EDO approximation of valve trumpet intonation

Hello all,

I've just updated my webpage on valve trumpet intonation,

http://tonalsoft.com/monzo/trumpet/trumpet-intonation.htm

greatly expanding the old table of notes to include the
monzos for each note, and also adding a new table which
groups the notes according to each blown harmonic with
all its valve combinations.

I was planning to use 72-edo HEWM to supplement the notation
for the notes actually sounded, but found that for some
notes it was quite innacurate.

Can someone please explore which EDOs give good approximations
to the notes in my table? Thanks.

Here's the essential data, to hopefully make it easier ...

harm. valves . --------- monzo ------------ .. cents
............... 2. 3. 5. 7 11 13 19 53 167

C6 ... 0 ..... [ 3, 0, 0, 0> ................ 3600.00
C6 ... 2 ..... [-1, 1, 1, 0, 0, 0, 0, 0, 0> . 3488.27
C6 ... 1 ..... [ 6,-2, 0, 0, 0, 0, 0, 0, 0> . 3396.09
Bb<5 . 0 ..... [ 0, 0, 0, 1> ............... 3368.83
C6 ... 1-2 ... [ 6, 1, 1, 0,-1,-1, 0, 0, 0> . 3296.42
C6 ... 3 ..... [ 2,-1, 1, 0, 0, 0, 0, 0, 0> . 3284.36
Bb<5 . 2 ..... [-4, 1, 1, 1, 0, 0, 0, 0, 0> . 3257.09
C6 ... 2-3 ... [ 3, 1, 1, 0, 0, 0,-1, 0, 0> . 3190.76
Bb<5 . 1 ..... [ 3,-2, 0, 1, 0, 0, 0, 0, 0> . 3164.92
C6 ... 1-3 ... [ 6, 0, 1, 0, 0, 0, 0,-1, 0> . 3112.81
G5 ... 0 ..... [ 1, 1, 0, 0> ................ 3101.96
Bb<5 . 1-2 ... [ 3, 1, 1, 1,-1,-1, 0, 0, 0> . 3065.25
Bb<5 . 3 ..... [-1,-1, 1, 1, 0, 0, 0, 0, 0> . 3053.18
C6 ... 1-2-3 . [ 6, 1, 1, 0, 0, 0, 0, 0,-1> . 3027.82
G5 ... 2 ..... [-3, 2, 1, 0, 0, 0, 0, 0, 0> . 2990.22
Bb<5 . 2-3 ... [ 0, 1, 1, 1, 0, 0,-1, 0, 0> . 2959.58
G5 ... 1 ..... [ 4,-1, 0, 0, 0, 0, 0, 0, 0> . 2898.04
Bb<5 . 1-3 ... [ 3, 0, 1, 1, 0, 0, 0,-1, 0> . 2881.64
G5 ... 1-2 ... [ 4, 2, 1, 0,-1,-1, 0, 0, 0> . 2798.38
Bb<5 . 1-2-3 . [ 3, 1, 1, 1, 0, 0, 0, 0,-1> . 2796.65
G5 ... 3 ..... [ 0, 0, 1, 0, 0, 0, 0, 0, 0> . 2786.31
E-5 .. 0 ..... [ 0, 0, 1, 0> ................ 2786.31
G5 ... 2-3 ... [ 1, 2, 1, 0, 0, 0,-1, 0, 0> . 2692.71
E-5 .. 2 ..... [-4, 1, 2, 0, 0, 0, 0, 0, 0> . 2674.58
G5 ... 1-3 ... [ 4, 1, 1, 0, 0, 0, 0,-1, 0> . 2614.76
E-5 .. 1 ..... [ 3,-2, 1, 0, 0, 0, 0, 0, 0> . 2582.40
G5 ... 1-2-3 . [ 4, 2, 1, 0, 0, 0, 0, 0,-1> . 2529.78
E-5 .. 1-2 ... [ 3, 1, 2, 0,-1,-1, 0, 0, 0> . 2482.74
E-5 .. 3 ..... [-1,-1, 2, 0, 0, 0, 0, 0, 0> . 2470.67
C5 ... 0 ..... [ 2, 0, 0, 0> ................ 2400.00
E-5 .. 2-3 ... [ 0, 1, 2, 0, 0, 0,-1, 0, 0> . 2377.07
E-5 .. 1-3 ... [ 3, 0, 2, 0, 0, 0, 0,-1, 0> . 2299.12
C5 ... 2 ..... [-2, 1, 1, 0, 0, 0, 0, 0, 0> . 2288.27
E-5 .. 1-2-3 . [ 3, 1, 2, 0, 0, 0, 0, 0,-1> . 2214.14
C5 ... 1 ..... [ 5,-2, 0, 0, 0, 0, 0, 0, 0> . 2196.09
C5 ... 1-2 ... [ 5, 1, 1, 0,-1,-1, 0, 0, 0> . 2096.42
C5 ... 3 ..... [ 1,-1, 1, 0, 0, 0, 0, 0, 0> . 2084.36
C5 ... 2-3 ... [ 2, 1, 1, 0, 0, 0,-1, 0, 0> . 1990.76
C5 ... 1-3 ... [ 5, 0, 1, 0, 0, 0, 0,-1, 0> . 1912.81
G4 ... 0 ..... [ 0, 1, 0, 0> ................ 1901.96
C5 ... 1-2-3 . [ 5, 1, 1, 0, 0, 0, 0, 0,-1> . 1827.82
G4 ... 2 ..... [-4, 2, 1, 0, 0, 0, 0, 0, 0> . 1790.22
G4 ... 1 ..... [ 3,-1, 0, 0, 0, 0, 0, 0, 0> . 1698.04
G4 ... 1-2 ... [ 3, 2, 1, 0,-1,-1, 0, 0, 0> . 1598.38
G4 ... 3 ..... [-1, 0, 1, 0, 0, 0, 0, 0, 0> . 1586.31
G4 ... 2-3 ... [ 0, 2, 1, 0, 0, 0,-1, 0, 0> . 1492.71
G4 ... 1-3 ... [ 3, 1, 1, 0, 0, 0, 0,-1, 0> . 1414.76
G4 ... 1-2-3 . [ 3, 2, 1, 0, 0, 0, 0, 0,-1> . 1329.78
C4 ... 0 ..... [ 1, 0, 0, 0> ................ 1200.00
C4 ... 2 ..... [-3, 1, 1, 0, 0, 0, 0, 0, 0> . 1088.27
C4 ... 1 ..... [ 4,-2, 0, 0, 0, 0, 0, 0, 0> .. 996.09
C4 ... 1-2 ... [ 4, 1, 1, 0,-1,-1, 0, 0, 0> .. 896.42
C4 ... 3 ..... [ 0,-1, 1, 0, 0, 0, 0, 0, 0> .. 884.36
C4 ... 2-3 ... [ 1, 1, 1, 0, 0, 0,-1, 0, 0> .. 790.76
C4 ... 1-3 ... [ 4, 0, 1, 0, 0, 0, 0,-1, 0> .. 712.81
C4 ... 1-2-3 . [ 4, 1, 1, 0, 0, 0, 0, 0,-1> .. 627.82

