Carlos S. answered • 03/26/20

Effective and resourceful Guitar and Music Production Tutor

Hello, Kelci! This is a really hard challenge. I'm closely related to this due to some of my music production activities. This kind of calculations are used in sound design for virtual synths. I hope you find this useful!

If you are ever interested in taking lessons with me online or on-location, please let me know! I teach Music Theory at all melodic and harmonic levels, Music Foundations, Ear Training, Logic ProX, Mixing, Mastering, Compositional resources, etc. Interactive reinforcement exercises are made for each student (tailored workshops) using cool but simple software! We can work online (or locally if you live in the Miami/Doral area)

Have a great week. Take care!

Carlos

I'd use these:

1.) **Equal Temperament Tuning:**

440 ∙ 2(22/12) = **1,567.982 **Hz

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2.) **Pythagorean Tuning**:

440 ∙ (3/2)–2 ∙ 23 = **1,564.444 **Hz

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3.) **Harmonic Series (key of A)**:

440 ∙ (7/4) ∙ 21 = **1,540 **Hz

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4.) **Harmonic series: you could use the Key of Ab**:

**Equation #1: Ab4 x (12/11) = 440 Hz. (which is A)**

(you have Ab4 and need to go up 1 minor second, which is 12/11 in Harmonic Series).

**Step 1.) Getting Ab4 **

First, you’ll need to divide both sides of Equation #1 by 12/11 (which means multiplying by 11/12) = 440 x 11/12 = 403.33333 Hz.

This is, Ab4 = 403.33333 Hz

**Step 2.) Finding G6: **

For this, you need to take your Ab4 and multiply by the fraction corresponding to a major seventh , then multiply again by 21^{. }

Thus, it would be 403.33333 ∙ (11/6) ∙ 21 = **1,478.889 **Hz

G6 (according to the Harmonic Series in the key of Ab) = **1,478.889 **Hz

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5.) **Just Intonation: You could use the Key of Ab again.**

Ab4 ∙ (16/15) = 440 Hz. (which is A)

**Step 1.)** You should divide both sides by 16/15 (this is, multiply by 15/16) to get A4b

When you do this, you’ll get Ab4 = 412.5 Hz

**Step 2.)** Finding G6:

You will take Ab4 and multiply by 15/8, which is a major seventh (in Just Intonation), then multiplying by 21

Thus, 412.5 ∙ (15/8) ∙ 21 = **1,546.875 **Hz (this is G6 according to Just Intonation)