Equal Temprament

Question 0

Explanation

Answer 0

Octaves are a exponential sequence. Vibration frequency doubles every octave.

Harmony intervals are whole fractions
5th (3/2 ratio,1.5)
4th (4/3 ratio 1.33)
Major 3 (5/4, 1.25)

Question 1

A4 concert pitch

Answer 1

A5 = 880  Hz   17th fret 1st string
A4 = 440         5th fret on 1st string
A3 = 220         2nd fret on 3rd string
A2 = 110         open 5th string
A1 = 55           open 2nd string on bass
A0 = 27.5 Hz
An = (27.5)2 power n, octaves, exponential sequence

Question 2

Bach solution

Answer 2

J.S. Bach painstakingly, and entirely by ear, devised a system of smoothing ‘equally out of tune’ in every key. A glorious compromise. Every interval except the octave is slightly out of natural tune.

Question 3

Middle C

Answer 3

C4 is 261.6 Hz. 
middle C (piano) on the guitar is the fifth fret G string, or 1st fret B string. NOT the third fret of the 5th string. 

The guitar is a transposing instrument. It plays an octave lower than it reads.

What most editions of guitar sheet music don’t say, is that guitar music is not written in treble clef, but in tenor clef.