Thanks for the book recommendation. I will check it out.
MonsterRadioMan, you are right. There are never diminished ninths or diminshed 13ths except in weird circumstances.
I found some answers about perfect intervals online.
Here they are in case anyone is interested :
"Why are perfect intervals lowered by only one semitone called diminished, while all other intervals must be lowered by 2 semitones to be called diminished?
I think it is because the perfect intervals were discovered first, before the Major and minor intervals.
The perfect intervals were the simplest to work out and were considered the most pleasing or consonant sounding.
They must have tried flattening or sharpening them by one semitone ( thereby coming up with ‘diminished’ and ‘augmented’ ) already, before they came up with the Major intervals and minor intervals.
“The term “perfect” originated due to the musical overtone series.”
“[The perfect intervals are] so called because of their simple pitch relationships and their high degree of consonance.”
“These sound qualities were first discovered and praised in the East.”
“Pythagoras was the first person from the West to explore this interesting observation.”
“The label of “perfect” in addition to a number describes the interval’s quality”
“These intervals are called perfect because the ratios of their frequencies are simple whole numbers.”
“They are labeled as “perfect” because the sound quality is much different from any other intervals.”
“Whether an interval is “perfect” or “major” depends on mathematical ratios of frequencies as determined by the Greeks.”
Mathematical ratios of frequencies regarding perfect intervals :
The perfect intervals are the simplest. They are the first three in the harmonic series.
1:1 = Tonic or Perfect Unison [full length of string / open string]
2:1 = Octave ( first overtone ) or Perfect Octave ( first interval ) [string split into two equal halves].
3:1 = Fifth above the octave ( second overtone ) 3:2 = Perfect Fifth ( the second interval )[3:2 is the other side of the string when 3:1 split is used]
4:1 = 2 Octaves ( the third overtone ) 4:3 = Perfect Fourth ( the third interval ) [4:3 is the other side of the string when 4:1 split / fretting / node is used]
Some Rules about Perfect intervals :
If any perfect interval is raised by one semitone, the interval becomes augmented
If any perfect interval is lowered by one semitone, the interval becomes diminished.
Intervals of a unison, 4th, 5th and octave can only be diminished, perfect or augmented.
Rules about Major and minor intervals :
If any major interval is raised by one semitone, the interval becomes augmented
If any major interval is lowered by one semitone, the interval becomes minor
If any major interval is lowered by two semitones, the interval becomes diminished
Intervals with a numeric value of 2nd, 3rd, 6th and 7th can be diminsished, minior, major or augmented.
Extra Information :
Typically consonant intervals are the unison, octave, fifth, sixth, and third.
Typically dissonant intervals are the second, seventh, and tritone, as well as all augmented or diminished intervals
( consonance is now considered a relative matter based on the harmonic series and context ).
( The tritone is defined as a musical interval composed of three adjacent whole tones, or 6 semitones, a diminished fifth ),