Re: The I-IV-V7-I cadence in different tunings

Monz, I said the D:F is "broken" in the 5-limit JI scale whose lattice is
A E B
F C G D
because it's a whole syntonic comma (21.5 c) short of being a 5:6. It's a
"wolf minor third". It certainly can't form an acceptable D:F:A triad.

Because of this, I think it would be stretching things a bit to call this a
diatonic scale. But I guess there is a lot of diatonic music with no ii chord.

You wrote 4:5:6|27:32 for the V7 in this scale. It can also be written
meaningfully as 9[4:5:6]:16. 4:5:6|5:6 is also 5[4:5:6]:9 or redundantly
5[4:5:6|5:6]9.

Which reminds me. Some folk (not Monz) have been writing the 5-limit just
minor triad as 1/(4:5:6). This violates the convention that pitches
increase from left to right. It should of course be 1/(6:5:4) since this is
shorthand for 1/6 : 1/5 : 1/4.

Monz, thanks for correcting my adaptive tuning scheme with the 4:5:6:7. I
actually was under the misaprehension that the G had to shift _up_ in pitch
going from the G7 to the C chord. I guess that JdL's algorithm would
produce something like this (the corrected version). I repeat that I don't
think there's anything 'natural' about it, at least not in a diatonic context.

You might like to add the following example. It's adaptive JI using the 5:9
instead of the 4:7. Instead of a single syntonic comma shift between F and
G7 we've spread it over the 3 transitions. This is equivalent to having the
roots in 1/3-comma meantone with vertical JI. I expect 5[4:5:6|5:6]9 would
be a lot easier to sing a cappella than 9[4:5:6|27:32]16 (because all but
one of its 6 intervals can "lock in" and the 6th one is far enough away
from anything simple that it will have no "pull" in any particular
direction), and I expect it will sound more natural in a diatonic context
than 4:5:6:7. Maybe this is the one that can satisfy both Dave and Jerry?

F 4/3 27/20
E 5/4 5/4
D 9/8
C 1/1 1/1 1/1
B 15/8
A 5/3
G 3/2 3/2 3/2

all all
+7.2c -7.2c

It would have been nice to give Jerry just this one and the adaptive
4:5:6:7 "barbershop" one in a blind test to see which he preferred, and
which he thought his singers were (or should be) closest to.

Thanks again Monz.

Regards,

-- Dave Keenan
http://dkeenan.com

[David C Keenan:]
>Some folk (not Monz) have been writing the 5-limit just minor triad
as 1/(4:5:6). This violates the convention that pitches increase from
left to right. It should of course be 1/(6:5:4) since this is
shorthand for 1/6 : 1/5 : 1/4.

Hmm, I used to intuitively write these frontward and backwards, i.e.,
a 4:5:6 as a 6:5:4, etc., and now in an attempt at improving their
meaning by taking up others thoughtful suggestions, I'm writing them
both incorrectly *and* counter-intuitively! Anyway, thanks for
pointing this out Dave.

Dan

Pity Monz had to go before implementing the adaptive JI version of the 5:9.

F 4/3 27/20
E 5/4 5/4
D 9/8
C 1/1 1/1 1/1
B 15/8
A 5/3
G 3/2 3/2 3/2
all all
+7.2c -7.2c

Can anyone else do it? Maybe edit his existing 5:9 one with the ugly
"lumped" comma.

I'll be unsubscribed when you read this. You'll have to email me if you
want me to read something.

Regards,

-- Dave Keenan
http://dkeenan.com