The simplest comma pump ever

...Might be something like C9 -> F6.

How in the heck do you guys deal with such occurances? To have the D
in the C9 be a comma sharp of the D in the F6 sounds absolutely
terrible to me, and to have the D be 27/16 in the F6 chord instead of
5/3 also sounds terrible. Is there some generally accepted solution
for this type of thing?

I should probably get this sorted out before I even hope to tackle any
sort of 11-limit comma pumps in Debussy.

-Mike

Well, 12:15:18:20 is obviously the best major sixth chord, but 16:20:24:27 is acceptable despite the wolf fourth, so I'd probably use 1/1 5/4 3/2 16/9 9/4 > 4/3 5/3 2/1 9/4. (I tried 1/1 5/4 3/2 16/9 20/9 for C9, i.e. 36:45:54:64:80, and it just rubbed me the wrong way.)

~D.

----- Original Message ----- From: "Mike Battaglia" <battaglia01@...>
To: <tuning@yahoogroups.com>
Sent: Thursday, 15 October, 2009 00:47
Subject: [tuning] The simplest comma pump ever

> ...Might be something like C9 -> F6.
>
> How in the heck do you guys deal with such occurances? To have the D
> in the C9 be a comma sharp of the D in the F6 sounds absolutely
> terrible to me, and to have the D be 27/16 in the F6 chord instead of
> 5/3 also sounds terrible. Is there some generally accepted solution
> for this type of thing?
>
> I should probably get this sorted out before I even hope to tackle any
> sort of 11-limit comma pumps in Debussy.
>
> -Mike
>
>
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Eh, I just checked the tuning-math outline, and I suppose this
wouldn't be called a "comma pump," but rather a "pun." Either way, it
sounds horrible.

-Mike

On Thu, Oct 15, 2009 at 1:47 AM, Mike Battaglia <battaglia01@...> wrote:
> ...Might be something like C9 -> F6.
>
> How in the heck do you guys deal with such occurances? To have the D
> in the C9 be a comma sharp of the D in the F6 sounds absolutely
> terrible to me, and to have the D be 27/16 in the F6 chord instead of
> 5/3 also sounds terrible. Is there some generally accepted solution
> for this type of thing?
>
> I should probably get this sorted out before I even hope to tackle any
> sort of 11-limit comma pumps in Debussy.
>
> -Mike
>

What precedes and follows these two chords? The voicings? Any tied tones? I can hardly imagine you're using block voicings, and absolute identity of inversion is 12-tET thinking... not to mention function
without context isn't exactly function, is it.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> ...Might be something like C9 -> F6.
>
> How in the heck do you guys deal with such occurances? To have the D
> in the C9 be a comma sharp of the D in the F6 sounds absolutely
> terrible to me, and to have the D be 27/16 in the F6 chord instead of
> 5/3 also sounds terrible. Is there some generally accepted solution
> for this type of thing?
>
> I should probably get this sorted out before I even hope to tackle any
> sort of 11-limit comma pumps in Debussy.
>
> -Mike
>

Mike wrote:

> ...Might be something like C9 -> F6.
>
> How in the heck do you guys deal with such occurances? To have
> the D in the C9 be a comma sharp of the D in the F6 sounds
> absolutely terrible to me, and to have the D be 27/16 in the
> F6 chord instead of 5/3 also sounds terrible. Is there some
> generally accepted solution for this type of thing?

You can root the F chord a comma sharp, since there's only
one common tone between the chords.

The standard solution is use meantone temperament. 1/4-comma
probably wouldn't be the ideal tuning, since its 9ths have
high error (1/2-comma). Something closer to 1/6-comma maybe.
But no meantone is going to be fantastic for 9th chords.

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Eh, I just checked the tuning-math outline, and I suppose this
> wouldn't be called a "comma pump," but rather a "pun."
> Either way, it sounds horrible.
>
> -Mike

Technically it's not a pun unless the two 9s are the same pitch,
which is why puns are usually considered a good thing. You might
call the situation a "comma problem".

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> ...Might be something like C9 -> F6.
>
> How in the heck do you guys deal with such occurances? To have the D
> in the C9 be a comma sharp of the D in the F6 sounds absolutely
> terrible to me, and to have the D be 27/16 in the F6 chord instead of
> 5/3 also sounds terrible. Is there some generally accepted solution
> for this type of thing?
> ...
> -Mike

One solution is to use some sort of adaptive JI. I would suggest lowering the D by 1/3 comma for the 2nd chord. If you make F:D an exact 3:5 in the 2nd chord, then the C will rise in pitch by 2/3 comma from the 1st to the 2nd chord.