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

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

> Here's the essential data, to hopefully make it easier ...
>
>
> harm. valves . --------- monzo ------------ .. cents
> ............... 2. 3. 5. 7 11 13 19 53 167
>
> C6 ... 0 ..... [ 3, 0, 0, 0> ................ 3600.00
> C6 ... 2 ..... [-1, 1, 1, 0, 0, 0, 0, 0, 0> . 3488.27
> C6 ... 1 ..... [ 6,-2, 0, 0, 0, 0, 0, 0, 0> . 3396.09
>
> <snip>

AARRRRRRRGGGGGHHH !!!!!!!!!

So no matter how much trouble a poster goes thru to format
a table correctly, Yahoo is determined to sabotage it.
Sucks.

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

>> harm. valves . --------- monzo ------------ .. cents
>> ............... 2. 3. 5. 7 11 13 19 53 167
>>
>> C6 ... 0 ..... [ 3, 0, 0, 0> ................ 3600.00
>> C6 ... 2 ..... [-1, 1, 1, 0, 0, 0, 0, 0, 0> . 3488.27
>> C6 ... 1 ..... [ 6,-2, 0, 0, 0, 0, 0, 0, 0> . 3396.09
>>
>> <snip>
>
>AARRRRRRRGGGGGHHH !!!!!!!!!
>
>So no matter how much trouble a poster goes thru to format
>a table correctly, Yahoo is determined to sabotage it.
>Sucks.

