[sdiy] Wavetable Design Update

[Scott Gravenhorst]

Tom Wiltshire <tom at electricdruid.net> wrote:
>
>On 2 Feb 2011, at 12:36, Scott Gravenhorst wrote:
>
>> Dave Manley <dlmanley at sonic.net> wrote:
>>> On 2/1/2011 10:28 PM, Matthew Smith wrote:
>>> 
>>>> * How to convert from my note numbers (these will be all the 
>>> MIDI-defined notes plus intermediate detune values) to the 
>>> prescaler/counter values to plug into AVR's onboard counter. I 
>>> would appear to > have two options: a lookup table (would not fit 
>>> in ATTINY2313 FLASH) or to calculate these at note-on. I'm 
>>> favouring the second approach for flexibility (would even allow 
>>> an actual frequency to be > specified rather than a note number) 
>>> but haven't the foggiest how to work out the algorithm required. 
>>> 
>>> roughly:
>>> 
>>> note number mod 12 -> note
>>> note number / 12 -> octave
>>> 
>>> 12 entry look up table followed by divide/mult by power of 2 for octaves
>> 
>> I did what Dave described for my phase accumulator oscillator designs.  What I
>> learned, however, was the it is best to consider the 12 values for note to be the
>> lowest pitches that will be produced and use the octave number to left shift.  This
>> ensures that octaves are true octaves.  If one right shifts, significant bits get
>> shifted into the bit bucket and notes that should be octaves will beat because the
>> are not exactly 1/2 the frequency of the higher one.
>
>How interesting to hear a justification for doing it the other way around!
>
>So it looks like there's a tradeoff to be made between higher 
>accuracy for the higher octaves (right shifting) or perfect, 
>beat-free octaves (left-shifting). You choose, I guess. 

To be sure that is true - I use 17 bit wide table, your point induces me to go back and calculate
the number of cents of error.  I don't hear an error in the high register, so I suspect it's <= 5
cents.

>>  I chose to calculate the octave
>> value in my MIDI microcontroller - which does not have a divide instruction - I did
>> the division with a "subtract 12 many times" loop which was plenty fast enough.  The
>> divide loop provided both the octave number (quotient) and the note number
>> (remainder).  This method works very well for me.
>
>Like I said, I hate division. Even the dsPIC which does have a 
>divide instruction spends 17 cycles doing it. Best avoided if 
>possible. 
>

I hate divides too, the divide I use happens only once at note start, so while it contributes a
tiny bit of latency (25 MIPs MCU) that amounts to a few microseconds, it is not required during
oscillator operation.  It was either that or a 128 location table for all possibe notes.

-- ScottG
________________________________________________________________________
-- Scott Gravenhorst
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