 The Clarinet BBoard
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Author: Nathan
Date: 2005-12-07 02:20
I'm trying to figure out what the frequency of the low Eb on a bass clarinet is. Thanks.
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Author: Low_Reed
Date: 2005-12-07 03:03
Look here for answers to Frequency Asked Questions:
http://www.contrabass.com/pages/frequency.html
Bruce
**Music is the river of the world!**
-- inspired by Tom Waits and a world full of music makers
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Author: Johnny Galaga
Date: 2005-12-07 05:38
How come the frequencies don't increase by the same amount for every half step? The spacing isn't even.
Is there a formula to calculate the freqeuncies?
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Author: GBK
Date: 2005-12-07 06:02
The note "A" is set at 440 Hz and all of the other notes are tuned off of that.
In the tempered scale, all of the notes are offset by the 12th root of 2 (roughly 1.0595).
Thus, if you take any note's frequency and multiply it by 1.0595, you get the frequency for the next note.
For example:
A = 440.0
A# = 466.1
B = 493.8
C = 523.2
C# = 554.3
D = 587.3
D# = 622.2
E = 659.2
F = 698.4
F# = 739.99
G = 783.99
G# = 830.61
A = 880.0
...GBK
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Author: David Peacham
Date: 2005-12-07 10:23
Johnny:
As GBK says, to get a scale you must move by the same ratio each time, not the same difference.
If you increase by the same number of Hertz each time, you get the harmonic series. For example, start at a low A of 55 Hz and increase by 55 Hz each time, you will get this:
A 55
A 110
E 165
A 220
C# 275
E 330
G (rather flat) 385
A 440
and so on ad infinitum
The G, as indicated, is quite a bit flat. The E and C# are almost - but not exactly - in line with the formula given by GBK.
These are exactly the notes played by a tenor trombone if you pull the slide out 8 cm or so. Any brass player can demonstrate this.
If you think about it, the notes of the scale could not possibly be at equal differences of frequency as your question implies. If they were, then you could play a descending scale until you got to 0 Hz - which makes little sense.
You have probably come across references to intervals measured in cents. These are a logarithmic scale, so an octave is always 1200 cents (and an equal-tempered semitone is 100 cents) whatever the frequency.
So A to A may be a difference of 55 to 110, or 110 to 220, or 220 to 440 etc, but it is always a ratio of 2:1 and it is always 1200 cents.
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If there are so many people on this board unwilling or unable to have a civil and balanced discussion about important issues, then I shan't bother to post here any more.
To the great relief of many of you, no doubt.
Post Edited (2005-12-07 10:24)
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Author: Johnny Galaga
Date: 2005-12-08 03:31
This is interesting. You'd think there'd be an even numerical distance between each note. I wonder what it would sound like if we had a music system like that.
So of all things, why is it that the 12th root multiples are what happens to sound appealing to us? Is it a matter of culture and upbringing, because that's simply what we're used to hearing?
What if we instead were all exposed to music only based on even-tempered scales since birth? Perhaps all of our tastes would be quite different.
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Author: David Peacham
Date: 2005-12-08 08:35
Johnny -
If there were an equal numerical difference between each note, it would sound exactly as I said in my previous post. You'd get the harmonic series. Bugle calls, if you like.
In point of fact, 12th root multiples don't sound appealing to us. They are an approximation forced on us by the fact that it is impractical to build pianos with many dozens of notes to each octave.
I don't know what you mean by "even-tempered scales". Equal-tempered scales are these twelfth-root-of-two things that pianos use and GBK has explained above.
But let's try a different explanation. If I play a C major scale in correct intonation, the ratios will be:
C to D is 9 to 8
D to E is 10 to 9
F to E is 16 to 15
F to G is 9 to 8
G to A is 10 to 9
A to B is 9 to 8
B to C is 16 to 15
If you multiply all those ratios together, you get 9x10x16x9x10x9x16 divided by 8x9x15x8x9x8x15, which works out as 2 to 1 as you'd expect.
But suppose we tuned a piano like that. It'd sound lovely in C major. But as soon as we played it in D major, it'd sound odd. Why? Because in D major, we want the interval D to E to have a ratio of 9 to 8, not 10 to 9.
The solution chosen by modern-day piano tuners is to make every semitone the same. We want twelve semitones to be an octave, which is 2 to 1. So each individual semitone must be the-twelfth-root-of-two to 1, not 16/15. Then each tone is the-sixth-root-of-two to 1, not 9 to 8 nor 10 to 9.
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If there are so many people on this board unwilling or unable to have a civil and balanced discussion about important issues, then I shan't bother to post here any more.
To the great relief of many of you, no doubt.
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Author: Johnny Galaga
Date: 2005-12-08 20:39
What I mean by even tempered scale would be something like this:
C 100 Hz
C# 102 Hz
D 104 Hz
D# 106 Hz
E 108 Hz
etc......
You'd think our scales would be like this. I just think it's odd that moving from one note to the next does not increase the Hz by a fixed amount each time
And if octaves are supposed to be exactly double, then why not just divide by 12 instead of using the 12th root?
C 144 Hz
C# 156 Hz
D 168 Hz
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.
.
C 288 Hz
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Author: Mark Charette
Date: 2005-12-08 20:48
Johnny Galaga wrote:
> You'd think our scales would be like this. I just think it's
> odd that moving from one note to the next does not increase the
> Hz by a fixed amount each time
>
> And if octaves are supposed to be exactly double, then why not
> just divide by 12 instead of using the 12th root?
Because then the octaves wouldn't be doubled frequencies, would they
Easy example:
120 - 240 Hz - / 12 = 10 Hz/step
240 - 480 Hz - / 12 = 20 Hz/step
The 12th root ratio (tempered because it isn't quite right but close) maintains the octaves.
There are (as has been discussed) many ways to temper the scale .
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