# MATLAB/Sound/Just and equal tuning

< MATLAB

The two codes play the same riff, both using *just* and *equal* tuning. The only difference between the two versions is whether the *just* or *equal* tuned riff is first. If the variable *testnote* equals *true*, then major sixth above the first note is played at the end, for comparison.

On our speaker, it feels as if the sharper note is also louder. If that is true, then this is not a true test of whether the human ear prefers the just major sixth.

The codes can be copied and pasted into MATLAB either directly, or by going into Edit mode. The advantage of the latter is that if you select only the section, you can "select all" and then delete the first and last lines (<pre> ... <\pre>) after pasting.

## justFirst.m

editclc; clear all; close all; % Most sound cards support sample rates between approximately 5,000 and 48,000 % hertz. Specifying sample rates outside this range can produce unexpected results. % User selected parameters: testnote=true; testnotes = [5/3, 2^(9/12)]; Repeats = 2; %Number of times the riff is repeated (in each tuning) Duration=.3; %sets how long each note should be played (in seconds) f0=221; % fundamental frequency omega0=2*pi*f0; %Sets the fundamental frequency fj=[1 3/2 5/3 3/2 5/3 3/2] % Bach prelude cello suite 1 bitf=.4; % This softens the tone burst. .2 < bitf < 1. % Most of these parameters never change: dt=1/8192; %is Matlab's default sampling rate (period) t = 0:dt:Duration; %sets the timeframe for a single note notesInRiff = size(fj,2); r = zeros(1,notesInRiff); %pre-assigns notes on 12-scale (logs) % pitches for equal tuning begin with notes on the 12-tone scale for notecount= 1:notesInRiff r(notecount)=round(12*log2(fj(notecount))); end %This rounds the just notes to logs fs=2.^(r/12) % begin comparison of riffs in the two tunings for count = 1:Repeats % just tuning begin for n = 1:notesInRiff omega=omega0*fj(n); y=sin(omega*t); % This section in required to soften the start and stop of the tone-burst dfc=.5*size(y,2); %finds "center" of the array y for j=1:size(y,2) % multiply y by a softened step function. % this complicated function creates the soften step function y(j)=y(j)*( 1 - ( (j-dfc)/dfc )^2 )^bitf; end% section required to soften the start and stop of the tone burst. soundsc(y); pause(Duration) end % just tuning end % equal tuning begin for n = 1:notesInRiff omega=omega0*fs(n); y=sin(omega*t); % This section in required to soften the start and stop of the tone-burst dfc=.5*size(y,2); %finds "center" of the array y for j=1:size(y,2) % multiply y by a softened step function. % this complicated function creates the soften step function y(j)=y(j)*( 1 - ( (j-dfc)/dfc )^2 )^bitf; end% section required to soften the start and stop of the tone burst. soundsc(y); pause(Duration); end %equal tuning end end; % This ends the code unless testnote = true % Hear the difference after a short pause if testnote==true pause(2*Duration); durd=5*Duration; % a different (longer) duration for the difference td = 0:dt:durd; %new (larger) time array for difference tones omega=omega0*testnotes(1); y=sin(omega*td) ; % This section in required to soften the start and stop of the tone-burst dfc=.5*size(y,2); %finds "center" of the array y for j=1:size(y,2) % multiply y by a softened step function. % this complicated function creates the soften step function y(j)=y(j)*( 1 - ( (j-dfc)/dfc )^2 )^bitf; end % ends section required to soften the start and stop of the tone burst soundsc(y); pause(1.1*durd); omega=omega0*testnotes(2); y=sin(omega*td) ; % This section in required to soften the start and stop of the tone-burst dfc=.5*size(y,2); %finds "center" of the array y for j=1:size(y,2) % multiply y by a softened step function. % this complicated function creates the soften step function y(j)=y(j)*( 1 - ( (j-dfc)/dfc )^2 )^bitf; end soundsc(y); end

## equalFirst.m

editclc; clear all; close all; % Most sound cards support sample rates between approximately 5,000 and 48,000 % hertz. Specifying sample rates outside this range can produce unexpected results. % % User selected parameters: testnote=true; testnotes = [5/3, 2^(9/12)]; Repeats = 2; %Number of times the riff is repeated (in each tuning) Duration=.3; %sets how long each note should be played (in seconds) f0=221; % fundamental frequency omega0=2*pi*f0; %Sets the fundamental frequency fj=[1 3/2 5/3 3/2 5/3 3/2] % Bach prelude cello suite 1 bitf=.4; % This softens the tone burst. .2 < bitf < 1. % Most of these parameters never change: dt=1/8192; %is Matlab's default sampling rate (period) t = 0:dt:Duration; %sets the timeframe for a single note notesInRiff = size(fj,2); r = zeros(1,notesInRiff); %pre-assigns notes on 12-scale (logs) % pitches for equal tuning begin with notes on the 12-tone scale for notecount= 1:notesInRiff r(notecount)=round(12*log2(fj(notecount))); end %This rounds the just notes to logs fs=2.^(r/12) % begin comparison of riffs in the two tunings for count = 1:Repeats % equal tuning begin for n = 1:notesInRiff omega=omega0*fs(n); y=sin(omega*t); % This section in required to soften the start and stop of the tone-burst dfc=.5*size(y,2); %finds "center" of the array y for j=1:size(y,2) % multiply y by a softened step function. % this complicated function creates the soften step function y(j)=y(j)*( 1 - ( (j-dfc)/dfc )^2 )^bitf; end% section required to soften the start and stop of the tone burst. soundsc(y); pause(Duration); end %equal tuning end % just tuning begin for n = 1:notesInRiff omega=omega0*fj(n); y=sin(omega*t); % This section in required to soften the start and stop of the tone-burst dfc=.5*size(y,2); %finds "center" of the array y for j=1:size(y,2) % multiply y by a softened step function. % this complicated function creates the soften step function y(j)=y(j)*( 1 - ( (j-dfc)/dfc )^2 )^bitf; end% section required to soften the start and stop of the tone burst. soundsc(y); pause(Duration) end % just tuning end end; % This ends the code unless testnote = true % Hear the difference after a short pause if testnote==true pause(2*Duration); durd=5*Duration; % a different (longer) duration for the difference td = 0:dt:durd; %new (larger) time array for difference tones omega=omega0*testnotes(2); y=sin(omega*td) ; % This section in required to soften the start and stop of the tone-burst dfc=.5*size(y,2); %finds "center" of the array y for j=1:size(y,2) % multiply y by a softened step function. % this complicated function creates the soften step function y(j)=y(j)*( 1 - ( (j-dfc)/dfc )^2 )^bitf; end % ends section required to soften the start and stop of the tone burst soundsc(y); pause(1.1*durd); omega=omega0*testnotes(1); y=sin(omega*td) ; % This section in required to soften the start and stop of the tone-burst dfc=.5*size(y,2); %finds "center" of the array y for j=1:size(y,2) % multiply y by a softened step function. % this complicated function creates the soften step function y(j)=y(j)*( 1 - ( (j-dfc)/dfc )^2 )^bitf; end % ends section required to soften the start and stop of the tone burst. soundsc(y); end