# Multiply-diminished intervals from a major

I know that starting from a perfect interval and shortening the interval by two semitones gives a doubly-diminished interval. But what about starting with a major interval?

For instance, starting with a major 6th, I have 9 semitones. If I shorten it to 8 semitones, I have a minor 6th, and 7 semitones is a diminished 6th. Would 6 semitones (3 less than were we started) be a double diminished 6th, or a triply diminished sixth?

In other words, is the "numeric name" of a diminished interval based on how many semitones it is below the "reference" interval (major or perfect), or how many semitones it is starting from singly diminished?

• Why would that need to happen? Technically I don't think it would be necessary to move the same name note down that far. – Tim Jul 11 '14 at 17:10
• I have no idea why, but it is possible and I've seen references to it. For instance A# to Eb is a doubly-diminished 5th. I guess I'm just assuming that the same applies to Major intervals, and even if it's not commonly used, it is at least sensical on a technical level. – brianmearns Jul 11 '14 at 17:14
• It happens, though admittedly rarely, in order to indicate rarer intervallic functions, usually in a complex contrapuntal framework. For example, Ligeti has need occasionally in Musica Ricercata to indicate a resolution on Bb and E, so he precedes it with Cb and D#, which is a doubly-augmented second. People argue about whether it's appropriate, but some composers and editors think it is. – Pat Muchmore Jul 11 '14 at 17:45