche Grammaphone that comes to mind. And
> no orchestras play accurately enough in 12 that the
> characteristic beat rates of the intervals can be heard, as
> they can in MIDI music.
>
> And that's a very good comparison. Check out your local
> orchestra, then come home and download some MIDI versions
> of what you just heard. Or use recordings in your library.
> The difference you hear is in large part due to the
> deviations from 12-tET in the intonation of the real
> orchestra.

I would like to believe this. Hopefully you are right, it makes
music a lot more interesting!

> > I am almost inclined to believe that if anything, choral
> > singing is close to Pythagorean tuning, where whole steps are
> > essentially 9/8 and half steps their square root.
>
> There's no square root of anything in Pythagorean intonation.

Sure there is. What about the tritone? I was taught 102 102 102 102
90 102 102 102 102 102 102 90 for Pythagorean. Am I misinformed?

>
> > Otherwise, music with augmented chords and arpeggios (Howells
> > comes to mind here) would have the diesis all over the place
> > and that just doesn't happen, C'mon, octaves off by 42 cents?
> > That's ridiculous!
>
> Melodic intonation can be different from harmonic intonation.

Well I goofed a little anyway cuz the last interval is a diminished
fourth not a major third. But you'd still be off 28 cents.
I don't think choral singers differentiate between melodic and
harmonic intonation. "Melody is harmony unfured, harmony is
melody furled" (A Scriabin). (Is "furled" a word?)

> > Tribal music of Africa probably is just.
>
> Why do you say that? Have you listened to much tribal music
> from Africa? I have. It's mostly percussion and chanting.
> Perhaps you're thinking of Mbube singing? That's not tribal
> music...

I'm not an expert. I am thinking of the kind of African singing,
usually three parts, with triads. That sounds just.
>
> > But those major (natural) thirds sound strange to our ears.
>
> I frankly don't think you would recognize one, or you wouldn't
> be complaining of their paucity. It's actually not uncommon
> for APers to have relatively poor relative pitch like this.

Ouch. I do recognize them. They sound "natural" but also flatter
than what I am used to. Erase your memory about the physics test
my friend did. That was in '84.

> > I just cannot imagine an orchestra
> > playing "Rite of Spring" in anything but 12-tET.
>
> The UC Berkeley orchestra did it in 2003 with no 12-tET
> intervals audible. The Firebird I mention above is Boulez,
> Chicago '93, Deutsche Grammophon 437-850-2.
>
> > So the same would apply for choirs singing choral music of
> > the 19th and 20th centuries.
>
> Why would the same thing be true of choirs as is of orchestras??
> They're completely different domains.

Just another comparison. Maybe not a good one. We do a lot of
big works with full orchestra. It all has to be in tune. I think
it's 12t-ET. Maybe it's not, convince me otherwise.

> > Having AP, I think I would know if I was singing 14 cents flat.
>
> Maybe you aren't. Is your AP sensitive to the thirds played
> by brass quintets?

It's possible I attack them in 12-tET and slide down a little
for sustained chords. I missed your post on that when I wrote
this one.

> > So maybe they should get rid of singers with AP, but I've never
> > been accused of singing sharp. Or singing minor thirds flat. I
> > think Occam's razor applies: It's just plain 12t-ET. Sorry to
> > rain on anyone's parade.
>
> Unfortunately intonation is not something that is understood
> by musicians.

> -Carl

Oh really now. That's like saying kinesthetic awareness isn't
something understood by athletes. Now you are making generalizations.

Cheers,

PGH

Unfortunately intonation is not something that is understood
by musicians.

-Carl

Please take this back, or rephrase, or something. There are plenty of
musicians that understand intonation a lot better than dilettantes, amateurs, and
most musicologists.

************************************** See what's free at http://www.aol.com.

> > > Sure, the strings have the flexibility of tuning intervals
> > > pure.
> >
> > ...as do all of the instruments.
>
> Some, with the lip as they say.

Enough, if you're a skilled player. Not to mention
all modern brass instruments have slides, not just the
trombone.

> > Saying orchestras intone in 12-tET is accurate at some level
> > of abstraction. The actual intonation of the ensemble depends
> > on the orchestra and the music. Then there is sectional
> > intonation, and finally the intonation of the individual
> > instruments.
> >
> > Instrument intonation can be viewed as sectional intonation
> > with small, random perturbations. And not so small if you're
> > most violin sections. :)
>
> ??? So you mean string ensembles tune closer to just?

Generally different instrument types have different
intonation tendencies. First of all, the theory we've been
discussing is very keyboard-centric. Discrete notes don't
exist in reality, they are an abstraction. If you look at
a pitch-tracker, you'll see that the majority of the time
a violin is playing, it's playing "connective tissue" (to
quote Eric Lindemann) between notes -- slides, glisses,
legato goo, etc. etc. So is this stuff in the realm of
intonation theory or not? Clearly, in an all-string
ensemble, players have more in common, so there's more
chance for them to sync up their intonation, and the stuff
listeners do when they extract "notes" from string playing
will all line up across instruments. The same kind of
thing holds true for winds and brass. In a big orchestra,
players intonate first with their section, and second
with the entire ensemble both for this reason, and also
because other instrument types are located far away and
can be hard to hear.

> > And that's a very good comparison. Check out your local
> > orchestra, then come home and download some MIDI versions
> > of what you just heard. Or use recordings in your library.
> > The difference you hear is in large part due to the
> > deviations from 12-tET in the intonation of the real
> > orchestra.
>
> I would like to believe this. Hopefully you are right, it makes
> music a lot more interesting!

Try the MIDI Comparison Challenge 2007! :)

> > > I am almost inclined to believe that if anything, choral
> > > singing is close to Pythagorean tuning, where whole steps are
> > > essentially 9/8 and half steps their square root.
> >
> > There's no square root of anything in Pythagorean intonation.
>
> Sure there is. What about the tritone? I was taught 102 102 102 102
> 90 102 102 102 102 102 102 90 for Pythagorean. Am I misinformed?

Cents are inherently irrational. Pythagorean intonation is
a form of JI, which under one definition of JI at least, means
everything is a rational.

> > > Otherwise, music with augmented chords and arpeggios (Howells
> > > comes to mind here) would have the diesis all over the place
> > > and that just doesn't happen, C'mon, octaves off by 42 cents?
> > > That's ridiculous!
> >
> > Melodic intonation can be different from harmonic intonation.
>
> Well I goofed a little anyway cuz the last interval is a
> diminished fourth not a major third. But you'd still be off
> 28 cents. I don't think choral singers differentiate between
> melodic and harmonic intonation.

They do. Otherwise it would not be possible, as you point
out, to hear as many measurably pure (using FFT) chords in
some choral performances and still finish pieces (measurably)
on-pitch. Now, I don't think they do precise adaptive JI,
where the commas are spread out evenly over all melodic
intervals. But whenever full harmony drops away, people's
sense of pitch causes them to right the comma drift. The
basses take a big leap, and they may insert a comma. Also,
I think people are generally glued to something closer to
12-tET intonation for the diatonic scale than JI, so that does
have an adaptive-JI effect.

> "Melody is harmony unfured, harmony is
> melody furled" (A Scriabin). (Is "furled" a word?)

There is a lot of truth to this. . .

> > > Tribal music of Africa probably is just.
> >
> > Why do you say that? Have you listened to much tribal music
> > from Africa? I have. It's mostly percussion and chanting.
> > Perhaps you're thinking of Mbube singing? That's not tribal
> > music...
>
> I'm not an expert. I am thinking of the kind of African singing,
> usually three parts, with triads. That sounds just.

Africa is a big place. That sort of singing is, as far as
I know, a post-colonial phenomenon. I agree it tends toward
5-limit JI.

> > > I just cannot imagine an orchestra
> > > playing "Rite of Spring" in anything but 12-tET.
> >
> > The UC Berkeley orchestra did it in 2003 with no 12-tET
> > intervals audible. The Firebird I mention above is Boulez,
> > Chicago '93, Deutsche Grammophon 437-850-2.
> >
> > > So the same would apply for choirs singing choral music of
> > > the 19th and 20th centuries.
> >
> > Why would the same thing be true of choirs as is of orchestras??
> > They're completely different domains.
>
> Just another comparison. Maybe not a good one. We do a lot of
> big works with full orchestra. It all has to be in tune. I
> think it's 12t-ET. Maybe it's not, convince me otherwise.

First let's talk about how closely you line up with the guy
(or gal) standing next to you. How close, in cents, do you
think, as a function of time a note is sutained?

> > > So maybe they should get rid of singers with AP, but I've never
> > > been accused of singing sharp. Or singing minor thirds flat. I
> > > think Occam's razor applies: It's just plain 12t-ET. Sorry to
> > > rain on anyone's parade.
> >
> > Unfortunately intonation is not something that is understood
> > by musicians.
>
> Oh really now. That's like saying kinesthetic awareness isn't
> something understood by athletes. Now you are making
> generalizations.

Hardly. How many musicians know what meantone is, or that
it was part of Western music for 300 years? How many know
the commas of the 12-tET kernel? How many know what
extended JI is, or have any practice singing or hearing
7- or 11-limit intervals? Heck, pianists don't even know
how to tune their own instruments in this culture. Can you
set equal temperament by ear on your piano? Have you ever
tried?

All this stuff is what I would consider basic, fundamental
stuff about intonation that every musician should know.
I've hung around some of the best conservatories, and their
students don't have this knowledge. Then consider that the
vast majority of musicians work in the rock and hip-hop
world...

-Carl

> Please take this back, or rephrase, or something. There are
> plenty of musicians that understand intonation a lot better
> than dilettantes, amateurs, and most musicologists.