Looks fine in my e-mail client. But, though I didn't read
your page, I generally don't like this sort of thing because
it tends to imply the trumpet's intonation is:

* Fixed
* The same in all octaves
* Even possible to control so that it would be fixed, if
that were desirable
* The same between sizes of trumpet (Bb, C, D, E, flugelhorns,
cornets, etc.)
* The same between brands of trumpet (Selmer, Conn, Yamaha, etc.)

-Carl

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

> Can someone please explore which EDOs give good approximations
> to the notes in my table? Thanks.

I'd reduce your data to the octave, create a Scala scl file, and do
"fit to et" on it.

At 05:32 PM 12/15/2006, you wrote:
>Hello all,
>
>I've just updated my webpage on valve trumpet intonation,
>
>http://tonalsoft.com/monzo/trumpet/trumpet-intonation.htm

I took a look. Note:

* The overblown notes of a trumpet aren't necessarily harmonics.

* 2 of the 3 valve slides are adjustable, and are adjusted
constantly during playing by competent musicians, by means of
spring-loaded triggers and so forth (which is why they're
called "slides").

-Carl

This happens because it is a slightly conical bore which they did to make playing in 12 ET easier.
Bruce Fowler pointed this out to me about the trombone when i played him a harmonic series some 20+ years ago.
He was immediately recognized the differences between this series and his instrument.

Carl Lumma wrote:
>
> At 05:32 PM 12/15/2006, you wrote:
> >Hello all,
> >
> >I've just updated my webpage on valve trumpet intonation,
> >
> >http://tonalsoft.com/monzo/trumpet/trumpet-intonation.htm > <http://tonalsoft.com/monzo/trumpet/trumpet-intonation.htm>
>
> I took a look. Note:
>
> * The overblown notes of a trumpet aren't necessarily harmonics.
>
> * 2 of the 3 valve slides are adjustable, and are adjusted
> constantly during playing by competent musicians, by means of
> spring-loaded triggers and so forth (which is why they're
> called "slides").
>
> -Carl
>
> -- 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

At 03:21 PM 12/16/2006, you wrote:
>This happens because it is a slightly conical bore which they did to
>make playing in 12 ET easier.
> Bruce Fowler pointed this out to me about the trombone when i played
>him a harmonic series some 20+ years ago.
> He was immediately recognized the differences between this series and
>his instrument.

The bore on all brass instruments is conical, and it was so
before anyone ever heard of 12-equal.

-Carl

>>This happens because it is a slightly conical bore which they did to
>>make playing in 12 ET easier.
>> Bruce Fowler pointed this out to me about the trombone when i played
>>him a harmonic series some 20+ years ago.
>> He was immediately recognized the differences between this series and
>>his instrument.
>
>The bore on all brass instruments is conical, and it was so
>before anyone ever heard of 12-equal.

The trumpets of baroque times were longer I think, which makes
it easier to play higher 'harmonics', which they had to do to
play scales. On the modern trumpet, one seldom plays above the
6th 'harmonic', I think, so the numbers on monz's table relating
to the 7th harmonic don't really apply. I think. Keep in mind
I haven't played the damn thing since 1995.

-Carl

yes at the end. but they are now from the start and don't believe this is always been the case.

Carl Lumma wrote:
>
> At 03:21 PM 12/16/2006, you wrote:
> >This happens because it is a slightly conical bore which they did to
> >make playing in 12 ET easier.
> > Bruce Fowler pointed this out to me about the trombone when i played
> >him a harmonic series some 20+ years ago.
> > He was immediately recognized the differences between this series and
> >his instrument.
>
> The bore on all brass instruments is conical, and it was so
> before anyone ever heard of 12-equal.
>
> -Carl
>
> -- 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

At 04:11 PM 12/16/2006, you wrote:
>yes at the end. but they are now from the start and don't believe this
>is always been the case.

Hm, may-bee. I don't know what effect that would have on
the modes of the instrument (the physics term for what we've
been calling 'harmonics', which are not necessarily the
same as the overtones of the timbre). I'm in over my head.
Where's our resident physicists?

-Carl

Carl Lumma wrote:
> At 04:11 PM 12/16/2006, you wrote:
>> yes at the end. but they are now from the start and don't believe this >> is always been the case.
> > Hm, may-bee. I don't know what effect that would have on
> the modes of the instrument (the physics term for what we've
> been calling 'harmonics', which are not necessarily the
> same as the overtones of the timbre). I'm in over my head.
> Where's our resident physicists?