Another solution is to allow a small amount of tempering, such as found in 72-equal, in which the pitch difference of the D shrinks to 16.7 cents. You can then split the difference by having the D shift downward and the C upward by half of that amount (in which case you're actually using 144-equal).

--George

cameron said:
> What precedes and follows these two chords? The voicings? Any tied tones? I can hardly imagine you're using block voicings, and absolute identity of inversion is 12-tET thinking... not to mention function
> without context isn't exactly function, is it.

This situation came up a number of times in my trying to regress
Reverie to 72-tet. Chords like Gm7, C9, Fmaj6 would pop up all the
time, which basically turned the piece into a comma nightmare. I dealt
with the Gm7 by making the Bb in the C9 chord 16/9, and then the "7"
of the Gm7 chord a fifth on top of that (so the F root), effectively
making the Gm7 into the Pythagorean version of the chord (which sounds
fine). But the C9 to Fmaj6 then ruins that.

The progressions that give me the most trouble are ones like F -> Dm9
-> Gm -> C9 -> F -> Am -> Dm -> Gm7 -> C7 -> F7.

Carl said:
> You can root the F chord a comma sharp, since there's only
> one common tone between the chords.

Er, the C and the D...?

> The standard solution is use meantone temperament. 1/4-comma
> probably wouldn't be the ideal tuning, since its 9ths have
> high error (1/2-comma). Something closer to 1/6-comma maybe.
> But no meantone is going to be fantastic for 9th chords.

gdsecor said:
> One solution is to use some sort of adaptive JI. I would suggest lowering the D by 1/3 comma for the 2nd chord. If you make F:D an exact 3:5 in the 2nd chord, then the C will rise in pitch by 2/3 comma from the 1st to the 2nd chord.
> Another solution is to allow a small amount of tempering, such as found in 72-equal, in which the pitch difference of the D shrinks to 16.7 cents. You can then split the difference by having the D shift downward and the C upward by half of that amount (in which case you're actually using 144-equal).

I was hoping to do the whole thing in 72-equal, but maybe 144-equal
really is what I want. This is a shame, because it means that 72-equal
isn't quite as useful as I thought it was going to be, if it can't
handle this sort of thing.

Thanks to all for the advice,
Mike

Hi Mike,

How in the heck do you guys deal with such occurances? To have the D
> in the C9 be a comma sharp of the D in the F6 sounds absolutely
> terrible to me, and to have the D be 27/16 in the F6 chord instead of
> 5/3 also sounds terrible. Is there some generally accepted solution
> for this type of thing?
>
> I should probably get this sorted out before I even hope to tackle any
> sort of 11-limit comma pumps in Debussy.
>

Yes I agree a comma shift is unacceptable.
And if the 27/16 in the F6 chord is not acceptable either then the solution
is probably:
1/1 5/4 3/2 20/9
4/3 5/3 20/9
With the key beeing F major.
If the key for that part is C major then it should be with 9/4 instead of
the 20/9.
It can even be as Carl pointed out 1/1 5/4 3/2 9/4 -> 27/20 27/16 9/4
Depends on the music.

Marcel

It would be very interesting to hear Debussy in Just Intonation of some
sort.

I for one will be looking forward to it.

On Thu, Oct 15, 2009 at 9:58 AM, Marcel de Velde <m.develde@...>wrote:

>
>
> Hi Mike,
>
> How in the heck do you guys deal with such occurances? To have the D
>> in the C9 be a comma sharp of the D in the F6 sounds absolutely
>> terrible to me, and to have the D be 27/16 in the F6 chord instead of
>> 5/3 also sounds terrible. Is there some generally accepted solution
>> for this type of thing?
>>
>> I should probably get this sorted out before I even hope to tackle any
>> sort of 11-limit comma pumps in Debussy.
>
>
> Yes I agree a comma shift is unacceptable.
> And if the 27/16 in the F6 chord is not acceptable either then the solution
> is probably:
> 1/1 5/4 3/2 20/9
> 4/3 5/3 20/9
> With the key beeing F major.
> If the key for that part is C major then it should be with 9/4 instead of
> the 20/9.
> It can even be as Carl pointed out 1/1 5/4 3/2 9/4 -> 27/20 27/16 9/4
> Depends on the music.
>
> Marcel
>
>

There are two 5-limit possibilities then. Since we want the high D in both octaves to be the same, and we'll call its ratio x:

I9 = {1/1 5/4 3/2 16/9 x}:
if x = 20/9, then C9 = {36:45:54:64:80}
if x = 9/4, then C9 = {36:45:54:64:81}

I9 would sound just as smooth either way.