I don't need to say anything. Everyone here already knows
that they are amateurs compared to you and the musicians you
work with.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > Sure, the strings have the flexibility of tuning intervals
> > > > pure.
> > >
> > > ...as do all of the instruments.
> >
> > Some, with the lip as they say.
>
> Enough, if you're a skilled player. Not to mention
> all modern brass instruments have slides, not just the
> trombone.
>
> > > Saying orchestras intone in 12-tET is accurate at some level
> > > of abstraction. The actual intonation of the ensemble depends
> > > on the orchestra and the music. Then there is sectional
> > > intonation, and finally the intonation of the individual
> > > instruments.
> > >
> > > Instrument intonation can be viewed as sectional intonation
> > > with small, random perturbations. And not so small if you're
> > > most violin sections. :)
> >
> > ??? So you mean string ensembles tune closer to just?
>
> Generally different instrument types have different
> intonation tendencies. First of all, the theory we've been
> discussing is very keyboard-centric. Discrete notes don't
> exist in reality, they are an abstraction. If you look at
> a pitch-tracker, you'll see that the majority of the time
> a violin is playing, it's playing "connective tissue" (to
> quote Eric Lindemann) between notes -- slides, glisses,
> legato goo, etc. etc. So is this stuff in the realm of
> intonation theory or not? Clearly, in an all-string
> ensemble, players have more in common, so there's more
> chance for them to sync up their intonation, and the stuff
> listeners do when they extract "notes" from string playing
> will all line up across instruments. The same kind of
> thing holds true for winds and brass. In a big orchestra,
> players intonate first with their section, and second
> with the entire ensemble both for this reason, and also
> because other instrument types are located far away and
> can be hard to hear.
>
> > > And that's a very good comparison. Check out your local
> > > orchestra, then come home and download some MIDI versions
> > > of what you just heard. Or use recordings in your library.
> > > The difference you hear is in large part due to the
> > > deviations from 12-tET in the intonation of the real
> > > orchestra.
> >
> > I would like to believe this. Hopefully you are right, it makes
> > music a lot more interesting!
>
> Try the MIDI Comparison Challenge 2007! :)
>
> > > > I am almost inclined to believe that if anything, choral
> > > > singing is close to Pythagorean tuning, where whole steps are
> > > > essentially 9/8 and half steps their square root.
> > >
> > > There's no square root of anything in Pythagorean intonation.
> >
> > Sure there is. What about the tritone? I was taught 102 102 102
102
> > 90 102 102 102 102 102 102 90 for Pythagorean. Am I misinformed?
>
> Cents are inherently irrational. Pythagorean intonation is
> a form of JI, which under one definition of JI at least, means
> everything is a rational.
>
> > > > Otherwise, music with augmented chords and arpeggios (Howells
> > > > comes to mind here) would have the diesis all over the place
> > > > and that just doesn't happen, C'mon, octaves off by 42 cents?
> > > > That's ridiculous!
> > >
> > > Melodic intonation can be different from harmonic intonation.
> >
> > Well I goofed a little anyway cuz the last interval is a
> > diminished fourth not a major third. But you'd still be off
> > 28 cents. I don't think choral singers differentiate between
> > melodic and harmonic intonation.
>
> They do. Otherwise it would not be possible, as you point
> out, to hear as many measurably pure (using FFT) chords in
> some choral performances and still finish pieces (measurably)
> on-pitch. Now, I don't think they do precise adaptive JI,
> where the commas are spread out evenly over all melodic
> intervals. But whenever full harmony drops away, people's
> sense of pitch causes them to right the comma drift. The
> basses take a big leap, and they may insert a comma. Also,
> I think people are generally glued to something closer to
> 12-tET intonation for the diatonic scale than JI, so that does
> have an adaptive-JI effect.
>
> > "Melody is harmony unfured, harmony is
> > melody furled" (A Scriabin). (Is "furled" a word?)
>
> There is a lot of truth to this. . .
>
> > > > Tribal music of Africa probably is just.
> > >
> > > Why do you say that? Have you listened to much tribal music
> > > from Africa? I have. It's mostly percussion and chanting.
> > > Perhaps you're thinking of Mbube singing? That's not tribal
> > > music...
> >
> > I'm not an expert. I am thinking of the kind of African singing,
> > usually three parts, with triads. That sounds just.
>
> Africa is a big place. That sort of singing is, as far as
> I know, a post-colonial phenomenon. I agree it tends toward
> 5-limit JI.
>
> > > > I just cannot imagine an orchestra
> > > > playing "Rite of Spring" in anything but 12-tET.
> > >
> > > The UC Berkeley orchestra did it in 2003 with no 12-tET
> > > intervals audible. The Firebird I mention above is Boulez,
> > > Chicago '93, Deutsche Grammophon 437-850-2.
> > >
> > > > So the same would apply for choirs singing choral music of
> > > > the 19th and 20th centuries.
> > >
> > > Why would the same thing be true of choirs as is of orchestras??
> > > They're completely different domains.
> >
> > Just another comparison. Maybe not a good one. We do a lot of
> > big works with full orchestra. It all has to be in tune. I
> > think it's 12t-ET. Maybe it's not, convince me otherwise.
>
> First let's talk about how closely you line up with the guy
> (or gal) standing next to you. How close, in cents, do you
> think, as a function of time a note is sutained?
>
> > > > So maybe they should get rid of singers with AP, but I've
never
> > > > been accused of singing sharp. Or singing minor thirds flat. I
> > > > think Occam's razor applies: It's just plain 12t-ET. Sorry to
> > > > rain on anyone's parade.
> > >
> > > Unfortunately intonation is not something that is understood
> > > by musicians.
> >
> > Oh really now. That's like saying kinesthetic awareness isn't
> > something understood by athletes. Now you are making
> > generalizations.
>
> Hardly. How many musicians know what meantone is, or that
> it was part of Western music for 300 years? How many know
> the commas of the 12-tET kernel? How many know what
> extended JI is, or have any practice singing or hearing
> 7- or 11-limit intervals? Heck, pianists don't even know
> how to tune their own instruments in this culture. Can you
> set equal temperament by ear on your piano? Have you ever
> tried?
>
> All this stuff is what I would consider basic, fundamental
> stuff about intonation that every musician should know.
> I've hung around some of the best conservatories, and their
> students don't have this knowledge. Then consider that the
> vast majority of musicians work in the rock and hip-hop
> world...
>
> -Carl

I need to finish some work so I will touch on all your points later.
But as for this last part, all I can say is remember about
"intuition" and "talent", and that Beethoven couldn't even make
change, or translate currencies (he hated math). Sure, most
professional singers aren't math-brains, but they can still sing
beautifully and in tune.

My friend is a vocal coach so I should ask him some of these
questions. He might not know kernel-commas, but do you know about
vowel-coloring, etc? It's like you said about "goo", it's hard
to pin anything down anyway. I read one article that even brings
in quantum mechanics to indicate you can't know the frequency
and position of a wave (Good grief) at any moment. Went over my head.

PGH

Hi Paul and Carl,

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

> > > > [Paul]
> > > > I am almost inclined to believe that if anything, choral
> > > > singing is close to Pythagorean tuning, where whole steps are
> > > > essentially 9/8 and half steps their square root.
> > >
> > > [Carl]
> > > There's no square root of anything in Pythagorean intonation.
> >
> > [Paul]
> > Sure there is. What about the tritone? I was taught
> > 102 102 102 102 90 102 102 102 102 102 102 90 for
> > Pythagorean. Am I misinformed?
>
> Cents are inherently irrational. Pythagorean intonation
> is a form of JI, which under one definition of JI at least,
> means everything is a rational.

Regardless of what definition one uses for "JI", pythagorean
tuning by definition is a rational tuning. So Carl is right.
Cents are only an approximate logarithmic measure of
the exact pythagorean ratios.

But Paul, i'm not quite sure what you're getting at with
either your remark about the tritone or your list of
cents values.

In integer cents values, the pythagorean major-2nd = 204
cents and minor-2nd = 90 cents. 102 cents is an exact 1/2 of
the major-2nd, but it is not a part of pythagorean tuning.

As for the tritone, perhaps you're thinking of the 12-edo
version, whose "ratio" is 2^(1/2) (i.e., the square-root of 2).
But in pythagorean tuning the tritone is the augmented-4th
whose exact ratio is 729/512 -- that is, (9/8)^3 or 2,3-monzo
[-9 6> -- expressed in decimal form as exactly 1.423828125,
with a logarithmic interval size of ~611.7300052 cents.

Here's my Encyclopedia page on the tritone:
http://tonalsoft.com/enc/t/tritone.aspx

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

--- In tuning@yahoogroups.com, "monz" <monz@...> wrote:
>
> Hi Paul and Carl,
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
>
> > > > > [Paul]
> > > > > I am almost inclined to believe that if anything, choral
> > > > > singing is close to Pythagorean tuning, where whole steps
are
> > > > > essentially 9/8 and half steps their square root.
> > > >
> > > > [Carl]
> > > > There's no square root of anything in Pythagorean intonation.
> > >
> > > [Paul]
> > > Sure there is. What about the tritone? I was taught
> > > 102 102 102 102 90 102 102 102 102 102 102 90 for
> > > Pythagorean. Am I misinformed?
> >
> > Cents are inherently irrational. Pythagorean intonation
> > is a form of JI, which under one definition of JI at least,
> > means everything is a rational.
>
>
> Regardless of what definition one uses for "JI", pythagorean
> tuning by definition is a rational tuning. So Carl is right.
> Cents are only an approximate logarithmic measure of
> the exact pythagorean ratios.
>
> But Paul, i'm not quite sure what you're getting at with
> either your remark about the tritone or your list of
> cents values.
>
> In integer cents values, the pythagorean major-2nd = 204
> cents and minor-2nd = 90 cents. 102 cents is an exact 1/2 of
> the major-2nd, but it is not a part of pythagorean tuning.
>
> As for the tritone, perhaps you're thinking of the 12-edo
> version, whose "ratio" is 2^(1/2) (i.e., the square-root of 2).
> But in pythagorean tuning the tritone is the augmented-4th
> whose exact ratio is 729/512 -- that is, (9/8)^3 or 2,3-monzo
> [-9 6> -- expressed in decimal form as exactly 1.423828125,
> with a logarithmic interval size of ~611.7300052 cents.
>
> Here's my Encyclopedia page on the tritone:
> http://tonalsoft.com/enc/t/tritone.aspx
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software

Thanks Monz. My bad. I actually got those numbers from, yes,
"The Encyclopedia Americana 1960" which Dad bought used. It
stuck in my memory. I think I looked at it when I was in high
school. It compared meantone, just, pythagorean and 12-tET.

Let's see: 408+90+102=600. Well it least I'm consistent albeit wrong.
(I upgraded to the Encylopedia Britannica back in the 80's. Much
nicer).

PGH

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> Thanks Monz. My bad. I actually got those numbers from,
> yes, "The Encyclopedia Americana 1960" which Dad bought used.
> It stuck in my memory. I think I looked at it when I was
> in high school. It compared meantone, just, pythagorean
> and 12-tET.
>
> Let's see: 408+90+102=600. Well it least I'm consistent
> albeit wrong. (I upgraded to the Encylopedia Britannica
> back in the 80's. Much nicer).

Well, all humility aside (ahem), i suggest that for
any information concerning tuning, you look at *my*
Encyclopedia first, and forget about what appears in
any other.

