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Why is the interval of 2 tones called a third? Indeed, the distance from note C to note E is 2 whole segments, and if we subtract 3 - 1 we get 2.

In Russian each interval has its own name, not an ordinal value. It is confusing.

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    What names are you thinking of in Russian? The ru:WP entry seems to be almost transliterated Latin, and "third" is Терция - see ru.wikipedia.org/wiki/… – Brian Chandler Oct 28 '18 at 6:45
  • (Amended comment) This is because in Russian you use the transliterated Italian/Latin names for 1st, 2nd, 3rd, i.e. прима, секунда, терциа, instead of первый, второй, тритий. But these are just translations of the same words (I don't know why прима is feminine? in Russian; it's ''primo'' in Italian.) – Brian Chandler Oct 28 '18 at 6:58
  • Russian is not the only language where you have names for the intervals. – Neil Meyer Oct 29 '18 at 6:04
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What a 'third' means is that you have moved two notes up - or down - from some other conceptually 'first' note in a scale, making it the 'third' note. As you rightly say, this is an ordinal number.

If you're a software developer, then you might be used to 'zero-indexing' sequences, so that the first one in the sequence is seen as zero. That might indeed make sense here, but most non-developers think of sequences as one-indexed, so it's not very surprising that we call the first note in a scale the 'first'.

Why the interval of 2 tones is called the third.

It doesn't have to be. You are welcome to refer to an interval of 2 tones, or 4 semitones, if that makes the most sense in the context in which you're speaking.

And of course you have to be careful as there are different sizes of 'third'. A 'third' isn't necessarily 2 tones - it could be 3 semitones, if we're talking about a minor third. And 2 tones isn't necessarily a 'third'. It could be a doubly augmented second.

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The first note mentioned is just that - the first note. C is the first, D second, taking us to the third, E.

It's also the case that a gap of two tones can be a diminished fourth, further confusing the issue!

As a corollary, a student recently discussing intervals, and their seeming illogicality, said 'maybe it's not an appropriate word...' Maybe there's something in that. Is there a more succinct word that would work better?

  • it is not that confusing – Neil Meyer Oct 28 '18 at 12:55
  • @NeilMeyer - makes me wonder why the question was ever posed, then. – Tim Oct 28 '18 at 13:27
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Hopefully I won't confuse the matter by pointing out that an interval is not always a whole tone. Tones and intervals are not the same thing. There are also semitones in the Major scale that are referred to as intervals. Tones and semitones are the space between two adjacent notes in a scale, and intervals describe distance between both adjacent notes and the rest of the notes without considering whether the space between notes are whole or half tones. This needs to be understood in order to avoid wondering why the interval of a perfect fourth is only two and a half tones. Also, counting intervals uses what is commonly called inclusive counting, counting tones does not.

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