# Transposing in Semitones

• Oct 2, 2020 - 12:49

I am revisiting an old friend who is still proving a tough nut to crack: transposing in semitones. All seemed clear after mike320 posted as per image below but now I've got a bit confused again. From my guitar fretboard I can show that there are 12 semitone steps needed to move a note up by 1 octave. However, the table shown seems to show that there are 14 half steps. What am I missing?

I can't understand this table at all; I don't know what a "step" is (not a "whole tone", for sure). The fact that this table doesn't show a major third the same as a diminished fourth (in equal-temperament/guitar frets) is a giveaway that something is amiss. I can count in semitones, diatonic intervals, or whole and half tones.

In equal temperament,
Unison = 0 semitones
Minor second = augmented unison = 1 semitone
Major second = diminished third = 2 semitones
Minor third = augmented second = 3 semitones
Major third = diminished fourth = 4 semitones
Perfect fourth = 5 semitones
Augmented fourth = diminished fifth = 6 semitones
Perfect fifth = diminished sixth = 7 semitones
Minor sixth = augmented fifth = 8 semitones
major sixth = diminished seventh = 9 semitones
minor seventh = augmented sixth = 10 semitones
major seventh = diminished octave = 11 semitones
perfect octave = 12 semitones.

My table was flawed. There are two points in every octave that have a 1/2 step between notes (B-C & E-F) that I didn't account for. BSG's is much better.

I would like to note that the Russian (superlative) composer and theorist Sergei Taneyev (or Taneev, Tane'ev) promoted the use of zero-based interval nomenclature so that intervals could be added and subtracted with ordinary arithmetic. It never caught on; maybe we should call him the zeroth person to advocate this.

Now I just need to raise an S5 for transposition in semitones. It's more natural for tabbers.

You wrote:
From my guitar fretboard I can show that there are 12 semitone steps needed to move a note up by 1 octave.

Great observation!
Another fact is that the 12th fret divides a string's length into 2 equal parts. A vibrating string cut in half will then vibrate at twice its original frequency - and so the octave of an open string is produced at the twelve fret. The very basis of harmonic theory.

Those 12 half steps comprise an octave. Not only on your guitar fretboard, but viewing a piano keyboard shows that any 12 consecutive (black and white) keys span an octave.

More lingo:

A half step is a semitone (i.e., 1 guitar fret).
A whole step is comprised of 2 semitones (or 2 half steps).
A musical scale is comprised of whole steps and half steps.
A major scale contains 2 half steps. One falls between the 3rd and 4th scale degrees (notes from the starting note). The other half step is between the 7th and 8th.

So... on the guitar, one can start on a fret on any string (try the second fret) play it, then move 2 frets, 2 frets, 1 fret, 2 frets, 2 frets, 2 frets, 1 fret. Doing this will play a major scale.
2+2+1+2+2+2+1 = 12 semitones.

This (the 12 semitones) is what you correctly observed on the fretboard. 1 fret =1 half step = 1 semitone.
The terms 'whole tone' and 'half tone' are also used for 'whole step' and 'half step'.

(I'm surprised no one noticed the flaw in mike320's original post. Probably TLDR ;-)

Not only does a major scale contain 2 and only 2 half-steps, but a (natural) minor scale, and every (church) modal scale, e.g., Dorian, Phrygian, etc. Just in different places relative to the "tonic" of the key.

"Another fact is that the 12th fret divides a string's length into 2 equal parts." - must be why twelfth fret harmonics work.

221,2221 is easy enough to remember. What's the pattern for minor scales?