Concert pitch vs. different tunings question

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Ozzlefinch
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Concert pitch vs. different tunings question

Post by Ozzlefinch »

Ok then....

I am working on unlocking the mysteries of the Deep Knowledge of music theory and I am having trouble understanding the idea of "concert pitch" as it relates to the various tunings of the trombone.

For example: All the music I've ever played was written for a trombone tuned to Bb using bass clef. From my understanding, that means my horn in 1st position blows a Bb at 440 pitch and I play a bass clef composition using common fingerings. But what about a trombone tuned to C or something else? My thought is that if I have an antique or old European made horn, in first position it will be tuned to C (or something else)? If I am understanding that correctly, then how does that translate to reading a modern script? Is it normal fingering, or transposed, or treble clef ??? For example, if I have an old pitched instrument, but wanted to play a modern composition along with modern instruments, what do I need to do to make this happen?

I am sorry if this is a dead simple question with an obvious answer, but I am just not getting the connections at this time. And I'm not even sure if I'm making sense with the question.

Thanks in advance!
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Re: Concert pitch vs. different tunings question

Post by hyperbolica »

Concert pitch means you play notes as they sound on piano. The note A is 440 hz. Strings and piano read music in concert pitch. Most instruments use this method. Bb and Eb trombone included (Eb alto trombone plays Eb in 1st position, but still reads concert pitch). The key of the trombone just means what note sounds as the harmonic fundamental - a function of the length of the instrument.

Tuba music is all written in concert pitch, whether Bb, C, Eb or F tuba. The player just uses different fingerings for each length tuba. Any key tuba can play a "tuba" part, just with different fingerings.

Some instrument players through tradition are taught to read transposed parts. Trumpet, clarinet, saxophone. Sometimes baritone and tuba parts (and sometimes even trombone parts) are transposed and written in treble clef, but it's mostly the Brits that do this..

Transposition is used to keep the same fingerings between alto and tenor sax, for example. So for sax, same fingerings for different notes, for tuba, different fingerings for the same notes.

The Bb trumpet is half the length of the Bb trombone, so it should be written an octave above the trombone, but it's written a 9th above. That is just out of tradition. A C trombone sounds C in 1st position, but music isn't written any different for a C trombone.

There can be two keys associated with an instrument. One is the way it is built (what note sounds in first position or open) and the other is how music is typically written for that instrument. Bb trombone (built in Bb) typically plays music in C (concert pitch). Bb trumpet (built in Bb) typically plays music in Bb (written a step higher than it sounds).

The system is inconsistent and confusing. Once you accept that, you're on your way.
Last edited by hyperbolica on Tue Jul 12, 2022 6:50 am, edited 2 times in total.
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Re: Concert pitch vs. different tunings question

Post by ithinknot »

Don't worry about the pitch reference side of it yet - historically, pitch standards varied (often for extremely practical reasons) but, for now, let's take A=~440Hz as a given. Technically, a valve trombone in 8ft C can be said to be "in Bb at A=494Hz", but that's conceptually unimportant and practically useless.

Then, https://en.wikipedia.org/wiki/Transposing_instrument

The basic advantage of transposing notation is to allow the same (C-based) fingerings to work across multiple instruments of differing sizes. On a natural horn/trumpet, you're only ever thinking about a C harmonic series, and then the length of the instrument and/or its crooks does the rest. In the British brass band tradition, all the instruments (except for the bass trombone, Because History) are notated in treble C, so any player could go from the Eb soprano cornet to BBb tuba without having to think about fingerings.

(Outside of these notated traditions, you still need to know what note you're actually playing...)

So, for your example: if you bought a C valve trombone, either

a. you 'relearn'/recontextualise the fingerings so that Bb is 1st valve, etc
or
b. you need music that's notated a tone lower in order to 'trick' you into using the necessary fingerings - we want to hear a Bb, so the page says Ab, you depress the 1st valve as you learned on a Bb instrument, Bb sounds. (But printed music transposing in this direction doesn't generally exist, so you'll have to learn how to do the former.)
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Re: Concert pitch vs. different tunings question

Post by Ozzlefinch »

Interesting.

