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\par }\pard\plain \s1\ql \li0\ri0\sb240\sa60\keepn\widctlpar\faauto\outlinelevel0\adjustright\rin0\lin0\itap0 \b\f1\fs32\lang1033\langfe1033\kerning32\cgrid\langnp1033\langfenp1033 {Audio and the Fourier Transform
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Why study audio in a class on images?
\par {\listtext\pard\plain\f3\fs20 \loch\af3\dbch\af0\hich\f3 \'b7\tab}}\pard \ql \fi-360\li720\ri0\widctlpar\jclisttab\tx720\faauto\ls1\adjustright\rin0\lin720\itap0 {Audio is an important part of games.
\par {\listtext\pard\plain\f3\fs20 \loch\af3\dbch\af0\hich\f3 \'b7\tab}MP-3 audio is part of the MPEG multimedia standard.
\par {\listtext\pard\plain\f3\fs20 \loch\af3\dbch\af0\hich\f3 \'b7\tab}It is easier to understand frequency concepts in 1-D audio than in 2-D images.  This is central to the Fourier Transform and the Discrete Cosine Transform used to compress JPEG.
\par }\pard \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 {We will study music, since it is easier than speech.
\par 
\par For audio, electrical engineers talk about "time domain" and "frequency domain".  The two are related by the (one dimensional) Fourier transform.  
\par The same thing applies to monochrome images, except that the image is two dimensional.  "Time" becomes the horizontal and vertical image luminance.  "Frequency" becomes spatial frequency.
\par 
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\par 
\par The frequency representation is an "}{\ul impulse}{", which requires some explanation.
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\par An impulse is zero everywhere except at one point.  At the one point where it has a value, it packs a lot of energy; so much energy that if you integrate the impulse over any interval that contains its non-zero value, you get 1.
\par The impulse can be defined as the limit of a rectangle as it gets skinnier and higher
\par 
\par The impulse can be thought of as the derivative of the unit step.
\par 
\par Calculus:  How do you integrate a discontinuous function?  What do you get?
\par 
\par The impulse isn't really a funct
ion.  To make all this precise, you have to work with the theory of distributions.  This is something that math majors would hit about the second year of grad school.  Engineers don't worry about it; an impulse just magically packs a lot of punch at its o
ne point.
\par 
\par The impulse is also sometimes called a \'93singularity function\'94 or \'93Dirac delta\'94
\par 
\par The impulse is sometimes defined by the sifting property:
\par For any function }{\i h}{(}{\i t}{) which is continuous at }{\i t}{ = }{\i x}{,
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\par }\pard\plain \s2\ql \li0\ri0\sb240\sa60\keepn\widctlpar\faauto\outlinelevel1\adjustright\rin0\lin0\itap0 \b\i\f1\fs28\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {{\*\bkmkstart _DFT}{\*\bkmkend _DFT}\page Basic Music Theory
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {To represent music we need to indicate:
\par }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2391 \cellx2283\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2164 
\cellx4447\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2639 \cellx7086\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr
\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2382 \cellx9468\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\ul Perceptual\cell }\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 
\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\b\ul Example\cell Physical\cell Example\cell }\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\b\ul \trowd 
\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2391 \cellx2283\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2164 \cellx4447
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2639 \cellx7086\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth2382 \cellx9468\row }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2391 \cellx2283\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2164 \cellx4447\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2639 \cellx7086
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2382 \cellx9468\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {Pitch  \cell }\pard\plain 
\s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {A}{\sub 4}{\cell Frequency \cell 440 Hz\cell }\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 
\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2391 \cellx2283\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2164 \cellx4447\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2639 \cellx7086
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2382 \cellx9468\row }\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 
\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Loudness\cell }\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {forte\cell Amplitude / Power\cell 60 db\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2391 \cellx2283\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2164 \cellx4447\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2639 \cellx7086
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2382 \cellx9468\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {Duration\cell Quarter note\cell Time
\cell 0.5 sec\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2391 \cellx2283\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2164 \cellx4447\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2639 \cellx7086
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2382 \cellx9468\row }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 
\trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth2391 \cellx2283\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2164 \cellx4447\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2639 \cellx7086\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2382 \cellx9468\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {Timbre\cell Clarinet\cell Spectrum\cell Odd harmonics\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl
\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr
\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2391 \cellx2283\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2164 \cellx4447\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2639 \cellx7086\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth2382 \cellx9468
\row }\pard\plain \s18\ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \f2\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Pitch and frequency are not exactly the same, especially at higher and lower frequencies.