From what I remember it's a horribly complex subject. A conical bore won't give harmonic-series modes (they're something like n-squared instead of n). But you can employ some kind of trickery to get something close by treating the first overblown mode as the fundamental. There are all kinds of imperfections to do with the valves and flare, so you're lucky if it vaguely works, and it won't work so well that you can say if either ET or JI is the true result.

I don't know about how far they're conical. If you're near a good library you could look at a book on musical acoustics. I know any instrument with a slide or valves must have sections of cylindrical tubing.

Graham

>>> yes at the end. but they are now from the start and don't believe this
>>> is always been the case.
>>
>> Hm, may-bee. I don't know what effect that would have on
>> the modes of the instrument (the physics term for what we've
>> been calling 'harmonics', which are not necessarily the
>> same as the overtones of the timbre). I'm in over my head.
>> Where's our resident physicists?
>
> From what I remember it's a horribly complex subject. A conical bore
>won't give harmonic-series modes (they're something like n-squared
>instead of n). But you can employ some kind of trickery to get
>something close by treating the first overblown mode as the fundamental.
> There are all kinds of imperfections to do with the valves and flare,
>so you're lucky if it vaguely works, and it won't work so well that you
>can say if either ET or JI is the true result.

Thanks for chiming in here, Graham.

>I don't know about how far they're conical. If you're near a good
>library you could look at a book on musical acoustics. I know any
>instrument with a slide or valves must have sections of cylindrical tubing.

I know you probably meant this last sentence with dry humor, but it
is technically possible to have a conical section through a valve.
Not a slide, though, I shouldn't think.

-Carl

i am sure someone will one make a 'virtual' one

Carl Lumma wrote:
>
> >>> yes at the end. but they are now from the start and don't believe > this
> >>> is always been the case.
> >>
> >> Hm, may-bee. I don't know what effect that would have on
> >> the modes of the instrument (the physics term for what we've
> >> been calling 'harmonics', which are not necessarily the
> >> same as the overtones of the timbre). I'm in over my head.
> >> Where's our resident physicists?
> >
> > From what I remember it's a horribly complex subject. A conical bore
> >won't give harmonic-series modes (they're something like n-squared
> >instead of n). But you can employ some kind of trickery to get
> >something close by treating the first overblown mode as the fundamental.
> > There are all kinds of imperfections to do with the valves and flare,
> >so you're lucky if it vaguely works, and it won't work so well that you
> >can say if either ET or JI is the true result.
>
> Thanks for chiming in here, Graham.
>
> >I don't know about how far they're conical. If you're near a good
> >library you could look at a book on musical acoustics. I know any
> >instrument with a slide or valves must have sections of cylindrical > tubing.
>
> I know you probably meant this last sentence with dry humor, but it
> is technically possible to have a conical section through a valve.
> Not a slide, though, I shouldn't think.
>
> -Carl
>
> -- 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

[ Attachment content not displayed ]

Hi Carl,

Did you *really* read my page? I mention all kinds of caveats,
including the fact that there are tuning slides, that the 7th
harmonic is rarely used, and that the embouchure plays a *huge*
role in intonation and that the intonation is therefore wildly
variable. I was just trying to pin down as much as i could
what's going on with the valve trumpet intonation.

When i originally posted the page several years ago, i asked
for feedback because i knew that what i wrote isn't the whole
story ... the only person who responded in any detail was
George Secor, and i put his entire reply onto my page.

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

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> >>This happens because it is a slightly conical bore which they did to
> >>make playing in 12 ET easier.
> >> Bruce Fowler pointed this out to me about the trombone when i played
> >>him a harmonic series some 20+ years ago.
> >> He was immediately recognized the differences between this series
and
> >>his instrument.
> >
> >The bore on all brass instruments is conical, and it was so
> >before anyone ever heard of 12-equal.
>
> The trumpets of baroque times were longer I think, which makes
> it easier to play higher 'harmonics', which they had to do to
> play scales. On the modern trumpet, one seldom plays above the
> 6th 'harmonic', I think, so the numbers on monz's table relating
> to the 7th harmonic don't really apply. I think. Keep in mind
> I haven't played the damn thing since 1995.
>
> -Carl
>

>Doesn't the extension from the valve to where it rejoins the main bore have to cylindrical or can it be conical with a different taper?
>My recollection is that the join is pretty close to the valve so the main bore hasn't changed much in diameter.

