Re: [Unschooling-dotcom] music and math
Alan & Brenda Leonard
> I am completely confused by your post.I regret that. I'll try to be more clear below.
Please understand that I answered your post after picking up digests.
Therefore, I learned after I'd already replied to it that you'd resolved the
issue with your son. This happens regularly here, because many people do
receive on digest. I wasn't trying to beat a dead horse.
> Regarding music, I play mutliple instruments, and I never even mentionedI don't know about everybody, being only one somebody, but I assumed that
> piano, so I'm not sure why everyone is assuming that I am talking about piano.
you were talking about piano because your vision of notation sounded limited
to the idea of one black spot, one place on the instrument. Only piano has
that kind of visual link.
>Not on a transposing instrument.
> In every instrument the notation of "C" means "C".
> OnBut here is my point. A note on the treble clef staff does not always send
> the violin, its a particular finger position. On the guitar, it is also a
> particular finger position.
you to a particular finger placement. For example, the "A" that is the
second space on the treble clef is an open string on my violin. But it's
also a stopped note on the two lower strings, and can be played with any of
the 4 fingers, for a total of 9 locations. It's even worse on guitar, with
more than 4 strings!
> On a saxophone or trumpet, it is a fingerOn the trumpet, those 3 little valves only improve the pitch. A great
> positioning, or a combination of finger positions that only vary depending on
> the octave involved.
trumpet player plays all the notes with the mouth by changing lip and tongue
positions and the speed and support of the breath. I don't know much about
saxaphone, sorry.
>Yep, it's c. But it's a lot more abstract than you made it sound.
> But "c" is still "c". That never changes.
>I do. I hope that it's more clear *why* I do. You can see it as not
> I don't see music as abstract at all.
abstract if you want.
> what way is it "multistep" other than to learn the notation and how itMultistep music. Okay. I'm a professional musician, and this is my concept
> accomplished on the particular instrument you are playing?
of the steps. The first 3 steps take about 3 seconds for me. I've spent
entire lessons working through them with kids, though.
New music:
Step 1: composer. That affects the way I look at the music. Not just in
interpretation, but also how I read the notes. Ornaments (turns, trills,
mordents, etc.) are read differently in differnet periods.
Step 2: key signature. quick scan to see if it changes anyplace.
Step 3: time signature, and a glace above at the tempo marking. Allegro is
a pretty abstract concept in itself (fast? how fast?). select tempo.
negotiate with other people if necessary, or take a look at what the
conductor wants.
Step 4:
notes. I make a million decisions every minute as I play. I take the notes
on the page and decide, while playing, where to play them on the instrument.
That's not interpretative, that's functional. Can I reach the next note if
I play this one here, with this finger.
and so on.
>I hope that what I've written above helps you understand why I say that
> After that, there are many ways to play the same note on a particular
> instrument. Take the violin for example. You can play a note, use vibrato, or
> use pizzacato, all of which is in the notation on the music. But you are
> still playing the same note, and each symbol on the paper represents one
> thing, and the technique to play the music the way its written never changes,
> even though the style might.
there are different techniques to play the notes the way they are written.
And vibrato, for the record, is never written into the music I play. That's
dropped about the 2nd year of playing. I make decisions about bow stroke,
vibrato, and such myself. But that's stylistic, which you aren't thinking
of as technical. I do, because there's a technical approach to each piece
of style, but that's neither here nor there.
>Of course. But if you understand the CONCEPT of what you are trying to do,
> In contrast to music, there are many technical ways to solve a single problem
> in math. When adding, you can add from right to left, you can add from left
> to right, you can estimate and subract, you can mentally compute it in your
> head by any combination of these methods.
than the notes fall into place. If you understand the CONCEPT of the math
problem you are trying to solve, then you choose the technical way that
makes the most sense to you.
Beginning players want to learn the technical steps without the concepts.