Yes, I want to learn how it is and not "fight" against it. I understand all about the distances between notes as a mathematical function, so I would assume that using different tunings is just kind of sliding that formula up or down the correct pitch distance to compensate?

I am interested to learn more about the fingerings being different vs. using the same fingerings on a transposed sheet of music. I will have to see if I can find alternate fingering charts- maybe seeing a visualization might help with my understanding (I didn't understand the idea of keys until I bought a wiz-wheel - then it was a "duh" moment).
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Re: Concert pitch vs. different tunings question

Post by BGuttman »

We read true pitch for the most part. There are some trombone parts that are in transposed treble clef; mostly used in British Brass Band nowadays, but used much more commonly 125 years ago. Parts in transposed treble clef can be read as tenor clef with a couple of odd accidentals to resolve (written C# is played as B natural and written F# is played as E natural).

Just a comment: Bb is never at 440 Hz -- the pitch standard is that A4 (3 lines above the bass staff) is at 440 Hz.

An older instrument could be in High Pitch or Low Pitch. High Pitch has A at around 460 Hz and Low Pitch has A at around 435 Hz. Low Pitch is pretty close to modern pitch and you could fit in an ensemble. A High Pitch instrument feels like it is in B natural. If you get into older music like Maximilien (LeTromboniste) you will find that pitch standards ran from 415 for A4 to 465 for A4. He has to keep a variety of crooks for his instruments to fit the pitch being played. Still, many modern groups play this old music at A4=440 Hz.

Tenor and Alto clef parts are also written in True Pitch. So you can use any trombone on any part and it reads the same. Of course the positions to play a particular note on an Eb alto, Bb tenor, or F bass are all different. I started teaching myself alto trombone by playing my Community Band parts on it (in bass clef). Since it had a Bb attachment, all the notes were there; just in different positions.

While the most common pitch of a trombone is Bb, there are other pitches. Alto is in Eb (or sometimes D), and some basses can be in G, F, or Eb. You learn to read true pitch parts on any of these instruments. There used to be a trombone in C (called a "Preacher Trombone). This instrument was intended to read lead line parts from a hymnal. You can actually do this on the Bb trombone (I've done so), but if you have a Preacher Trombone, 1st position is C, 2nd is B natural, 3rd is Bb, etc. Again, you need to learn the true pitches on that instrument.

To try to answer your second question:

The idea behind the transposing instruments seems to date back to the mid 19th Century. A set of valved brasses in Eb and Bb all using the same 3 valves can thus be played by anybody who was familiar with the valve fingerings. So you can use the same method book for a Bb cornet, Eb alto, Bb baritone, or Eb tuba. This had very practical implications for American bands of the Civil War era. Bandsmen doubled as stretcher bearers and if somebody got injured or killed, anybody else could just sub in on a part (you wouldn't miss an Eb "peck horn" but you would miss the solo Eb cornet). Note that a written C on any of the parts will sound either Eb or Bb depending on which instrument you were playing. Same goes for saxophones. I believe the choice of these keys was somewhat arbitrary and dates back to Adolphe Sax, who developed the reed instruments and the valved brasses.

There are other transposing instruments in the band or orchestra. Clarinets come in Bb and A. The A clarinet works better in the sharp keys so popular in orchestral music. The parts read Bb Clarinet or A Clarinet and you would choose the appropriate instrument. It is possible to play A clarinet parts on a Bb clarinet if you can adjust the fingerings, but they will be more awkward. Similar for a Bb part on an A clarinet. At one time cornets came with a "transposing" valve to put them in A as well.

Trumpets and Horns were developed long before there were valves, and as such there are whole families of instruments. Horns often came with a big chest of crooks to put the basic instrument in a variety of keys. Modern horn players learn to transpose these parts on sight. Trumpets come in a variety of keys; some of which are variants. For example, the Eb trumpet often comes with a set of valve slides to put it in D. Modern trumpets are commonly in Bb or C (at least orchestral ones are). Often a player will use one or the other and transpose parts written for different instruments.