There can't be a single taper for the horn in both valved and unvalved
states, that's for sure. But neither *has* to be cylindrical.

>If the extension came in at a different diameter from the bore, I'd expect an impedance mismatch and the possibility of reflections. But I'm a woodwind player and mathematician so what do I know about the physics of brass instruments.

Hm, interesting point. I don't know either, but FWIW all the
instruments I've seen have had the following characteristics...

1. Severe taper inside the mouthpiece to diameter x (most drawings
I've seen show a linear taper).

2. Main slide and valve sections nearly cylindrical at diameter
x + 2t, where t is the thickness of the wall of the mouthpiece
shank at its open end.

3. Moderate but exponential taper down the bell.

-Carl

At 08:18 PM 12/17/2006, you wrote:
>Hi Carl,
>
>Did you *really* read my page? I mention all kinds of caveats,
>including the fact that there are tuning slides, that the 7th
>harmonic is rarely used, and that the embouchure plays a *huge*
>role in intonation and that the intonation is therefore wildly
>variable. I was just trying to pin down as much as i could
>what's going on with the valve trumpet intonation.
>
>When i originally posted the page several years ago, i asked
>for feedback because i knew that what i wrote isn't the whole
>story ... the only person who responded in any detail was
>George Secor, and i put his entire reply onto my page.
>
>-monz
>http://tonalsoft.com
>Tonescape microtonal music software

I'm sorry I didn't have time to read your page completely. I
said only that I took "a look". I don't feel that caveats are
strong enough to make the page read in a way that reflects the
point I feel should be made about trumpet intonation, so I was
offering that view here.

I saw George's remarks on your page, but not here on the list.

I saw this paragraph: "one last _caveat_: the way the player uses
his lips has a *tremendous* affect on trumpet intonation. these
cents-values are only theoretical, and may vary widely. also, i
know nothing about variabilities of tube-length for the valves
among different makes and models of trumpet." Apparently it
wasn't the last caveat.

I saw the phrase: "of course, most of the ones which really
deviate far from 12edo are those that are produced in conjunction
with the lips sounding the 7th harmonic", but didn't read the
rest of the paragraph about the infrequent use of the 7th
harmonic. Except "harmonic" isn't the right word -- I think
"mode" is. Moreover, as I said, you can't assume there will
be a mode with the same pitch as the 7th harmonic of the 1st
mode of the pipe.

I saw the sentence: "and certainly good players could also use
the 9th, 11th, and 13th harmonics for microtonal high notes" but
I'm not sure it's true. Maybe Jon Faddis can hit these modes,
but that's about it.

I saw the paragraph beginning "ONE IMPORTANT NOTE", but all horns
have adjustable 1st and 3rd slides, and all pro-level horns make
those adjustments available to the player in real-time, and the
overwhelming majority of professional players use them constantly
during performance. Certain valve combinations require their use,
in fact. 1 + 3 usually requires extension of the 3rd slide to
about 2/3 of its total length, for example. This would fit with
your observation that the valve combinations make more complex
ratios... if I could remember all the recommended slide positions,
I'd tell you.

As for George's proposal, his thumb valve is reminiscent of that
on the French horn, though it is only a two-position valve which
typically transposes the instrument by a fourth.

I like his suggestion in general, but it isn't clear to me how he
addresses the lost functionality of the thumb re. current trumpet
technique. Meanwhile, he apparently doesn't know that orchestral
trumpets are almost always pitched in C.

He also doesn't discuss the possibility of making the total
speaking length of the instrument greater, to make the higher
modes of the instrument more accessible. It's one reason French
horn is a much better microtonal instrument than the trumpet,
I think.

Of course none of this mentions the most microtonal of all brass
instruments -- the trombone. There are all sizes of trombone for
all registers, though some of them are hard to find in mass
production.