If it says this black dot, do I play D string with second finger? Getting
beyond that is the first step to really playing music.
School children are told to learn the technical steps without the concepts.
And then they forget the steps. Getting beyond that is the route to really
understanding math.
>But my point is the same. You must understand the concept before you can
>>>> What difference does it make
> that you flip the fraction over and mulitply if you haven't got any idea WHY
> you would do that. If you understand the concepts, you see why that works.<<<
>
> It was a question I asked for myself. That one had nothing to do with my son.
teach it.
Great violinists do not always make great teachers. I've studied with great
players who could not explain what they did to save their life. They just
don't know. And that's no help to me or anyone else. Great teachers are
people who understand WHY you do what you do, and don't just do something
instinctually. They can explain it.
>>> If you don't get it, why are you trying to teach him to not get it? <<The impression I feel like you had given here was that you were teaching
>
> Because he asked me to teach him the way his friends learn. I thought that
> was what he wanted, so thats what I did.
your son. Teaching. If you don't understand the concepts behind it, you
can't teach it. That was my point.
I'm glad that you put the book away. But I hope that you don't fall into
this trap again. You don't have to teach him anything, but if asked to
teach something, by someone, it should be something you really understand.
In my humble opinion.
brenda
Have a Nice Day!
THank you SO much for writing this. I really appreciate the time and thought you put into it. See comments below.
Please understand that I answered your post after picking up digests.
Therefore, I learned after I'd already replied to it that you'd resolved the
issue with your son. This happens regularly here, because many people do
receive on digest. I wasn't trying to beat a dead horse.<<
No problem. I figured it was something like that :o). I noticed I've been getting some posts out of order myself. Thats why I recapped.
Ok, this is new to me. I'll look it up, but if you feel like it, I'd be glad to hear more about it. Given your example of a violin, I assume that is considered a "transposing instrument". I've never heard it called that. I'll check it out.
second space on the treble clef is an open string on my violin.<<<
True. I guess I always considered "open" to be another finger position.
positions and the speed and support of the breath. I don't know much about
saxaphone, sorry.<<<
I didn't know that about the trumpet, but it does make sense since there are only so many combinations of fingerings with 3 valves.
of the steps. The first 3 steps take about 3 seconds for me. I've spent
entire lessons working through them with kids, though.
<snip>
You know something, I totally agree with you. I think when we are talking about music, what I call stylistic differences (allegro, etc), you call abstract. And I do think stylistic differences *are* abstract.
When I think of technical issues, I'm thinking of the notes themselves, or the notation for "up bow" or "down bow", pizz, etc. Those things mean something specific, but other things mean something of creative license.
And creative license is abstract, even though there are also techniques to style.
I *think* we agree, but we were maybe saying it different ways.
can't teach it. That was my point.<<
teach something, by someone, it should be something you really understand.
In my humble opinion.<<
I completely agree with you. Thank you so much for going back and explaining it. I hope I don't fall into that trap again too. The truth is, I fall back on textbooks (especially in math) because I *don't* understand everything, and even when I do, I have a hard time teaching it.
But given the fact he appeared interested, I was hoping it would all make more sense in spite of me.
Kristen
[Non-text portions of this message have been removed]
> I am completely confused by your post.I regret that. I'll try to be more clear below.
Please understand that I answered your post after picking up digests.
Therefore, I learned after I'd already replied to it that you'd resolved the
issue with your son. This happens regularly here, because many people do
receive on digest. I wasn't trying to beat a dead horse.<<
No problem. I figured it was something like that :o). I noticed I've been getting some posts out of order myself. Thats why I recapped.
> In every instrument the notation of "C" means "C".Not on a transposing instrument.
Ok, this is new to me. I'll look it up, but if you feel like it, I'd be glad to hear more about it. Given your example of a violin, I assume that is considered a "transposing instrument". I've never heard it called that. I'll check it out.