There are even some "oddball" pitched instruments. One is the piccolo in Db. That's a trap for the unwary flute player looking for a double. A Db piccolo sounds a half tone HIGHER than played. A Db piccolo reading a C part in a flute section can be a very jarring experience.

I hope this helps a bit.
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Re: Concert pitch vs. different tunings question

Post by Ozzlefinch »

That is indeed very helpful. It will take me a while to sort through what you said and see if I can wrap my head around it all and then apply it to a real world situation.

Thanks for clarifying the A=440 pitch. I think I misstated it on my question, but I do understand what you are saying about that.

I have been playing since 1978 and this is the first time I've really tried to explore the relationship of tuning to composition and so forth. It's quite the rabbit hole! I am having fun learning about it. I don't like mysteries and not knowing what people are talking about when discussing this subject so I decided that this will be the year I will edgumakate myself on the topic.
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Re: Concert pitch vs. different tunings question

Post by Clovenhoof81 »

It is my understanding that A440 hz is a fixed tone.
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Re: Concert pitch vs. different tunings question

Post by BGuttman »

Clovenhoof81 wrote: Tue Jul 12, 2022 12:26 pm It is my understanding that A440 hz is a fixed tone.
The note A (common orchestral tuning note) has been standardized at 440 Hz since the mid 19th Century (although not universally adopted until 125 years later). Talking about A=440 Hz is something called a Pitch Standard. All other notes are based on A4 at 440 Hz. You can see frequency values for all notes based on A4 at 440 Hz in many lists on line.

A4 has not been consistently at 440 Hz in the past. Different areas used different values for A4, ranging from 415 Hz to around 465 Hz. Musical instruments are built to meet these different standards. Here the orchestral strings (violin, viola, cello, bass) have an advantage since you can tune to different pitch standards simply by changing the tension on the string. Other instruments may not have enough adjustment length to meet the requirements of the other tuning standard. In fact, in some pitch standards (known as "High Pitch", with A4 around 460 Hz) a standard length trombone would be in A rather than the Bb we know now.
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Re: Concert pitch vs. different tunings question

Post by robcat2075 »

Ozzlefinch wrote: Tue Jul 12, 2022 5:55 am But what about a trombone tuned to C or something else?
Is that a common thing?

Well... the standard convention for wind instruments that read music in bass clef is that they shall produce the pitches that are written (as if you played the note on a piano) and use whatever fingering or slide position it takes to do that.

So for any given note on the bass clef staff the C tuba, the Eb tuba, the F tuba and the Bb tuba will all sound the same pitch even though they will each need a different fingering to make that note happen on their horn.

If you actually had a C trombone the normal expectation would be that you produce the pitches that are indicated on the bass clef staff and the expectation would not be that you play the slide positions as if you were still on a Bb trombone and thus produce pitches one step higher than indicated.

There are confusing instances in orchestral music where the composer or part copyist didn't understand the above conventions and created bass clef parts that are transposed from the desired pitches. Those are rare however.


AFAIK, the only standard exception to the bass clef rule is low-register horn music written in bass clef, which is transposed in F.


All of this is a different issue from tuning standards like A440 or whatever.
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Re: Concert pitch vs. different tunings question

Post by Ozzlefinch »

Right, good. Thank you all for the detailed answers. I have thought about it overnight and I think I have an idea of how it all works. (however, thinking isn't my strong point :) )

I am trying to create a 3-D model in my head of the relationship of fingering to the tunings - if I can do that, then I can make any corrections or adjustment I need to on any instrument. Attached is a standard chart showing the notes on each slide position, and by extension it transfers to standard 3 and 4 valve fingerings as well. This I understand without problem as the relationships between notes is a mathematical relationship.

Now, from what I think I know so far, if I have a 'bone in Eb for example, then this fingering chart will shift a full step to the left so that now Eb is in 1st, D in 2nd and so forth? Is this correct or am I off on a flight of fancy?

