Full thread (9 messages)
From: Gene Ward Smith (2006-10-19)
Subject: Kirkwood gaps scale
How about Kirkwood gaps as a scale construction idea?
http://en.wikipedia.org/wiki/Kirkwood_gap
This would give [5/3, 2, 7/3, 5/2, 8/3, 3, 7/2, 4, 9/2]/ Reduced to
an octave, that becomes:
! kirkwood.scl
Scale based on Kirkwood gaps of the asteroid belt
8
!
9/8
7/6
5/4
4/3
3/2
5/3
7/4
2
All the intervals are superparticular, and the scale is fairly nicely
structured. The scale is the union of two otonal pentads a fifth
apart, and so various other chords are present, of course.
Harmonizing the music of the (lesser) spheres would be very
straightforward.
From: Robin Perry (2006-10-20)
Subject: Re: Kirkwood gaps scale
That's quite amazing!...
The music of the spheroids. Thanks for that.
--- In [email protected], "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> How about Kirkwood gaps as a scale construction idea?
>
> http://en.wikipedia.org/wiki/Kirkwood_gap
>
> This would give [5/3, 2, 7/3, 5/2, 8/3, 3, 7/2, 4, 9/2]/ Reduced
to
> an octave, that becomes:
>
> ! kirkwood.scl
> Scale based on Kirkwood gaps of the asteroid belt
> 8
> !
> 9/8
> 7/6
> 5/4
> 4/3
> 3/2
> 5/3
> 7/4
> 2
>
> All the intervals are superparticular, and the scale is fairly
nicely
> structured. The scale is the union of two otonal pentads a fifth
> apart, and so various other chords are present, of course.
> Harmonizing the music of the (lesser) spheres would be very
> straightforward.
>
From: Robert walker (2006-10-20)
Subject: Re: Kirkwood gaps scale
Welcome to the Alternate Tunings Mailing List.Hi Gene,
Nice scale :-), and I like the astronomical connection.
Just did one of my short fun pieces in it. Hope you enjoy it.
http://www.tunesmithy.netfirms.com/tunes/tunes.htm#kirkwood_gaps
Robert
From: Gene Ward Smith (2006-10-20)
Subject: Re: Kirkwood gaps scale
--- In [email protected], "Robert walker" <robertwalker@...> wrote:
>
> Welcome to the Alternate Tunings Mailing List.Hi Gene,
>
> Nice scale :-), and I like the astronomical connection.
>
> Just did one of my short fun pieces in it. Hope you enjoy it.
>
> http://www.tunesmithy.netfirms.com/tunes/tunes.htm#kirkwood_gaps
Lovely little thing, thank you. I wonder what tuning George thinks it
sounds melodically best in?
From: Robert walker (2006-10-23)
Subject: re: Kirkwood gaps scale
Welcome to the Alternate Tunings Mailing List.
Thanks again for the scale. I think you often make interesting scales :-).
I'd say your tuning is a lyrical one , at least I found it so. I wonder if one can maybe say that certain scales are on islands of lyricism, by analogy with the islands of stability in the periodic table, then one can ask if they are on the same island or the same archipelago, though I don't know how one would answer. I noticed yours has a third tone sized semitone though don't know if there are any other resemblances to 17-et.
It is interesting that a fair number of people independently can come up with a feeling that a tuning is particularly lyrical. I came to that conclusion myself about 17-et as a result of trying it out a few years ago independently of what anyone else has said, and it seems that others have found it so too, if not necessarily everyone.
One idea I have is that sometimes if a piece is composed in one tuning and then played in a quite different tuning, perhaps sometimes something of the flavour of the one can carry through into the other, just because the original piece was written for that particular tuning, so I suppose the composer makes particular choices based on the tuning that it originated in, different perhaps from the ones one might make in the tuning it is played in finally.
I had a go at retuning it to 17-et - a similarly sized semitone though not otherwise very close, anyway, this is the mode I used, closest to your scale:
0 3 4 6 7 10 13 14 17
and here is the result:
http://www.tunesmithy.netfirms.com/tunes/kirkwood_gaps_nearest_17-et.mid
Compare:
http://www.tunesmithy.netfirms.com/tunes/kirkwood_gaps.mid
Thanks,
Robert
From: Gene Ward Smith (2006-10-23)
Subject: Re: Kirkwood gaps scale
--- In [email protected], "Robert walker" <robertwalker@...> wrote:
> I had a go at retuning it to 17-et - a similarly sized semitone
though not otherwise very close, anyway, this is the mode I used,
closest to your scale:
> 0 3 4 6 7 10 13 14 17
> and here is the result:
Here are retunings to 31, 34 (the sharp 7 version), 46, 68, and 99,
as well as the JI original. I'm fond of the extra shimmer 99 adds on,
though it generally sounds a lot like the JI version. Anyway, people
can compare to 31 and see if sharp fifths are really melodically
better as George claims.
http://bahamas.eshockhost.com/~xenharmo/midi/examples/kirkwood/
From: Robert walker (2006-10-24)
Subject: Re: Kirkwood gaps scale
HI Gene,
Thanks for the retunings. I liked the 99 too.