> Onyou to a particular finger placement. For example, the "A" that is the
> the violin, its a particular finger position. On the guitar, it is also a
> particular finger position.
>>>But here is my point. A note on the treble clef staff does not always send
second space on the treble clef is an open string on my violin.<<<
True. I guess I always considered "open" to be another finger position.
>>On the trumpet, those 3 little valves only improve the pitch. A greattrumpet player plays all the notes with the mouth by changing lip and tongue
positions and the speed and support of the breath. I don't know much about
saxaphone, sorry.<<<
I didn't know that about the trumpet, but it does make sense since there are only so many combinations of fingerings with 3 valves.
> what way is it "multistep" other than to learn the notation and how itMultistep music. Okay. I'm a professional musician, and this is my concept
> accomplished on the particular instrument you are playing?
of the steps. The first 3 steps take about 3 seconds for me. I've spent
entire lessons working through them with kids, though.
<snip>
You know something, I totally agree with you. I think when we are talking about music, what I call stylistic differences (allegro, etc), you call abstract. And I do think stylistic differences *are* abstract.
When I think of technical issues, I'm thinking of the notes themselves, or the notation for "up bow" or "down bow", pizz, etc. Those things mean something specific, but other things mean something of creative license.
And creative license is abstract, even though there are also techniques to style.
I *think* we agree, but we were maybe saying it different ways.
>But my point is the same. You must understand the concept before you canteach it.
>>Great violinists do not always make great teachers. I've studied with greatplayers who could not explain what they did to save their life. <<
>>The impression I feel like you had given here was that you were teachingyour son. Teaching. If you don't understand the concepts behind it, you
can't teach it. That was my point.<<
>>I'm glad that you put the book away. But I hope that you don't fall intothis trap again. You don't have to teach him anything, but if asked to
teach something, by someone, it should be something you really understand.
In my humble opinion.<<
I completely agree with you. Thank you so much for going back and explaining it. I hope I don't fall into that trap again too. The truth is, I fall back on textbooks (especially in math) because I *don't* understand everything, and even when I do, I have a hard time teaching it.
But given the fact he appeared interested, I was hoping it would all make more sense in spite of me.
Kristen
[Non-text portions of this message have been removed]
[email protected]
In a message dated 2/8/03 3:17:15 AM, abtleo@... writes:
<< I make a million decisions every minute as I play. I take the notes
on the page and decide, while playing, where to play them on the instrument.
That's not interpretative, that's functional. Can I reach the next note if
I play this one here, with this finger.
But my main instrument lately is recorder. It's fairly crude, but even
there, I see the note, and I feel in my hands whether I have an F instrument
or a C instrument. If I've been just playing one for a whole hour, I'm not
thinking that anymore, but in the set of music we've been doing lately I
switch between alto and soprano a fair amount.
A G on the paper is a different combo of fingers depending which recorder I
have. Good. I'm going.
When I get to (on an alto, I'll use as an example) a low E, there are two
equally good fingerings to use, and it depends which notes it's next to which
one I'm going to use. No sense moving three fingers when I can just move
one. Other combos are better with the other fingering.
In a fast run, I can use a trill/alternate fingering sometimes.
On my Küng recorder, the high A is sharp, always, and so I shade that by
putting my fourth finger, right hand, close to the surface of a hole. If I'm
using the Moeck or a plastic Yamaha, that A is fine without shading it down.
But those other two have a harder time going above high C.
I've been playing that same recorder since I was 19, off and on, though, and
I remember it.
That's not abstraction, that's detailed particulars.
The idea that one note represents one set of fingerings isn't true of all
instruments. Bass recorders famously have to be learned, each one, by each
musician. The notes in the middle of the range are likely to be good as on
higher pitched recorders. But when you get to the higher and lower notes you
kinda have to find each one for that particular instrument. It's not a wild
search, there are likelihoods and physical (as in physics) realities. But
nobody here can say "On any bass recorder, a low A is fingered like this."
