Yahoo Tuning Groups Ultimate Backup tuning Scriabin's chord in JI

I'm following the discussion on the use of the golden ratio as an
interval (and I have used it rhythmically as a "lazy swing" beat). It
just so happens I'm writing something using the ratio, or rather an
approximation of 833 1/3 cents, or 25/36 octave. Right now I only have
an arpeggio of C Ab+ F- C# A+ F#- D (plus and minus indicate a pitch
shift of 33 1/3 cents).

Anyway, my question regards the "Mystic chord" of Alexander Scriabin,
commonly written as C F# Bb E A D, and a message from March 2003:

/tuning/topicId_43033.html#43033

Leonid Sabaneyev theorized that Scriabin was implying an overtone series
in the chord, the odd ones up to 13. The chord would then be voiced as
8:11:14:20:26:36. I came up with four interpretations of my own, two in
11-limit, two in 7-limit. The first, third and fourth use 27/8 instead
of 13/4, because I see the 13th harmonic as much more minor than major.
The last two treat the first four notes as an altered French sixth (i.e.
C F# A# E) and use more "orthodox" ratios equating to 26/53 or 35/72 of
an octave.

* 8:11:14:20:27:36
* 24:33:42:60:80:108 (replacing 27/8 with 10/3)
* 32:45:56:80:108:144 (if the tritone is 45/32)
* 40:56:70:100:135:180 (if the tritone is 7/5)

I still need to familiarize myself better with Prometheus though. Any
thoughts?

~D.

🔗caleb morgan <calebmrgn@...>

sorry for hasty post-and-run, back tomorrow!

none of these i'm posting seem like unproblematic choices.

fwiw, a prosaic 5-limit version:
8/9 5/4 8/5 9/8 3/2 1/1 in D?
problem: 5/4 to 8/5 ain't so wonderful (solution: play the whole chord, never expose only that interval?)

7-limit:
root on Ab?
5/4 7/4 9/8 8/5 16/15 64/45

5-limit:
root on Gb?
45/32 (too low!) 1/ 5/4 8/9 32/27 64/81

On Feb 4, 2009, at 5:41 PM, Danny Wier wrote:

> I'm following the discussion on the use of the golden ratio as an
> interval (and I have used it rhythmically as a "lazy swing" beat). It
> just so happens I'm writing something using the ratio, or rather an
> approximation of 833 1/3 cents, or 25/36 octave. Right now I only have
> an arpeggio of C Ab+ F- C# A+ F#- D (plus and minus indicate a pitch
> shift of 33 1/3 cents).
>
> Anyway, my question regards the "Mystic chord" of Alexander Scriabin,
> commonly written as C F# Bb E A D, and a message from March 2003:
>
> /tuning/topicId_43033.html#43033
>
> Leonid Sabaneyev theorized that Scriabin was implying an overtone > series
> in the chord, the odd ones up to 13. The chord would then be voiced as
> 8:11:14:20:26:36. I came up with four interpretations of my own, two > in
> 11-limit, two in 7-limit. The first, third and fourth use 27/8 instead
> of 13/4, because I see the 13th harmonic as much more minor than > major.
> The last two treat the first four notes as an altered French sixth > (i.e.
> C F# A# E) and use more "orthodox" ratios equating to 26/53 or 35/72 > of
> an octave.
>
> * 8:11:14:20:27:36
> * 24:33:42:60:80:108 (replacing 27/8 with 10/3)
> * 32:45:56:80:108:144 (if the tritone is 45/32)
> * 40:56:70:100:135:180 (if the tritone is 7/5)
>
> I still need to familiarize myself better with Prometheus though. Any
> thoughts?
>
> ~D.
>
>
>

🔗Marcel de Velde <m.develde@...>

You could see it as a 1/1 3/2 16/9 5/2 10/3 40/9 with a lowered 3/2 (for
instance 64/45)Lowered 3/2 may be 5 limit or 7 limit haven't checked in
numbers and can't play it right now since my little studio is a mess
rewiring things.

Marcel

On Thu, Feb 5, 2009 at 1:24 AM, caleb morgan <calebmrgn@...> wrote:

> sorry for hasty post-and-run, back tomorrow!
>
> none of these i'm posting seem like unproblematic choices.
>
>
> fwiw, a prosaic 5-limit version:
> 8/9 5/4 8/5 9/8 3/2 1/1 in D?
> problem: 5/4 to 8/5 ain't so wonderful (solution: play the whole chord,
> never expose only that interval?)
>
> 7-limit:
> root on Ab?
> 5/4 7/4 9/8 8/5 16/15 64/45
>
> 5-limit:
> root on Gb?
> 45/32 (too low!) 1/ 5/4 8/9 32/27 64/81
>
>
>
> On Feb 4, 2009, at 5:41 PM, Danny Wier wrote:
>
> I'm following the discussion on the use of the golden ratio as an
> interval (and I have used it rhythmically as a "lazy swing" beat). It
> just so happens I'm writing something using the ratio, or rather an
> approximation of 833 1/3 cents, or 25/36 octave. Right now I only have
> an arpeggio of C Ab+ F- C# A+ F#- D (plus and minus indicate a pitch
> shift of 33 1/3 cents).
>
> Anyway, my question regards the "Mystic chord" of Alexander Scriabin,
> commonly written as *C F# Bb E A D*, and a message from March 2003:
>
> /tuning/topicId_43033.html#43033
>
> Leonid Sabaneyev theorized that Scriabin was implying an overtone series
> in the chord, the odd ones up to 13. The chord would then be voiced as
> 8:11:14:20:26:36. I came up with four interpretations of my own, two in
> 11-limit, two in 7-limit. The first, third and fourth use 27/8 instead
> of 13/4, because I see the 13th harmonic as much more minor than major.
> The last two treat the first four notes as an altered French sixth (i.e.
> C F# A# E) and use more "orthodox" ratios equating to 26/53 or 35/72 of
> an octave.
>
> * 8:11:14:20:27:36
> * 24:33:42:60:80:108 (replacing 27/8 with 10/3)
> * 32:45:56:80:108:144 (if the tritone is 45/32)
> * 40:56:70:100:135:180 (if the tritone is 7/5)
>
> I still need to familiarize myself better with Prometheus though. Any
> thoughts?
>
> ~D.
>
>
>
>

🔗Marcel de Velde <m.develde@...>

Yeah, it's most likely 1/1 64/45 16/9 5/2 10/3 40/9 (though I can't hear it
right now)
But it could be many other things. Depends on the rest of the compostition
(which I haven't heard / seen).
Marcel

On Thu, Feb 5, 2009 at 3:11 AM, Marcel de Velde <m.develde@...> wrote:

> You could see it as a 1/1 3/2 16/9 5/2 10/3 40/9 with a lowered 3/2 (for
> instance 64/45)Lowered 3/2 may be 5 limit or 7 limit haven't checked in
> numbers and can't play it right now since my little studio is a mess
> rewiring things.
>
> Marcel
>
>
> On Thu, Feb 5, 2009 at 1:24 AM, caleb morgan <calebmrgn@...> wrote:
>
>> sorry for hasty post-and-run, back tomorrow!
>>
>> none of these i'm posting seem like unproblematic choices.
>>
>>
>> fwiw, a prosaic 5-limit version:
>> 8/9 5/4 8/5 9/8 3/2 1/1 in D?
>> problem: 5/4 to 8/5 ain't so wonderful (solution: play the whole chord,
>> never expose only that interval?)
>>
>> 7-limit:
>> root on Ab?
>> 5/4 7/4 9/8 8/5 16/15 64/45
>>
>> 5-limit:
>> root on Gb?
>> 45/32 (too low!) 1/ 5/4 8/9 32/27 64/81
>>
>>
>>
>> On Feb 4, 2009, at 5:41 PM, Danny Wier wrote:
>>
>> I'm following the discussion on the use of the golden ratio as an
>> interval (and I have used it rhythmically as a "lazy swing" beat). It
>> just so happens I'm writing something using the ratio, or rather an
>> approximation of 833 1/3 cents, or 25/36 octave. Right now I only have
>> an arpeggio of C Ab+ F- C# A+ F#- D (plus and minus indicate a pitch
>> shift of 33 1/3 cents).
>>
>> Anyway, my question regards the "Mystic chord" of Alexander Scriabin,
>> commonly written as *C F# Bb E A D*, and a message from March 2003:
>>
>> /tuning/topicId_43033.html#43033
>>
>> Leonid Sabaneyev theorized that Scriabin was implying an overtone series
>> in the chord, the odd ones up to 13. The chord would then be voiced as
>> 8:11:14:20:26:36. I came up with four interpretations of my own, two in
>> 11-limit, two in 7-limit. The first, third and fourth use 27/8 instead
>> of 13/4, because I see the 13th harmonic as much more minor than major.
>> The last two treat the first four notes as an altered French sixth (i.e.
>> C F# A# E) and use more "orthodox" ratios equating to 26/53 or 35/72 of
>> an octave.
>>
>> * 8:11:14:20:27:36
>> * 24:33:42:60:80:108 (replacing 27/8 with 10/3)
>> * 32:45:56:80:108:144 (if the tritone is 45/32)
>> * 40:56:70:100:135:180 (if the tritone is 7/5)
>>
>> I still need to familiarize myself better with Prometheus though. Any
>> thoughts?
>>
>> ~D.
>>
>>
>>
>>
>
>

🔗Marcel de Velde <m.develde@...>

Ah I'm sorry.Gave it a bit more thought and I really can''t say yet what it
should be.
It's exactly in the area which I'm still working on.
Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to me.