Sorry again if the question seems simplistic or if I'm just being dense about it all. Most likely I'm making it much harder than it needs to be....



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Re: Concert pitch vs. different tunings question

Post by ithinknot »

robcat2075 wrote: Tue Jul 12, 2022 10:40 pm
Ozzlefinch wrote: Tue Jul 12, 2022 5:55 am But what about a trombone tuned to C or something else?
Is that a common thing?
In valve trombone world, not uncommon. C valve instruments (often the 'short' wrap configuration) show up in Catalan cobla bands and various Central and South American traditions.
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Re: Concert pitch vs. different tunings question

Post by ithinknot »

Ozzlefinch wrote: Wed Jul 13, 2022 5:51 am Now, from what I think I know so far, if I have a 'bone in Eb for example, then this fingering chart will shift a full step to the left so that now Eb is in 1st, D in 2nd and so forth?
In Eb (i.e. an alto) the chart shifts a *perfect 4th* (5 semitones) to the left. Yes, Eb series in 1st, A in 7th.
In C (i.e. certain valve trombones that you should resist the urge to buy) the chart moves a whole tone (2 semitones) to the left. C in 1st, F# in 7th.
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Re: Concert pitch vs. different tunings question

Post by elmsandr »

Ozzlefinch wrote: Wed Jul 13, 2022 5:51 am Right, good. Thank you all for the detailed answers. I have thought about it overnight and I think I have an idea of how it all works. (however, thinking isn't my strong point :) )

I am trying to create a 3-D model in my head of the relationship of fingering to the tunings - if I can do that, then I can make any corrections or adjustment I need to on any instrument. Attached is a standard chart showing the notes on each slide position, and by extension it transfers to standard 3 and 4 valve fingerings as well. This I understand without problem as the relationships between notes is a mathematical relationship.

Now, from what I think I know so far, if I have a 'bone in Eb for example, then this fingering chart will shift a full step to the left so that now Eb is in 1st, D in 2nd and so forth? Is this correct or am I off on a flight of fancy?

Sorry again if the question seems simplistic or if I'm just being dense about it all. Most likely I'm making it much harder than it needs to be....



Image
I would not say you shift it a full step to the left... I assume there you are looking at the top row, you need to look at the bottom. The Bb in the lower left spins until THAT is an Eb. You go up a 4th, not down a step. The F on the top becomes a Bb.

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Re: Concert pitch vs. different tunings question

Post by BGuttman »

Your chart is missing one partial just under the one at the top. It is a very out of tune Eb (if I remember correctly) in 1st. Also there is a pedal register an octave below your bottom line.

And you are right that a "continuation" of the chart moved to the left with Eb in 1st position on the bottom row makes the chart appropriate for an Eb alto or Eb bass trombone.

Note that the tendencies for pure overtones on a cylindrical wave guide get modified by the effect of the enlargement at one end and any tapers in the tubing. Instrument makers have known this for a long time and have made instruments to compensate for these foibles, although I doubt anybody had created a perfectly mean-tempered instrument where all the positions line up perfectly. Then again, chords tune better off the mean tempered scale. Often you need to compensate the note based on where it is in the chord. I forget whether the 3rd needs to be flattened and the fifth sharpened or vice versa (but my ears will tell me in a split second).
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Re: Concert pitch vs. different tunings question

Post by Ozzlefinch »

At least I'm barking up the right tree. I'm 74.3% confident that I properly understand what is going on now with the different instrument tunings.

