# Are 13 and 20 semitone intervals diminished 9th and diminished 13th?

In the context of the following chords, should the 13 and 20 semitone intervals be properly descirbed as diminished 9th and diminished 13th ( or minor 9th and minor 13th )?

m7b9 - ( 0 3 7 10 13 ) ( root m3 P5 m7 d9 )

[root, minor third = 3st, Perfect fifth = 7st, minor seventh = 10 st, ??diminished ninth = 13st?? ]

9b13 - ( 0 4 7 10 14 20 ) ( M3 P5 m7 M9 d13 )

[root, Major third = 4st, Perfect fifth = 7st, minor seventh = 10st, Major ninth = 14st, ??diminished 13th = 20st?? ]

Whats the correct way to describe the b9 ( 13 semitone ) and b13 ( 20 semitone ) intervals, diminished or minor?

There is no such thing as a diminished 9th. I mean theoretically there is, but normally you wouldn’t say that. A diminished 9th is an octave. Same with a diminished 13th, that’s a perfect 5th. So yeah, you would call it a minor. In fact there’s a joke in Buffy the Vampire Slayer where they make a reference to the E diminished 9th as one of Oz’s ambitions in life (it’s a power chord! ).

To clarify, a diminished 9th is possible, but no one would ever use it since it’s sort of meaningless. A b9 is a minor 9th.

Or rather, there’s a theoretical relevance to it, in that you may come across a diminished 9th in some pieces, like if you had an E chord but were suddenly confronted with an Fb for whatever reason. Rare, but it could happen. But it makes little harmonic sense when spelling out a chord to say “diminished 9”. I hope that makes sense.

A diminished 9th is an octave. Same with a diminished 13th, that’s a perfect 5th.

Diminished usually means that a Major interval has been flattened by 2 semitones, whereas minor usually means a Major interval that has been flattened by 1 semitone.

Thats why I thought a 13 semitone interval being described as ‘diminished 9th’ and a 20 semitone interval being described as ‘diminished 13th’ was unusual.

A Major 9th is 14 semitones. I can understand why someone would say that a minor 9th would be 13 semitones and a diminished 9th would be 12 semitones ( as one octave = 12 semitones ).

A Major 13th is 21 semitones. I can understand that by taking away 2 semitones from 21 you would get 19 semitones, which is a perfect 5th above the octave ( for example, C4 to G5 ).

However in the case of a 6 semitone interval ( a perfect fifth flattened by 1 semitone ) it is often described as a diminished fifth.

I wonder if a 9th ( 14 semitones ), flattened by 1 semitone to 13 can also be described as diminished in some contexts?

How about a 13th ( 21 semitones ), flattened by 1 semitone being described as diminished in certain contexts?

Or does the rule ‘diminished is a Major interval flattened by 2 semitones’ apply to all intervals except for one ( the perfect fifth, which is 7 semitones but becomes diminished when flattened by 1 semitone ).

I just want to make sure… in the case of the following chords are the d9 and d13 interval descriptions ( for 13 and 20 semitones ) definitely incorrect? ( If they are it just means that the book I am working from is incorrect ).

m7b9 - ( 0 3 7 10 13 ) ( root m3 P5 m7 d9 )

[root, minor third = 3st, Perfect fifth = 7st, minor seventh = 10 st, ??diminished ninth = 13st??]

9b13 - ( 0 4 7 10 14 20 ) ( M3 P5 m7 M9 d13 )

[root, Major third = 4st, Perfect fifth = 7st, minor seventh = 10st, Major ninth = 14st, ??diminished 13th = 20st??]

A perfect fifth is an interval it would be neither major, nor minor. just a root and the fifth. you would need the 3rd, or flatted 3rd to make it either major or minor.

If you want to listen to somebody with a great understanding of diminished 5ths you should check out the band Dokken, he’s famous for them. The diminished scale is a whole tone scale with every other note dropped a semi tone. Its an 8 note scale. A 9th in jazz adds 7 and 9.

Adding 7 and 8 would be very dissonant instead you play something like edim7

http://dokken.net/

O.K. Thanks.

Why is it that a perfect fifth ( 7 semitone interval ) flattened by 1 semitone ( to a 6 semitone interval ) is called diminished while all the other non-perfect intervals must be flattened by 2 semitones to be called diminished?

Maybe its something to do with what you said about it being neither Major nor minor, that is to say, it is a perfect interval.

I can see that the other perfect intervals must only be flattened by only one semitone to become diminished as well, so it may be a general rule that applies to all perfect intervals ( they become diminished when flattened by only one semitone ).

For example :

P4 ( Perfect Fourth, 5st ) - 1st = 4st ( diminished fourth ).

P5 ( Perfect Fifth, 7st ) - 1st = 6st ( diminished fifth ).

P8 ( Perfect Octave, 12st ) - 1st = 11st ( diminished octave ).

P11 ( Perfect eleventh, 17st ) - 1st = 16st ( diminiahed eleventh ).

P12 ( Perfect Twelfth, 19st ) - 1st = 18st (diminished twelfth ).

P15 ( Perfect Fifthteenth, 24 semitones - 1st = 23st ( diminished fifthteenth ).

In any case, I think diminished 9th ( as 13 semitone interval ) and diminished 13th ( as 20 semitone interval ) must be wrong as MonsterRadioMan indicated above.

Why are perfect intervals called perfect? Is it something to do with dividing the string up, like the harmonic series? Sorry, I’m learning this stuff for the first time.

“Perfect intervals,” are not major or minor ie named perfect, or an interval can be major, “major 7th,” or minor, “minor 7th.”

The book below is one of my all time favorite books on music theory. It is marketed as an, “introduction to jazz theory,” which is a laugh. I’m still, “beyond confused,” by the subject as a whole

https://www.amazon.com/Jazz-Theory-Practice-Jeffrey-Hellmer/dp/0882847228

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.

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 ),