Re: Descending aug and dim intervals

"David Webber" <dave@[EMAIL PROTECTED]
> wrote in message 
news:ftnt9n$bgk$2$8300dec7@[EMAIL PROTECTED]
>
> "Tom K." <tkorth1@[EMAIL PROTECTED]
> wrote in message 
> news:E8-dnVay7JzSh2PanZ2dnUVZ_qmlnZ2d@[EMAIL PROTECTED]
>
>> Not following you here, Ian.  An interval is just a measured distance 
>> whether reckoned up or down.  By the same token, if I'm driving from
New 
>> York to Miami, am I supposed to measure the mileage from south to north

>> instead of the north-south route I'm actually traveling?  And will the 
>> results differ depending on which method I use?
>
> The really interesting thing is that and interval is not "just a
measured 
> distance" :-)
>
> One can associate a distance measure with an interval, not in a unique 
> way. In fact two such measures are in common use:
>
> The number of semitones in the interval.
> The logarithm of the frequency ratio of the notes forming the interval.
>
> Both are additive but they are only equivalent in equal temperament.
>

Sorry, being a keyboard player, I tend to think more in ET.

> And give that they are additive (with 0 being associated with a unison) 
> they are also directional: nothing breaks down if you associate a
negative 
> distance with a downward interval.

What is a "negative distance" in terms of musical intervals, Dave?  Sounds
a 
bit like like our late, unlamented "Diminished Prime"!  I guess my point
is 
that intervals may be undirected (harmonic) or directed (melodic), and 
directed intervals may be measured either up or down, forwards or
backwards 
without any difference in the result.  Of course, with some performers, 
there may also be misdirected intervals...:-)

> Intervals themselves add in a much more interesting way: a minor 7th
plus 
> a minor 7th is a minor 13th and so on.   And in adding intervals both
the 
> distance measures above also add.    (But while you can find either 
> distance measure from the interval, you can't get the interval from the 
> distance measure: there is enharmonic ambiguity.)

Unless you are assuming ET and measuring in semitones.  Then your
m7+m7=m13 
becomes 10+10=20.

Tom K.