Marcel

On Thu, Feb 5, 2009 at 3:15 AM, Marcel de Velde <m.develde@...> wrote:

> Yeah, it's most likely 1/1 64/45 16/9 5/2 10/3 40/9 (though I can't hear it
> right now)
> But it could be many other things. Depends on the rest of the compostition
> (which I haven't heard / seen).
> Marcel
>
>
> On Thu, Feb 5, 2009 at 3:11 AM, Marcel de Velde <m.develde@...>wrote:
>
>> You could see it as a 1/1 3/2 16/9 5/2 10/3 40/9 with a lowered 3/2 (for
>> instance 64/45)Lowered 3/2 may be 5 limit or 7 limit haven't checked in
>> numbers and can't play it right now since my little studio is a mess
>> rewiring things.
>>
>> Marcel
>>
>>
>> On Thu, Feb 5, 2009 at 1:24 AM, caleb morgan <calebmrgn@...> wrote:
>>
>>> sorry for hasty post-and-run, back tomorrow!
>>>
>>> none of these i'm posting seem like unproblematic choices.
>>>
>>>
>>> fwiw, a prosaic 5-limit version:
>>> 8/9 5/4 8/5 9/8 3/2 1/1 in D?
>>> problem: 5/4 to 8/5 ain't so wonderful (solution: play the whole chord,
>>> never expose only that interval?)
>>>
>>> 7-limit:
>>> root on Ab?
>>> 5/4 7/4 9/8 8/5 16/15 64/45
>>>
>>> 5-limit:
>>> root on Gb?
>>> 45/32 (too low!) 1/ 5/4 8/9 32/27 64/81
>>>
>>>
>>>
>>> On Feb 4, 2009, at 5:41 PM, Danny Wier wrote:
>>>
>>> I'm following the discussion on the use of the golden ratio as an
>>> interval (and I have used it rhythmically as a "lazy swing" beat). It
>>> just so happens I'm writing something using the ratio, or rather an
>>> approximation of 833 1/3 cents, or 25/36 octave. Right now I only have
>>> an arpeggio of C Ab+ F- C# A+ F#- D (plus and minus indicate a pitch
>>> shift of 33 1/3 cents).
>>>
>>> Anyway, my question regards the "Mystic chord" of Alexander Scriabin,
>>> commonly written as *C F# Bb E A D*, and a message from March 2003:
>>>
>>> /tuning/topicId_43033.html#43033
>>>
>>> Leonid Sabaneyev theorized that Scriabin was implying an overtone series
>>> in the chord, the odd ones up to 13. The chord would then be voiced as
>>> 8:11:14:20:26:36. I came up with four interpretations of my own, two in
>>> 11-limit, two in 7-limit. The first, third and fourth use 27/8 instead
>>> of 13/4, because I see the 13th harmonic as much more minor than major.
>>> The last two treat the first four notes as an altered French sixth (i.e.
>>> C F# A# E) and use more "orthodox" ratios equating to 26/53 or 35/72 of
>>> an octave.
>>>
>>> * 8:11:14:20:27:36
>>> * 24:33:42:60:80:108 (replacing 27/8 with 10/3)
>>> * 32:45:56:80:108:144 (if the tritone is 45/32)
>>> * 40:56:70:100:135:180 (if the tritone is 7/5)
>>>
>>> I still need to familiarize myself better with Prometheus though. Any
>>> thoughts?
>>>
>>> ~D.
>>>
>>>
>>>
>>>
>>
>>
>

🔗Marcel de Velde <m.develde@...>

or more likely 1/1 10/7 25/14 5/2 10/3 40/9
Marcel

On Thu, Feb 5, 2009 at 4:09 AM, Marcel de Velde <m.develde@...> wrote:

> Ah I'm sorry.Gave it a bit more thought and I really can''t say yet what
> it should be.
> It's exactly in the area which I'm still working on.
> Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
> In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to me.
>
> Marcel
>
>
> On Thu, Feb 5, 2009 at 3:15 AM, Marcel de Velde <m.develde@...>wrote:
>
>> Yeah, it's most likely 1/1 64/45 16/9 5/2 10/3 40/9 (though I can't hear
>> it right now)
>> But it could be many other things. Depends on the rest of the compostition
>> (which I haven't heard / seen).
>> Marcel
>>
>>
>> On Thu, Feb 5, 2009 at 3:11 AM, Marcel de Velde <m.develde@...>wrote:
>>
>>> You could see it as a 1/1 3/2 16/9 5/2 10/3 40/9 with a lowered 3/2 (for
>>> instance 64/45)Lowered 3/2 may be 5 limit or 7 limit haven't checked in
>>> numbers and can't play it right now since my little studio is a mess
>>> rewiring things.
>>>
>>> Marcel
>>>
>>>
>>> On Thu, Feb 5, 2009 at 1:24 AM, caleb morgan <calebmrgn@...>wrote:
>>>
>>>> sorry for hasty post-and-run, back tomorrow!
>>>>
>>>> none of these i'm posting seem like unproblematic choices.
>>>>
>>>>
>>>> fwiw, a prosaic 5-limit version:
>>>> 8/9 5/4 8/5 9/8 3/2 1/1 in D?
>>>> problem: 5/4 to 8/5 ain't so wonderful (solution: play the whole
>>>> chord, never expose only that interval?)
>>>>
>>>> 7-limit:
>>>> root on Ab?
>>>> 5/4 7/4 9/8 8/5 16/15 64/45
>>>>
>>>> 5-limit:
>>>> root on Gb?
>>>> 45/32 (too low!) 1/ 5/4 8/9 32/27 64/81
>>>>
>>>>
>>>>
>>>> On Feb 4, 2009, at 5:41 PM, Danny Wier wrote:
>>>>
>>>> I'm following the discussion on the use of the golden ratio as an
>>>> interval (and I have used it rhythmically as a "lazy swing" beat). It
>>>> just so happens I'm writing something using the ratio, or rather an
>>>> approximation of 833 1/3 cents, or 25/36 octave. Right now I only have
>>>> an arpeggio of C Ab+ F- C# A+ F#- D (plus and minus indicate a pitch
>>>> shift of 33 1/3 cents).
>>>>
>>>> Anyway, my question regards the "Mystic chord" of Alexander Scriabin,
>>>> commonly written as *C F# Bb E A D*, and a message from March 2003:
>>>>
>>>> /tuning/topicId_43033.html#43033
>>>>
>>>> Leonid Sabaneyev theorized that Scriabin was implying an overtone series
>>>> in the chord, the odd ones up to 13. The chord would then be voiced as
>>>> 8:11:14:20:26:36. I came up with four interpretations of my own, two in
>>>> 11-limit, two in 7-limit. The first, third and fourth use 27/8 instead
>>>> of 13/4, because I see the 13th harmonic as much more minor than major.
>>>> The last two treat the first four notes as an altered French sixth (i.e.
>>>> C F# A# E) and use more "orthodox" ratios equating to 26/53 or 35/72 of
>>>> an octave.
>>>>
>>>> * 8:11:14:20:27:36
>>>> * 24:33:42:60:80:108 (replacing 27/8 with 10/3)
>>>> * 32:45:56:80:108:144 (if the tritone is 45/32)
>>>> * 40:56:70:100:135:180 (if the tritone is 7/5)
>>>>
>>>> I still need to familiarize myself better with Prometheus though. Any
>>>> thoughts?
>>>>
>>>> ~D.
>>>>
>>>>
>>>>
>>>>
>>>
>>>
>>
>

🔗Danny Wier <dawiertx@...>

On Thu, 2009-02-05 at 04:09 +0100, Marcel de Velde wrote:
> Ah I'm sorry.
> Gave it a bit more thought and I really can''t say yet what it should
> be.
> It's exactly in the area which I'm still working on.
> Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
> In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to me.

