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SineWave as Octave - Music Notes

🔗Dan Amateur <xamateur_dan@...>

10/10/2006 7:40:45 PM

Hello,

recently I read the site page;

http://www.dovesong.com/centuries/Spiral.asp

Where they discuss the sine wave as an octave.

I found the below text as well. If we begin the sine
wave at zero degrees with the note of C, at what
degrees will the rest of the notes be found?

Octave as a Sine Wave and 1.2 AC waveforms

1.2. AC WAVEFORMS 7

Angle Sine(angle)
in degrees

0 0.0000 -- zero
15 0.2588
30 0.5000
45 0.7071
60 0.8660
75 0.9659
90 1.0000 -- positive peak
105 0.9659
120 0.8660
135 0.7071
150 0.5000
165 0.2588
180 0.0000 -- zero
195 -0.2588
210 -0.5000
225 -0.7071
240 -0.8660
255 -0.9659
270 -1.0000 -- negative peak
285 -0.9659
300 -0.8660
315 -0.7071
330 -0.5000
345 -0.2588
360 0.0000 � zero

When an alternator produces AC voltage, the voltage
switches polarity over time, but does so in a very
particular manner. When graphed over time, the "wave"
traced by this voltage of alternating polarity from an
alternator takes on a distinct shape, known as a sine
wave:
+- Time Graph of AC voltage
over time (the sine wave) In the voltage plot from an
electromechanical alternator, the change from one
polarity to the other is a smooth one, the voltage
level changing most rapidly at the zero ("crossover")
point and most slowly at its peak. If we were to graph
the trigonometric function of "sine" over a horizontal
range of 0 to 360 degrees, we would �nd the exact same
pattern:

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🔗misterbobro <misterbobro@...>

10/11/2006 1:35:58 AM

"degrees" are a convenient but arbitrary unit of measurement- you
won't find what you're looking for using them. Use radians.

--- In MakeMicroMusic@yahoogroups.com, Dan Amateur
<xamateur_dan@...> wrote:
>
> Hello,
>
> recently I read the site page;
>
> http://www.dovesong.com/centuries/Spiral.asp
>
> Where they discuss the sine wave as an octave.
>
> I found the below text as well. If we begin the sine
> wave at zero degrees with the note of C, at what
> degrees will the rest of the notes be found?
>
> Octave as a Sine Wave and 1.2 AC waveforms
>
> 1.2. AC WAVEFORMS 7
>
>
> Angle Sine(angle)
> in degrees
>
> 0 0.0000 -- zero
> 15 0.2588
> 30 0.5000
> 45 0.7071
> 60 0.8660
> 75 0.9659
> 90 1.0000 -- positive peak
> 105 0.9659
> 120 0.8660
> 135 0.7071
> 150 0.5000
> 165 0.2588
> 180 0.0000 -- zero
> 195 -0.2588
> 210 -0.5000
> 225 -0.7071
> 240 -0.8660
> 255 -0.9659
> 270 -1.0000 -- negative peak
> 285 -0.9659
> 300 -0.8660
> 315 -0.7071
> 330 -0.5000
> 345 -0.2588
> 360 0.0000 – zero
>
> When an alternator produces AC voltage, the voltage
> switches polarity over time, but does so in a very
> particular manner. When graphed over time, the "wave"
> traced by this voltage of alternating polarity from an
> alternator takes on a distinct shape, known as a sine
> wave:
> +- Time Graph of AC voltage
> over time (the sine wave) In the voltage plot from an
> electromechanical alternator, the change from one
> polarity to the other is a smooth one, the voltage
> level changing most rapidly at the zero ("crossover")
> point and most slowly at its peak. If we were to graph
> the trigonometric function of "sine" over a horizontal
> range of 0 to 360 degrees, we would ¯nd the exact same
> pattern:
>
>
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam? Yahoo! Mail has the best spam protection around
> http://mail.yahoo.com
>

🔗dar kone <zarkorgon@...>

10/11/2006 5:45:29 PM

Hey, thanks for the feedback - ok, radians then. But how?

misterbobro <misterbobro@...> wrote: "degrees" are a convenient but arbitrary unit of measurement- you
won't find what you're looking for using them. Use radians.

--- In MakeMicroMusic@yahoogroups.com, Dan Amateur
<xamateur_dan@...> wrote:
>
> Hello,
>
> recently I read the site page;
>
> http://www.dovesong.com/centuries/Spiral.asp
>
> Where they discuss the sine wave as an octave.
>
> I found the below text as well. If we begin the sine
> wave at zero degrees with the note of C, at what
> degrees will the rest of the notes be found?
>
> Octave as a Sine Wave and 1.2 AC waveforms
>
> 1.2. AC WAVEFORMS 7
>
>
> Angle Sine(angle)
> in degrees
>
> 0 0.0000 -- zero
> 15 0.2588
> 30 0.5000
> 45 0.7071
> 60 0.8660
> 75 0.9659
> 90 1.0000 -- positive peak
> 105 0.9659
> 120 0.8660
> 135 0.7071
> 150 0.5000
> 165 0.2588
> 180 0.0000 -- zero
> 195 -0.2588
> 210 -0.5000
> 225 -0.7071
> 240 -0.8660
> 255 -0.9659
> 270 -1.0000 -- negative peak
> 285 -0.9659
> 300 -0.8660
> 315 -0.7071
> 330 -0.5000
> 345 -0.2588
> 360 0.0000 – zero
>
> When an alternator produces AC voltage, the voltage
> switches polarity over time, but does so in a very
> particular manner. When graphed over time, the "wave"
> traced by this voltage of alternating polarity from an
> alternator takes on a distinct shape, known as a sine
> wave:
> +- Time Graph of AC voltage
> over time (the sine wave) In the voltage plot from an
> electromechanical alternator, the change from one
> polarity to the other is a smooth one, the voltage
> level changing most rapidly at the zero ("crossover")
> point and most slowly at its peak. If we were to graph
> the trigonometric function of "sine" over a horizontal
> range of 0 to 360 degrees, we would ¯nd the exact same
> pattern:
>
>
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam? Yahoo! Mail has the best spam protection around
> http://mail.yahoo.com
>

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