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

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > > > Sure, the strings have the flexibility of tuning intervals
> > > > pure.
> > >
> > > ...as do all of the instruments.
> >
> > Some, with the lip as they say.
>
> Enough, if you're a skilled player. Not to mention
> all modern brass instruments have slides, not just the
> trombone.

But trombone is the only one where you can adjust on the fly of
course. Not just a main tuning slide (you know)

> > > Saying orchestras intone in 12-tET is accurate at some level
> > > of abstraction. The actual intonation of the ensemble depends
> > > on the orchestra and the music. Then there is sectional
> > > intonation, and finally the intonation of the individual
> > > instruments.
> > >
> > > Instrument intonation can be viewed as sectional intonation
> > > with small, random perturbations. And not so small if you're
> > > most violin sections. :)
> >
> > ??? So you mean string ensembles tune closer to just?
>
> Generally different instrument types have different
> intonation tendencies. First of all, the theory we've been
> discussing is very keyboard-centric. Discrete notes don't
> exist in reality, they are an abstraction. If you look at
> a pitch-tracker, you'll see that the majority of the time
> a violin is playing, it's playing "connective tissue" (to
> quote Eric Lindemann) between notes -- slides, glisses,
> legato goo, etc. etc. So is this stuff in the realm of
> intonation theory or not? Clearly, in an all-string
> ensemble, players have more in common, so there's more
> chance for them to sync up their intonation, and the stuff
> listeners do when they extract "notes" from string playing
> will all line up across instruments. The same kind of
> thing holds true for winds and brass. In a big orchestra,
> players intonate first with their section, and second
> with the entire ensemble both for this reason, and also
> because other instrument types are located far away and
> can be hard to hear.

So it's not all quantifiable? A lot of people don't believe
music (or art) is quantifiable AT ALL. Most people, when
I talk about math and music either say "Well it's the same
thing" (Not true) Or --- Wow, those things don't have
anything in common! (Also, Not true)

> > > And that's a very good comparison. Check out your local
> > > orchestra, then come home and download some MIDI versions
> > > of what you just heard. Or use recordings in your library.
> > > The difference you hear is in large part due to the
> > > deviations from 12-tET in the intonation of the real
> > > orchestra.
> >
> > I would like to believe this. Hopefully you are right, it makes
> > music a lot more interesting!
>
> Try the MIDI Comparison Challenge 2007! :)

I will

> > > > I am almost inclined to believe that if anything, choral
> > > > singing is close to Pythagorean tuning, where whole steps are
> > > > essentially 9/8 and half steps their square root.
> > >
> > > There's no square root of anything in Pythagorean intonation.
> >
> > Sure there is. What about the tritone? I was taught 102 102 102
102
> > 90 102 102 102 102 102 102 90 for Pythagorean. Am I misinformed?
>
> Cents are inherently irrational. Pythagorean intonation is
> a form of JI, which under one definition of JI at least, means
> everything is a rational.

See my response to monz
>
> > > > Otherwise, music with augmented chords and arpeggios (Howells
> > > > comes to mind here) would have the diesis all over the place
> > > > and that just doesn't happen, C'mon, octaves off by 42 cents?
> > > > That's ridiculous!
> > >
> > > Melodic intonation can be different from harmonic intonation.
> >
> > Well I goofed a little anyway cuz the last interval is a
> > diminished fourth not a major third. But you'd still be off
> > 28 cents. I don't think choral singers differentiate between
> > melodic and harmonic intonation.
>
> They do. Otherwise it would not be possible, as you point
> out, to hear as many measurably pure (using FFT) chords in
> some choral performances and still finish pieces (measurably)
> on-pitch. Now, I don't think they do precise adaptive JI,
> where the commas are spread out evenly over all melodic
> intervals. But whenever full harmony drops away, people's
> sense of pitch causes them to right the comma drift. The
> basses take a big leap, and they may insert a comma. Also,
> I think people are generally glued to something closer to
> 12-tET intonation for the diatonic scale than JI, so that does
> have an adaptive-JI effect.

Maybe. So you are saying, insert a comma to fix commatic drift? Would
that be an anti-comma? I totally agree with your last sentence.
That's my pseudo-pythagorean-scale: 204-204-90-204-204-204-204-90<-
>200-200-100-200-200-200-200-100!

> > "Melody is harmony unfured, harmony is
> > melody furled" (A Scriabin). (Is "furled" a word?)
>
> There is a lot of truth to this. . .
>
> > > > Tribal music of Africa probably is just.
> > >
> > > Why do you say that? Have you listened to much tribal music
> > > from Africa? I have. It's mostly percussion and chanting.
> > > Perhaps you're thinking of Mbube singing? That's not tribal
> > > music...
> >
> > I'm not an expert. I am thinking of the kind of African singing,
> > usually three parts, with triads. That sounds just.
>
> Africa is a big place. That sort of singing is, as far as
> I know, a post-colonial phenomenon. I agree it tends toward
> 5-limit JI.
>
> > > > I just cannot imagine an orchestra
> > > > playing "Rite of Spring" in anything but 12-tET.
> > >
> > > The UC Berkeley orchestra did it in 2003 with no 12-tET
> > > intervals audible. The Firebird I mention above is Boulez,
> > > Chicago '93, Deutsche Grammophon 437-850-2.

Boulez should know what he is doing I guess. Didn't he start IRCAM?
Can you cite the UC Berkeley 2003 recording? I want it!!!

> > > > So the same would apply for choirs singing choral music of
> > > > the 19th and 20th centuries.
> > >
> > > Why would the same thing be true of choirs as is of orchestras??
> > > They're completely different domains.
> >
> > Just another comparison. Maybe not a good one. We do a lot of
> > big works with full orchestra. It all has to be in tune. I
> > think it's 12t-ET. Maybe it's not, convince me otherwise.
>
> First let's talk about how closely you line up with the guy
> (or gal) standing next to you. How close, in cents, do you
> think, as a function of time a note is sutained?

Do you mean, close to each other, over time, as a note is sustained?
Hopefully not off by more than a few cents, especially if sustained
for more than a quarter note! I would imagine it quickly gets
closer together. Usually stronger singers set the pitch. (Not always
louder singers, just stronger ones)

We sit in sections. However, 10 years ago, under another director,
we say mixed, I never understood that.

> > > > So maybe they should get rid of singers with AP, but I've
never
> > > > been accused of singing sharp. Or singing minor thirds flat. I
> > > > think Occam's razor applies: It's just plain 12t-ET. Sorry to
> > > > rain on anyone's parade.
> > >
> > > Unfortunately intonation is not something that is understood
> > > by musicians.
> >
> > Oh really now. That's like saying kinesthetic awareness isn't
> > something understood by athletes. Now you are making
> > generalizations.
>
> Hardly. How many musicians know what meantone is, or that
> it was part of Western music for 300 years? How many know
> the commas of the 12-tET kernel? How many know what
> extended JI is, or have any practice singing or hearing
> 7- or 11-limit intervals? Heck, pianists don't even know
> how to tune their own instruments in this culture. Can you
> set equal temperament by ear on your piano? Have you ever
> tried?

Yes, I learned about temperament bars real early. I worked as a piano
technician (even though I didn't tune, I knew the theory.) However,
I did retune my Conover grand to the celebrated "5 and 7's"
temperament: Black keys: 5t-ET Whites: 7-tET Offset so they balance.
>
> All this stuff is what I would consider basic, fundamental
> stuff about intonation that every musician should know.
> I've hung around some of the best conservatories, and their
> students don't have this knowledge. Then consider that the
> vast majority of musicians work in the rock and hip-hop
> world...
>
> -Carl

I do get frustrated with other musicians and don't agree with the way
things are. But I think that is changing. With all the technology
now, and it's importance, people are owning up to science. Music
used to be a science (back in the day of Mozart and Haydn) and it
is high time it become one again. I say: Open up the conservatories
to jazz, rock, hip hop whatever! But also teach a little science.
Musicians who balance heat (emotion) with light (intellect) do the
best. Doesn't change the fact that music is, yes, emotion.

We have our work cut out for us. There are musicians who don't even
know the octave is 2/1. In high school my friend played in a rock
group where the lead singer didn't even know what an octave WAS.
Had to show him on the piano!

PGH

> But as for this last part, all I can say is remember about
> "intuition" and "talent", and that Beethoven couldn't even make
> change, or translate currencies (he hated math). Sure, most
> professional singers aren't math-brains, but they can still sing
> beautifully and in tune.

I said "knowledge" not "skill".

> My friend is a vocal coach so I should ask him some of these
> questions. He might not know kernel-commas, but do you know about
> vowel-coloring, etc?

I've practiced a lot of vowel stuff with singing.
Barbershoppers are obsessed with it.

> It's like you said about "goo", it's hard
> to pin anything down anyway. I read one article that even brings
> in quantum mechanics to indicate you can't know the frequency
> and position of a wave (Good grief) at any moment.

There's something called the Classical Uncertainty Principle,
which doesn't have to do with quantum mechanics, but does
limit simultaneous frequency and time -domain resolution.
So you can never know the exact onset of a sound and its
frequency. I don't know the fourier math behind it, but I've
always fancied that it follows from the fact that frequency
has time units.

-Carl

> > > > > Sure, the strings have the flexibility of tuning intervals
> > > > > pure.
> > > >
> > > > ...as do all of the instruments.
> > >
> > > Some, with the lip as they say.
> >
> > Enough, if you're a skilled player. Not to mention
> > all modern brass instruments have slides, not just the
> > trombone.
>
> But trombone is the only one where you can adjust on the fly of
> course. Not just a main tuning slide (you know)

Typical trumpets have two realtime slides.

> > > > Instrument intonation can be viewed as sectional intonation
> > > > with small, random perturbations. And not so small if you're
> > > > most violin sections. :)
> > >
> > > ??? So you mean string ensembles tune closer to just?

Here I meant that many (even pro) orchestral violin sections
are not able to play in unison without an audible "chorusing"
effect. String players in early music ensembles don't tend
to have this problem, and are usually trained to pay much
closer attention to intonation than a classical violinist.

