Convert octave to pitch

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1

Someone asked on Discord. Posting an answer here for reference.

I have some mallet sounds when a user types (in the key of A Major), and i need to transpose it based off what song is playing in the background (for example a song in C Major needs to go up 3 semi-tones or half-steps)

An octave means that the ratio between two frequences is 2:1 (e.g. pitch for one octave higher is 2, for 2 = 4, etc.), so the pitch becomes:

pitch = 2 ** octaves;

Say, you have 12 semitones in an octave, then it becomes:

pitch = 2 ** (semitones / 12);

For an absolute pitch, like F4, you can represent it as a MIDI note 64 (you can google those). So, in the end, if you want to find a pitch of MIDI note C4 (60) using a sample of MIDI note D4 (62), it becomes:

// 2 ** ((D4 - C4) / 12);
pitch = 2 ** ((62 - 60) / 12);

If you need cents for say vibrato, you can divide semitone accordingly - there are 100 cents in semitone:

// 10 cents = 0.1 semitones
const D4 = 62 + 10 / 100;
pitch = 2 ** ((D4 - 60) / 12);

Hope that helps.

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2

I have also solved it in this way! I needed to be able to transpose a note up from like A to C for example, and notes in a scale are not equally divided into 12 even though there are 12 notes in a scale. Its all about the ratios!

with this chart: C5S1_Intervals
you can see the ratios of each note in a chromatic scale compared to the input note. Here is a function to transpose up. So if you are playing an A note in a soundSlot but you want it to play a C you could do

soundSlot.pitch = this.transposeUpSemiTones(3)
soundSlot.play

With the transpose function being:

AudioController.prototype.transposeUpSemiTones = function(semitones){
    if (newKey == 0){
        return 1;
    }
    else if (newKey == 1){
        return 16/15;
    }
    else if (newKey == 2){
        return 9/8;
    }
    else if (newKey == 3){
        return 6/5;
    }
    else if (newKey == 4){
        return 5/4;
    }
    else if (newKey == 5){
        return 4/3;
    }
    else if (newKey == 6){
        return 45/32;
    }
    else if (newKey == 7){
        return 3/2;
    }
    else if (newKey == 8){
        return 8/5;
    }
    else if (newKey == 9){
        return 5/3;
    }
    else if (newKey == 10){
        return 9/5;
    }
    else if (newKey == 11){
        return 15/8;
    }
    return 1; //Not specified
};
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