\par Perceived loudness depends on both amplitude and frequency:
\par }{\cf6 [ Fig 18-3 from Levine and Shefner. ]
\par }\pard\plain \s18\ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \f2\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\f0 The American Standards Association defines }{\f0\ul timbre}{\f0 
 as covering all the ways that two sounds of the same pitch, loudness, and apparent duration may differ.  
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {
\par Ancient Greek music theory held that harmonious tones are those related by the ratios of small numbers.
\par 
\par }{\ul Octave}{: Double the frequency
\par Example:
\par }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 
\cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\ul Note\cell CSound\cell 
Frequency (Hz)\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644
\row }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 0}{\cell 4.09\cell 27.5\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 1}{\cell 5.09\cell 55\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644
\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 2}{\cell 6.09\cell 110\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 3}{\cell 7.09\cell 220\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644
\row }\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {A}{\sub 4}{\cell }\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 
\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {8.09\cell 440\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr
\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 
\cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr
\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 5}{\cell 9.09\cell 880\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd 
\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 6}{\cell 10.09\cell 1760
\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644
\row }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 7}{\cell 11.09\cell 3520\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard\plain \s18\ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \f2\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\f0 
\par The range of a piano is A}{\f0\sub 0}{\f0  to C}{\f0\sub 8}{\f0  (27.5 to 4186 Hz).
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\ul 
\par Harmonics}{ are multiples of the fundamental frequency.
\par Example:
\par }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 
\cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\ul Note\cell Harmonic\cell 
Frequency (Hz)\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644
\row }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 2}{\cell Fundamental\cell 110\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 3}{\cell 2\cell 220\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644
\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {E}{\sub 4}{\cell 3\cell 330\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {A}{\sub 4}{\cell 
}\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {4\cell 440\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt
\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {C#}{\sub 5}{\cell 5\cell 550\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644
\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {E}{\sub 5}{\cell 6\cell 660\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {approx G}{\sub 5}{\cell 7\cell 770\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644
\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 5}{\cell 8\cell 880\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv
\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 
\cellx4644\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {B}{\sub 5}{\cell 9\cell 990\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 
\trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx2772\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4644\row }\pard \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 {
\par }{\cf6 [Figure: Notes]
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa60\keepn\widctlpar\faauto\outlinelevel1\adjustright\rin0\lin0\itap0 \b\i\f1\fs28\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\page Scales
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Western music divides the octave into 12 semitones.
\par In the Equal Tempered Chromatic scale, each note increases by the 12}{\super th}{ root of 2:  1.0595.  This can be considered a compromise that does not exactly preserve the ratios of \'93just intonation\'94.