> > Generally different instrument types have different
> > intonation tendencies. First of all, the theory we've been
> > discussing is very keyboard-centric. Discrete notes don't
> > exist in reality, they are an abstraction. If you look at
> > a pitch-tracker, you'll see that the majority of the time
> > a violin is playing, it's playing "connective tissue" (to
> > quote Eric Lindemann) between notes -- slides, glisses,
> > legato goo, etc. etc. So is this stuff in the realm of
> > intonation theory or not? Clearly, in an all-string
> > ensemble, players have more in common, so there's more
> > chance for them to sync up their intonation, and the stuff
> > listeners do when they extract "notes" from string playing
> > will all line up across instruments. The same kind of
> > thing holds true for winds and brass. In a big orchestra,
> > players intonate first with their section, and second
> > with the entire ensemble both for this reason, and also
> > because other instrument types are located far away and
> > can be hard to hear.
>
> So it's not all quantifiable? A lot of people don't believe
> music (or art) is quantifiable AT ALL. Most people, when
> I talk about math and music either say "Well it's the same
> thing" (Not true) Or --- Wow, those things don't have
> anything in common! (Also, Not true)

It's not that it isn't quantifiable, it's just that the
keyboard-centric view is a simplification that leaves
some bits out. Those bits are needed if you want to make
a synthesizer sound like a violin. Are they needed in
music theory? I guess that depends what you're trying
to do. I'm suggestion they come up in a discussion of
ensemble intonation.

> > > > Melodic intonation can be different from harmonic intonation.
> > >
> > > Well I goofed a little anyway cuz the last interval is a
> > > diminished fourth not a major third. But you'd still be off
> > > 28 cents. I don't think choral singers differentiate between
> > > melodic and harmonic intonation.
> >
> > They do. Otherwise it would not be possible, as you point
> > out, to hear as many measurably pure (using FFT) chords in
> > some choral performances and still finish pieces (measurably)
> > on-pitch. Now, I don't think they do precise adaptive JI,
> > where the commas are spread out evenly over all melodic
> > intervals. But whenever full harmony drops away, people's
> > sense of pitch causes them to right the comma drift. The
> > basses take a big leap, and they may insert a comma. Also,
> > I think people are generally glued to something closer to
> > 12-tET intonation for the diatonic scale than JI, so that does
> > have an adaptive-JI effect.
>
> Maybe. So you are saying, insert a comma to fix commatic drift?
> Would that be an anti-comma?

It's the same comma, just inserted all at once instead of
spread out like in mathematically-perfect adaptive JI.

> > > > > I just cannot imagine an orchestra
> > > > > playing "Rite of Spring" in anything but 12-tET.
> > > >
> > > > The UC Berkeley orchestra did it in 2003 with no 12-tET
> > > > intervals audible. The Firebird I mention above is Boulez,
> > > > Chicago '93, Deutsche Grammophon 437-850-2.
>
> Boulez should know what he is doing I guess.

He's a good conductor.

> Didn't he start IRCAM?

May have. Lindemann (quoted earlier) was a big IRCAM player
in the '80s, I believe.

> Can you cite the UC Berkeley 2003 recording? I want it!!!

I don't know if a recording was made. My friend had the
bassoon solo; I'll write to him and see if he has it.

> > > Just another comparison. Maybe not a good one. We do a lot of
> > > big works with full orchestra. It all has to be in tune. I
> > > think it's 12t-ET. Maybe it's not, convince me otherwise.
> >
> > First let's talk about how closely you line up with the guy
> > (or gal) standing next to you. How close, in cents, do you
> > think, as a function of time a note is sutained?
>
> Do you mean, close to each other, over time, as a note is
> sustained?

Yes. You sing in unison with your section-mates. How close
can you get? Within a few cents for a whole note (the voice
naturally wavers by a couple cents at a time). In a run,
14 cents probably wouldn't break the bank.

> Hopefully not off by more than a few cents, especially if sustained
> for more than a quarter note! I would imagine it quickly gets
> closer together. Usually stronger singers set the pitch. (Not
> always louder singers, just stronger ones)

Yes.

> We sit in sections. However, 10 years ago, under another director,
> we say mixed, I never understood that.

It's a good rehearsal technique. I've never heard it from
the audience... wonder what it sounds like.

> We have our work cut out for us. There are musicians who don't even
> know the octave is 2/1. In high school my friend played in a rock
> group where the lead singer didn't even know what an octave WAS.
> Had to show him on the piano!

Yes, that sounds more typical to me.

-Carl

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

> I don't know the fourier math behind it, but I've
> always fancied that it follows from the fact that frequency
> has time units.

One way to think about it is this: a precise frequency means a periodic
waveform. But a periodic waveform, by definition, extends from -infinity
to infinity in terms of time. If it is time-limited, it must involve
more than one frequency.

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

> Discrete notes don't
> exist in reality, they are an abstraction. If you look at
> a pitch-tracker, you'll see that the majority of the time
> a violin is playing, it's playing "connective tissue" (to
> quote Eric Lindemann) between notes -- slides, glisses,
> legato goo, etc. etc. So is this stuff in the realm of
> intonation theory or not?

It certainly is, in EON theory at least, which views "partials" as
regions, and judges tuning and intonation in light of the various
weights of those regions (with an ear on their psychoacoustic
byproducts) within the overall sound. If the fuzz and goo is
statistically weighted, so to speak, in regions which characterize the
overall tuning, it is going to be "in tune". These "weights"
can't be entirely measured by machine because expression and
interpretation lend their own weights to different events: a
dissonance, false and forte, can be outweighed in the overall scheme
of things by a consonance in a pianissimo resolution,
that kind of thing.

Paul- when you hear "xenharmonic" music, does it always sound
out of tune to you?

-Cameron Bobro

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
>
> > Discrete notes don't
> > exist in reality, they are an abstraction. If you look at
> > a pitch-tracker, you'll see that the majority of the time
> > a violin is playing, it's playing "connective tissue" (to
> > quote Eric Lindemann) between notes -- slides, glisses,
> > legato goo, etc. etc. So is this stuff in the realm of
> > intonation theory or not?
>
> It certainly is, in EON theory at least, which views "partials" as
> regions, and judges tuning and intonation in light of the various
> weights of those regions (with an ear on their psychoacoustic
> byproducts) within the overall sound. If the fuzz and goo is
> statistically weighted, so to speak, in regions which characterize
the
> overall tuning, it is going to be "in tune". These "weights"
> can't be entirely measured by machine because expression and
> interpretation lend their own weights to different events: a
> dissonance, false and forte, can be outweighed in the overall
scheme
> of things by a consonance in a pianissimo resolution,
> that kind of thing.
>
> Paul- when you hear "xenharmonic" music, does it always sound
> out of tune to you?
>
> -Cameron Bobro

Usually, even though I like 31t-ET, that sounds the best. Haven't
listened to much lately
>

Occam's Razor has nothing to do with the discussion. In order to 'sing
12-ET' (or play it) in any meaningful sense, you need to make both
melodic and harmonic intervals
1) impure, i.e. 'out of tune' and (if harmonic) beating
2) impure / beating by a particular, rather exact amount

and I contend that this is impossible for singers with or without
piano accompaniment.

Sure, you can try to sing fifths a tiny bit flat and thirds rather
sharp; but the result will NOT be ET in any meaningful sense, unless
yon can learn to sing melodic intervals to an accuracy of 2 cents. It
is more likely to be a chaotic mess that only sounds acceptable (if at
all) by chance, or because some singers naturally try to approach pure
intervals.

Or you can try to take your pitches from a piano; in which case the
result may sometimes sound similar to ET, but is likely to deviate
significantly from it in many cases, because one can't vocally
reproduce or remember a pitch from the piano with all that much
accuracy. Not that one would want to, since the piano doesn't even
have 2:1 octaves.

Due to the piano's inharmonicity it is really impossible to take a
pitch from it to any accuracy: if your fundamental is right, your
second harmonic will be wrong.

Actually, Occam's razor does come in. Unless we see some definite
evidence to the contrary, I think it is simplest to assume that
*no-one* can sing a melodic interval, or take a pitch from a piano,
with 2c accuracy. *Pure* harmonic intervals might be achieved with
this accuracy by using 'locking' between voices - i.e. beats - but it
takes a tiny fraction of a second for this to be achieved.

Piano tuners manage to achieve ET by very careful attention to the
beats in certain intervals, which they listen to in isolation, after
checking that they are on the right side of the pure interval. (NB: a
fifth that is 2c sharp sounds identical to one that is 2c flat, unless
you do a direct comparison one after the other!)
Choral singing is a totally different situation with, usually, much
wider tolerances. In rapidly changing or dissonant harmonies, large
deviations from any theoretical scheme are both possible and probable
without causing noticeable artistic problems.

In practice, one starts with bad choral intonation, then works to
improve it. I propose that this work is mostly and best done by
singers *listening to each other* and, by using their ears, being able
to approach purity both within a voice and between voices. Pure
intervals are the only ones one can reliably hear and try to approach
in harmony.

Not that pure intervals may ever really be reached: but that intervals
become *sufficiently* pure for their musical context.

How do several basses singing the same line manage to be in tune with
each other? Absolutely NOT by all listening to the piano and then
independently trying to reproduce its pitches. The beating of a
mistuned unison between similar timbres is strong enough that (if they
listen at all!) they are practically forced into an almost-pure unison
within a fraction of a second. This unison will be, of course, not so
far away from the piano's, but need not and cannot be identical to it.

In the same Max Planck article, we read that 'some choir directors
already know that in a quiet, long-held final major chord the third is
to be taken somewhat flatter.' What can this mean apart from that
purity of intonation is desirable in some circumstances and can be
achieved if a chord is to be sustained for some time?

At the same time, choirs that sing with piano cannot get too far away
from its broad intonational framework. Again, due to inharmonicity
and/or in rapid passages, it is really impossible to sing in tune with
a piano very accurately. But it is not necessary either. It is only
possible and necessary to be *sufficiently* in tune with it, given the
very different timbres and envelopes of the piano and the voice.

What deviations are allowed while one remains *sufficiently* pure or
in tune is an experimental question - which hasn't received that much
attention, probably because of its difficulty.

Another experimental question is how well someone can detect
deviations from ET in single pitches, if they have 'absolute pitch'.
Why not try tuning a piano note by note, without ever playing an
interval or chord; then get out the electronic gadget and see how far
off you are.

To say 'I could easily notice 14 cents deviation' without ever having
tested yourself is absurd.

I think choirs, even excellent ones with spotless intonation, probably:
Sing differently in chromatic or diatonic passages
Sing differently in religious or secular music
Sing differently in slow or fast passages
Sing differently in Renaissance or 20th century music
Since each of these factors is likely to affect intonation, to try and
describe real choral tuning by any fixed system of twelve (or more!)
pitches is futile.

What can realistically be done? One can listen to actual pieces being
performed by actual choirs and try to pick out significant features of
their tuning and see if any of these theoretical prejudices can
possibly be correct. Hence my link to the page with the Hilliard
Ensemble sample. No, their thirds are not absolutely pure: but they
are much nearer than ET is.