Surely the point in the paper is that 17-et is a special tuning with its own characteristics. Part of the appeal, apart from the lyricism, is the way that ones expectations are somewhat turned on their heads, so that the major third is no longer an important consonance, and that possibly even depending how one composed, the fifth even needn't be so much the most important structuring element as it is in some other tunings - because since it is a prime number, any of the intervals will make a complete cycle, and the fifth is no longer necessarily the only one to use.
I get the impression there are several strands to microtonal interest, and one starts with common practice music and one is looking for tunings to explore the same kinds of chords and progressions, but better tuned than in 12-et or else to bring out particular characteristics - or maybe one has things like using septimal intervals, but still basically the same kind of harmonic ethos in a way. Or the other approach is that one is interested in tunings that turn ones expectations on their head so that one needs to start with a new framework, or start from scratch, which some find enjoyable (and others maybe aren't trained enough in the common practice music to have such a big transition to make anyway).
So - for instance if one wanted everything turned on its head one might be interested in 7-et maybe, or 11-et 13-et, or some such, or the hexanies and eikosanies, or various other tunings discussed here that just won't cut the ice at all with common practice music.
Or one might want to explore 31-et or 53-et or just intonation twelve tone scales and lattices and comma shifts if one is very into nicely tuned common practice music.
If one is into medieval music then that's Margo's line where you follow all sorts of tunings in a medieval style where the fifth is still important as a consonance but the third needn't be particularly. Then there are other possibliities as well, e.g. gamelan where it isn't so much really normal conventional harmony that one is aiming for in a way.
17-et then is one that is sort of a bit familiar and can do 12-t type music not too badly, enough so that it seems familiar but not very good at it perhaps except that it may feel surprisingly lyrical. If one follows through, it may be that it brings out a different style altogether, coming to relish the somewhat discordant thirds no longer as a consonance but as something else, another kind of element in the music. Then George's paper suggests there may be other more exotic ways of exploring it as well using other intervals instead of the fifth to structure ones music.
So given that background, one wouldn't really expect it to show up very well with transcriptions of common practice music. Well my little piece though isn't that either, as it is likely to be a bit unorthodox as it was written to a particular j.i. scale, just using the harmonic resources in that scale. So anyway all you can really find out is whether my somewhat unorthodox little piece in a particular ji.i. scale hybridises well with various ets apart from the ones it was originally written for.
So anyway, quite fun, and I'm interested enough to hear how it turns up. However, I don't think one can conclude much about the melodic virtues or otherwise e.g. of sharp fifths or small semitones in a more general way.
Sometime it woudl be nice to settle down and do some composing in 17-et for instance. Most of my pieces have been very short first impression type pieces of various tunings, and that also is nice to do, like ones first impressions of a place or person, quick sketch, could be interesting to look back on later, and it also often has a kind of freshness to it which is appealing. So I think it is a valid and nice thing to do to kind of dash off a little piece in a tuning that you haven't really explored that much. Just so long as it isn't taken as the outcome of long considered exploration and if one doesn't take it too seriously or try to generalise about what one found out in ones little test piece :-).
So anyway, yes I think 17-et is a very lyrical tuning (amongst others) and some time it would be nice to really explore it and try and bring out what I feel seems to come across when improvising in it. But I don't think there is any shortcut to doing that and particularly with this tuning, retuning a piece written in another tuning gives a hybrid which can be interesting in its own right, but doesn't really tell one that much about 17-et as such, rather just about what happens when you hybridise it with this other particular tuning and also perhaps only really about what happens with a particualr piece, in short I'm not sure one can generalise very much.
Thanks,
Thanks,
Robert
From: Gene Ward Smith (2006-10-24)
Subject: Re: Kirkwood gaps scale
--- In [email protected], "Robert walker" <robertwalker@...>
wrote:
> I get the impression there are several strands to microtonal
interest, and one starts with common practice music and one is
looking for tunings to explore the same kinds of chords and
progressions, but better tuned than in 12-et or else to bring out
particular characteristics - or maybe one has things like using
septimal intervals, but still basically the same kind of harmonic
ethos in a way.