I'm going to make a cylinder slide wiz-wheel thingy later today to help me visualize what's happening. Hopefully I will have some time to try out some "modified" fingerings and see how the theory chart matches to practical application. Unfortunately, as a grown up, I have little time for fun stuff like this :(

Now, for the practical application, if I am playing a standard composition in bass clef where normally a Bb would be in 1st etc, if I am playing an Eb trombone, then Bb would be in 3rd? and the rest follows along according to the harmonic series. I wouldn't have to transpose anything, just use the fingerings based on the chart shifts?
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Re: Concert pitch vs. different tunings question

Post by timothy42b »

Ozzlefinch wrote: Wed Jul 13, 2022 6:44 am
Now, for the practical application, if I am playing a standard composition in bass clef where normally a Bb would be in 1st etc, if I am playing an Eb trombone, then Bb would be in 3rd? and the rest follows along according to the harmonic series. I wouldn't have to transpose anything, just use the fingerings based on the chart shifts?
Kinda sorta. On Eb trombone, top of the bass clef staff is in 1st, and 2cnd line Bb is in 6th. That's because that top Bb is a 5th above the Eb pitch of the horn, and the lower one a 4th below, EXACTLY like the respective F and C are on the Bb trombone. But yes, you don't transpose, and the harmonic series is followed, you just start in a different place.

Sometimes on Eb trombone you forget the middle F is in 6th, and you try to play it in short 1st and bang your mouth.
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Re: Concert pitch vs. different tunings question

Post by Kdanielsen »

6th position of an Eb alto is the same as 1st position of a Bb tenor.

The Eb and Bb don’t indicate a notated transposition; they indicate the harmonic series available in first position. This is true of some instruments (like F tuba) and not of others (like Bb clarinet where it indicates a written transposition).
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Re: Concert pitch vs. different tunings question

Post by OneTon »

Just to make sure confusion reigns supreme:

If I blow into a Bb clarinet without depressing any keys or covering any holes, the note that sounds is f. The notation in treble clef is written as g. This, the most common clarinet, is characterized as “Bb” even though Bb is one of if not the sorriest sounding note on the instrument, particularly for students. The trombones only think they have it bad. It may actually make sense for band directors to tune the group to the tuba’s f.
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Re: Concert pitch vs. different tunings question

Post by harrisonreed »

Ozzlefinch wrote: Wed Jul 13, 2022 6:44 am
Now, for the practical application, if I am playing a standard composition in bass clef where normally a Bb would be in 1st etc, if I am playing an Eb trombone, then Bb would be in 3rd? and the rest follows along according to the harmonic series. I wouldn't have to transpose anything, just use the fingerings based on the chart shifts?
Nope. Bb is in first position, in the partial where F usually is on tenor. I think you're confusing written music with fingerings or transpositions. There are no transpositions in trombone world. You want to say "say I want to play a standard composition in bass clef where normally a Bb would still be a Bb. Even though I switch to alto, a Bb is a Bb. I'd still have to figure out how to play Bb on alto because the music doesn't change at all"

The easiest way to think of it is like this:

The alto trombone still has 7 positions, it's just shorter, so everything is higher. A 4th higher. So all your Bbs are now Ebs. All your Fs are now Bbs. All your D's are now Gs. Abs C#/Db. C's become Fs. And that's just the basic structure of the harmonic series -- it's not like a Bb actually became an Eb, it just always was an Eb in that spot on alto. You have to learn it like a new instrument. So if your first position on alto is pedal Eb, Eb, Bb, Eb, G, Bb, C#, Eb, F, then you can build your position chart off that, going down through the 7 positions chromatically.

The other trick is to learn that the pitch of an instrument doesn't necessarily mean it uses transposed music. A Bb trumpet reads transposed music in Bb, and most trumpeters will have music transposed for whatever pitch trumpet they are using. They play a Bb on an open Bb trumpet, a Bb comes out, and they call it a C. On C trumpet, they play the open horn, a C comes out, and they call it a C too. A Bb trombone reads concert pitch music in C. You play a Bb in first, on the open horn, a Bb comes out, and we call it a Bb (NOT a C). An Eb trombone also reads concert pitch music in C. You play an Eb in first, an Eb comes out, and we call it an Eb (not a Bb or C). As a trombonist, you live in C, regardless of the pitch of trombone you are playing.
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Re: Concert pitch vs. different tunings question

Post by JohnL »

It's easier to make sense of the whole thing if you keep the key of the instrument and the key of the music being read separate.