-Carl

--- In tuning-math@yahoogroups.com, "monz" <monz@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "monz" <monz@> wrote:
>
> > Here's the essential data, to hopefully make it easier ...
> >
> >
> > harm. valves . --------- monzo ------------ .. cents
> > ............... 2. 3. 5. 7 11 13 19 53 167
> >
> > C6 ... 0 ..... [ 3, 0, 0, 0> ................ 3600.00
> > C6 ... 2 ..... [-1, 1, 1, 0, 0, 0, 0, 0, 0> . 3488.27
> > C6 ... 1 ..... [ 6,-2, 0, 0, 0, 0, 0, 0, 0> . 3396.09
> >
> > <snip>
>
>
> AARRRRRRRGGGGGHHH !!!!!!!!!
>
> So no matter how much trouble a poster goes thru to format
> a table correctly, Yahoo is determined to sabotage it.
> Sucks.
>
>
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software

Hey, Monz:

1) Calm down.

2) While viewing this message, look to the right for the
selection "show message option" and click on it.

3) Then look below that, and click on "use fixed width font".

Or if you're viewing the list of messages, click on the "expanded"
option, which defaults to a fixed-width font.

--George

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> At 08:18 PM 12/17/2006, you wrote:
> >Hi Carl,
> >
> >Did you *really* read my page? I mention all kinds of caveats,
> >including the fact that there are tuning slides, that the 7th
> >harmonic is rarely used, and that the embouchure plays a *huge*
> >role in intonation and that the intonation is therefore wildly
> >variable. I was just trying to pin down as much as i could
> >what's going on with the valve trumpet intonation.
> >
> >When i originally posted the page several years ago, i asked
> >for feedback because i knew that what i wrote isn't the whole
> >story ... the only person who responded in any detail was
> >George Secor, and i put his entire reply onto my page.
> >
> >-monz
> >http://tonalsoft.com
> >Tonescape microtonal music software
>
> I'm sorry I didn't have time to read your page completely. I
> said only that I took "a look". I don't feel that caveats are
> strong enough to make the page read in a way that reflects the
> point I feel should be made about trumpet intonation, so I was
> offering that view here.
>
> I saw George's remarks on your page, but not here on the list.
>
> I saw this paragraph: "one last _caveat_: the way the player uses
> his lips has a *tremendous* affect on trumpet intonation. these
> cents-values are only theoretical, and may vary widely.

The bore of all brass instruments is partially conical (at each end)
and partially cylindrical (in the middle, where the valves and tuning
slides are located). I'm not sure exactly what effect this has on
the harmonic series, but the player has several ways of coping with
this: the embouchure, the position of the back of the tongue,
adjusting slides, and trying out an instrument before you buy it.

> ...
> I saw the paragraph beginning "ONE IMPORTANT NOTE", but all horns
> have adjustable 1st and 3rd slides, and all pro-level horns make
> those adjustments available to the player in real-time, and the
> overwhelming majority of professional players use them constantly
> during performance. Certain valve combinations require their use,
> in fact. 1 + 3 usually requires extension of the 3rd slide to
> about 2/3 of its total length, for example. This would fit with
> your observation that the valve combinations make more complex
> ratios... if I could remember all the recommended slide positions,
> I'd tell you.
>
> As for George's proposal, his thumb valve is reminiscent of that
> on the French horn, though it is only a two-position valve which
> typically transposes the instrument by a fourth.
>
> I like his suggestion in general, but it isn't clear to me how he
> addresses the lost functionality of the thumb re. current trumpet
> technique.

1) The thumb-trigger on a trumpet is operated by the *left* thumb,
whereas the valves (including my proposed thumb-valve) are operated
by the *right* hand.

2) The purpose of the the 1st- and 3rd-valve slides is to compensate
for the shortfall in tube length that results when tubing lengths are
added in combination. My microtonal plan specifies that "a
compensating mechanism is intended to be employed when the 3rd valve
is used in combination with other valves, which brings into play a
second (longer) set of slide tubing that corrects most of the
shortfall in length. (My spreadsheet gives the error in cents for
each valve combination in each division.)"

Compensating mechanisms already exist and I'm told that they work
very well; they're not very common however, because they make the
instrument more expensive.

