On May 30, 8:53 pm, Danny Schorr <.@[EMAIL PROTECTED]
> wrote:
> On Fri, 30 May 2008 22:45:27 +0200, "Alain Naigeon" <anaig...@[EMAIL PROTECTED]
>
> wrote:
>
> >"Tom K." <tkor...@[EMAIL PROTECTED]
> a =E9crit dans le message de news:
> >_cCdnYOzBbGH_d3VnZ2dnUVZ_rTin...@[EMAIL PROTECTED]
>
> >> "Alain Naigeon" <anaig...@[EMAIL PROTECTED]
> wrote in message
> >>news:48405157$0$11995$426a74cc@[EMAIL PROTECTED]
> >>> "Steve Latham" <llat...@[EMAIL PROTECTED]
> a =E9crit dans le message de
news=
:
> >>> JmL%j.10928$4c.1530@[EMAIL PROTECTED]
>
> >>>> "Danny Schorr" <.@[EMAIL PROTECTED]
> wrote in message
> >>>>news:e41u34dmfg7nr00rb8tdtni6h1n8uplukq@[EMAIL PROTECTED]
> >>>>> On Thu, 29 May 2008 08:17:39 GMT, Danny Schorr <.@[EMAIL PROTECTED]
> wrote:
>
> >>>>>>When does an interval become a leap?
>
> >>>>>>When a melody moves by an interval greater than a whole step.
>
> >>>> I was going to quiz you on the very same thing.
>
> >>>> But your definition actually stands:
>
> >>>> Whole Tone.
>
> >>>> Bb to C# is, yes, a leap - even though the letters are consecutive,
i=
t's
> >>>> still larger than a whole step.
>
> >>>> And it has nothing to do with "scale" - just interval. So even
though=
> >>>> A-C are "adjacent scale steps" in a pentatonic scale, it's still
larg=
er
> >>>> than a whole step, thus leap.
>
> >>> Ok, now, let's imagine a scale in which every step is greater than a
t=
one
> >>> (for example a strange C Eb Gb A) ;
> >>> would you still call a leap such an atomic step like C Eb ? ;-)
>
> >> But Alain, even in our collective imaginations, C Eb Gb A wouldn't be
> >> termed a "scale". Call it a dim. 7th chord, a tetrachord, or perhaps
a=
4
> >> PC set - but not a scale!
> >> Tom K.
>
> >Tom, where is it written that a scale must have 7 notes, or more than
fou=
r,
> >or that it should contain at least one interval not greater than some
> >inferior
> >limit, or..?
> >In other words, I'm not necessarly disagreeing with your answer, but
I'd
> >then ask : how can we turn our common feeling of a scale to a rational
> >definition ?
>
> Alain, your inquiry is actually along the same lines as my musing upon
whe=
n
> it is that a step becomes a leap.
> Hindemith said that 7 notes are the minimum requirement for a succesion
o=
f
> notes that move by step and not by leap. I pondered this for a while,
and
> as far as I can tell he is right ( he derived the 7 note scale from
> Pythagoras's metheod, moving lower and higher from the original
derivation=
> of fifths to arrive at the 7 note scale, before filling out the
chromatic
> with all twelve notes. I can give the details in another post if you are
> interested.)
> My intertest was piqued by something Steve said to someone in another
> thread - that although there are 12 notes in the chromatic scale, early
> music at first used 7 of the notes ( or something like that : Steve -
feel=
> free to restate what you said if I am mis-representing that)
>
> So, anyway, I started to think about it - the only counter-example I
could=
> think of was the whole-tone scale - say, CDEF#G#A#B#(C) - but that
doesn't=
> have a P5 in it,so that won't fly. I was interested to know how the
> pentatonic scales figured into things - the only conclusion I can reach
at=
> present is that people just happen to like the sound of them - highly
> unscientific indeed!
>
> Danny
The pentatonic scale is created with 5 consecutive Pythagorean 5ths
as well as the first 5 different tones of the harmonic series if you
use the lower note of the 6/b7 interpretation of the 7th partial. How
scientific does it have to be?
Now, this is of no matter if you go by the traditional definitions of
"leap". The ones that I have found refer to an interval greater than a
second. Strange that none of these definitions limited the second to a
major second! so that would allow for the Bb ->C# in a d harmonic
scale to be a step as it is a second but would allow the pentatonic
scale to have 2 leaps in its diatonic movement of notes because the
"names" of the intervals are more than a second. But then again, this
would allow the diminished scale that wold have a C C# D# to call the
C to D# to be called a step and not a "leap" even though it is both
the same interval (in semitones) as the minor third of the pentatonic
scale AND it "skips" one of the notes of the scale! And then if you
have something like a Locrian #7 (B C D E F G A# B) or its rotations,
the "skip" from the A# to the C is in semitones only a major second.
So with this ambiguity when applied to more modern concepts one has to
conclude that this definition of "anything more than a major second"
is specific to a limited number of styles of music. I suspect that the
Hindemith (or was it Piston) definition would be in a book that dealt
with CPP conventions as well as Dolmetsh and Virginia State and other
definitions that define a skip in this manner. So as I said before, it
depends on your context. In the CPP context, this definition may work.
In the broader spectrum of music, it just doesn't seem to make any
sense. When confronted with a conundrum (with the: a paradoxical,
insoluble, or difficult problem; a dilemma: connotation rather than a
riddle. Hmm, maybe someone can solve this with a play on words or pun
to make it the other conundrum!) we were likely to venture our own
definitionsince the ones that we found didn't work, why not?
That is why I would look at it from the context of the Scale. The
scale definition being that a "skip" is the movement from one note to
another that skips a note in the scale. This would make the Pentatonic
scale "sans skip" as well as allowing Alain's example to work,
assuming that the notes that he chose would fit the requirements of a
scale. His particular choice does have a rather unstable quality, but
then again, so does the whole tone scale. The whole tone scale has 6
notes, the Pentationic has 5 so why could there not be a 4 note scale,
and in this case the four notes happen to also be a diminished 7th
chord. I can imagine Alain's scale expanded to a two octave scale of
C Eb Gb A B# D# F# Gx C. In this case if you combined the major second
definition and the second definition, Gb to A would be a step and so
would A to B# although the B# to D# could be a skip and the etc, etc,
etc, well you get the idea! And only I have mentioned the Chromatic
scale and the Diminished scale.
So I have to come back to the context. The definition I use that bases
it on skipping a note in the scale adapts to the various contexts by
the definition of the scale. Thus it will work not only in the CPP
context quite nicely, but is also will accommodate the more modern
aspects of music that may use non CPP scale structures just as
easily.
LJS
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