And yes, sometimes I hear choirs who sing thirds mighty sharp, but
that doesn't make them ET; it just makes them sharp. If one absolutely
wants the chord to sound shrill and aggressive then it is
indispensable (and one had also better sing a slightly sharp fifth!!).

If you forced me at gunpoint to say what most choirs mostly sing I
would have to say something like 'approximate 12-ET-based adaptive
JI'. Which means that the roots of chords progress approximately by ET
intervals, while the other voices make approximately pure intervals
with the roots. The degree of approximation depends, as I said, very
heavily on the context, and may (by absolute standards) be very good
one minute but lousy the next.

~~~T~~~

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Please take this back, or rephrase, or something. There are
> > plenty of musicians that understand intonation a lot better
> > than dilettantes, amateurs, and most musicologists.
>
> I don't need to say anything. Everyone here already knows
> that they are amateurs compared to you and the musicians you
> work with.
>
> -Carl
>

'Everyone'? Gee.

It just happens that I earned 100 Euros for two performances of the
lead vocal part in the Schuetz 'Seven Last Words' over Easter.

It just happens that next week I am giving two short harpsichord
concerts in the main church here in Heidelberg, on a historically
based Italian-style single manual instrument, I'm going to tune the
instrument myself (modified 1/5 comma meantone), and I'll go head to
head with anyone on the list in doing so.

By the way, and not so much on a professional level, did I advertise
my clavichord home recordings here? Not that they are of much formal
tuning interest, since the instrument is fretted fairly near ET and it
seems to come out slightly differently every time I temper it. They
can be found by searching Google for 'Thomas Dent clavichord'.
~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
>
> Occam's Razor has nothing to do with the discussion. In order
to 'sing
> 12-ET' (or play it) in any meaningful sense, you need to make both
> melodic and harmonic intervals
> 1) impure, i.e. 'out of tune' and (if harmonic) beating
> 2) impure / beating by a particular, rather exact amount
>
> and I contend that this is impossible for singers with or without
> piano accompaniment.
>
> Sure, you can try to sing fifths a tiny bit flat and thirds rather
> sharp; but the result will NOT be ET in any meaningful sense, unless
> yon can learn to sing melodic intervals to an accuracy of 2 cents.
It
> is more likely to be a chaotic mess that only sounds acceptable (if
at
> all) by chance, or because some singers naturally try to approach
pure
> intervals.
>
> Or you can try to take your pitches from a piano; in which case the
> result may sometimes sound similar to ET, but is likely to deviate
> significantly from it in many cases, because one can't vocally
> reproduce or remember a pitch from the piano with all that much
> accuracy. Not that one would want to, since the piano doesn't even
> have 2:1 octaves.
>
> Due to the piano's inharmonicity it is really impossible to take a
> pitch from it to any accuracy: if your fundamental is right, your
> second harmonic will be wrong.
>
> Actually, Occam's razor does come in. Unless we see some definite
> evidence to the contrary, I think it is simplest to assume that
> *no-one* can sing a melodic interval, or take a pitch from a piano,
> with 2c accuracy. *Pure* harmonic intervals might be achieved with
> this accuracy by using 'locking' between voices - i.e. beats - but
it
> takes a tiny fraction of a second for this to be achieved.
>
> Piano tuners manage to achieve ET by very careful attention to the
> beats in certain intervals, which they listen to in isolation, after
> checking that they are on the right side of the pure interval. (NB:
a
> fifth that is 2c sharp sounds identical to one that is 2c flat,
unless
> you do a direct comparison one after the other!)
> Choral singing is a totally different situation with, usually, much
> wider tolerances. In rapidly changing or dissonant harmonies, large
> deviations from any theoretical scheme are both possible and
probable
> without causing noticeable artistic problems.
>
> In practice, one starts with bad choral intonation, then works to
> improve it. I propose that this work is mostly and best done by
> singers *listening to each other* and, by using their ears, being
able
> to approach purity both within a voice and between voices. Pure
> intervals are the only ones one can reliably hear and try to
approach
> in harmony.
>
> Not that pure intervals may ever really be reached: but that
intervals
> become *sufficiently* pure for their musical context.
>
> How do several basses singing the same line manage to be in tune
with
> each other? Absolutely NOT by all listening to the piano and then
> independently trying to reproduce its pitches. The beating of a
> mistuned unison between similar timbres is strong enough that (if
they
> listen at all!) they are practically forced into an almost-pure
unison
> within a fraction of a second. This unison will be, of course, not
so
> far away from the piano's, but need not and cannot be identical to
it.
>
> In the same Max Planck article, we read that 'some choir directors
> already know that in a quiet, long-held final major chord the third
is
> to be taken somewhat flatter.' What can this mean apart from that
> purity of intonation is desirable in some circumstances and can be
> achieved if a chord is to be sustained for some time?
>
> At the same time, choirs that sing with piano cannot get too far
away
> from its broad intonational framework. Again, due to inharmonicity
> and/or in rapid passages, it is really impossible to sing in tune
with
> a piano very accurately. But it is not necessary either. It is only
> possible and necessary to be *sufficiently* in tune with it, given
the
> very different timbres and envelopes of the piano and the voice.
>
> What deviations are allowed while one remains *sufficiently* pure or
> in tune is an experimental question - which hasn't received that
much
> attention, probably because of its difficulty.
>
> Another experimental question is how well someone can detect
> deviations from ET in single pitches, if they have 'absolute pitch'.
> Why not try tuning a piano note by note, without ever playing an
> interval or chord; then get out the electronic gadget and see how
far
> off you are.
>
> To say 'I could easily notice 14 cents deviation' without ever
having
> tested yourself is absurd.
>
> I think choirs, even excellent ones with spotless intonation,
probably:
> Sing differently in chromatic or diatonic passages
> Sing differently in religious or secular music
> Sing differently in slow or fast passages
> Sing differently in Renaissance or 20th century music
> Since each of these factors is likely to affect intonation, to try
and
> describe real choral tuning by any fixed system of twelve (or more!)
> pitches is futile.
>
> What can realistically be done? One can listen to actual pieces
being
> performed by actual choirs and try to pick out significant features
of
> their tuning and see if any of these theoretical prejudices can
> possibly be correct. Hence my link to the page with the Hilliard
> Ensemble sample. No, their thirds are not absolutely pure: but they
> are much nearer than ET is.
>
> And yes, sometimes I hear choirs who sing thirds mighty sharp, but
> that doesn't make them ET; it just makes them sharp. If one
absolutely
> wants the chord to sound shrill and aggressive then it is
> indispensable (and one had also better sing a slightly sharp
fifth!!).
>
> If you forced me at gunpoint to say what most choirs mostly sing I
> would have to say something like 'approximate 12-ET-based adaptive
> JI'. Which means that the roots of chords progress approximately by
ET
> intervals, while the other voices make approximately pure intervals
> with the roots. The degree of approximation depends, as I said, very
> heavily on the context, and may (by absolute standards) be very good
> one minute but lousy the next.
>
> ~~~T~~~

Some good thoughts.

I have tested my pitch by retuning my own keyboard (easy to do)
14 cents is almost 1/7 of a half step, very easy to distinguish.
So I don't agree with you on that.

I don't agree that inharmonicity is a problem. Choirs only have
(about) a four octave range, and most of the music is in two
octaves.

I don't agree that switching from secular to sacred music (an
artificial division anyway) or classical to popular (another
artificial division) is going to affect how I tune or harmonize.
An exception would be barbershop quartet singing. I agree with you
there.

I got a little lost in your discussion of pure intervals. Do you
mean pure tempered or just ones? Obviously there is no beating
in just intervals.

Wow being a second bass, guess (according to you) I am setting
the pitch, since I always sing the lowest line. I'm afraid I
don't think it is that simple. Even though it is funny that you
are saying the bassline is essentially 12-tET.

Slow or fast is a relative term. How slow is slow? It's true that
in fast singing, you just do your best and come close.

Diatonic / chromatic is a relative term. It's true, some music
has almost no accidentals, some is cluttered with them. So is
F-F# chromatic, while F-Gb diatonic? Do I sing them differently?
I know that I don't.

You have some good points, but I've been singing (almost unbroken)
in some kind of choir or another since I was 5. It's fun to
try to reconcile what I have learned about tuning with what I
experience. (Also sang in St. Olaf Choir 3 years, mostly all
a capella singing, always from memory, if you don't know, that this
choir traditionally set the standard for this kind of singing
in the midwest for most of the 20th century). I am just saying
I have a little experience. Doesn't mean I think I'm right about
everything. I just don't think it's that cerebral, and I don't think
tuning varies as much as you are saying it does.

2 cents accuracy? No of course not. The tempered fifth is so
close that it is essentially a non-issue.

I agree with you about approximate 12-ET based adaptive JI" and
although few would agree with me, I would almost say "approximate
12-ET based adaptive Pythagorean tuning" even though I am sure
most of you would jump on me for indicating major thirds as big
as 81/64.

Would like to see some experimental data. Otherwise we might
as well be arguing about string theory.

PGH

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@> wrote:
> >
> > > Please take this back, or rephrase, or something. There are
> > > plenty of musicians that understand intonation a lot better
> > > than dilettantes, amateurs, and most musicologists.
> >
> > I don't need to say anything. Everyone here already knows
> > that they are amateurs compared to you and the musicians you
> > work with.
> >
> > -Carl
> >
>
> 'Everyone'? Gee.
>
> It just happens that I earned 100 Euros for two performances of the
> lead vocal part in the Schuetz 'Seven Last Words' over Easter.
>
> It just happens that next week I am giving two short harpsichord
> concerts in the main church here in Heidelberg, on a historically
> based Italian-style single manual instrument, I'm going to tune the
> instrument myself (modified 1/5 comma meantone), and I'll go head to
> head with anyone on the list in doing so.
>
> By the way, and not so much on a professional level, did I advertise
> my clavichord home recordings here? Not that they are of much formal
> tuning interest, since the instrument is fretted fairly near ET and
it
> seems to come out slightly differently every time I temper it. They
> can be found by searching Google for 'Thomas Dent clavichord'.
> ~~~T~~~

The fact that you are a keyboard player and professional singer
