Doppler Pairs

Whistle
1

In my earlier thread on C music transposition I noted this pair:

  • music written in the key of G played on a C whistle will be transposed into sounding in the key of F
  • music written in the key of C played on a G whistle will be transposed into sounding in the key of F

And similarly:

  • music written in the key of A played on a C whistle will be transposed into sounding in the key of G
  • music written in the key of C played on a A whistle will be transposed into sounding in the key of G
    and so on with the others …

Why does it not seem to matter in the pairs which is the music key and which is the whistle?

I see some connection to the Doppler Shift others have mentioned where source, observer and medium could be applied to whistle, music and listener i.e. it doesn’t matter which of the source, observer or medium is stationary and which is moving, however, in this scenario the whistle analogy seems to fall apart if one moves each of the three which if it held should yield triplets instead of pairs.

Anyway Physics aside, some kind of easy music theory answer would be helpful.

2

This sounds like CPT theory for particles applied to whistles. There are three variants here, whistle key, fingering, and resultant music key. You can always change two such that the third is constant. Unlike CPT theory, however, the changes here are multivalued, rather than binary - thus demonstrating that whistle theory is more complicated than quantum theory.

3

Sorry, I didn’t mean to make this sound like I intended anything deep. I have a slight bit of Physics and no music theory at all. The transpositions I mention where done using a chart not from theory. So honestly is my assumption correct that the basic theory behind doing this transposition is simply counting semitones up or down? But why can the music played key and the whistle played be interchanged and still give the same resultant transposition? What is the basis behind this?

4

I think I just may have a glimmer at a possible answer. Is it because the fingering is concert pitch and is a match for the music? In other words, if I didn’t use concert pitch fingering, would these pairs no longer jive?

5

OK, lets start with some basic music theory, the Circle of Fifths. Lets start on F. Count F as 1 and go up to 5:

1 - F
2 - G
3 - A
4 - Bb
5 - C

So, C is a fifth above F. If we keep going, we get a list of keys that are a fifth apart:

F - F G A Bb C D E F
C - C D E F G A B C
G - G A B C D E F# G
D - D E F# G A B C# D
A - A B C# D E F# G# A

Notice that keys a fifth apart differ by exactly one sharp or flat.

Let’s now look at the D whistle. If we play it with no-half-holes or forked fingerings, I get the D scale. If I half-hole or use a forked fingering (OXX OOO, for instance) to get a Cnat instead of a C sharp, I am now playing G scale (the only difference between the D scale and the G scale is the C#/Cnat). I have moved the scale a fifth, G and D are a fiflth apart.

Now pick up an A whistle. If you play the G# (OOO OOO on an A whistle or the “C# fingering”) as a G (OXX OOO) you are now playing a D scale. Just like on the D whistle, when you flatten OOO OOO to OXX OOO, you move a fifth.

Looking at your first two examples:

  1. Music in G played on a C whistle sounds in F. If we played music in G on a D whistle, we would get G, one fifth up the list above. So, if we do the same fingering on a C whistle, we get one fifth up the list from C or F.

  2. Music in C played on G whistle sounds in F. If we played C music on a D whistle, we would play Cnat instead of C# (OXX OOO vs OOO OOO) and Fnat instead of F# (XXX X / O vs XXX XOO, where / is a half-hole). We would move up two fifths on the list above from D to C. So, if we do the same fingering on a G whistle, we also move up two fifths on the list from G to F.

Your remaining two examples are left as a problem for the student. Hope this helps.

Edited to add: The complete Circle of Fifths is

C
G
D
A
E
B
F#
Db (same as C#)
Ab
Eb
Bb
F
C

Each key on the list is a fifth from the ones just above and below it on the list and differs from those keys by exactly one flat or sharp.

6

http://www.edly.com/mtfpp.html :wink:

7

wallrii - This is exactly what I needed. Thank you wallrii for taking the time to put together a detailed answer. It is much appreciated.
Before breakfast it clicked, but after breakfast not as well so I’ll paste your answer to a file and print it out to reread several times to get it to stick. Having the theory applied directly to whistles does seem to help.

MTGuru - A year ago I had borrowed my son’s “Idiot’s Guide to Music Theory”, but I found it just OK and wouldn’t give it much of a recommendation so I just ordered “Edly’s Music Theory for Practical People” that you referenced. Hopefully it will have more “practical” application for things like the rule of fifths that obviously didn’t make much of an impression first time through.

Again, thank you both for your help.

8

Wallrii - To help anyone else with the same transposition issues I’ve finished the examples and reworded your lesson slightly by adding the words “flatten” and “sharpen” in a few spots to clarify:

In this all whistles are played using “D whistle fingering” or “concert pitch fingering”.

OK, lets start with some basic music theory, the Circle of Fifths. Lets start on F. Count F as 1 and go up to 5:
1 - F
2 - G
3 - A
4 - Bb
5 - C

So, C is a fifth above F. If we keep going, we get a list of keys that are a fifth apart:
F - F G A Bb C D E F
C - C D E F G A B C
G - G A B C D E F# G
D - D E F# G A B C# D
A - A B C# D E F# G# A

The complete Circle of Fifths is below. Each key on the list is a fifth from the ones just above and below it on the list and differs from those keys by exactly one flat or sharp. Moving to the right sharpens and moving to the left flattens.

C G D A E B F# Db/C# Ab Eb Bb F C

F - 1 flat
C - no accidentals
G - 1 sharp
D - 2 sharps
A - 3 sharps
etc.