I originally wanted 5/2 10/3 40/9 for the top three notes, but combined
with 1/1 7/5 7/4 (I'll just use those for this reply), they produce a
chord of 180:252:315:450:600:800. That's not something I'd want to
resolve a progression with, if 1/1 is the root or key. If it's
dissonance you want, or if you want to emphasize the 5/2 and up over all
the other notes, then the chord would probably do fine.

The simpler alternatives, mathwise, would be having 5/2 27/8 9/2 on top
(40:56:70:100:135:180), or 5/2 10/3 9/2 (60:84:105:150:200:270). I'd say
either way you'd win. But these may only look better on paper; I'd have
to actually listen to these chords with various synth instruments. And a
lot would depend on context within a composition.

But it all goes back to what I commented about a while back: wolf
fourths are not anathema. Not to me at least, but I have a high
tolerance for dissonance.

~D.

🔗Marcel de Velde <m.develde@...>

Hi Danny,

I originally wanted 5/2 10/3 40/9 for the top three notes, but combined
> with 1/1 7/5 7/4 (I'll just use those for this reply), they produce a
> chord of 180:252:315:450:600:800.
>

Ah yes I shouldn't have written 7/5 7/4 I take it back :)
Wrote that without looking at it properly to state it can be a 7th thing.
10/7 25/14 is way more likely.

But I'm having serious trouble saying when the 7th should be there instead
of 225/128 etc that kind of thing.
Long story.

So my fair guess based on experience and some theory that's not yet up to
this would say either 1/1 64/45 16/9 5/2 10/3 or 1/1 10/7 25/14 5/2 10/3
40/9
I can't listen to it now but don't imagine I could tell by listening which
of the ones it should be, either one should sound correct.

> The simpler alternatives, mathwise, would be having 5/2 27/8 9/2 on top
> (40:56:70:100:135:180), or 5/2 10/3 9/2 (60:84:105:150:200:270). I'd say
> either way you'd win. But these may only look better on paper; I'd have
> to actually listen to these chords with various synth instruments. And a
> lot would depend on context within a composition.
>

I wouldn't get too hung up on how it looks on paper in this way, I've found
that simpler low prime intervals between notes matter far more (to keep a
very long story short)

But it all goes back to what I commented about a while back: wolf
> fourths are not anathema. Not to me at least, but I have a high
> tolerance for dissonance.
>

Yes I agree but I see no reason for wolf fourths here.

But, I replied too fast in my first message and after further thought I
really don't know what's the most likely chord :)

Marcel

🔗Marcel de Velde <m.develde@...>

Try playing 1/1 10/7 25/14 5/2 10/3 40/9 -> 15/14 10/7 25/14 20/7 25/7 30/7and
1/1 64/45 16/9 5/2 10/3 40/9 -> 16/15 64/45 16/9 128/45 32/9 64/15

Marcel

On Thu, Feb 5, 2009 at 7:16 AM, Marcel de Velde <m.develde@...> wrote:

> Hi Danny,
>
> I originally wanted 5/2 10/3 40/9 for the top three notes, but combined
>> with 1/1 7/5 7/4 (I'll just use those for this reply), they produce a
>> chord of 180:252:315:450:600:800.
>>
>
> Ah yes I shouldn't have written 7/5 7/4 I take it back :)
> Wrote that without looking at it properly to state it can be a 7th thing.
> 10/7 25/14 is way more likely.
>
> But I'm having serious trouble saying when the 7th should be there instead
> of 225/128 etc that kind of thing.
> Long story.
>
> So my fair guess based on experience and some theory that's not yet up to
> this would say either 1/1 64/45 16/9 5/2 10/3 or 1/1 10/7 25/14 5/2 10/3
> 40/9
> I can't listen to it now but don't imagine I could tell by listening which
> of the ones it should be, either one should sound correct.
>
>
>
>> The simpler alternatives, mathwise, would be having 5/2 27/8 9/2 on top
>> (40:56:70:100:135:180), or 5/2 10/3 9/2 (60:84:105:150:200:270). I'd say
>> either way you'd win. But these may only look better on paper; I'd have
>> to actually listen to these chords with various synth instruments. And a
>> lot would depend on context within a composition.
>>
>
> I wouldn't get too hung up on how it looks on paper in this way, I've found
> that simpler low prime intervals between notes matter far more (to keep a
> very long story short)
>
>
> But it all goes back to what I commented about a while back: wolf
>> fourths are not anathema. Not to me at least, but I have a high
>> tolerance for dissonance.
>>
>
> Yes I agree but I see no reason for wolf fourths here.
>
> But, I replied too fast in my first message and after further thought I
> really don't know what's the most likely chord :)
>
> Marcel
>
>
>

🔗Ben Miller <bencole.miller@...>

this is a super topic!! can you let me hear this stuff?

On Thu, Feb 5, 2009 at 12:48 AM, Danny Wier <dawiertx@...> wrote:

> On Thu, 2009-02-05 at 04:09 +0100, Marcel de Velde wrote:
> > Ah I'm sorry.
> > Gave it a bit more thought and I really can''t say yet what it should
> > be.
> > It's exactly in the area which I'm still working on.
> > Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
> > In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to me.
>
> I originally wanted 5/2 10/3 40/9 for the top three notes, but combined
> with 1/1 7/5 7/4 (I'll just use those for this reply), they produce a
> chord of 180:252:315:450:600:800. That's not something I'd want to
> resolve a progression with, if 1/1 is the root or key. If it's
> dissonance you want, or if you want to emphasize the 5/2 and up over all
> the other notes, then the chord would probably do fine.
>
> The simpler alternatives, mathwise, would be having 5/2 27/8 9/2 on top
> (40:56:70:100:135:180), or 5/2 10/3 9/2 (60:84:105:150:200:270). I'd say
> either way you'd win. But these may only look better on paper; I'd have
> to actually listen to these chords with various synth instruments. And a
> lot would depend on context within a composition.
>
> But it all goes back to what I commented about a while back: wolf
> fourths are not anathema. Not to me at least, but I have a high
> tolerance for dissonance.
>
> ~D.
>
>
>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Ah I'm sorry.Gave it a bit more thought and I really can't
> say yet what it should be.
> It's exactly in the area which I'm still working on.
> Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
> In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to me.
>
> Marcel
>

I'm a bit curious why participants in this thread seem to
assume that any chord one can play in 12-ET has some 'true'
version in JI. It ain't so. Chords are what they are, and
every chord, JI or not, potentially has unique musical
applications.
Obviously, JI chords are attractors and if you get close
enough to one it would be meaningful to say, for instance,
that 0-390-702 cents "is" 4:5:6. But with larger chords
the areas of attraction overlap and even in pure JI it's
not clear when some chords approximate others. Nearly all
large chords in 12-ET will have multiple JI versions that
can stand in, depending on the musical context in which
the 12-ET version occurs.

-Carl

🔗Petr Parízek <p.parizek@...>

I more or less agree with Carl that this particular chord is so specific to 12-equal that I don't find any "meaningful" representation for it in JI.

And then, have you ever, whether Danny or Marcel or anyone interested, heard Steve Reich's "The Desert Music" or "Sextet"? In many cases, there are lots of chords like "C#-F-B-E-A-D-G" with the C# being "doubled" in some lower octaves. And in some cases, particularly in the "Sextet", when this chord is used repeatedly to accompany other melodic voices, those melodic voices are sometimes constrained to an ordinary pentatonic scale which excludes the bass tone (like G-A-B-D-E). This means that the chord starts, counting from the lowest tone, with the diminished fourth followed by an augmented fourth (and even Scriabins Prometheus itself contains lots of these instances of the chord). When you play this thing in 12-equal, the diminished fourth has such a "tendency" to be used like a major third that you would immediately find the chord "out of tune" if you tried to tune this interval to a diminished fourth in, say, 5-limit JI. The only suggestion I can think of at the moment (should we really use JI) is to use 3-limit Pythagorean intonation. But again, a Pythag. dim. fourth is only about 2 cents away from a pure major third so I'm asking what's the point if real Pythag. major thirds don't sound so "synchronous" as dim. fourths. And anyway, the Pythag. F-B is much closer to 10/7 rather than 7/5, so the 7th won't work either.