\par 
\par }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 
\cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr
\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\ul Note\cell CSound\cell Interval\cell Ratio to Tonic\cell ETC frequency\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b\ul \trowd \trgaph108\trleft-108\trbrdrt
\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb
\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 
\cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b C}{\b\sub 4}{\b  (middle C)
\cell 8.00\cell Tonic\cell 1:1\cell }\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\b 261.63\cell }\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 
\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\b \trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {C#}{\sub 4}{\cell 8.01\cell \cell 16:15\cell 277.18\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd 
\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {D}{\sub 4}{\cell }\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {8.02\cell Second\cell }\pard\plain 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {9:8\cell 293.66\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 
\cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {Eb}{\sub 4}{\cell 8.03
\cell Minor Third\cell 6:5\cell 311.13\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 
\trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b E}{\b\sub 4}{\b \cell 8.04\cell Third\cell 5:4\cell 329.63\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b \trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {F}{\sub 4}{\cell 8.05\cell Fourth\cell 4:3\cell 349.23\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd 
\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard\plain 
\s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {F#}{\sub 4}{\cell }\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 
\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {8.06\cell \cell 7:5\cell 369.99\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb
\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt
\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b G}{\b\sub 4}{\b \cell 8.07\cell 
Fifth (dominant)\cell 3:2\cell 392.00\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b \trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 
\trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {G#}{\sub 4}{\cell 
}\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {8.08\cell \cell 8:5\cell 415.30\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd 
\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {A}{\sub 4}{\cell 8.09\cell Sixth\cell 5:3\cell }\pard\plain \s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {440.00\cell 
}\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 
\trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {Bb}{\sub 4}{\cell 8.10\cell \cell 9:5\cell }\pard\plain 
\s15\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {466.16\cell }\pard\plain \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 
\fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 
\trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {B}{\sub 4}{\cell 8.11\cell Seventh\cell 15:8\cell 493.88\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\trowd 
\trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl
\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484
\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 
\trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 \trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 
\clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 
\clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 
\cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b C}{\b\sub 5}{\b \cell 9.00
\cell Octave\cell 2:1\cell 523.25\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\b \trowd \trgaph108\trleft-108\trbrdrt\brdrs\brdrw10 \trbrdrl\brdrs\brdrw10 \trbrdrb\brdrs\brdrw10 \trbrdrr\brdrs\brdrw10 \trbrdrh\brdrs\brdrw10 
\trbrdrv\brdrs\brdrw10 \trftsWidth1\trpaddl108\trpaddr108\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx1332\clvertalt\clbrdrt
\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1152 \cellx2484\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 
\cltxlrtb\clftsWidth3\clwWidth1872 \cellx4356\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 \clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1440 \cellx5796\clvertalt\clbrdrt\brdrs\brdrw10 \clbrdrl\brdrs\brdrw10 
\clbrdrb\brdrs\brdrw10 \clbrdrr\brdrs\brdrw10 \cltxlrtb\clftsWidth3\clwWidth1728 \cellx7524\row }\pard \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 {
\par Keys: pick 7 of the 12 semitones to use.  The key is named for its tonic note.  A major scale follows the step pattern: full, full, semi, full, full, full, semi.
\par C Major: No sharps or flats.
\par G Major: Use F#
\par A Major: Use F#, C#, G#.
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa60\keepn\widctlpar\faauto\outlinelevel1\adjustright\rin0\lin0\itap0 \b\i\f1\fs28\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\page Representation
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\cf6 [Star Wars Theme sheet music]
\par }{The lines of the treble clef are : EGBDF; the spaces are FACE
\par On the bass clef, the lines are GBDFA; the spaces are ACEG
\par Middle C (261 Hz) is between the treble and bass clefs.
\par Duration is shown by half notes, quarter notes, eighth notes, etc.  The time signature (4/4) means that there are 4 beats per measure (top 4) and that one beat is a quarter note (bottom 4).
\par 
\par There are several systems for computer representation of musical scores:
\par IRCAM (Institute for Research on Musical Acoustics)
\par MIDI (Musical Instrument Digital Interface)
\par CSound: free from 
\par ftp://ftp.maths.bath.ac.uk/pub/dream/newest/
\par See also: 
\par http://mitpress.mit.edu/e-books/csound/frontpage.html
\par http://depts.washington.edu/smccweb
\par 
\par With CSound, you define an instrument file (.orc) and a score file (.sco).  The software will convert this to a WAVE file.  (Be sure to use the -W command line argument)
\par 
\par }{\f2 \page ;  a sine wave function table
\par      f1 0 256 10 1
\par ;  Star Wars Main Theme (with chords)
\par      t    0   320   ; tempo: starting from time 0, 320 units/sec
\par ;instr start duration amp note 
\par      i1   0    1   5000. 8.02
\par      i1   1    .    .    .