adds a lot of weight (for me) in what you say. I already responded
to your other post...let me think about things for a day or two.

Carl, Music is very competitive, the best musicians have to be smart.
Some are prodigies who were also math whizzes as kids, good at
languages, well-read etc. You know that don't you? However, I do
agree that some are off in their own artistic world, doesn't mean
they can't arrive at some of the same conclusions...

Tom wrote...

> In order to 'sing 12-ET' (or play it) in any meaningful
> sense, you need to make both melodic and harmonic intervals
> 1) impure, i.e. 'out of tune' and (if harmonic) beating
> 2) impure / beating by a particular, rather exact amount
> and I contend that this is impossible for singers with or
> without piano accompaniment.

I think there are meaningful senses to say music is
performed in 12-ET. 12 is a natural phenomenon -- it's
one of the best temperaments -- and it's all around us,
and many musicians are taught to use a piano as a
tuning reference. If somebody sings music whose score
assumes the 12-ET kernel and ends on the same pitch they
started... I think on some level we can say they sang in
12-ET. But just saying that, it can be misinterpreted.
I don't think it's accurate in the sense Paul originally
seemed to mean it.

If you want to try an experiment, Paul, record yourself
at your next rehearsal. If you mount a small mic on
your lapel you may get a clean signal. Else, you can
place a 2nd mic in the audience and then subtract that
recording from your lapel recording later on your
computer (with any standard sound editing software --
the free Audacity should do it).

Feed that monophonic part into a pitch tracker. There
are freely available pitch trackers, I'm sure. I think
Praat can do it. Then time-domain transform the pitch
data with a window the duration of an entire piece. Now
you can see to what extent you sing in 12, by looking at
how far the *pitches* of 12 rise above the background!

> Due to the piano's inharmonicity it is really impossible to
> take a pitch from it to any accuracy: if your fundamental
> is right, your second harmonic will be wrong.

The piano isn't *that* inharmonic in the center octaves
where most of the action takes place. In any case, the
brain's pitch processor has no problem reporting single
pitches for notes of the center four octaves of any decent
instrument. What inharmonicity there is will effect the
size of beatless intervals, but only very minimally the
perceived pitch, and not at all the fact that only one
pitch is perceived.

> Actually, Occam's razor does come in. Unless we see some
> definite evidence to the contrary, I think it is simplest to
> assume that *no-one* can sing a melodic interval, or take a
> pitch from a piano,

Melodic discrimination isn't much worse than harmonic,
actually. I think the JND is around 3 cents or something.
Anyway, accurate enough to distinguish Pythagorean, 12-ET,
and 5-limit major thirds.

> At the same time, choirs that sing with piano cannot get too
> far away from its broad intonational framework. Again, due to
> inharmonicity and/or in rapid passages, it is really impossible
> to sing in tune with a piano very accurately.

???

> Another experimental question is how well someone can detect
> deviations from ET in single pitches, if they have 'absolute
> pitch'.

You're asking the right guy (Paul). But remember, there are
degrees of AP.

> To say 'I could easily notice 14 cents deviation' without
> ever having tested yourself is absurd.

Actually the different in melodic sound between pure and
equal-tempered thirds is well above the melodic JND for
most people.

> I think choirs, even excellent ones with spotless intonation,
> probably:
> Sing differently in chromatic or diatonic passages
> Sing differently in religious or secular music
> Sing differently in slow or fast passages
> Sing differently in Renaissance or 20th century music
> Since each of these factors is likely to affect intonation, to
> try and describe real choral tuning by any fixed system of
> twelve (or more!) pitches is futile.

I think I can agree with this.

-Carl

> 'Everyone'? Gee.

That was a sarcastic remark. Johnny has been posting
here about amateurs vs. his famed ability to spontaneously
perform intervals with 1-cent accuracy for neigh a decade.

> It just happens that I earned 100 Euros for two performances
> of the lead vocal part in the Schuetz 'Seven Last Words' over
> Easter.

Cool. I've never been paid for singing, even though I've
been in more public performances as a singer than anything
else. I did earn US$150 for a piano gig once. I'm sure
that's nothing compared to what Johnny's AFMM musicians
earn in NYC, alas.

> By the way, and not so much on a professional level, did I
> advertise my clavichord home recordings here? Not that they
> are of much formal tuning interest, since the instrument is
> fretted fairly near ET and it seems to come out slightly
> differently every time I temper it. They can be found by
> searching Google for 'Thomas Dent clavichord'.
> ~~~T~~~

Why not post a link? This list is the very color of
self-promotion.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> Tom wrote...
>
> > In order to 'sing 12-ET' (or play it) in any meaningful
> > sense, you need to make both melodic and harmonic intervals
> > 1) impure, i.e. 'out of tune' and (if harmonic) beating
> > 2) impure / beating by a particular, rather exact amount
> > and I contend that this is impossible for singers with or
> > without piano accompaniment.
>
> I think there are meaningful senses to say music is
> performed in 12-ET. 12 is a natural phenomenon -- it's
> one of the best temperaments -- and it's all around us,
> and many musicians are taught to use a piano as a
> tuning reference. If somebody sings music whose score
> assumes the 12-ET kernel and ends on the same pitch they
> started... I think on some level we can say they sang in
> 12-ET. But just saying that, it can be misinterpreted.
> I don't think it's accurate in the sense Paul originally
> seemed to mean it.
>
> If you want to try an experiment, Paul, record yourself
> at your next rehearsal. If you mount a small mic on
> your lapel you may get a clean signal. Else, you can
> place a 2nd mic in the audience and then subtract that
> recording from your lapel recording later on your
> computer (with any standard sound editing software --
> the free Audacity should do it).
>
> Feed that monophonic part into a pitch tracker. There
> are freely available pitch trackers, I'm sure. I think
> Praat can do it. Then time-domain transform the pitch
> data with a window the duration of an entire piece. Now
> you can see to what extent you sing in 12, by looking at
> how far the *pitches* of 12 rise above the background!
>
> > Due to the piano's inharmonicity it is really impossible to
> > take a pitch from it to any accuracy: if your fundamental
> > is right, your second harmonic will be wrong.
>
> The piano isn't *that* inharmonic in the center octaves
> where most of the action takes place. In any case, the
> brain's pitch processor has no problem reporting single
> pitches for notes of the center four octaves of any decent
> instrument. What inharmonicity there is will effect the
> size of beatless intervals, but only very minimally the
> perceived pitch, and not at all the fact that only one
> pitch is perceived.
>
> > Actually, Occam's razor does come in. Unless we see some
> > definite evidence to the contrary, I think it is simplest to
> > assume that *no-one* can sing a melodic interval, or take a
> > pitch from a piano,
>
> Melodic discrimination isn't much worse than harmonic,
> actually. I think the JND is around 3 cents or something.
> Anyway, accurate enough to distinguish Pythagorean, 12-ET,
> and 5-limit major thirds.
>
> > At the same time, choirs that sing with piano cannot get too
> > far away from its broad intonational framework. Again, due to
> > inharmonicity and/or in rapid passages, it is really impossible
> > to sing in tune with a piano very accurately.
>
> ???
>
> > Another experimental question is how well someone can detect
> > deviations from ET in single pitches, if they have 'absolute
> > pitch'.
>
> You're asking the right guy (Paul). But remember, there are
> degrees of AP.
>
> > To say 'I could easily notice 14 cents deviation' without
> > ever having tested yourself is absurd.
>
> Actually the different in melodic sound between pure and
> equal-tempered thirds is well above the melodic JND for
> most people.
>
> > I think choirs, even excellent ones with spotless intonation,
> > probably:
> > Sing differently in chromatic or diatonic passages
> > Sing differently in religious or secular music
> > Sing differently in slow or fast passages
> > Sing differently in Renaissance or 20th century music
> > Since each of these factors is likely to affect intonation, to
> > try and describe real choral tuning by any fixed system of
> > twelve (or more!) pitches is futile.
>
> I think I can agree with this.
>
> -Carl
>

I'm not sure. We sing music from 1500-2000, with every degree of
chromaticism, I sure don't notice any tuning differences. Just
because something makes sense intellectually doesn't mean it
actually happens. So, would I tune differently in "Ode to Joy"
(secular) and "Missa Solemnis" (sacred), both by Beethoven?
Would I tune differently in Rachmaninoff (chromatic) and Tallis
(diatonic?) Sing differently in older church music, and more modern
(let's say, both pretty diatonic for example?) I'm just not seeing
it. Maybe I am wrong.

PGH

Paul wrote...
> We sing music from 1500-2000, with every degree of
> chromaticism, I sure don't notice any tuning differences. Just
> because something makes sense intellectually doesn't mean it
> actually happens. So, would I tune differently in "Ode to Joy"
> (secular) and "Missa Solemnis" (sacred), both by Beethoven?
> Would I tune differently in Rachmaninoff (chromatic) and Tallis
> (diatonic?) Sing differently in older church music, and more
> modern (let's say, both pretty diatonic for example?) I'm just
> not seeing it. Maybe I am wrong.

I'm sure it depends. Groups that specialize in early music
tend to sing in a different style than groups coming from
a common-practice angle (like yours), and that includes
intonation. As for your group, I'm sure intonation depends
on the sustain of consonances in the score. For something
like a chorale (which both the Missa Solemnis and the 9th
Symphony contain), where every beat is a quarter-note triad,
you will be pulled to JI vertically. You may not succeed,
but if you can hear the other parts at all (admitedly this
depends on the size of your sections and the room you
rehearse in), you can scarcely be pulled any other way. In
faster-moving passages, or when singing more complex chords,
the story may be different. If a piano is playing the parts
(not a separate keyboard part), that will also have an effect.

In the broader picture, the primary type of chord used to
make harmony (i.e. triads or tetrads) in music is also an
intonation issue (something we study on these lists), on top
of the issue of how close to JI they are typically performed.

On another note: have you ever heard a harpsichord in
equal temperament? This is not something that's easy to
find. You have to go back to recordings from the '50s and
'60s. If you have heard one, did you find it objectionable?
Most early music buffs do -- one friend of mine rebuffed me
for it immediately upon entering my car, where I was
playing a Scarlatti recording by Valenti.

-Carl

Carl Lumma wrote:

> Melodic discrimination isn't much worse than harmonic,
> actually. I think the JND is around 3 cents or something.
> Anyway, accurate enough to distinguish Pythagorean, 12-ET,
> and 5-limit major thirds.