Petr

🔗caleb morgan <calebmrgn@...>

you are right, sir

On Feb 5, 2009, at 1:11 PM, Petr Parízek wrote:

>
> I more or less agree with Carl that this particular chord is so
> specific to 12-equal that I don't find any "meaningful"
> representation for it in JI.
>
> And then, have you ever, whether Danny or Marcel or anyone
> interested, heard Steve Reich's "The Desert Music" or "Sextet"? In
> many cases, there are lots of chords like "C#-F-B-E-A-D-G" with the
> C# being "doubled" in some lower octaves. And in some cases,
> particularly in the "Sextet", when this chord is used repeatedly to
> accompany other melodic voices, those melodic voices are sometimes
> constrained to an ordinary pentatonic scale which excludes the bass
> tone (like G-A-B-D-E). This means that the chord starts, counting
> from the lowest tone, with the diminished fourth followed by an
> augmented fourth (and even Scriabins Prometheus itself contains lots
> of these instances of the chord). When you play this thing in 12-
> equal, the diminished fourth has such a "tendency" to be used like a
> major third that you would immediately find the chord "out of tune"
> if you tried to tune this interval to a diminished fourth in, say, 5-
> limit JI. The only suggestion I can think of at the moment (should
> we really use JI) is to use 3-limit Pythagorean intonation. But
> again, a Pythag. dim. fourth is only about 2 cents away from a pure
> major third so I'm asking what's the point if real Pythag. major
> thirds don't sound so "synchronous" as dim. fourths. And anyway, the
> Pythag. F-B is much closer to 10/7 rather than 7/5, so the 7th won't
> work either.
>
> Petr
>
>
>
>

🔗Kraig Grady <kraiggrady@...>

🔗Marcel de Velde <m.develde@...>

Hi Carl,

> I'm a bit curious why participants in this thread seem to
> assume that any chord one can play in 12-ET has some 'true'
> version in JI. It ain't so.
>

Oh I must strongly disagree if you mean by this that 12-ET has chords that
exist correctly in 12-ET and do not have a fundamentel basis in JI.
What I mean is that all 12-ET chords are out of tune JI chords.

Yes many different JI chords may become thesame 12-ET chord.
But I do see that there are usually more likely candidate JI chords at the
basis of a 12-ET chord.
For instance take C-E-G, yes it can be many different JI chords depending on
the context of the composition but the most likely one is 1/1 5/4 3/2
One has to have a very very strong reason and a very very complex
compositional context to make this into something like 1/1 19/15 40/27 (also
giving C-E-G in 12-ET)

What I do see is that some correct JI chords may sound more consonant in
12-ET.
Like I beleive an interval like 75/64 gets it's consonance from it's
proximity to 7/6.
I mean that in many cases the correct interval is really 75/64, but we may
rate it's consonance as 7/6.
Same story for some dissonant JI intervals that because of 12-ET get closer
to a consonant JI interval.
Strong examples for this are JI intervals in complex chords that are fairly
close to 3/2 or 4/3 that because of 12-ET become a 12-ET forth or fifth.

Marcel

🔗Kraig Grady <kraiggrady@...>

🔗Marcel de Velde <m.develde@...>

🔗Petr Parízek <p.parizek@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> Hi Carl,
>
> > I'm a bit curious why participants in this thread seem to
> > assume that any chord one can play in 12-ET has some 'true'
> > version in JI. It ain't so.
>
> Oh I must strongly disagree if you mean by this that 12-ET has
> chords that exist correctly in 12-ET and do not have a
> fundamentel basis in JI. What I mean is that all 12-ET chords
> are out of tune JI chords.

Do you have an answer for the dim7 (that works in all inversions)?

> For instance take C-E-G, yes it can be many different JI chords
> depending on the context of the composition but the most likely
> one is 1/1 5/4 3/2

I think I said that.

> Like I believe an interval like 75/64 gets it's consonance from it's
> proximity to 7/6.

I'd agree with that.

-Carl

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> > Scriabin thought of it as a 13th chord, but he exploited that
> > the tritone divided the octave in half. along with all its
> > other ambiguities One will see his music progressing up the
> > harmonic series.
>
> Ok interesting.
> But why does this mean his music progresses up the harmonic
> series? A 13th chord does not have anything to do with the
> 13th harmonic, it's just the 13th key of the diatonic system.

That's true, but by coincidence, diatonic 7ths, 9ths, 11ths,
and 13ths can approximate their respective harmonics! Only
3rds and 5ths can't do this (they're reversed with respect
to their harmonics).

That's not to say they do so in this chord. But in general,
the music of Ravel, at least, evokes extended JI, somehow.
I haven't heard enough Scriabin to comment definitively.
Jazz can too, but not as well as Ravel for some reason...
perhaps because of its heavy use of the major 7th, whereupon
the 15th harmonic tends to be voiced too low.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

Petr,

With respect, if JI is based on the harmonic series, if one choose a root to
base a specific harmonic series, the corresponding notes of Scriabin's chord
would be found somewhere in that series and then transposition by octaves to
reach the proper pitch class.

It seems to me the difficulty comes in assigning the correct root to that
fairly ambgious chord. It is of course a given that the exact frequencies
for a particular note will be different from 12-TET.

Does that make any sense?

Chris

On Thu, Feb 5, 2009 at 4:13 PM, Petr Parízek <p.parizek@...> wrote:

> Marcel wrote:
>
> > What I mean is that all 12-ET chords are out of tune JI chords.
>
> Maybe, but the various combinations of intervals with different degrees of
> „out-of-tuneness" can create chords which have no „correct" or „unique"
> equivalent in JI. If you play a 12-equal chord where the ambiguity between
> „C#-E#-B" and „C#-F-B" is one of the „core" properties, you can't say what
> JI intervals could be the „proper" origin of the chord. And therefore, I
> don't find any great point in saying that a JI version of such a chord
> should probably sound more like „this" rather than „that" because of ...
> whatever. -- Clear enough?
>
> Petr
>
>
>
>
>
>

🔗Marcel de Velde <m.develde@...>

🔗Mike Battaglia <battaglia01@...>

> That's true, but by coincidence, diatonic 7ths, 9ths, 11ths,
> and 13ths can approximate their respective harmonics! Only
> 3rds and 5ths can't do this (they're reversed with respect
> to their harmonics).

That always tripped me out. Unfortunately the pattern is broken at 14 and 15.

> That's not to say they do so in this chord. But in general,
> the music of Ravel, at least, evokes extended JI, somehow.
> I haven't heard enough Scriabin to comment definitively.
> Jazz can too, but not as well as Ravel for some reason...
> perhaps because of its heavy use of the major 7th, whereupon
> the 15th harmonic tends to be voiced too low.

As does Debussy. Debussy really nails it. I'm actually retuning his
"Reverie" to be in 72tet now. There are a few instances in which the
best overall tuning of a certain chord seems to line up with 12-tet,
but sometimes JI chords really do sound like they nail what he was
going for.

I don't know if you're familiar with that piece, but the beginning
works very very well if the major thirds are tuned 9/7, for some
reason I might never know.

I think Stravinsky also approximates higher-limit JI in the Rite of
Spring, especially 17/16 and 19/16, although I don't know if he was
thinking in terms of the overtone series when he came up with some of
his chords.

-Mike

🔗Marcel de Velde <m.develde@...>

🔗Carl Lumma <carl@...>

🔗Danny Wier <dawiertx@...>

On Thu, 2009-02-05 at 17:22 +0000, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> >
> > Ah I'm sorry.Gave it a bit more thought and I really can't
> > say yet what it should be.
> > It's exactly in the area which I'm still working on.
> > Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
> > In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to me.
> >
> > Marcel
> >
>
> I'm a bit curious why participants in this thread seem to
> assume that any chord one can play in 12-ET has some 'true'
> version in JI. It ain't so. Chords are what they are, and
> every chord, JI or not, potentially has unique musical
> applications.

That may be so, at least for a patently atonal work (twelve-tone music
especially), and I don't mean to insist all ET music be "converted" to
JI. But Scriabin's work, as well as that of Bartók, Hindemith and
pre-twelve-tone Schoenberg, is still tonal, though its tonality is
mercurial, not fixed on a particular major, minor or even modal key.

