::@Pfly. The several discussions that led to replacing List of musical intervals, first merely by a link to this page, then by the disambiguation page that it now became, are spread on the talk pages of both articles. In the history of List of musical intervals, you'll see that the existing list has been removed three times in less than a month (and restored twice). The whole could have happened in a less aggressive way. 
 ::I think that vulgarization is not about replacing difficult concepts by approximations, but about trying to explain them as simply as possible. "Pitch interval" is not a good expression because a pitch is a frequency (e.g. 440 Hz) associated with a note name (e.g. A4). The intervals discussed in this article are not between pitches properly speaking, if only because they are independent from any particular frequency. The expression can be understood, which is why it has not (yet) been changed, but I persist thinking that it is essentially wrong. 
 ::A "musical interval", to me, is an interval used in music, and not in the discourse about music – otherwise it should be renamed as something like "music theoretic interval", or "intervals used in tunings and temperaments". But neither of these are really satisfying. A cent, an eptameride, a savard are not intervals, they are merely units for measuring intervals. The 12-TET intervals (and most others listed in the column headed TET) cannot be expressed as fractions and cannot be factorized (they are irrational). These are but a few of the approximations of the article.  
 ::I agree that computers make everything possible (or so it seems). Yet, many of the intervals in this list result from excessive "digitalisation", i.e. express in numbers what in real music can neither be perceived, nor even conceived in this manner. You speak yourself of a music that "shifts between tuning systems". Many historical tunings similarly have been shifting between segments of simpler tunings. 'Just intonation' (of Zarlino's type) can be described as segments of Pythagorean tuning shifted by a syntonic comma; this does not mean that the syntonic comma was used as a musical interval. 18th-century irregular temperaments make use of all sorts of shifts, many of which cannot be expressed as ragisma or breedsma or anything of the kind, merely because they cannot be expressed as fractions. 
 ::All this considered, it appears to me that what the List of pitch intervals article does is digitalizing intervals, i.e. approximating them in whole numbers. But the article does not say so, is not even aware of doing so. These intervals may or may not have been used in music. Let's admit that they all could be used in music – it is not exactly the same... The article rests on implicit notions of what a note is, of what a pitch is, of what an interval is, and supposes that these notions are universal. This to me is both vulgarization and eurocentrism at their worst. 
 ::