Guitar and Bass Tuner Library
Teensy 3.1 v2.0

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_o 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.

  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 ( n² ) for finding the fundamental frequency f_o, it is tuned to skip certain tau () 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.

AudioTuner.h

/****************************************************************/
#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). 

YIN Algorithm

1. Difference Function - Squared difference of the (signal - signal lag())
   
2. Cumulative Mean Normalized Difference Function - Calculate the cumulative mean on the normalized difference signal
   
3. Absolute Threshold - Fix for subharmonic error with Autocorrelation, choose () that gives a minimum