I listened to "Prometheus" earlier today, and I can hear the overtone
series implied in the piano parts. But I was asking how one could or
should tune the chord not to try to "improve" the composer's work, but
to get an idea how I would voice the chord if I ever decide to use a
chord like it.

> Obviously, JI chords are attractors and if you get close
> enough to one it would be meaningful to say, for instance,
> that 0-390-702 cents "is" 4:5:6. But with larger chords
> the areas of attraction overlap and even in pure JI it's
> not clear when some chords approximate others. Nearly all
> large chords in 12-ET will have multiple JI versions that
> can stand in, depending on the musical context in which
> the 12-ET version occurs.

True, and I decided there's probably no "best" way to voice a complex
chord like Mystic/Prometheus, Tristan, the "Purple Haze" E7#9 and all
those augmented sixths, though there are naturally some very bad
voicings.

~D.

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > That's true, but by coincidence, diatonic 7ths, 9ths, 11ths,
> > and 13ths can approximate their respective harmonics! Only
> > 3rds and 5ths can't do this (they're reversed with respect
> > to their harmonics).
>
> That always tripped me out. Unfortunately the pattern is broken at
14 and 15.
>
> > That's not to say they do so in this chord. But in general,
> > the music of Ravel, at least, evokes extended JI, somehow.
> > I haven't heard enough Scriabin to comment definitively.
> > Jazz can too, but not as well as Ravel for some reason...
> > perhaps because of its heavy use of the major 7th, whereupon
> > the 15th harmonic tends to be voiced too low.
>
> As does Debussy. Debussy really nails it.

I've never heard it so much from Debussy.

> I don't know if you're familiar with that piece, but the beginning
> works very very well if the major thirds are tuned 9/7, for some
> reason I might never know.

I'll look it up. Or if you have a recording or MIDI to
share, please do.

> I think Stravinsky also approximates higher-limit JI in the Rite of
> Spring,

In places, yes. But it's a gestalt for Ravel.

-Carl

🔗Marcel de Velde <m.develde@...>

🔗Charles Lucy <lucy@...>

Scriabin's theory was that each note in the octave could be associated
with a specific colour, and in Prometheus, the Poem of Fire, he wrote
the colours and music to match. His arrangement was:

C Db D Eb E F F# G Ab A Bb B
Red Violet Yellow Steel Pale
Blue

Dark
Red

Bright
Blue

Orange Purple Green Steel Pale
Blue

On 5 Feb 2009, at 21:55, Chris Vaisvil wrote:

> Petr,
>
> With respect, if JI is based on the harmonic series, if one choose a
> root to base a specific harmonic series, the corresponding notes of
> Scriabin's chord would be found somewhere in that series and then
> transposition by octaves to reach the proper pitch class.
>
> It seems to me the difficulty comes in assigning the correct root to
> that fairly ambgious chord. It is of course a given that the exact
> frequencies for a particular note will be different from 12-TET.
>
> Does that make any sense?
>
> Chris
>
>
> On Thu, Feb 5, 2009 at 4:13 PM, Petr Parízek <p.parizek@chello.cz>
> wrote:
>
> Marcel wrote:
>
> > What I mean is that all 12-ET chords are out of tune JI chords.
>
> Maybe, but the various combinations of intervals with different
> degrees of „out-of-tuneness" can create chords which have no
> „correct" or „unique" equivalent in JI. If you play a 12-equal chord
> where the ambiguity between „C#-E#-B" and „C#-F-B" is one of the
> „core" properties, you can't say what JI intervals could be the
> „proper" origin of the chord. And therefore, I don't find any great
> point in saying that a JI version of such a chord should probably
> sound more like „this" rather than „that" because of ... whatever.
> -- Clear enough?
>
> Petr
>
>
>
>
>
>

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

🔗Mike Battaglia <battaglia01@...>

🔗Marcel de Velde <m.develde@...>

Hi Mike,

> No waay rite of spring uses a prime higher than 7.
> > This is not JI.
>
> Why do you say that? 17/16 and 19/16 are well approximated in 12-tet.

Since when is JI about approximating 12-tet?

Modes / tonality / chords / music is perfect and has to do with relations
between sounds.
To keep a very long story short, these start with simple relations like 1/1
2/1, 1/1 3/2, etc.
Music you could see as a sort of play of the possibilities.
If you see it as a construction of simple relations / intervals going to
higher relations / intervals you can take the harmonic series for this.
If you take up to the 5th harmonic you allready have many possibilities. The
way I view it you have a complexity of 1*2*3*4*5
If you take it to 6th harmonic you have 1*2*3*4*5*6 complexity
possibilities.
I know this will probably not make much sense now but I can explain it much
better but it takes a long story but you should be able to accept that you
get many possibilities more with every added harmonic in some sort of
exponential curve.
By the time you get to the 19th harmonic you have such an incredible amount
of simpler musical constructions that will aproximate the interval you think
is for instance 19/16 to within a fraction of a cent. You better make a very
strong case with the music / chord before your mind will see it as the 19th
harmonic.
Music and harmonic overtones are 2 different things.

Here for example some very simple 5 limit modes that you get when building
musical structures with nothing more than the 6th harmonic:

1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
9/8 : 10/9 32/27 4/3 40/27 5/3 16/9 2/1
5/4 : 16/15 6/5 4/3 3/2 8/5 9/5 2/1
4/3 : 9/8 5/4 45/32 3/2 27/16 15/8 2/1
3/2 : 10/9 5/4 4/3 3/2 5/3 16/9 2/1
5/3 : 9/8 6/5 27/20 3/2 8/5 9/5 2/1
15/8: 16/15 6/5 4/3 64/45 8/5 16/9 2/1

1/1 9/8 6/5 4/3 3/2 8/5 9/5 2/1
9/8: 16/15 32/27 4/3 64/45 8/5 16/9 2/1
6/5: 10/9 5/4 4/3 3/2 5/3 15/8 2/1
4/3: 9/8 6/5 27/20 3/2 27/16 9/5 2/1
3/2: 16/15 6/5 4/3 3/2 8/5 16/9 2/1
8/5: 9/8 5/4 45/32 3/2 5/3 15/8 2/1
9/5: 10/9 5/4 4/3 40/27 5/3 16/9 2/1

1/1 9/8 5/4 4/3 3/2 8/5 15/8 2/1
9/8 : 10/9 32/27 4/3 64/45 5/3 16/9 2/1
5/4 : 16/15 6/5 32/25 3/2 8/5 9/5 2/1
4/3 : 9/8 6/5 45/32 3/2 27/16 15/8 2/1
3/2 : 16/15 5/4 4/3 3/2 5/3 16/9 2/1
8/5 : 75/64 5/4 45/32 25/16 5/3 15/8 2/1
15/8: 16/15 6/5 4/3 64/45 8/5 128/75 2/1

1/1 9/8 5/4 4/3 3/2 5/3 9/5 2/1
9/8: 10/9 32/27 4/3 40/27 8/5 16/9 2/1
5/4: 16/15 6/5 4/3 36/25 8/5 9/5 2/1
4/3: 9/8 5/4 27/20 3/2 27/16 15/8 2/1
3/2: 10/9 6/5 4/3 3/2 5/3 16/9 2/1
5/3: 27/25 6/5 27/20 3/2 8/5 9/5 2/1
9/5: 10/9 5/4 25/18 40/27 5/3 50/27 2/1

1/1 9/8 6/5 4/3 3/2 8/5 15/8 2/1
9/8 : 16/15 32/27 4/3 64/45 5/3 16/9 2/1
6/5 : 10/9 5/4 4/3 25/16 5/3 15/8 2/1
4/3 : 9/8 6/5 45/32 3/2 27/16 9/5 2/1
3/2 : 16/15 5/4 4/3 3/2 8/5 16/9 2/1
8/5 : 75/64 5/4 45/32 3/2 5/3 15/8 2/1
15/8: 16/15 6/5 32/25 64/45 8/5 128/75 2/1

1/1 9/8 6/5 4/3 3/2 5/3 9/5 2/1
9/8: 16/15 32/27 4/3 40/27 8/5 16/9 2/1
6/5: 10/9 5/4 25/18 3/2 5/3 15/8 2/1
4/3: 9/8 5/4 27/20 3/2 27/16 9/5 2/1
3/2: 10/9 6/5 4/3 3/2 8/5 16/9 2/1
5/3: 27/25 6/5 27/20 36/25 8/5 9/5 2/1
9/5: 10/9 5/4 4/3 40/27 5/3 50/27 2/1

