Is a Major Interval the same as a Pure Interval?

I've been making electronic music for the past year but recently decided that I need to sit down and learn some actual theory. So, I picked up a copy of Guide to the Practical Study of Harmony by Tchaikovsky and I had a quick question about how he's describing major/pure intervals.

For example:

Thus, we learn, that a major or a pure interval is converted into a minor, diminished or augmented interval by lowering or raising the upper tone...

In this passage, and a few others in the introduction, he seems to be using Major and Pure interchangeably in his sentence.

So, I'm just looking for clarification here, are Major and Pure intervals the same thing? Or, I suppose this is possible, that the rule he's describing just applies to both intervals and that's why he's using the terms interchangeably in a sentence?

Nevermind. I found the answer here.

A perfect interval identifies the distance between the first note of a major scale and the unison, 4th, 5th or octave. Only those intervals can be given the extra attached name as “perfect”.

• The problem is that your question is about the word "pure" as used by Tchaikovsky, and your answer is about the word "perfect". I think Tchaikovsky probably does mean "pure" to mean "major", mainly because unisons, fourths, fifths, and octaves are not called "minor" when they are lowered by a half step, but major intervals are. – Todd Wilcox Jun 2 '18 at 17:15
• I usually think of pure intervals as just intoned intervals. I'm not sure what Tchaikovsky had in mind here, but perfect intervals and pure intervals can't be the same thing in his thinking, since there is no such thing as converting a perfect interval to a minor interval. – ex nihilo Jun 2 '18 at 22:05
• @DavidBowling - for me, as well, a pure interval is a just interval. But from the context it's clear that Tchaikovsky mean "perfect interval" in its normal modern sense of simply being a unison, a fourth, a fifth, or an octave. Of course, there's nothing really "perfect" about a tempered fourth or fifth, but that's another topic..... – Scott Wallace Jun 3 '18 at 18:47
• @DavidBowling -- well, it says "a major or a pure interval is converted into a minor, diminished or augmented interval by lowering or raising the upper tone". I think he's saying- sloppily- that the major becomes minor and the "pure" becomes diminished when the upper tone is lowered a semitone, not that pure intervals also become minor. It's in any case ambiguous and shouldn't be in a textbook. – Scott Wallace Jun 3 '18 at 18:56
• @ScottWallace -- I get it now; Tchaikovsky is giving major and perfect (pure) intervals as two fundamental types to be modified.... – ex nihilo Jun 3 '18 at 18:57