# Renaming intervals to avoid fractions

Any two consecutive piano keys make an interval of 1/2 step (e.g. C to C#, or E to F). Why not just rename that to be a whole step, and avoid having to use fractions? Then, for example, C to F would be 5 steps instead of 2.5, and an octave would be 12 steps.

Just wondering if there is a good reason why it is the way it is, other than, "That's the way it has always been." Would music theory be drastically different if intervals had been named this way all along?

• Some people count semitones. If you can forget that "semi" means "half" that works. I doubt it would make much difference, because music theory is more a description of what works than a prescription that makes things work. – Peter Aug 3 '20 at 22:14
• so the steps of the major/minor scales will then be called what, steps and double steps? how is that better than whole and half steps? – Michael Curtis Aug 4 '20 at 12:51
• Actually the steps in a major scale are called seconds, so a step in a scale can be either a minor second or a major second. Thus the term step can mean both of these intervals, but unfortunately the term is also used in a different way when you talk about a half step and a whole step. – Lars Peter Schultz Aug 5 '20 at 21:09

Half steps and whole steps (or tones and semitones) are used to build scales, not to define intervals. Intervals consist of two measurements one which is number of semitones the other is letter name distance. So people would never describe the interval of C to F as 2.5 steps, but a perfect fourth (P4). If there ever is a need to talk in pure chromatic steps which can happen when taking outside of letter names, the term semitones will be used (a P4 is 5 semitones) since it is the smaller unit.

The steps are used in context of talking about the distance between one letter name and the next in a scale. The whole step is the typical step size with the major scale consisting of 5 whole and 2 half steps. If the name half and whole are hard to get over, treat them as "small" step and "big" step respectively.

• Since a semitone = 1 fret, guitarists talk about a number of frets - thus C>F is 5 frets. A lot wouldn't even consider P4! – Tim Aug 4 '20 at 6:32

If we hadn't used 'tone' and 'semi-tone' (the slightly more cumbersome 'whole-step' and 'half-step' are, I think, a later Americanism) we'd doubtless have coined something like 'gap' and 'double-gap'. I doubt that Western music would have leapt straight into Dodecaphonism.

• More cumbersome, perhaps, but certainly less ambiguous, given that "tone" can also be a synonym for "pitch." – phoog Aug 5 '20 at 4:53
• Yeah, I guess. Though I'm struggling to think of a context where there could be confusion. Got anything? – Laurence Payne Aug 5 '20 at 8:16
• The example that prompted my comment was Tim's comment on an answer to his recent question: "The higher the tension the higher the tone? But one tone is a difference in pitch, so that doesn't sound too plausible" – phoog Aug 5 '20 at 12:32

Only because it's called Semitone shouldn't mean that you have to think in terms of fractions. Even if it seems a little silly at first, once we think of Semitone as 1 and Tone as 2, everything is clear.

Once you get over the name, you can easily understand and visualize scales as combinations of tones and semitones, i.e. steps and half steps.

For example, major scale: T T S T T T S, which is the same as 2 2 1 2 2 2 1, etc.

Why call the first Tone and the second Semi-tone? I'm no historian by these names didn't start as English names, they were translations of Italian or perhaps Latin names used in the late middle ages, and whatever was first used back then stuck until now.

• Interesting. There are more whole steps than half steps in the major scale, so maybe that influenced the names. As in, "We should call the more common interval in the scale a whole step." – DreiCleaner Aug 4 '20 at 16:34
• @DreiCleaner perhaps it was something like that, though the terminology was settled on long before the major scale came into existence. – phoog Aug 5 '20 at 5:07