The most they can say is "Might be, on an F bass, like this; try it."
And still people play recorders!! <bwg>
And people still love math, if they love it, because of the patterns and the
flow of ideas and relationships between things, not because the formulas are
pretty on paper. Because they liked and understood math first and THEN
wanted to learn the notation so someone could show them some cool other
stuff. School's math methods can kill that dead for all but the lucky few
who understood math in their heads, on their fingers, on chessboards, or in
their yards on the fencewire before they got there.
Sandra
Sandra
<< I make a million decisions every minute as I play. I take the notes
on the page and decide, while playing, where to play them on the instrument.
That's not interpretative, that's functional. Can I reach the next note if
I play this one here, with this finger.
>>I make a dozen decisions, not a million. <g>
But my main instrument lately is recorder. It's fairly crude, but even
there, I see the note, and I feel in my hands whether I have an F instrument
or a C instrument. If I've been just playing one for a whole hour, I'm not
thinking that anymore, but in the set of music we've been doing lately I
switch between alto and soprano a fair amount.
A G on the paper is a different combo of fingers depending which recorder I
have. Good. I'm going.
When I get to (on an alto, I'll use as an example) a low E, there are two
equally good fingerings to use, and it depends which notes it's next to which
one I'm going to use. No sense moving three fingers when I can just move
one. Other combos are better with the other fingering.
In a fast run, I can use a trill/alternate fingering sometimes.
On my Küng recorder, the high A is sharp, always, and so I shade that by
putting my fourth finger, right hand, close to the surface of a hole. If I'm
using the Moeck or a plastic Yamaha, that A is fine without shading it down.
But those other two have a harder time going above high C.
I've been playing that same recorder since I was 19, off and on, though, and
I remember it.
That's not abstraction, that's detailed particulars.
The idea that one note represents one set of fingerings isn't true of all
instruments. Bass recorders famously have to be learned, each one, by each
musician. The notes in the middle of the range are likely to be good as on
higher pitched recorders. But when you get to the higher and lower notes you
kinda have to find each one for that particular instrument. It's not a wild
search, there are likelihoods and physical (as in physics) realities. But
nobody here can say "On any bass recorder, a low A is fingered like this."
The most they can say is "Might be, on an F bass, like this; try it."
And still people play recorders!! <bwg>
And people still love math, if they love it, because of the patterns and the
flow of ideas and relationships between things, not because the formulas are
pretty on paper. Because they liked and understood math first and THEN
wanted to learn the notation so someone could show them some cool other
stuff. School's math methods can kill that dead for all but the lucky few
who understood math in their heads, on their fingers, on chessboards, or in
their yards on the fencewire before they got there.
Sandra
Sandra
Tia Leschke
> > On a saxophone or trumpet, it is a fingerdepending on
> > positioning, or a combination of finger positions that only vary
> > the octave involved.tongue
>
> On the trumpet, those 3 little valves only improve the pitch. A great
> trumpet player plays all the notes with the mouth by changing lip and
> positions and the speed and support of the breath.Not quite. A certain fingering on trumpet or French horn will get you into
a series of partials. Which of the partials you get depends on the lip. So
on horn, an open fingering will get you the C two octaves below middle
(written) C, the C above that, the G above that, middle C, then E, G, C, D,
E, G, A, C. There are also some other notes you can get, but they don't
tend to be in tune. As you can see, the higher you go in the partial, the
closer together the notes are. And *that's* the reason horn players tend to
miss more notes than other instrumentalists. They play high in the
partials. Trumpets play lower in theirs. If I remember my one quarter of
trombone correctly, the positions work the same way as the fingerings on
trumpet or horn. The position gets you into the right partial. Then your
lips decide where in the partial.
As for improving the pitch, I can't remember how it's done on the trumpet.
On the horn, you do it some with your lips, but you also move the right hand
in and out of the bell for tuning.
Tia