\par      i1   2    .    .    .
\par ; bar 1
\par      i1   3    6    .    8.07
\par      i1   .    .    .    8.02
\par      i1   .    .    .    7.11
\par      i1   9    .    .    9.02
\par      i1   .    .    .    8.11
\par      i1   .    .    .    8.07
\par ; bar 2
\par      i1  15    1    .    9.00
\par      i1   .    .    .    8.07
\par      i1   .    .    .    8.04
\par      i1  16    .    .    8.11
\par      i1  17    .    .    8.09
\par      i1  18    6    .    9.07
\par      i1   .    .    .    9.02
\par      i1   .    .    .    8.11
\par      i1  24    3    .    9.02
\par      i1   .    .    .    8.11
\par      i1   .    .    .    7.07
\par ; bar 3
\par      i1  27    1    .    9.00
\par      i1   .    .    .    8.07
\par      i1   .    .    .    8.04
\par      i1  28    .    .    8.11
\par      i1  29    .    .    8.09
\par      i1  30    6    .    9.07
\par      i1   .    .    .    9.02
\par      i1   .    .    .    9.00
\par      i1  36    3    .    9.02
\par      i1   .    .    .    8.11
\par      i1   .    .    .    8.07
\par ; bar 4
\par      i1  39    1    .    9.00
\par      i1   .    .    .    8.09
\par      i1   .    .    .    8.05
\par      i1  40    .    .    8.11
\par      i1  41    .    .    9.00
\par      i1  42    6    .    8.09
\par      i1   .    .    .    8.06
\par      i1   .    .    .    8.02
\par }{\page }{\cf6 [Play StarWars_sine.wav]
\par [Play Star Wars CD]
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa60\keepn\widctlpar\faauto\outlinelevel1\adjustright\rin0\lin0\itap0 \b\i\f1\fs28\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {{\*\bkmkstart _CS320_IDAT}{\*\bkmkend _CS320_IDAT}Real Instruments
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Now consider what a physical musical instrument sounds like.  Here is an analysis of the sustained part of B}{\f1 b}{\sub 3}{
 on clarinet:
\par 
\par }\trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 Harmonic\cell Frequency
\par (Hz)\cell Relative Power\cell Phase (degrees)\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\trowd 
\trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone 
\clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone 
\clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\pard \qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 1\cell 234\cell 7\cell 26\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone 
\cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone 
\cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard \qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {
\f1\cf1\cgrid0 3\cell 702\cell 4\cell -87\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard 
\qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 5\cell 1170\cell 30\cell 0\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd 
\trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone 
\clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone 
\clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard \qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 7\cell 1638\cell 9\cell -43\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone 
\cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone 
\cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard \qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {
\f1\cf1\cgrid0 8\cell 1872\cell 8\cell -34\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard 
\qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 9\cell 2106\cell 21\cell -150\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd 
\trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone 
\clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone 
\clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard \qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 10\cell 2340\cell 2\cell -137\cell }\pard 
\ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone 
\cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone 
\cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard \qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {
\f1\cf1\cgrid0 11\cell 2574\cell 9\cell -27\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard 
\qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 13\cell 3042\cell 1\cell 124\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd 
\trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone 
\clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone 
\clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr
\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr
\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\pard \qr \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {
\f1\cf1\cgrid0 15\cell 3510\cell 5\cell -26\cell }\pard \ql \li0\ri0\widctlpar\intbl\faauto\adjustright\rin0\lin0 {\f1\cf1\cgrid0 \trowd \trgaph30\trrh250\trleft-30\trftsWidth1\trpaddl30\trpaddr30\trpaddfl3\trpaddfr3 \clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx978\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx1986\clvertalt\clbrdrt\brdrnone \clbrdrl
\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx2994\clvertalt\clbrdrt\brdrnone \clbrdrl\brdrnone \clbrdrb\brdrnone \clbrdrr\brdrnone \cltxlrtb\clftsWidth3\clwWidth1008 \cellx4002\row }\pard 
\ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 {
\par The magnitude of the spectrum is:
\par }{\cf6 [figure Harmonics-234]
\par }{The frequencies present in the spectrum are called }{\ul partial}{ tones.  Some instruments have both harmonic and inharmonic partials. You can add up the partials in the tone to reconstruct the time domain representation:
\par }{\cf6 [sequence of figures]
\par [Play StarWars_clar.wav]
\par [Play StarWars_sine.wav]
\par 
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa60\keepn\widctlpar\faauto\outlinelevel1\adjustright\rin0\lin0\itap0 \b\i\f1\fs28\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\page Phase
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {Note that the harmonics in the clarinet tone have a phase relationship between
 them; Not all the sine waves start at the same time.  If they did, you would get a different signal:
\par }{\cf6 [figure Harmonics-Phases]
\par }{You should be able to hear the difference:
\par }{\cf6 [Play StarWars_zero.wav]
\par [Play StarWars_clar.wav]
\par }{
\par This means that the magnitude spec
trum by itself is not enough to define the signal.  We also need the phase.  Thus the location of each frequency component is an ordered pair: (frequency, phase).  While the time domain representation is a function of a single real variable, the frequency
 domain representation is a function of two real variables or of one complex variable.
\par 
\par }{\cf6 [Figure Harmonics-234 phase]
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa60\keepn\widctlpar\faauto\outlinelevel1\adjustright\rin0\lin0\itap0 \b\i\f1\fs28\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\page Subbands
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {
We have shown how to break a triangle wave into high and low frequency components.  We can do this either with analog electronics or with Fourier series.  We don\rquote 
t have to limit ourselves to two ranges.  Either method can be used to split the signal into as many frequency subbands as we want.  It turns out that this is a great idea for audio compression.
\par 
\par }{\cf6 [Figure Ear.jpg]
\par }{Consider ho
w the ear is structured.  The inner ear contains the cochlea, a tapered spiral tube that looks like a snail shell.  Sound hits the eardrum, making it vibrate.  Three tiny bones link these vibrations on the eardrum to the cochlea.  The cochlea is mechanica
l
ly designed so that different regions vibrate in response to different frequencies.  The regions have hair cells that vibrate and produce an electrical signal that is sent to the brain.  There are 26 different frequency bands in the cochlea.  The bandwidt
hs vary, giving less resolution at higher frequencies.
\par 
\par The result is that human hearing exhibits }{\i masking}{.  If a tone contains a 1000 Hz component and a softer 1100 Hz component, we cannot hear the 1100 Hz.  It is totally masked by the stronger component.  
We can use this in compression.  Thus there is no need to encode the 1100 Hz at all.  We can break the original signal into subbands and drastically compress each subband.  This is the main trick used by MP3.
\par 
\par }\pard\plain \s2\ql \li0\ri0\sb240\sa60\keepn\widctlpar\faauto\outlinelevel1\adjustright\rin0\lin0\itap0 \b\i\f1\fs28\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {\page MP-3
\par }\pard\plain \ql \li0\ri0\widctlpar\faauto\adjustright\rin0\lin0\itap0 \fs20\lang1033\langfe1033\cgrid\langnp1033\langfenp1033 {MPEG-1 defines three layers of audio, wi
th Layer 1 being the simplest and layer 3 providing higher quality but more complexity.  MP-3 is Layer 3 of MPEG-1 audio.
\par 
\par The MPEG standard tells how to decode a bitstream, but does not specify a compression method.
\par 
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