1/1 9/8 5/4 4/3 3/2 8/5 9/5 2/1
9/8: 10/9 32/27 4/3 64/45 8/5 16/9 2/1
5/4: 16/15 6/5 32/25 36/25 8/5 9/5 2/1
4/3: 9/8 6/5 27/20 3/2 27/16 15/8 2/1
3/2: 16/15 6/5 4/3 3/2 5/3 16/9 2/1
8/5: 9/8 5/4 45/32 25/16 5/3 15/8 2/1
9/5: 10/9 5/4 25/18 40/27 5/3 16/9 2/1

1/1 9/8 6/5 4/3 3/2 5/3 15/8 2/1
9/8 : 16/15 32/27 4/3 40/27 5/3 16/9 2/1
6/5 : 10/9 5/4 25/18 25/16 5/3 15/8 2/1
4/3 : 9/8 5/4 45/32 3/2 27/16 9/5 2/1
3/2 : 10/9 5/4 4/3 3/2 8/5 16/9 2/1
5/3 : 9/8 6/5 27/20 36/25 8/5 9/5 2/1
15/8: 16/15 6/5 32/25 64/45 8/5 16/9 2/1

1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
9/8 : 16/15 10/9 32/27 4/3 64/45 40/27 8/5 5/3 16/9 2/1
6/5 : 25/24 10/9 5/4 4/3 25/18 3/2 25/16 5/3 15/8 2/1
5/4 : 16/15 6/5 32/25 4/3 36/25 3/2 8/5 9/5 48/25 2/1
4/3 : 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1
3/2 : 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1
8/5 : 25/24 9/8 75/64 5/4 45/32 3/2 25/16 5/3 15/8 2/1
5/3 : 27/25 9/8 6/5 27/20 36/25 3/2 8/5 9/5 48/25 2/1
9/5 : 25/24 10/9 5/4 4/3 25/18 40/27 5/3 16/9 50/27 2/1
15/8: 16/15 6/5 32/25 4/3 64/45 8/5 128/75 16/9 48/25 2/1

Every single one of the above 7 note modes is a valid mode.
You don't want to know how much larger this list gets when you go up 1
number in complexity and add the 7th harmonic.

Marcel

🔗Claudio Di Veroli <dvc@...>

A list of historical colour-scale associations is found in.
http://homepage.eircom.net/~musima/visualmusic/visualmusic.htm

Of the 11 alternatives shown there, I find that NONE agrees with my personal
feeling (which I had and did not change since I was first introduced to
music as a child): in particular, I feel very strongly that C is black, D
green, F brown, F# orange, G ocean blue and A red.
This is obviously subconscious.
Does anybodyknow why do we have those associations?
And why everybody seems to have a different one?

Kind regards

Claudio

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
Mike Battaglia
Sent: 06 February 2009 00:14
To: tuning@yahoogroups.com
Subject: Re: [tuning] Re: Scriabin's and Colour. FYI

I've heard that, but I have completely different color associations
than those Scriabin listed. Note that Scriabin has a few cases where
notes a fifth apart from each other have the same or similar "colors"
- Eb-Bb, E-B, B-F#, Db-Ab... Also notice that C is red and D is yellow
with G being in the middle at orange. As someone with AP, the
phenomenon between notes that are fifths apart is extremely similar -
C and G sound far more similar than C and C#.

Musicians have been arguing over what color a certain chord or note is
since time immemorial... I wonder if all synesthesia is accumulated
associations in this way.

-Mike

🔗Charles Lucy <lucy@...>

I have also seen/read of many different pitch to colour arrangements, yet Scriabin's system makes no sense to me.

On 6 Feb 2009, at 00:14, Mike Battaglia wrote:

> I've heard that, but I have completely different color associations
> than those Scriabin listed. Note that Scriabin has a few cases where
> notes a fifth apart from each other have the same or similar "colors"
> - Eb-Bb, E-B, B-F#, Db-Ab... Also notice that C is red and D is yellow
> with G being in the middle at orange. As someone with AP, the
> phenomenon between notes that are fifths apart is extremely similar -
> C and G sound far more similar than C and C#.
>
> Musicians have been arguing over what color a certain chord or note is
> since time immemorial... I wonder if all synesthesia is accumulated
> associations in this way.
>
> -Mike
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

🔗Daniel Forro <dan.for@...>

Yes, such color assigning is just Scriabin's idea, other person can have different one or feel no connection between sound and color. Music itself will have no harm in any case. This all is a pure mysticism, Scriabin was under strong influence of theosofy.

Daniel Forro

On 6 Feb 2009, at 9:14 AM, Mike Battaglia wrote:

🔗Marcel de Velde <m.develde@...>

🔗Daniel Forro <dan.for@...>

In the diatonic usually only 7 notes are supposed, not more :-)

If you order tones of Mixolydian diatonic scale in thirds, you will get 13th chord, which follows to some degree (and by concidence) odd tones of harmonic series. Reason for using flat 7th (when we start on C) is that this chord was originally constructed as a Dominant class chord, later such complex chords were used on other tones in a scale.
Of course a chord which follows harmonic series would be rather 13/11+, that one started to be used by Debussy, Scriabin and later overused in jazz even as ending chord. It's based on the Lydian/Mixolydian scale C - D - E - F# - G - A - Bb, which has a narrow connection with flute overblowing (and Scriabin's Prometheus chord!). Therefore we can find this scale in all cultures using flute as a main instrument, usually shepherd's music, in Europe it's for example Carpathian music from Bulgaria to Slovakia, South Poland and eastern Moravia where this type of musical culture ends (which was found and used by many composers - Bartok, Janacek especially, Haba, Killar - his Krzesany is an excellent example for this scale...). This "natural harmonic" scale has a name "goralska" or "podhalanska" tonality in High Tatra Mountains and it can be easily played on regional instrument - long flute called "fujara" and other flutes.

Long time composers were not aware of this, but when accordics has reached 13th in the middle of 19th century, and when composers started to be interested in folklore and were influenced by it, there were some composers who started not to use 13th chord in a traditional way (e.g. with omitted third and fifth, like for example Bb7maj on C bass - such chords were used by Chopin and Liszt), but with 11+, third and fifth to simulate harmonic series even in common 12 ET. It's interesting but not surprising that composers-pianists started with this, as they could find such "nice sounding" chords easily with pressed pedal. We can find such chords in Chopin, Liszt (maybe not intentional use, just as a color) and especially Debussy who was for sure aware of this. Chopin used 7th and 9th chords in this way. Debussy has this in his Isle joyeuse (BTW I consider it as a great breakthrough work, there's a clear connection to harmonic series with Lydian 4th and Mixolydian 7th, it would sound great in JI) and other works. This line in music continued in Stravinskij, Janacek, Bartok, Messiaen, Killar, Reich and many others (not forget myself in more works).

But it's necessary to emphasize that it's only a simulation of harmonic series. I'm not aware of any attempts from the side of those composers to use JI, nothing to say about jazz.

Daniel Forro

On 6 Feb 2009, at 5:33 AM, Marcel de Velde wrote:

>
>
> Scriabin thought of it as a 13th chord, but he exploited that the
> tritone divided the octave in half. along with all its other > ambiguities
> One will see his music progressing up the harmonic series.
>
>
> Ok interesting.
> But why does this mean his music progresses up the harmonic series?
> A 13th chord does not have anything to do with the 13th harmonic, > it's just the 13th key of the diatonic system.
>
> Marcel

🔗Graham Breed <gbreed@...>

Marcel de Velde wrote:
> A specific feature of the 12-et dim7 chord is that it DOES sound the
> same in all inversions, and its ambiguity in that sense is musically
> exploited often.
> > > Another specific feature of 12-et is that it's allways out of tune, and every > interval sounds thesame, and it puts a boring gray haze over all music played in it.
> > Anything done in 12-et with the dim7 that sounds musical you can do in JI better.
> That it doesn't sound exactly thesame in all keys is a good thing and doesn't > take away musical possibilities.

I'm with you on this, anyway. A dim7 is always presented in a musical context. In that context it can be tuned to JI. It doesn't matter that a different inversion would be tuned differently. And it doesn't matter that the intervals would be unequal because I really don't think listeners are going to spot the patterns and lose the ambiguity.

