Chromatic scales

Chromatic scales are useful tools with useful musical properties. As
an example, assume you're playing in extended meantone: meantone[12]
is always sort of there under the radar. This is probably somewhat
because of acculturation, but not really, because it's pretty easy to
discover meantone[12] even if you're just playing in meantone[7]; just
interpolate melodically between diatonic notes, or modulate to the
parallel minor, and you're bound to discover meantone[12]'s existence
soon enough.

Here's a sample situation which comes up all the time when you use
unequal chromatic scales. Say you're in 19-EDO, and you want to play C
minor - note that Eb is in this pitch set. Then, say you modulate
around for a while, ultimately ending up at C lydian #2, specifically
the C-E-F#-B-D# voicing, which is a beautiful chord everyone should
play a lot. Note that D# is in this pitch set.

Now you need Eb and D#! What do you do? What are your options?
1) Don't play that chord progression. (Too limiting.)
2) Limit yourself to a 12-note subset of meantone, pick one of those
choices, and use just use the enharmonic equivalent in the other case.
(Intonationally uneven.)
3) Pick a larger MOS of meantone, like meantone[19], and use that MOS
instead of meantone[12]. (On the right track.)

While #3 is clearly the best, practical constraints permitting, I
suggest that this solution is even better

4) Pick a larger MOS of meantone, like meantone[19]. Continue to use
meantone[12] as a prominent subset within this larger MOS, and just
change the mode of meantone[12] you're using on the fly when stuff
like this happens.

In other words, I'm saying, use a larger MOS as your gamut, but then
don't forget about meantone[12]. If this seems trivial, then try
replacing meantone[12] with orwell[13] or porcupine[15] above or the
14-note Fokker block of your choice, and maybe it'll make some
xenharmonic sense too.

A good analogy for the effect I've found this to create is the concept
of playing a fast line of parallel thirds in the major scale. Despite
the changing specific intervals, it's audible that they're both
"thirds" and share the same generic interval class. To do the above
with a set of parallel chromatic scale modes in a larger enharmonic
scale likewise helps to create a strong sense of generic interval
class for the generic intervals in the chromatic scale, and hence a
clear sense of chromatic "scale degrees" on which simpler melodies can
be built.

It would be really nice to do this for chromatic scales containing a
number of notes not equal to 12. For instance, the 22-EDO pitch set
suddenly pops into a more well-defined existence when you view it as
an enharmonic scale containing a prominent 15-tone chromatic scale
system. I also note that EDOs of around 17 and higher contain more
than one potential chromatic scale in this way - for instance, 19-EDO
has not only meantone[12] but sensi[11], wholetone[13], semaphore[14],
hanson[15], magic[16], etc. And 22-EDO contains not only porcupine[15]
but pajara[12], orwell[13], hedgehog[14], astrology[16],
superpyth[17], etc.

I think that this approach can serve useful for higher-rank systems as
well - there's no reason why you couldn't pick a Fokker block as a
chromatic scale and then shift around the different domes and modes of
it when necessary, still keeping the sense that there exists some
constant set of chromatic generic intervals in the background. I also
strongly suspect that the creation of such generic chromatic intervals
will strongly aid the development of what I was previously calling
"interval categories" for a tuning system, but which I now believe are
much more complex and possibly related to lifelong memories of nearly
subconscious musical features such as this. I'll try to come up with
some musical examples sometime soon when I'm not drowning in work.

-Mike

Hi Mike,

Here's my attempt, back in 1995, of "An algorithm for dynamically choosing the best 12 notes from an extended meantone".
http://dkeenan.com/Music/AdaptiveMeantone.htm

Hi Dave - very neat idea! I suppose I was thinking of doing something
like this, but manually, as a performer, in realtime. For instance,
you say this:

"Truly chromatic music is just not going to work. For example
attempting to play a chromatic scale up from C will result in the
sequence C,C#,D,D#,E,E#,F#,F##,G#,G##,Bb,B,C."

This solves that problem, because then the performer will have a good
sense of which notes go where.

My compositional idea with this is that a chromatic scale gives you a
strong sense of there being a background set of pitches, or more like
"generic pitches" of which "specific pitches" exist. Put another way,
there's a strong sense of background chromatic "generic interval
classes" in which specific "enharmonic variants" or "commatic
variants" can exist or whatever.

I don't see why this couldn't work with Fokker blocks too. For
instance, on one extreme, there's the idea of JI giving you all these
notes so you might as well play totally freeform and not worry about
scales too much. On the other extreme, there are people who stick
specifically to x-note subsets of JI and don't modulate past those.

This is what I feel to be the optimal compromise between the two. You
imply a "generic chromatic scale" and work with different modes and
domes of it as the music you're writing dictates, keeping some kind of
constant ground all the while.

You get bonus points if your generic chromatic scale is -not- 12
notes. 15 note generic chromatic scales in 11-limit JI plz.

-Mike

On Fri, May 18, 2012 at 8:58 PM, dkeenanuqnetau <d.keenan@...> wrote:
>
> Hi Mike,
>
> Here's my attempt, back in 1995, of "An algorithm for dynamically choosing the best 12 notes from an extended meantone".
> http://dkeenan.com/Music/AdaptiveMeantone.htm