One thing I've found is that my melodies can sound very out of tune if I solo them, but fine in context with the other parts where the harmony makes sense. I don't know what other people hear, but I'm open to the idea that somebody would be able to pick out a 3 cent difference in an isolated melody but ignore a 10 cent difference towards JI in a choir. Melody and harmony aren't orthogonal.

Graham

Orchestra players too. and this list is quite expandable. What human beings do cannot be measured because the context is constantly changing through rapid situations we have no words for.
Different cultures too with their different tunings also. The longer and older any tuning is used by human beings the more complex will human beings make the tuning extend how they need it to be.
to say which might never be said otherwise

Tom Dent pointed out~
I think choirs, even excellent ones with spotless intonation, probably:
Sing differently in chromatic or diatonic passages
Sing differently in religious or secular music
Sing differently in slow or fast passages
Sing differently in Renaissance or 20th century music
Since each of these factors is likely to affect intonation, to try and
describe real choral tuning by any fixed system of twelve (or more!)
pitches is futile.
--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/index.html>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main/index.asp> 88.9 FM Wed 8-9 pm Los Angeles

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> In order to 'sing
> 12-ET' (or play it) in any meaningful sense, you need to make both
> melodic and harmonic intervals
> 1) impure, i.e. 'out of tune' and (if harmonic) beating
> 2) impure / beating by a particular, rather exact amount

in
www.farago.info/hobby/stimmungen/Stimmungen_von_Tasteninstrumenten.pdf
Zolatan Farago wrote about that problem on p.10

"Für die vokale Kirchen-Musik ist in den meisten Fällen die
natürliche Stimmung vorzuziehen. Beim Gesang führt die häufige
Unterstützung in gleichschwebender Stummung
zu permanenten Intonations-Problem und schließlich zur Unfähigkeit
a capella zu singen. A-capella-Chöre singen in der Regel und der
Stimmung der höchsten Konsonanz, nämlich in der natürlichen Stimmung"
tr:
For vocal church-music one should prefer in most cases JI.
In sining, the frequent accomppainment by ET causes/yields
permanent remaining problems in proper pitch-intonation
and finally in the long run to the inablility to sing in
"a-capella" correctly.
A-capella choirs sing regulary in the tuning of
the most consonance, namely in JI."
>
> Or you can try to take your pitches from a piano; in which case the
> result may sometimes sound similar to ET, but is likely to deviate
> significantly from it in many cases, because one can't vocally
> reproduce or remember a pitch from the piano with all that much
> accuracy. Not that one would want to, since the piano doesn't even
> have 2:1 octaves.
That's the reason why good dirigents avoid the deviating piano,
when disturbing the intended JI all to much.
>

> In the same Max Planck article, we read that 'some choir directors
> already know that in a quiet, long-held final major chord the third >is
> to be taken somewhat flatter.'
...
> At the same time, choirs that sing with piano cannot get too far away
> from its broad intonational framework.

Agreed, for singers that are still insecure in pitch,
it's better to have that support by an 12EDO detuned piano,
that disturbes JI in the 3rds about ~14 Cents sharp.

> I think choirs, even excellent ones with spotless intonation, probably:
> Sing differently in chromatic or diatonic passages
> Sing differently in religious or secular music
> Sing differently in slow or fast passages
> Sing differently in Renaissance or 20th century music
> Since each of these factors is likely to affect intonation, to try and
> describe real choral tuning by any fixed system of twelve (or more!)
> pitches is futile.
>
In short terms:
Good singers are able to discriminate the SC 81/80
more or less properly
by as well by ears as voice
in perception und production of pitches.

Hence such guys alike Newton, Helmholtz and Planck
preferred the corresopnding 53-EDO approx. model
for sining barely plain by voices.

>
> If you forced me at gunpoint to say what most choirs mostly sing I
> would have to say something like 'approximate 12-ET-based adaptive
> JI'. Which means that the roots of chords progress approximately by ET
> intervals, while the other voices make approximately pure intervals
> with the roots. The degree of approximation depends, as I said, very
> heavily on the context, and may (by absolute standards) be very good
> one minute but lousy the next.

Just distinct inbetween the 2 cases, considering:

1. melodic 3rd or ditonus: 81/64 <<==>> ~2*9 = ~18 steps wide in 53EDO
vs:
2. harmonic 3rd: 5/4 <<==>> ~17 steps in 53EDO approx.

the preferable usage depends here
on the musical desired context.

12EDO is simple to coarse
lacking the needed precision,
in order to represent such fine nuances.

A.S.

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> Sing differently in older church music, and more modern
> (let's say, both pretty diatonic for example?) I'm just not seeing
> it. Maybe I am wrong.

You've never noticed that some choirs can sing Renassiance music with a
kind of suavity which depends, among other things, on getting the
chords close to 5-limit JI? 12-et triads are not suave.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@>
> wrote:
>
> > Sing differently in older church music, and more modern
> > (let's say, both pretty diatonic for example?) I'm just not
seeing
> > it. Maybe I am wrong.
>
> You've never noticed that some choirs can sing Renassiance music
with a
> kind of suavity which depends, among other things, on getting the
> chords close to 5-limit JI? 12-et triads are not suave.

Okay. This is a situation where the accompaniment would have to
be in the same tuning style, of course. I'll have to listen to
some Renaissance music. I also like even older music, like Ars Nova
and Ars Antiqua...

PGH

--- In tuning@yahoogroups.com, "Andreas Sparschuh" <a_sparschuh@...>
wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <stringph@> wrote:
> >
> > In order to 'sing
> > 12-ET' (or play it) in any meaningful sense, you need to make both
> > melodic and harmonic intervals
> > 1) impure, i.e. 'out of tune' and (if harmonic) beating
> > 2) impure / beating by a particular, rather exact amount
>
> in
>
www.farago.info/hobby/stimmungen/Stimmungen_von_Tasteninstrumenten.pdf
> Zolatan Farago wrote about that problem on p.10
>
> "Für die vokale Kirchen-Musik ist in den meisten Fällen die
> natürliche Stimmung vorzuziehen. Beim Gesang führt die häufige
> Unterstützung in gleichschwebender Stummung
> zu permanenten Intonations-Problem und schließlich zur Unfähigkeit
> a capella zu singen. A-capella-Chöre singen in der Regel und der
> Stimmung der höchsten Konsonanz, nämlich in der natürlichen
Stimmung"
> tr:
> For vocal church-music one should prefer in most cases JI.
> In sining, the frequent accomppainment by ET causes/yields
> permanent remaining problems in proper pitch-intonation
> and finally in the long run to the inablility to sing in
> "a-capella" correctly.
> A-capella choirs sing regulary in the tuning of
> the most consonance, namely in JI."
> >
> > Or you can try to take your pitches from a piano; in which case
the
> > result may sometimes sound similar to ET, but is likely to deviate
> > significantly from it in many cases, because one can't vocally
> > reproduce or remember a pitch from the piano with all that much
> > accuracy. Not that one would want to, since the piano doesn't even
> > have 2:1 octaves.
> That's the reason why good dirigents avoid the deviating piano,
> when disturbing the intended JI all to much.
> >
>
> > In the same Max Planck article, we read that 'some choir directors
> > already know that in a quiet, long-held final major chord the
third >is
> > to be taken somewhat flatter.'
> ...
> > At the same time, choirs that sing with piano cannot get too far
away
> > from its broad intonational framework.
>
> Agreed, for singers that are still insecure in pitch,
> it's better to have that support by an 12EDO detuned piano,
> that disturbes JI in the 3rds about ~14 Cents sharp.
>
>
> > I think choirs, even excellent ones with spotless intonation,
probably:
> > Sing differently in chromatic or diatonic passages
> > Sing differently in religious or secular music
> > Sing differently in slow or fast passages
> > Sing differently in Renaissance or 20th century music
> > Since each of these factors is likely to affect intonation, to
try and
> > describe real choral tuning by any fixed system of twelve (or
more!)
> > pitches is futile.
> >
> In short terms:
> Good singers are able to discriminate the SC 81/80
> more or less properly
> by as well by ears as voice
> in perception und production of pitches.
>
> Hence such guys alike Newton, Helmholtz and Planck
> preferred the corresopnding 53-EDO approx. model
> for sining barely plain by voices.
>
> >
> > If you forced me at gunpoint to say what most choirs mostly sing I
> > would have to say something like 'approximate 12-ET-based adaptive
> > JI'. Which means that the roots of chords progress approximately
by ET
> > intervals, while the other voices make approximately pure
intervals
> > with the roots. The degree of approximation depends, as I said,
very
> > heavily on the context, and may (by absolute standards) be very
good
> > one minute but lousy the next.
>
> Just distinct inbetween the 2 cases, considering:
>
> 1. melodic 3rd or ditonus: 81/64 <<==>> ~2*9 = ~18 steps wide in
53EDO
> vs:
> 2. harmonic 3rd: 5/4 <<==>> ~17 steps in 53EDO approx.
>
> the preferable usage depends here
> on the musical desired context.
>
> 12EDO is simple to coarse
> lacking the needed precision,
> in order to represent such fine nuances.
>
> A.S.
>

This is really interesting. 53-tET is a very good meantone
temperament of course. Thanks for naming the ditonus. I am starting
to think maybe there are some situations that the syntonic comma
comes into play with choirs.

If one looks at these things in binary (sliding decimal point) you
get kind of a perspective on it:

JI Major third: 10100000
Approximate 12-tET Major third: 1010000101..
Ditonus: 1010001

Doesn't look so bad that way, does it?

> This is really interesting. 53-tET is a very good meantone
> temperament of course.

53 isn't considered a meantone, since 81:80 isn't tempered out.

-Carl

He also confused me with that statement. Maybe it is a typo for 55-tET?

Oz.

----- Original Message -----
From: "Carl Lumma" <clumma@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: 15 Haziran 2007 Cuma 18:46
Subject: [tuning] Re: Tuning Twelve Pitches

> > This is really interesting. 53-tET is a very good meantone
> > temperament of course.
>
> 53 isn't considered a meantone, since 81:80 isn't tempered out.
>
> -Carl
>

--- In tuning@yahoogroups.com, "Ozan Yarman" <ozanyarman@...> wrote:
>
> He also confused me with that statement. Maybe it is a typo for 55-
tET?
>
> Oz.
>
> ----- Original Message -----
> From: "Carl Lumma" <clumma@...>
> To: <tuning@yahoogroups.com>
> Sent: 15 Haziran 2007 Cuma 18:46
> Subject: [tuning] Re: Tuning Twelve Pitches
>
>
> > > This is really interesting. 53-tET is a very good meantone
> > > temperament of course.
> >
> > 53 isn't considered a meantone, since 81:80 isn't tempered out.
> >
> > -Carl

Oops. Hadn't had my coffee yet. It's schismic, right? I just meant
it is a very good temperament < 100 My bad

Hi Paul,

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > This is really interesting. 53-tET is a very good meantone
> > temperament of course.
>
> 53 isn't considered a meantone, since 81:80 isn't tempered out.

In fact 53-edo is a very good approximation of 5-limit JI,