Graham

🔗Daniel Forro <dan.for@...>

Don't forget please that in practical music life nothing like pure 12 ET exists :-) It's only theoretical model. Even keyboard instruments (except electronic ones) don't use it, nothing to say about orchestras, choirs... So there ARE differences in tuning between different keys and chords. So it's definitely not boring (if music itself is not boring).

And there is tendency to tune chords in real time more near to nice sounding ones when not JI. So it's NOT always out of tune.

Intervals don't sound the same, it depends on musical context, and direction (up, down) and their position in the chord (root, third, fifth or other...). Lot of good performers are aware of this and use it (of course only if they can tune individual notes in real time).

Also dim7 chord can be tuned depending on its harmonic function and position between two other chords. For sure there is difference between G# - B - D - F, Ab - B - D - F, G# - B - D - E# and Ab - Cb - D - F as a resolution will be different (in traditional music supposed composer is aware what enharmonicity is) and there's more possibilities. Minimally good string quartet of choir a capella with perform this well (that means differently than 12 ET).

Daniel Forro

On 6 Feb 2009, at 9:40 AM, Marcel de Velde wrote:

>
>
> A specific feature of the 12-et dim7 chord is that it DOES sound the
> same in all inversions, and its ambiguity in that sense is musically
> exploited often.
>
> Another specific feature of 12-et is that it's allways out of tune, > and every interval sounds thesame, and it puts a boring gray haze > over all music played in it.
>
> Anything done in 12-et with the dim7 that sounds musical you can do > in JI better.
> That it doesn't sound exactly thesame in all keys is a good thing > and doesn't take away musical possibilities.
>
> Marcel

🔗Marcel de Velde <m.develde@...>

>
> Don't forget please that in practical music life nothing like pure 12
> ET exists :-) It's only theoretical model. Even keyboard instruments
> (except electronic ones) don't use it, nothing to say about
> orchestras, choirs... So there ARE differences in tuning between
> different keys and chords. So it's definitely not boring (if music
> itself is not boring).
>
> And there is tendency to tune chords in real time more near to nice
> sounding ones when not JI. So it's NOT always out of tune.
>

Ok this is true for string quartets, choirs, trombones etc
I agree with you here for a large part. (if the performers have great ears
and skill which is not allways the case)
But with full orchestras they're allready in trouble and play mostly 12tet.
I think in general we can say most western music is roughly 12tet and in
tune music is preserved for few music.

> Intervals don't sound the same, it depends on musical context, and
> direction (up, down) and their position in the chord (root, third,
> fifth or other...). Lot of good performers are aware of this and use
> it (of course only if they can tune individual notes in real time).
>

Yes but where else than in a good choir or string quartet can i hear the
difference between 10/9 and 9/8?
Most instruments can't tune individual notes.
Besides this I don't trust performers to tune correctly even if they have
the ability to tune every single note :)But there's another reason I hate
12tet. It limits the composers.
Just listen to arabic music. You can't play this on a piano and western
composers won't compose these notes.

Marcel

🔗Marcel de Velde <m.develde@...>

I mean the difference between 9/5 and 50/27 is less than 50 cents, but don't
really know if you could label it a minor 7th.Hmm probably not on second
thought.

1/1 10/9 5/4 25/18 40/27 5/3 16/9 2/1
This one is valid too but 25/18 and 16/9 makes 32/25.
Hmm although.. that doesn't look too bad.
Going to have a listen how they all sound.

Marcel

On Fri, Feb 6, 2009 at 3:17 AM, Marcel de Velde <m.develde@...> wrote:

> If it is indeed based on the Lydian / Mixolydian scale it will probably
>> be this:
>> 1/1 9/8 5/4 45/32 3/2 27/16 9/5 2/1
>>
>
> Which doesn't make much sense for the chord :)
>
> Could also be this: 1/1 10/9 5/4 25/18 40/27 5/3 50/27 2/1 which is a
> valid mode too.
>
> Very interesting. Didn't comsider this before but this makes the F# and Bb
> not a major third but a fourth!
> Makes a perfect chord in numbers. Wonder how it sounds.
>
> Marcel
>

🔗Daniel Forro <dan.for@...>

On 6 Feb 2009, at 11:06 AM, Marcel de Velde wrote:
> Ok this is true for string quartets, choirs, trombones etc
>
> I agree with you here for a large part. (if the performers have > great ears and skill which is not allways the case)
> But with full orchestras they're allready in trouble and play > mostly 12tet.
> I think in general we can say most western music is roughly 12tet > and in tune music is preserved for few music.

Yes, it's so.

> Yes but where else than in a good choir or string quartet can i > hear the difference between 10/9 and 9/8?
> Most instruments can't tune individual notes.

Most orchestral instruments can - bowed strings, brass, woodwinds. +/- 15 cents is no problem, and that's enough for such tuning corrections. Not yet enough for quartertones :-)
Only acoustic keyboards (including tuned mallet percussions) and harp can't do it.

> Besides this I don't trust performers to tune correctly even if > they have the ability to tune every single note :)

That's the main problem, performer's ability, lack of education in this direction. Probably many of them are even not aware of this possibility. Then it's also problem of conductor, he should balance not only dynamics, tempo changes, articulation, phrasing and expression, but tuning as well. Maybe this is one of the things which made some orchestra's good fame...

> But there's another reason I hate 12tet. It limits the composers.

That's true to some degree, and despite the fact lot of possibilities were discovered and used, there are still some interesting regions. I work a lot last years with symmetry, and chords created mathematically, to name just some of possibilities. It's quite exciting, there's still some potential.

> Just listen to arabic music. You can't play this on a piano and > western composers won't compose these notes.

Yes, it's different style, they just talk different languages. It doesn't mean western music is worse. As well we can't say that Arabic music is inferior because they don't use complex chords.
But we don't need to go in such far distance to find different languages - what about classical music and jazz or pop?
>

Daniel Forro

🔗Marcel de Velde <m.develde@...>

> Most orchestral instruments can - bowed strings, brass, woodwinds.
> +/- 15 cents is no problem, and that's enough for such tuning
> corrections. Not yet enough for quartertones :-)
> Only acoustic keyboards (including tuned mallet percussions) and harp
> can't do it.
>

Ok wow, I had no idea!
Haha thanks for letting me know, you'd think I should know this :)

That's true to some degree, and despite the fact lot of possibilities
> were discovered and used, there are still some interesting regions. I
> work a lot last years with symmetry, and chords created
> mathematically, to name just some of possibilities. It's quite
> exciting, there's still some potential.
>

Oh yes I can see it too.
The musical landscape is great.
Maybe the easy days are over for creating new things but I feel the greatest
music is yet to be written.

Marcel

🔗Kraig Grady <kraiggrady@...>

quite funny then cause i heard the chord in Gershwin without
mistake. Rhapsody in blue just before the last theme. I cannot off
hand think of an instance of this chord in either Stravinsky or
Bartok, but if you understand what they are doing you could surely
get this chord.

There i s a Reich ensemble in L.A. where the leader has perfect
pitch, so good that someone did a piece where they would hit a
cluster of 11 notes and ask which note was left out. He nailed
every time without hesitation. I will ask him

Posted by: "Petr Parï¿½zek"

When I was in Slovakia in 2005, Reich came to have a presentation there and he said that he had found his inspiration for those chords when carefully studiing music of Stravinski and Bartï¿½k.
--

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere: North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

🔗William Gard <billygard@...>

🔗Marcel de Velde <m.develde@...>

🔗Daniel Forro <dan.for@...>

Yes, his first works were inspired by Chopin, we can see him like a direct follower of Chopin. Very soon he started with more complex chords and alterations, which lead him to whole tone scale and augmented chords on one side (Debussy's influence?), and diminished chord and diminished mode on the other side (Chopin, Liszt). Whole tone scale as well as diminished chord and diminished scale has lot of tritones (he loved this interval, maybe because of that numerological symbol - it has 6 halftones, and it was always called "diabolus in musica", so he used it a lot in his works, like Satanic Poem, Black Mess sonata etc). It's not so far from the idea of using fourths as a base for chords (same was discovered by Satie, later Debussy - probably derived from pentatonics, later Schoenberg). In his last pieces he was not far from atonality, but differently then Schoenberg.

What's fabion bowers? That book can be interesting.