I'd say my approach starts from the 7-limit, which I take as basic,
but taking the 5-limit as basic makes a lot of sense also. In fact,
things like marvel tempering allow you to start from five and layer
seven on top. That's not the same as starting from common practice,
but if you can't produce a decent major triad I'd hope at least you
can do no-threes or no-fives triads. George and Margo seem to start
from the 3-limit as basic, so no-fives seems to work pretty well for
them.
> Or the other approach is that one is interested in tunings that
turn ones expectations on their head so that one needs to start with
a new framework, or start from scratch, which some find enjoyable
(and others maybe aren't trained enough in the common practice music
to have such a big transition to make anyway).
But I prefer it when the result is not painful to listen to. Your
version of Kirkwood Gaps would be an example of that, but often it
seems to me the assumption is that any old collection of notes will
do, and that's what I want to get away from.
> So - for instance if one wanted everything turned on its head one
might be interested in 7-et maybe, or 11-et 13-et, or some such, or
the hexanies and eikosanies, or various other tunings discussed here
that just won't cut the ice at all with common practice music.
From my point of view these are very different things. Hexanies and
eikosanies are JI, and 11 explores a system of subgroup-type harmony,
in effect, I think. 7 strikes me as a boring alternative to the
diatonic scale, and 13 is weird.
> Or one might want to explore 31-et or 53-et or just intonation
twelve tone scales and lattices and comma shifts if one is very into
nicely tuned common practice music.
53 is a schismatic system and not suitable for common practice music.
It would be great for medieval music, though.
> If one is into medieval music then that's Margo's line where you
follow all sorts of tunings in a medieval style where the fifth is
still important as a consonance but the third needn't be
particularly. Then there are other possibliities as well, e.g.
gamelan where it isn't so much really normal conventional harmony
that one is aiming for in a way.
Gamelan is indeed a completely different concept.
> So anyway, quite fun, and I'm interested enough to hear how it
turns up. However, I don't think one can conclude much about the
melodic virtues or otherwise e.g. of sharp fifths or small semitones
in a more general way.
What would be a good set of JI pieces to draw melidic conclusions
from?
> So anyway, yes I think 17-et is a very lyrical tuning (amongst
others) and some time it would be nice to really explore it and try
and bring out what I feel seems to come across when improvising in it.
Is it lyrical in a sense 19, say, isn't? They don't sound the same,
certainly.
From: George D. Secor (2006-10-24)
Subject: Re: Kirkwood gaps scale
--- In [email protected], "Gene Ward Smith" <genewardsmith@...>
wrote:
>
> --- In [email protected], "Robert walker" <robertwalker@>
wrote:
>
> > I had a go at retuning it to 17-et - a similarly sized semitone
> though not otherwise very close, anyway, this is the mode I used,
> closest to your scale:
> > 0 3 4 6 7 10 13 14 17
> > and here is the result:
>
> Here are retunings to 31, 34 (the sharp 7 version), 46, 68, and 99,
> as well as the JI original. I'm fond of the extra shimmer 99 adds
on,
> though it generally sounds a lot like the JI version. Anyway, people
> can compare to 31 and see if sharp fifths are really melodically
> better as George claims.
>
> http://bahamas.eshockhost.com/~xenharmo/midi/examples/kirkwood/
Hi Gene & Robert,
I got a chance to listen to the Kirkwood gaps (original & all of the
retunings) last night (several times) to decide if I had any
preferences. I observed that 34 is the only tuning that has both a
good 5/4 and 5/3 and also has the Archytas comma tempered out in the
upward jump of the fifth between 7/4 and 4/3 (at 0:27-0:28). But I
can't say that it's clearly my favorite for that reason, because I
also liked 46 and 68 better than the others.
In the paper, I didn't mean to give the impression that wide fifths
are necessarily better melodically under all circumstances -- I was
writing specifically about a diatonic scale, where wide fifths result
in significantly narrower-than-12ET diatonic semitones. Several
times in the paper (pp. 59, 74, 75), I made statements to the effect
that chromatic semitones in 31-ET could be used to enhance the
melodic effect of that (narrow-fifth) tuning, so the size of the
fifths is, under more general circumstances, beside the point.
If your tuning has dozens of tones/octave, you then have
opportunities to alter the mood on the fly by making subtle
substitutions in your scale subset, so it's not wise to draw
conclusions too quickly about one of these tunings vs. another.
--George