Yahoo Tuning Groups Ultimate Backup tuning More Newbie Q re: modulation, progressions

Paul H. Erlich wrote:
>>(i) play E major so it has 1 5/4 3/2 ratios, then Ab is played as 25/16 =
>>1.56 of C instead of the "original" ratio of 8/5 = 1.6 of C
>
>That's good but the third of E major is G#, not Ab. G# is usually considered
>to be 25/16 relative to C in JI anyway.

I'm looking for an algorithmic approach that is easy to implement and play
on my keyboard with foot pedals. This is the reason I've phrased things the
way I have. For example, the above scenario would be played by me
specifying with the foot pedals where the "root" or "tonic" is going to be
by pressing the E pedal key a bit before changing to the Emaj chord on the
keyboard. Then the Emaj would be played with 1 5/4 3/2 ratios, so
distinguishing between G# and Ab is done by the "root" selection. I would
just be thinking of it as a "JI major triad on E". This seems much simpler
to me to play than coming up with a way to specify whether the black key I'm
hitting should be a sharp or flat in the present circumstance.

I was also intending to keep the pedal pressed keys in a FIFO stack - so my
sequencer would know I just came from C, so if I played foot pedal C it
would take me back to the C pitch of the C I came from rather than to the
new C pitch based on the scale starting at E. I haven't worked out the
mechanics for specifiying whether I want to step back further in the stack
if I foot pedal a key which occured further back in the progression, but
probably a foot pedal switch which says "look back".

Thus I'm not as interested in finely divided fixed scales as I am in a
simple scale with algorithm approach that in practice would play more finely
divided fixed scales if looked at from that point of view. Or in other
words a set of 12 tone scales combined with algorithms rather than a fixed
scale. I say set of 12 tone scales because it is easy to switch the mapping
in the sequencer on the fly. (I hope this isn't too muddled an explanation.)

>>I find that Ab F C Eb (descend from Ab, rise to Eb) depends quite a bit on
>>the minor third intervals. Played high on the keyboard, it sounds awful to
>>me in 12Tet, and takes on a different feel depending on the minor third
>>intervals played.
>
>So you like the melody better when the minor third intervals are tuned as
>_________?

6/5 sounds way better to me than 300 cents, maybe even sharper than 6/5,
especially for the Eb.

John Link wrote:
>A very important example is the movement from IImin7 to V7 to Imaj7. For
>concreteness, let's consider the key of C, so we're talking about D-7 going
>to G7 going to Cmaj7. Here's a lattice diagram of the tones related by 5/4
>(up and to the left) or 3/2 (up and to the right):
>
>
> B D
>
> E G
>
> A C
>
> D F
>
>
>I won't waste my time trying to draw the usual lines. Since we're in C we
>have C=1/1. Here is my conjecture of what good a cappella singers do:
>
> C 1/1 B 15/16 B 15/16
> A 5/8 G 3/2 G 3/2
> F 4/3 F 21/16 E 5/4
> D 10/9 D 9/8 C 1/1
>
>Going from D-7 to G7 note that BOTH common notes adjust. Also note that
>while the two different D's are both in the lattice diagram, the second F
>is not, because relative to G it is 7/4, and I drew the lattice only for
>5/4 and 3/2.

I presume you use a 7/4 ratio for the G7 minor7th because it's the 7th
harmonic of G, no? And it's this choice that requires the adjustment of
pitch of F.

Anyways, here's some possibilities to translate into the foot pedal sheme above.

Ignoring how I get the pitch of D to start from, I would play FP D, Dmin7,
FP C, G7, Cmaj7. I believe this would then give me exactly the chord
intervals you have written above, except the 7th interval in the G7 would be
16/9 instead of 7/4.

ie: Dmin7 1, 6/5, 3/2, 9/5
G7 1, 5/4, 3/2, 16/9 (instead of 7/4)
Cmaj7 1, 5/4, 3/2, 15/8

If I had started in C by playing FP C before the FP D, then all the pitches
of the Dmin7 would be shifted up by a syntonic comma compared to your
example above, including the C, so if it was held from a previous tonic
chord or something, it would shift up at the beginning of the Dmin7. (Too
weird for words?) All the other pitches would be the same, except the F in
the G7 would be 4/3, so it would shift down from the F in the Dmin7.

If I also included scale switching, I could switch to a scale which used
10/9 for the major 2nd interval before playing FP D, then switch back to a
scale which uses 9/8 for this interval before playing FP C. This would give
me exactly the pitches you describe (except for the aforementioned G7 minor
7, although harder to play.

If, in addtion to the above scale switching, I also included a scale with
the minor 7th as 7/4 instead of 9/5, and switched to this scale and played
FP G before the G7, then switched back to the major 2nd = 9/8 scale and
played FP C before the Cmaj7, it would be exactly what you've given I think.
But now it's getting much more complicated to play, having to set a scale
and a root or tonic before each chord.

Comments?

Jim Savage

More Newbie Q re: modulation, progressions

🔗Jim Savage <waldpond@xxxxx.xxxx>

🔗johnlink@xxxx.xxxxxxxxxxxxxx)