\input texinfo
@settitle Intervals
@setfilename theory-intervals-pre
@chapter Interval names
In music theory we use the word @emph{interval} when we talk about the
distance between two tones.
Interval names consist of two parts, the general and the specific part.
You find the general name by counting the lines and spaces between two notes:
@lilypond[raggedright,staffsize=16]
\score{
<<
\new Staff\new Voice\notes{ 
	<c' c'>1 <c' d'> <c' e'> <c' f'> <c' g'>
	<c' a'> <c' b'> <c' c''> <c' d''>
	}
\new Lyrics\lyrics{ 
	unison second third fourth fifth sixth seventh octave ninth
}
>>
\paper{}
\midi{ \tempo 1=60 }
}
@end lilypond

Not all intervals with the same general name has the exact same size.
From the tone @emph{c} to the tone @emph{d} there is two semitone steps,
but from @emph{e} to @emph{f} there is only one semitone step. Both
intervals are called a @emph{second}, but the first interval is a
@emph{major second} and the second is a @emph{minor second}.
The specific name of an interval tell you the exact size of the interval.

@lilypond[raggedright,staffsize=16]
\score{
	<<
		\new Staff\notes{ <c' d'>1 <e' f'> }
		\new Lyrics\lyrics{ major minor }
		\new Lyrics\lyrics{ second second }
	>> 
	\paper{}
	\midi{}
}
@end lilypond

The easy way to remember the specific names of
intervals is to think of a major scale starting from the lowest of the
two notes. 

@lilypond[raggedright,staffsize=16]
\score {
	<<
		\new Staff\new Voice\notes{ 
			<c' c'>1 <c' d'> <c' e'> <c' f'> <c' g'>
			<c' a'> <c' b'> <c' c''> <c' d''>
		}
		\new Lyrics\lyrics{ 
			perfect major major perfect perfect major
			major perfect major
		}
		\new Lyrics\lyrics{ 
			unison "2nd" "3rd" "4th" "5th" "6th" "7th" "8ve" "9th"
		}
	>>
	\paper{}
	\midi{ \tempo 1=60}
}
@end lilypond

If the upper note is higher or lower than the scale note, then we find
the name by counting how many semitone steps larger of smaller the
interval is comparted to the interval from the major scale. 
@itemize @bullet
@item A minor interval is on semitone step smaller than a major interval.
@item A diminished interval is one semitone step smaller than a minor or a
perfect interval.
@item An augmented interval is one semitone step larger than a major or a
perfect interval.
@end itemize
Examples:
@lilypond[raggedright,staffsize=16]
\score{
	<<
		\new Staff\new Voice\notes{
			<g' b'>1 <g' bes'> <g' bis'> \bar "||"
			<e' ges'> <e' g'> <e' gis'>
			<d' a'>1 <d' aes'> <d' ais'>
		}
		\new Lyrics\lyrics{
			major minor augmented diminished minor major
			perfect diminished augmented
		}
		\new Lyrics\lyrics{
			third third third third third third
			fifth fifth fifth
		}
	>>
	\paper{}
	\midi{ \tempo 1=60 }
}
@end lilypond
@bye