Let’s now look at the D whistle. If we play it with no-half-holes or forked fingerings, I get the D scale. If I half-hole or use a cross/forked fingering (OXX OOO, for instance) to get a Cnat instead of a C sharp, I am now playing G scale (the only difference between the D scale and the G scale is the C#/Cnat). I have moved the scale a fifth, G and D are a fifth apart.

Now pick up an A whistle. If you play the G# (OOO OOO on an A whistle or the “C# fingering”) as a G (OXX OOO) you are now playing a D scale. Just like on the D whistle, when you flatten OOO OOO to OXX OOO, you move a fifth.

Examples:

  1. Music in G played on a C whistle sounds in F:
    If we played music in G on a D whistle, we would get G, one fifth flatter in the list above. So, if we do the same fingering on a C whistle, we get one fifth flatter in the list from C to F.

  2. Music in C played on G whistle sounds in F.
    If we played C music on a D whistle, we would play Cnat instead of C# (OXX OOO vs OOO OOO) and Fnat instead of F# (XXX X / O vs XXX XOO, where / is a half-hole). We would move two fifths flatter in the list above from D to C. So, if we do the same fingering on a G whistle, we also move two fifths flatter in the list from G to F.

  3. Music in A played on a C whistle sounds in G:
    If we played music in A on a D whistle, we would get A, one fifth sharper in the list above. So, if we do the same fingering on a C whistle we move one fifth sharper to G.

  4. Music in C played on an A whistle sounds in G:
    If we played music in C on a D whistle, we would get G, two fifths flatter. So, if we do the same fingering on an A whistle we move two fifths flatter to G.

Similarly:
5. Music in A played on an F whistle sounds in C.
6. Music in C played on a C whistle sounds in Bb.

9

:astonished: Eyes glazing over :astonished:

I think it’s fine to dive into the theory and mathematics, especially if you’re of an analytical bent. I’m one of the first to advocate a grounding in music theory, if only to add depth to one’s knowledge of this music, or any music.

But here’s the thing. This is not the way to deal with transposition issues, especially on the fly. It’s far simpler than that.

Here’s a typical situation. You’re at a session, and the fiddler launches into Porthole of the Kelp in D Dorian. You pick up your good old D whistle and think, ugh, I don’t want to deal with those F-nats. But you know from experience (or, yes, from theory) that you can easily finger an E Dorian scale.

Now E is one tone UP from D. In order to play along, you’re going to have to choose a whistle to compensate by bringing you one tone back DOWN again. And one tone down from D is C. So you pick up your C whistle, and off you go, playing along in your transposed key of E Dorian.

Similarly, you might also realize that you can easily finger an A Dorian scale. A is 4 tones UP from D. So to compensate, you count 4 tones DOWN from D, which gives you G. So you pick up your G whistle and off you go.

Sure, there are more complicated ways of calculating this. For example, in the case of D-> E, you can think: Hmmm, going up a Major 2nd interval takes me 2 steps clockwise around the circle of 5ths (5th + 5th → Major 9th, which reduces to Major 2nd). And 2 steps add 2 sharps to my key signature. So I need to choose a whistle that subtracts 2 sharps from my D whistle. And since D Major has 2 sharps, subtracting 2 sharps gives me zero sharps. And the key with zero sharps is C major. So I need to choose a C whistle.

But I can almost guarantee you that no one does it like this. Calculating by intervals is so much easier. :wink:

10

Maybe whistle isn’t the right instrument for everyone.
Perhaps I might humbly suggest trying a kazoo to get around all those horrid key issues?

11

funny how easy transposing is on one o’dem, innit!

12

MTGuru - Thank you for pointing out the practical application.

So then, EASY INTERVALS IT WILL BE!

13

I actually do the mental math much as you describe MT. However, being the analytical type, the simple approach didn’t satisfy until I’d thought the theory through. Once I had the theory firmly in mind, the simple approach became “oh, so that’s why we do it that way.” But then, I still have the quadratic formula memorized from high school.

14

I think that’s a good way to put it, walrii. I’m certainly not anti-theory, as everyone knows. :slight_smile: Understanding the relationships gives you multiple paths to the same calculated result, and there’s an elegance in the ways those paths reinforce each other. It also makes sense to pick the easiest path for solving practical problems.

I’m looking forward to reactions to the Edly book (Music Theory for Practical People) from pipebender and others who have now bought it.

15

Re: Edly’s Music Theory for Practical People by Ed Roseman

I’ve read the first 12 chapters so far and looking at the remainder of the book I suspect for the average person this is the only book one would ever need on music theory. Note that this book is strictly music theory and it does not deal with how to read music.

Mind you I find it easy to read for the most part, but it is so jam-packed with information that it’s a little difficult to take it all in on the first reading. I can see myself going back to it as a great reference. It spends a fair amount on chords, but I expect any book on music theory would probably do so as the author/writer/composer would most likely be proficient at the piano. Since anything more than the introductory chapters on chords doesn’t seem to be particularly relevant to the tin whistle, I’ll probably skip the more advanced chapters on chords at this stage.

I’m looking forward to the chapters on “modes” as I find this another area where I’m in the dark, however, it may be that I’m just not used to the buzz words yet.

Thanks for the recommendation!

16

Very glad to hear that, Pipe Bender. Thanks for your impressions! I think it’s great that you’re tackling this on your own terms and at your own pace. Bravo!

17

Yeah, well done. I particularly enjoyed the Groucho Marks one.