Consider the modern orchestral horn player. The vast majority use a double horn in Bb and F. They "natively" read music in the key of F, but are regularly faced with music in any one of a half dozen (or more) other keys.
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Re: Concert pitch vs. different tunings question

Post by Ozzlefinch »

Ok then. I have a short video of my understanding of what this is all about. Before you look at it, I misspoke when I said "treble clef" when I meant to say "bass clef". I know full well everything is in bass clef for the purposes of this discussion. Sorry for the error, sometimes my knuckles drag the ground so hard it hurts my brain....


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Re: Concert pitch vs. different tunings question

Post by JohnL »

You need to have all 11 pitches on the bottom line so you don't need to move vertically; by moving vertically, you place yourself at a different spot in the overtone series.
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Re: Concert pitch vs. different tunings question

Post by harrisonreed »

Ozzlefinch wrote: Wed Jul 13, 2022 6:38 pm Ok then. I have a short video of my understanding of what this is all about. Before you look at it, I misspoke when I said "treble clef" when I meant to say "bass clef". I know full well everything is in bass clef for the purposes of this discussion. Sorry for the error, sometimes my knuckles drag the ground so hard it hurts my brain....


Your chart is not correct. I don't know why you have a C in the first position, but I think it's because you shifted your chart down. Whatever you are doing with that chart, sliding it left and right and up and down is not the way it works. Here you go, an Eb alto position chart:

..... I. II. III. IV. V. VI. VII
8. F. E. Eb. D. Db. C. B.
7. Eb. D. Db. C. B. Bb. A
6. Db. C. B. Bb. A. Ab. G
5. Bb. A. Ab. G. F#. F. E
4. G. F#. F. E. Eb. D. Db
3. Eb. D. Db. C. B. Bb. A.
2. Bb. A. Ab. G. F#. F. E
1. Eb. D. Db. C. B. Bb. A
Pedal. Eb. D. Db. C. B. Bb. A
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Re: Concert pitch vs. different tunings question

Post by BGuttman »

Here's a little more weeds to dig through:

The set of resonant vibrations in a fixed length tube is a simple series comprised of the fundamental times n, where n is a whole number. We call the fundamental the pedal range and the Bb in 1st position is Bb1. Its frequency is 58.27 Hz based on A4 being 440 Hz. Thus:

Low Bb is 116.5 (2F)
F is 174.81 (3F)
Bb above that is 233.08 (4F)
D above that is 291.35 (5F)
F above that is 349.62 (6F)
Ab above that is 407.89 (7F) but proper pitch for that note is 415.32, so it's VERY flat)
Bb above that is 466.16 (8F)
C above that is 524.43 (9F)

I think you get the picture. If we had an alto trombone in Eb, its fundamental (pedal) pitch is 77.78 Hz and you can construct the series based on that.

If you compare the pitches to "proper" note pitches from one of the Web sites that give these (I used http://techlib.com/reference/musical_no ... encies.htm ) you can find out that these multiples are not quite proper and you need to adjust the slide position to compensate (hence the admonition to play 1st position off the bumpers).

To throw some more gasoline on the fire, musical instrument makers have learned that altering the shape of the instrument (tapers and bends) can alter these multiples a bit so they can be in better tune -- D being a little flat and F being a little sharp for example.

We could now get into the tuning tendencies of 3-valve instruments, but I think that's another topic for another day.
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Re: Concert pitch vs. different tunings question

Post by Ozzlefinch »

Ok, I got it wrong. Not the first time. Last night I was playing around a bit with the wheel I made and it wasn't adding up in some places, now I see why.

I'll think over the feedback I got and see if I can construct something that makes more sense- that is to say something that actually works and reflects reality.

At the very least, I am having fun learning about this.
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Re: Concert pitch vs. different tunings question

Post by jthomas105 »

Please delete that video from YouTube so that it doesn't confuse someone with the wrong information.
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Re: Concert pitch vs. different tunings question

Post by robcat2075 »

Ozzlefinch wrote: Wed Jul 13, 2022 6:38 pm I have a short video of my understanding of what this is all about.
With your device, to correctly indicate results for an Eb trombone, you'd need to slide the palette horizontally, not diagonally, from Bb until an Eb (in that lowest row of possible fundamentals) was in 1st position.