IV6 = {4/3 5/3 2/1 x}:
if x = 20/9, then F6 = {12:15:18:20}
if x = 9/4, then F6 = {16:20:24:27}

Both versions of I9 and IV6 together form {36:45:48:54:60:64:72:80} and {36:45:48:54:60:64:72:81} respectively.

Earlier, I suggested 9/4, but turns out that 20/9 would sound somewhat better if F6 is the final chord in a progression. 9/4 should be used if F6 is followed by a chord that uses 9/4, and you won't have to have that comma slide.

~D.

----- Original Message ----- From: Marcel de Velde
To: tuning@yahoogroups.com
Sent: Thursday, 15 October, 2009 08:58
Subject: Re: [tuning] The simplest comma pump ever

Hi Mike,

How in the heck do you guys deal with such occurances? To have the D
in the C9 be a comma sharp of the D in the F6 sounds absolutely
terrible to me, and to have the D be 27/16 in the F6 chord instead of
5/3 also sounds terrible. Is there some generally accepted solution
for this type of thing?

I should probably get this sorted out before I even hope to tackle any
sort of 11-limit comma pumps in Debussy.

Yes I agree a comma shift is unacceptable.
And if the 27/16 in the F6 chord is not acceptable either then the solution is probably:
1/1 5/4 3/2 20/9
4/3 5/3 20/9
With the key beeing F major.
If the key for that part is C major then it should be with 9/4 instead of the 20/9.
It can even be as Carl pointed out 1/1 5/4 3/2 9/4 -> 27/20 27/16 9/4
Depends on the music.

>
> There are two 5-limit possibilities then.
>

There are 3. The third one in my mail, the one Carl first mentioned is also
5-limit.

First one (most likely it seems to me without having seen the musical
context)
In major mode:
3/2 15/8 9/4 10/3 (dominant ninth chord, 8/3 can be played too)
1/1 2/1 5/2 10/3 (tonic sixth)

Second one
In major mode:
1/1 5/4 3/2 9/4 (tonic ninth chord, can be played with 15/8)
2/3 4/3 5/3 9/4 (subdominant sixth chord)

Third one
4/3 5/3 2/1 3/1 (subdominant ninth chord, can play 5/2 too)
9/10 9/5 9/4 3/1 (I don't know how to call it sixth chord, certainately left
major mode here)

Since we want the high D in
> both octaves to be the same, and we'll call its ratio x:
>
> I9 = {1/1 5/4 3/2 16/9 x}:
> if x = 20/9, then C9 = {36:45:54:64:80}
> if x = 9/4, then C9 = {36:45:54:64:81}
>
> I9 would sound just as smooth either way.
>
> IV6 = {4/3 5/3 2/1 x}:
> if x = 20/9, then F6 = {12:15:18:20}
> if x = 9/4, then F6 = {16:20:24:27}
>
> Both versions of I9 and IV6 together form {36:45:48:54:60:64:72:80} and
> {36:45:48:54:60:64:72:81} respectively.
>
> Earlier, I suggested 9/4, but turns out that 20/9 would sound somewhat
> better if F6 is the final chord in a progression. 9/4 should be used if
> F6 is followed by a chord that uses 9/4, and you won't have to have that
> comma slide.
>

I've found that best works to look at the key of the particular section.
Could be a large part is in thesame key, could be rapid modulations and only
a short part is in thesame key. Known progressions to indicate key help
decide which key it is, as well as your ear. It's often chords resolving to
a certain chord (often major) that indicates the key.
I've found it doesn't work well for JI to look at simple diatonic major
minor scales.
Instead I use a full 12tone JI scale of 1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2
8/5 5/3 9/5 15/8 2/1 and decide the key from this.
For instance D F A -> A C# E I find to be in C# key, making 1/1 4/3 8/5 ->
1/1 5/4 3/2, beeing a mode other than major or minor.
Hope this helps.
Will comming time post several pieces put in JI in this way.

Marcel