which meantone most emphatically is not.

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

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:
>

(Probably not a good idea if we quote the ENTIRETY of a previous
message when replying to it...)

I didn't say that choral tuning always comes from the bass up
(although that is a good approximation in many circumstances!) - I
said it comes from the *root* of the chord.

OK, maybe you can take each individual note from the piano in a
meaningful way. But you can't take pure, or even equal-tempered, 15ths
or 17ths or triple octaves.

Although inharmonicity is not a large effect, consider as follows:

The soprano can sing 3 octaves above the bass.
An upright piano will have certainly have more than 2 cents
inharmonicity in each of the octaves around the middle, probably more.
Should the soprano then sing more than 6 cents sharp to the bass in a
wide voiced chord?

How about major seventeenths? There you get 14 cents sharpness from ET
and 5 cents or more from stretching on the piano. Is that really not
too sharp?

As to what size of pitch difference you can detect, the question is
not whether you can detect it when the two almost-identical pitches
are played one after the other. The question is how precisely you can
distinguish *by listening to one pitch or one interval once*.
Absolute, not relative, pitch or interval recognition. Or, how
precisely can you sing this or that interval without accompaniment.
(Slightly different from the test of extracting one's own part from a
choral texture.)

And it's not a question of being able to tell apart an ET third from a
JI from a Pythagorean. That's not difficult, if you *know* that what
you are hearing is one of those 3 possibilities. The problem is when
in performance you get something in between. For example how well can
you distinguish thirds that are somewhere between 5:4 and ET? That's,
I hope, where most good choral performances actually lie.

Incidentally I think the solution to my Pythagorean third problem is
19:15, which is 1.4 cents sharp of 81:64.

Has anyone produced circulating temperaments or tunings using 19:15?
(Aaron KJ?) They might then actually be tunable by ear. ... Perhaps
Werckmeister was heavily into the 19-limit without knowing it.

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <stringph@...> wrote:
>
> --- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@>
> wrote:
> >
>
> (Probably not a good idea if we quote the ENTIRETY of a previous
> message when replying to it...)

Agreed. I never know what to chop. Of course, you don't want
to chop too much.

> I didn't say that choral tuning always comes from the bass up
> (although that is a good approximation in many circumstances!) - I
> said it comes from the *root* of the chord.

You do realize that even that is open to interpretation:

F#-A-C-E, F# is the root of a half-diminished chord, A is the root
of an A minor-6 chord

> OK, maybe you can take each individual note from the piano in a
> meaningful way. But you can't take pure, or even equal-tempered,
15ths
> or 17ths or triple octaves.

You got me there. I always thought maybe it was less than 1 cent per
octave. And I thought this was mostly done at the far ends, not at
all in the middle of the piano. Anyway, don't physical properties of
inharm. on the piano compensate for the retuning?

> And it's not a question of being able to tell apart an ET third
from a
> JI from a Pythagorean. That's not difficult, if you *know* that what
> you are hearing is one of those 3 possibilities. The problem is when
> in performance you get something in between. For example how well
can
> you distinguish thirds that are somewhere between 5:4 and ET?
That's,
> I hope, where most good choral performances actually lie.

Good question. I think looking at things in binary help with this:

1.0100000 Just
1.010000101... Tempered
1.010001 Ditonus

Then the sweet spot, (according to you) is around 1.01000001,
which is about 256 + 64 + 1 / 256 = 321/256 = 1.25390625. Of
course 1.255 could be considered the "choice" this is 253/200.

PGH

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> 53-tET is a very good meantone
> temperament of course.
nothing doing,
because in meantonic the 3rd: 5/4 is constructed
by 4 consecutive 5ths each narrowed by SC^(1/4)
but
http://en.wikipedia.org/wiki/53_equal_temperament#History
the 3rd is approximated schismatically by 8 times 4ths.

>Thanks for naming the ditonus.
http://en.wikipedia.org/wiki/Pythagorean_interval
"ditone 81/64 ~407.8 Cents"
also called "Pythagorean 3rd"
http://de.wikipedia.org/wiki/Ditonus
The <english> entry for that in WIKI is still lacking.

> I am starting
> to think maybe there are some situations that the syntonic comma
> comes into play with choirs.
That depends -alike in proper vilolin intonation-
on the harmonically 5/4 syntonic
or melodically 81/64 = (9/8)^2 pyth.
meaning induced by the musically context.
>
> If one looks at these things in binary (sliding decimal point) you
> get kind of a perspective on it:
>
> JI Major third: 10100000
> Approximate 12-tET Major third: 1010000101..
> Ditonus: 1010001
>
5/4 and 81/64 consist in:
http://en.wikipedia.org/wiki/Dyadic_fraction

That binary stuff belongs but rather into:
/tuning-math/

A.S.

> Oops. Hadn't had my coffee yet. It's schismic, right? I just meant
> it is a very good temperament < 100 My bad

Yep, but we've changed to calling it schismatic, to be
more in line with Greek or something.

-Carl

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> This is really interesting. 53-tET is a very good meantone
> temperament of course.

You mean 55?

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@...> wrote:
>
> > Oops. Hadn't had my coffee yet. It's schismic, right? I just meant
> > it is a very good temperament < 100 My bad
>
> Yep, but we've changed to calling it schismatic, to be
> more in line with Greek or something.

A Wikipedia editor was frothing at the mouth and denouncing Graham
because of "schismic", so I started using "schismatic". I hate to see
people frothing. However, I still like "schismic" really.

--- In tuning@yahoogroups.com, "Paul G Hjelmstad" <paul.hjelmstad@...>
wrote:

> > > 53 isn't considered a meantone, since 81:80 isn't tempered out.
> > >
> > > -Carl
>
> Oops. Hadn't had my coffee yet. It's schismic, right? I just meant
> it is a very good temperament < 100 My bad

53-et is the unique regular 5-limit temperament tempering out both the
schisma, 32805/32768, and the kleisma, 15625/15552. Since these are
both such strong 5-limit commas, the combination proves interesting.

You can have some fun conjoining any two 5-limit commas of comparable
accuracy and good quality, to see what you get.

On 6/17/07, Gene Ward Smith <genewardsmith@sbcglobal.net> wrote:
> A Wikipedia editor was frothing at the mouth and denouncing Graham
> because of "schismic", so I started using "schismatic". I hate to see
> people frothing. However, I still like "schismic" really.

"Schismic" is a bastard word. It's no more legitimate than
"schismous", "schismish", or "schismular". If those don't bother you,
go ahead and use "schismic".

Keenan

Keenan Pepper wrote:
> On 6/17/07, Gene Ward Smith <genewardsmith@sbcglobal.net> wrote:
> >>A Wikipedia editor was frothing at the mouth and denouncing Graham
>>because of "schismic", so I started using "schismatic". I hate to see
>>people frothing. However, I still like "schismic" really.

This is Gene's usual over-dramatisation. I don't remember being denounced although somebody did point out that I invented the spelling and it had only ever been used online.

As it's nice to agree on spellings I prefer "schismatic" now. It's also the natural Anglicisation of Helmholtz's original German. But I still prefer "diaschismic" over "diaschismatic" if that word survives.

> "Schismic" is a bastard word. It's no more legitimate than
> "schismous", "schismish", or "schismular". If those don't bother you,
> go ahead and use "schismic".

"Irregular" is the correct term. I can't see it's any worse than "systemic" which, like it or not, is part of the English language.

A schismous temperament is one that tempers out the schisma, but in which all notes aren't reachable by a chain of fifths from the tonic (that is, not a strictly linear temperament). A schismish temperament is one that looks like schismatic, but isn't quite; for example the Indian shruti system interpreted as JI but with a schismatic logic. A schismular temperament is one that's both schismous and regular but needn't be linear in either the strict or loose (rank 2) sense. You can get some neat notations for the 11-limit and beyond from schismular temperaments.

I don't see why these terms should bother you. But they aren't in widespread use so we can always revise them.

Graham

On 6/17/07, Graham Breed <gbreed@gmail.com> wrote:
> A schismous temperament is one that tempers out the schisma,
> but in which all notes aren't reachable by a chain of fifths
> from the tonic (that is, not a strictly linear temperament).
> A schismish temperament is one that looks like schismatic,
> but isn't quite; for example the Indian shruti system
> interpreted as JI but with a schismatic logic. A schismular
> temperament is one that's both schismous and regular but
> needn't be linear in either the strict or loose (rank 2)
> sense. You can get some neat notations for the 11-limit and
> beyond from schismular temperaments.

LOL, you made up definitions for all those. Now do ones for
"schismal", "schismical", and "schismaticular".

Keenan

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...>
wrote:
>
> On 6/17/07, Graham Breed <gbreed@...> wrote:
> > A schismous temperament is one that tempers out the schisma,
> > but in which all notes aren't reachable by a chain of fifths
> > from the tonic (that is, not a strictly linear temperament).
> > A schismish temperament is one that looks like schismatic,
> > but isn't quite; for example the Indian shruti system
> > interpreted as JI but with a schismatic logic. A schismular
> > temperament is one that's both schismous and regular but
> > needn't be linear in either the strict or loose (rank 2)
> > sense. You can get some neat notations for the 11-limit and
> > beyond from schismular temperaments.
>
> LOL, you made up definitions for all those. Now do ones for
> "schismal", "schismical", and "schismaticular".
>
> Keenan

Don't forget "schismine", or my favorite temperament of them
all, "schismalicious", which tempers out 1/1.

-Cameron Bobro

Cameron Bobro wrote:
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> > wrote:
> >>On 6/17/07, Graham Breed <gbreed@...> wrote:
>>
>>>A schismous temperament is one that tempers out the schisma,
>>>but in which all notes aren't reachable by a chain of fifths
>>>from the tonic (that is, not a strictly linear temperament).
>>> A schismish temperament is one that looks like schismatic,
>>>but isn't quite; for example the Indian shruti system
>>>interpreted as JI but with a schismatic logic. A schismular
>>>temperament is one that's both schismous and regular but
>>>needn't be linear in either the strict or loose (rank 2)
>>>sense. You can get some neat notations for the 11-limit and
>>>beyond from schismular temperaments.
>>
>>LOL, you made up definitions for all those. Now do ones for
>>"schismal", "schismical", and "schismaticular".

Well, "schismal" and "schismical" are Bristolian for the schisma and the temperament class you get by removing it. A "schimsaticular" is a specific tuning of schismatic(al)?.

> Don't forget "schismine", or my favorite temperament of them > all, "schismalicious", which tempers out 1/1. Hey, try and find a temperament that *doesn't* temper out 1/1! That'd be schismoksha: the ideal tuning for one hand clapping.

Graham