Difference between revisions of "Half step"

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==<u><b><i>Page in progress</i></b></u>==
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A [[half step]] is one twelfth of an [http://en.wikipedia.org/wiki/Octave octave].
  
This <u>should</u> be the formula to get a half step:
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=== Formula for a Half Step ===
<ol type="1">
 
<li>Measure the frequencies of two notes an octave apart. In this example, 440 and 880.</li>
 
<li>Average F1 (440) with F2 (880). You get F3 (660), or 6 half steps.</li>
 
<li>Average F1 with F3. You get F4, 550.  That's 3 half steps.</li>
 
<ol type="a">
 
<li>That's close enough; you could go on forever and not get it.</li>
 
</ol>
 
</ol>
 
  
== But wait! ==
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Since an octactave has a frequency ratio of 2, a half-step has a frequency of 2^(1/12), or approximately 1.0595.
  
Look! Let's use easier numbers as an example:
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For example, if the note A has a frequency of 440 Hz, then one half-step up is 440*1.0595 = 466.2 Hz. One half-step down is 440/1.0595 = 415.3 Hz.
In this example (E1), F1 will be 200 and we will try to find a half step up. We do the above proceedure (referred to from now on as HSP). F4 is 75. The difference between F1 and F4 is 75.
 
  
In E2, F1 is 200 and we will go <i>down</i> an octave. Do HSP, except go down instead of up. F4 ends up being 187.5. The difference between F1 and F4 is not 75, like before! It is 13.5, a totally unrelated number!
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(Just like an octave, a half-step interval is a ratio obtained through division, not a difference obtained through subtraction.  One octave above 440 Hz is 880 Hz, while one octave below is 220 Hz. The size of the octaves in Hz is different, but the ratio is the same.)
  
Why is this? Put it on the [[Talk:It Doesn't Work!]] page if you find out.
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Different "tempereraments" actually have slightly different half-steps.  See the Wikipedia article [http://en.wikipedia.org/wiki/Half_step Half Step] for details.
<<Back to [[Music]]
 

Revision as of 16:19, 5 April 2006

A half step is one twelfth of an octave.

Formula for a Half Step

Since an octactave has a frequency ratio of 2, a half-step has a frequency of 2^(1/12), or approximately 1.0595.

For example, if the note A has a frequency of 440 Hz, then one half-step up is 440*1.0595 = 466.2 Hz. One half-step down is 440/1.0595 = 415.3 Hz.

(Just like an octave, a half-step interval is a ratio obtained through division, not a difference obtained through subtraction. One octave above 440 Hz is 880 Hz, while one octave below is 220 Hz. The size of the octaves in Hz is different, but the ratio is the same.)

Different "tempereraments" actually have slightly different half-steps. See the Wikipedia article Half Step for details.