New retunings of Galticeran

I was trying to figure out what was going on in my 22-equal retuned version
of Galticeran -- it wasn't any kind of comma pump that I've seen before,
but it clearly seemed to have problems lining up. The equivalent spot in
the 15-equal version didn't have the same problem, so I got the idea that
it must have something to do with the cycle of major thirds, taking
advantage of the vanishing 128/125 of 12-equal and 15-equal. It turns out
that there aren't any of the usual comma pumps that rely on the 81/80
anywhere, which is why the rest of the 22-equal version seems to work fine.

The problem, it turns out, is that there's a chord in the sequence that I
was interpreting as an Eb major in the treble and a G major in the bass.
The sequence is G# minor / "Eb major + G major" / E minor. The G# minor
chord shares a B with the G major chord and a D# with the Eb major chord.
Both the Eb major and G major chords also have a G in common. This only
works because of the equivalence between D# and Eb.

So I had to reinterpret the harmony to get it to fit 22-equal more
naturally. It turns out that the main seven-note scale used in Galticeran,
B D Eb F Gb A Bb (with various transpositions), only has this one
enharmonic equivalent!

D# A#=Bb (Is there a name for this scale as a subset of 12-TET?)
B F#
D A
A#=Bb F

This suggested the possibility of trying other tunings that divide the
octave into three equal parts. I tried 21- and 27-equal, and they fit like
a glove. So now I've got two new versions (and one slightly altered old
one) on my web page as MIDI files.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
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stuff about what happens when the music wants 5/4=cuberoot(2) and
the best 5/4 doesn't do it in the tuning snipped. I'm looking
forward to attempting Giant Steps in 31tet when I get the guitar.

> So I had to reinterpret the harmony to get it to fit 22-equal more
> naturally. It turns out that the main seven-note scale used in Galticeran,
> B D Eb F Gb A Bb (with various transpositions), only has this one
> enharmonic equivalent!
>
> D# A#=Bb (Is there a name for this scale as a subset of 12-TET?)
> B F#
> D A
> A#=Bb F
>
A#
Jazz polychordal folk would notate the implied chord as ----
B
and other jazzers would call it a maj7#9#11#13.

In neither case would real musicians know what they were talking about,
so you'd verbally explain, "make a scale from a Bmaj7 with a Bb triad
on top of it" (since A# would get funny looks). When that fails, you'd
say, "just alternate major and minor thirds, now stick it in one octave,
1 #9 3 #11 5 #13 and 7. Okay, 1 b3 3 b5 5 b7 7 if you'd like".

Its a great sound and has no 'standard' name to my knowledge, unless
it got one in Slonimskys Thesaurus, although if it shows up there its
probably in the back of the book a a chord.

I went to your site for the first time last night and bookmarked it,
there is some good listenning there and I'll check this one out.

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

/tuning/topicId_24329.html#24343

> In neither case would real musicians know what they were talking
about, so you'd verbally explain, "make a scale from a Bmaj7 with a
Bb triad on top of it" (since A# would get funny looks). When that
fails, you'd say, "just alternate major and minor thirds, now stick
it in one octave, 1 #9 3 #11 5 #13 and 7. Okay, 1 b3 3 b5 5 b7 7 if
you'd like".
>
> Its a great sound and has no 'standard' name to my knowledge, unless
> it got one in Slonimskys Thesaurus, although if it shows up there
its probably in the back of the book a a chord.
>

Of course, a similar procedure with an Eb-7th chord and a
simultaneous E major chord underneith is the famous "Sacre du
Printemps" chord, correct??

_________ ________ ________
Joseph Pehrson

Herman Miller wrote:
> D# A#=Bb (Is there a name for this scale as a subset of 12-TET?)
> B F#
> D A
>A#=Bb F

There are several names for 1 3 1 2 1 3 1, Major Gipsy is one, see
http://www.xs4all.nl/~huygensf/doc/modename.html.

Manuel