You can't just put any Eb there, it has to be a fundamental.

It is surprising to hear that you have been playing for so long and yet the relationship of positions to partials remains mysterious. I wonder how common that is.
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Re: Concert pitch vs. different tunings question

Post by robcat2075 »

Print this out, then cutout the green bar.

Put the "1st" underneath any note in the "Fundamental" row, then you can slide it vertically to see positions for notes on any "partial" above the fundamental.

The blue cells are the normal Bb trombone.
Notes.jpg
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Re: Concert pitch vs. different tunings question

Post by OneTon »

Not knowing partials is common. The first step in putting partials in the toolbox is wanting to learn, followed up with practice.
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Re: Concert pitch vs. different tunings question

Post by harrisonreed »

I want to revisit your original post. I think you are still trying to put too many concepts together all at once, after looking at your video.
Ozzlefinch wrote: Tue Jul 12, 2022 5:55 am All the music I've ever played was written for a trombone tuned to Bb using bass clef. From my understanding, that means my horn in 1st position blows a Bb at 440 pitch
A 440 means that we have agreed to call the sound made at 440hz "A", and that we tune our instruments so that when we play an "A", it's as close to 440hz (or for trombones usually an octave lower, 220hz) as we can get it. We could call it a 仝 and it would still be the same sound. This is important, because transposing instruments might be calling their tuning note 荻 but the absolute pitch will still be 440hz or 220hz, or some other octave of that pitch. This is our "tuning convention". Usually in America it's A=440, but in Japan they tune their A to 442hz. Some places do A444.

So point one, "different tunings", usually this term will refer to the "tuning convention" which is just a fancy way to say "we've decided 440hz is what we are calling "A" on the piano."
and I play a bass clef composition using common fingerings.
The term fingerings might also be hindering you. The trombone only has positions and partials.
But what about a trombone tuned to C or something else? My thought is that if I have an antique or old European made horn, in first position it will be tuned to C (or something else)? If I am understanding that correctly, then how does that translate to reading a modern script? Is it normal fingering, or transposed, or treble clef ???
This is a different puzzle to unravel, unrelated to the pitch convention. For the trombone, we historically DO NOT transpose music to fit the instrument we play. So the music is unchanged. Your C trombone would have a new set of positions and partials to learn, like with the alto position charts that are posted up above. If you play the first position, fundamental note on your C trombone, the absolute pitch "C", just like a C on a piano, would come out. You could choose to call that noteゞ if you wanted to, but the frequency would be unchanged. This is what is meant by the "instrument's pitch". You can experiment with this on your tenor. In fact, you change the fundamental pitch of your trombone hundreds of times a day, all while the music on your stand remains unchanged. Move your slide to second position and you now have a trombone pitched in A. Same with trumpet. Push down the first valve and your trumpet is now pitched in Ab. Doing this won't cause you to need new, transposed music, because you already know how to play your tenor or your trumpet.
For example, if I have an old pitched instrument,
Break the habit of thinking of differently pitched instruments as old. They are just different lengths of pipe.
but wanted to play a modern composition along with modern instruments, what do I need to do to make this happen?
You would need to learn the new positions/ harmonic series for whatever horn you are playing. The music won't change, unless you want to transpose it and lie to yourself, so that absolute Ebs from the original score are written as Bb in your part. The sliding chart is cool and fun, but at the end of the day it won't really be faster than learning the new horn from scratch.

I am sorry if this is a dead simple question with an obvious answer, but I am just not getting the connections at this time. And I'm not even sure if I'm making sense with the question.
It's just a lot of different questions that seem related, but really aren't. The pitch of the horn, for trombones at least, is not related to the music on the page, or the clef. If it's in tenor or alto clef, you're supposed to know how to read that too. The C might be on a different line, but what you do to play that C is unique to the Bb or Eb trombone you are playing, and you need to know how to do it.
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