<p align="center">
<b>Guitar and Bass Tuner Library</b><br>
<b>Teensy 3.1 v2.0</b><br>
</p>
>Software algorithm ([YIN]) for guitar and bass tuning using a Teensy Audio Library. This audio object's algorithm can be some what memory and processor hungry but will allow you to detect with fairly good accuracy the fundamental frequencies f<sub>o</sub> from electric guitars and basses.
>>You can install this as a normal Arduino Library and will work with the Audio Library, no need to edit the Audio libraries source now.
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Hookup Guide - 1.2v DC Bias and High Pass Filter - No Amplification
*--------------------------------------------------*
| |
| Pull Down Resistor | ' | |
*------------/\/\/\-------------* |' '| |
| 47K | _|_'_|_ |
| | |` ` ` `| |
*---)|+---* | | ` ` ` | |
| 10uF | | |` ` ` `| |
TEENSY 3.1 | | | | ` ` ` | |
_______________ *-/\/\/\--* | |` ` ` `| |
|GND |_____| Vin| | 2.2K | | | ` ` ` | |
|0 ----- AGND|<-* | | |` ` ` `| |
|1 |`````| 3.3V|>---/\/\/\--*--/\/\/\--* | | ` ` ` | |
|2 | | 23| 10K 47K | | |` ` ` `| |
|3 ----- 22| | | | ` ` ` | |
|4 |'| 21| | | \=====/ |
|5 ------ 20| | | | '`| |
|6 |::::::::| 19| | REMOVE | | S`| |
|7 |::::::::| 18| | DC | | H`| |
|8 |::::::::| 17| | BIAS | | I`| |
|9 ------A2/16|<---SIGNAL-1.2v-BIAS---*---+|(----* | E`|>--ANGD--*
|10 --- 15| 1.2VDC 10uF | | L`|
|11 |(`)| 14| | | D`|
|12 --- 13| | | `|
--------------- | |===|
| \_/
| /T\
| .-I-.
*---<\ P /
\_/
>Many optimizations have been done to the [YIN] algorithm for frequencies between 29-360Hz.
>>While its still using a brute force method ( n<sup>2</sup> ) for finding the fundamental frequency f<sub>o</sub>, it is tuned to skip certain <b>tau</b> (<img src="http://latex.numberempire.com/render?%5Cinline%20%5Chuge%20%5Cmathbf%7B%5Ctau%7D&sig=845639da85c0dd8e2de679817b06639c"/></img>) values and focus mostly on frequencies found in the bass and guitar.
>>>The input is double buffered so while you are processing one buffer it is filling the other to double throughput.
>>>>There are a few parameters that can be adjusted to "dial in" the algorithm for better estimations. The defaults are what I found that have the best trade off for speed and accuracy.
<h4>AudioTuner.h</h4>
```
/****************************************************************/
#define SAMPLE_RATE_DIVIDE_BY_1 1 // 44100 sample rate
#define SAMPLE_RATE_DIVIDE_BY_2 2 // 22050 sample rate
#define SAMPLE_RATE_DIVIDE_BY_4 4 // 11025 sample rate
#define SAMPLE_RATE_DIVIDE_BY_8 8 // 5512.5 sample rate
#define SAMPLE_RATE_DIVIDE_BY_16 16 // 2756.25 sample rate
#define SAMPLE_RATE_DIVIDE_BY_32 32 // 1378.125 sample rate
/****************************************************************
* Safe to adjust these values below *
****************************************************************/
// Adjust number of samples to collect in buffer here, also effects
// convergence speed and resolution.
#define NUM_SAMPLES 2048 // make a power of two
// larger the divide-by, less resolution and lower the frequency for
// a given number of samples that can be detected. Also effects
// convergence speed.
#define SAMPLE_SKIP SAMPLE_RATE_DIVIDE_BY_2
/****************************************************************/
```
```
SAMPLE_RATE_DIVIDE_BY_x --> This sets 'SAMPLE_SKIP' to pass on every (x) data point from
the Audio Block being saved to the buffer, it determines the
sample rate.
```
```
NUM_SAMPLES --> This the size of each buffer, there two for double buffering.
```
```
SAMPLE_SKIP --> This sets your sample window length and sampling rate. Sample Window Size
is (NUM_SAMPLES * SAMPLE_SKIP) of the ~44100 samples every second. Sample
Rate is (AUDIO_SAMPLE_RATE_EXACT / SAMPLE_SKIP).
```
<div>
<b>YIN Algorithm</b>
<ol>
<li><b>Difference Function -</b> Squared difference of the (signal - signal lag(<img src="http://latex.numberempire.com/render?%5Cinline%20%5Chuge%20%5Cmathbf%7B%5Ctau%7D&sig=845639da85c0dd8e2de679817b06639c"/></img>))<br>
<img src="http://latex.numberempire.com/render?%5Chuge%20d_%7Bt%7D%20%5Cbig%28%20%5Ctau%20%5Cbig%29%20%3D%20%5Csum_%7Bj%3D1%7D%5EW%20%20%5Cbig%28x_%7Bj%7D-x_%7Bj%2B%5Ctau%7D%5Cbig%29%5E%7B2%7D&sig=da6a2a10a134437679df399dbb9327df" /></li>
<li><b>Cumulative Mean Normalized Difference Function -</b> Calculate the cumulative mean on the normalized difference signal<br><img src="http://latex.numberempire.com/render?%5Cinline%20%5Chuge%20d%27_%7Bt%7D%20%5Cbig%28%20%5Ctau%20%5Cbig%29%20%3D%5Cbegin%7Bcases%7D1%2C%20%26%20%5Ctau%20%3D%200%5C%5Cd_%7Bt%7D%20%5Cbig%28%20%5Ctau%20%5Cbig%29%5Cdiagup%20%26%5Cleft%5B%28%5Cfrac%7B1%7D%7B%5Ctau%7D%29%5Csum_%7Bj%3D1%7D%5E%5Ctau%20%20d_%7Bt%7D%20%28j%29%5Cright%5D%5Cend%7Bcases%7D&sig=15a0b31a37bd5db3074f854711119bb3" /></li>
<li><b>Absolute Threshold -</b> Fix for subharmonic error with Autocorrelation, choose (<img src="http://latex.numberempire.com/render?%5Cinline%20%5Chuge%20%5Cmathbf%7B%5Ctau%7D&sig=845639da85c0dd8e2de679817b06639c"/></img>) that gives a minimum <img src="http://latex.numberempire.com/render?%5Chuge%20d%27&sig=ec41ac0239b48a3c53617da8e4ca64c7"/></li>
</ol>
</div>
[YIN]:http://recherche.ircam.fr/equipes/pcm/cheveign/pss/2002_JASA_YIN.pdf