I consider a compensating mechanism essential for microtonal valved-
brass instruments. Because the distances between adjacent tones in a
microtonal tuning are typically much smaller than in 12-ET, the
errors resulting from shortfalls in tube length are more significant
when reckoned as percentages of scale degrees. For example, if your
trumpet is in 31-ET (39 cents between adjacent tones) and your
shortfall is around 20 cents, then the error puts you halfway between
tones, which is IMO unacceptable. A compensating mechanism would
keep the error to within 5 cents for most of the regular fingerings
and to within 7 cents for the (worst-case) alternate fingerings;
errors that small can very easily be corrected by the player's
embouchure, which would make valve-slide triggers *totally
unnecessary.*

You can see how small these errors are in my spreadsheet:
/tuning-math/files/secor/Brass.xls
(This is included in the text Monz quoted from me, but unfortunately
it's not there as hypertext.)

> Meanwhile, he apparently doesn't know that orchestral
> trumpets are almost always pitched in C.

I've since learned that the parts are often written in C, and it's up
to the player to sight-transpose the part, if necessary, to whichever
instrument he/she happens to be using. This is something that even
non-orchestral players (such as myself) learn to do, since it's not
unusual for a jazz or commercial Bb-trumpet player to be expected to
read from (generic) sheet music.

> He also doesn't discuss the possibility of making the total
> speaking length of the instrument greater, to make the higher
> modes of the instrument more accessible.

That would make the instrument more difficult (and treacherous) to
play, because the harmonics would be closer together. The reason for
the thumb valve on the French horn is to shorten the total tube
length (thereby putting the harmonics farther apart) when playing in
the upper part of the range. (BTW, this is the most common example
of a compensating mechanism, in which there are two sets of valve
slides for the finger-operated valves.)

> It's one reason French
> horn is a much better microtonal instrument than the trumpet,
> I think.

Yes, I agree. There's an additional possibility for microtones with
a conventional F/B-flat double horn. If you switch the two pieces of
tubing for the 3rd-valve slides with one another, you'll be able to
produce many non-12 pitches with the 3rd valve depressed, even in the
lower range (with lots of room for adjustment).

--George

>1) The thumb-trigger on a trumpet is operated by the *left* thumb,
>whereas the valves (including my proposed thumb-valve) are operated
>by the *right* hand.

Aha!

>2) The purpose of the the 1st- and 3rd-valve slides is to compensate
>for the shortfall in tube length that results when tubing lengths are
>added in combination. My microtonal plan specifies that "a
>compensating mechanism is intended to be employed when the 3rd valve
>is used in combination with other valves, which brings into play a
>second (longer) set of slide tubing that corrects most of the
>shortfall in length. (My spreadsheet gives the error in cents for
>each valve combination in each division.)"

I wonder how much tubing/complexity this would add to the
instrument...

>I consider a compensating mechanism essential for microtonal valved-
>brass instruments. Because the distances between adjacent tones in a
>microtonal tuning are typically much smaller than in 12-ET, the
>errors resulting from shortfalls in tube length are more significant
>when reckoned as percentages of scale degrees.

Sure, but it's already unacceptable for the very accurate 5-limit
JI intonation of brass quintets. And the existing trumpet, for
all its faults, does pretty well at this. Higher limits are
another story.

>> Meanwhile, he apparently doesn't know that orchestral
>> trumpets are almost always pitched in C.
>
>I've since learned that the parts are often written in C, and it's up
>to the player to sight-transpose the part, if necessary, to whichever
>instrument he/she happens to be using.

Correct. And to avoid this, and generally get a better fit for the
music, any player even in a small-town orchestra uses a C trumpet.
And any major-city player carries horns in several other keys for
scores that require them.

Sight-transposing is still something that a pro player is generally
expected to do. But Bb trumpets are typical in wind bands, and
virtually unheard of in orchestras.

>> He also doesn't discuss the possibility of making the total
>> speaking length of the instrument greater, to make the higher
>> modes of the instrument more accessible.
>
>That would make the instrument more difficult (and treacherous) to
>play, because the harmonics would be closer together.

There's a centuries-old tradition of playing such instruments.
Check out any "natural trumpet" recordings.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <ekin@...> wrote:
>
> >1) The thumb-trigger on a trumpet is operated by the *left* thumb,
> >whereas the valves (including my proposed thumb-valve) are operated
> >by the *right* hand.
>
> Aha!
>
<snip>

Hey guys ... my initial post on this has generated a big
discussion which is almost entirely off-topic for this list.
I wish i had spoken up about this sooner, so please move it
to the main tuning list if you want to continue.

I'm still hoping that someone can find an EDO approximation
to the pitches i have listed on my webpage.

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