Daniel Forro

On 6 Feb 2009, at 11:53 AM, Kraig Grady wrote:

> If you look at Scriabins music as a whole , he started with dominants
> then 9th, then 11 and 13th chords.
> there is a book on fabion bowers which also covers his harmonic > systems.
> The story is though when he would play many of his one minute prelude
> live , each one he would take out to 20 minutes.
> -->
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

🔗Daniel Forro <dan.for@...>

As far as I know, there is often used a chord 11+ in this work, and whole tone chords progressions shifted by chromatic, both mainly in bridge music, and it's the most boring cliche in this work. Both has here no connection with jazz, more with Liszt, Debussy and Tchaikovsky, but such chords were later used in jazz, and in a better way than here.

Daniel Forro

On 6 Feb 2009, at 12:04 PM, Kraig Grady wrote:

>
> quite funny then cause i heard the chord in Gershwin without
> mistake. Rhapsody in blue just before the last theme. I cannot off
> hand think of an instance of this chord in either Stravinsky or
> Bartok, but if you understand what they are doing you could surely
> get this chord.
>
> There i s a Reich ensemble in L.A. where the leader has perfect
> pitch, so good that someone did a piece where they would hit a
> cluster of 11 notes and ask which note was left out. He nailed
> every time without hesitation. I will ask him
>

🔗Daniel Forro <dan.for@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> > Most orchestral instruments can - bowed strings, brass,
> > woodwinds. +/- 15 cents is no problem, and that's enough
> > for such tuning corrections. Not yet enough for
> > quartertones :-) Only acoustic keyboards (including
> > tuned mallet percussions) and harp can't do it.
> >

Of course the problem becomes coordination of such a large
group. Often I hear what I would call "sectional intonation" --
the woodwinds may tune well together, the brass may tune well
together, the strings very rarely but sometimes do tune
well together, but these sections only very very rarely tune
well all together. Nevertheless, I have heard it a few
times. The MET orchestra (New York Metropolitan Opera) tends
to be good -- one might speculate that their relatively small
numbers and their habit of playing in the pit may help.

This is one of the reasons I have generally preferred chamber
music since I was a boy.

-Carl

🔗Daniel Forro <dan.for@...>

On 6 Feb 2009, at 5:21 PM, Carl Lumma wrote:
>
> Of course the problem becomes coordination of such a large
> group. Often I hear what I would call "sectional intonation" --
> the woodwinds may tune well together, the brass may tune well
> together, the strings very rarely but sometimes do tune
> well together, but these sections only very very rarely tune
> well all together.
>
Reason can be they have divided rehearsals by sections. But even so, we are used to it and take it as normal... Honky tonk piano and accordeon included :-)
> Nevertheless, I have heard it a few
> times. The MET orchestra (New York Metropolitan Opera) tends
> to be good -- one might speculate that their relatively small
> numbers and their habit of playing in the pit may help.
>
>
I've heard some Mozart top symphony with minimal orchestra setting as he wrote it, and without vibrato (specialty of that conductor) and it was good, too.
> This is one of the reasons I have generally preferred chamber
> music since I was a boy.
>
> -Carl
>
I was always tortured hearing string quartets or piano trios...

Daniel Forro

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:
>
>
> On 6 Feb 2009, at 5:21 PM, Carl Lumma wrote:
> >
> > Of course the problem becomes coordination of such a large
> > group. Often I hear what I would call "sectional intonation" --
> > the woodwinds may tune well together, the brass may tune well
> > together, the strings very rarely but sometimes do tune
> > well together, but these sections only very very rarely tune
> > well all together.
>
> Reason can be they have divided rehearsals by sections.

I think the more fundamental reasons are:
1. The inability to hear other sections, sitting far
away or on a stage where acoustics are poor.
2. The difference in timbre between instrument types.
It is harder to tune a trumpet to a violin than to
another trumpet.

> But even so, we are used to it and take it as normal... Honky
> tonk piano and accordeon included :-)

I hate honky tonk pianos, the chorused stops on accordion,
"chorus" effects in electronic music, the string sections
of most orchestras, romantic-style string playing in general
(vibrato), and so on.

> > This is one of the reasons I have generally preferred chamber
> > music since I was a boy.
>
> I was always tortured hearing string quartets or piano trios...

Top professional string quartets generally sound OK
to me. Or did you mean "quintets" (with a piano)?
I generally think that's a bad combination, but it can
work in certain cases, if the rhythms given to piano
and to the strings are different enough.

-Carl

🔗Ben Miller <bencole.miller@...>

Good point.

On 2/5/09, Petr Parízek <p.parizek@...> wrote:
> I more or less agree with Carl that this particular chord is so specific to
> 12-equal that I don't find any "meaningful" representation for it in JI.
>
> And then, have you ever, whether Danny or Marcel or anyone interested, heard
> Steve Reich's "The Desert Music" or "Sextet"? In many cases, there are lots
> of chords like "C#-F-B-E-A-D-G" with the C# being "doubled" in some lower
> octaves. And in some cases, particularly in the "Sextet", when this chord is
> used repeatedly to accompany other melodic voices, those melodic voices are
> sometimes constrained to an ordinary pentatonic scale which excludes the
> bass tone (like G-A-B-D-E). This means that the chord starts, counting from
> the lowest tone, with the diminished fourth followed by an augmented fourth
> (and even Scriabins Prometheus itself contains lots of these instances of
> the chord). When you play this thing in 12-equal, the diminished fourth has
> such a "tendency" to be used like a major third that you would immediately
> find the chord "out of tune" if you tried to tune this interval to a
> diminished fourth in, say, 5-limit JI. The only suggestion I can think of at
> the moment (should we really use JI) is to use 3-limit Pythagorean
> intonation. But again, a Pythag. dim. fourth is only about 2 cents away from
> a pure major third so I'm asking what's the point if real Pythag. major
> thirds don't sound so "synchronous" as dim. fourths. And anyway, the Pythag.
> F-B is much closer to 10/7 rather than 7/5, so the 7th won't work either.
>
> Petr
>
>
>

--
Sent from my mobile device

🔗Mike Battaglia <battaglia01@...>

> Another specific feature of 12-et is that it's allways out of tune, and
> every interval sounds thesame, and it puts a boring gray haze over all music
> played in it.

First off, your reasoning is circular. It's out of tune relative to
the chord you specified above. It's perfectly "in tune" if that's what
it's meant to be.

The fact that 4 equal divisions of the octave produces a dim7 that
sounds identical in all keys is a feature, not a bug. The fact that
you label it to be a malformation of 12-tet doesn't take away from its
practicality. In this case, the fact that it is completely ambiguous
and could resolve any which way is a property that has been exploited
for years.

> Anything done in 12-et with the dim7 that sounds musical you can do in JI
> better.

Except sound the same in every inversion.

> That it doesn't sound exactly thesame in all keys is a good thing and
> doesn't take away musical possibilities.

It takes away the possibility of having an unexpected resolution to a
different chord than you would expect.

There are chords out there that have nothing to do with JI. Go look up
some of the recent discussions on metastable ratios, for example. Such
chords aren't against the law.

-Mike

🔗Kraig Grady <kraiggrady@...>

🔗Mike Battaglia <battaglia01@...>

Debussy was the first person to use this chord, as far as I know. He
uses it in his work "Hommage a Rameau", for one. It's a dominant 7 #11
chord, which is "classically" derived from the Lydian Dominant scale:
C D E F# G A Bb C, which is the fourth mode of the melodic minor
scale.
-Mike

On Thu, Feb 5, 2009 at 10:04 PM, Kraig Grady <kraiggrady@...> wrote:
>
> quite funny then cause i heard the chord in Gershwin without
> mistake. Rhapsody in blue just before the last theme. I cannot off
> hand think of an instance of this chord in either Stravinsky or
> Bartok, but if you understand what they are doing you could surely
> get this chord.
>
> There i s a Reich ensemble in L.A. where the leader has perfect
> pitch, so good that someone did a piece where they would hit a
> cluster of 11 notes and ask which note was left out. He nailed
> every time without hesitation. I will ask him
>
> Posted by: "Petr Parízek"
>
> When I was in Slovakia in 2005, Reich came to have a presentation there
> and he said that he had found his inspiration for those chords when
> carefully studiing music of Stravinski and Bartók.
> --
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
>

🔗Kraig Grady <kraiggrady@...>

🔗Marcel de Velde <m.develde@...>

Hi Mike,

No you're wrong.

First off, your reasoning is circular. It's out of tune relative to
> the chord you specified above. It's perfectly "in tune" if that's what
> it's meant to be.
>

I can agree with you that if it's ment to be out of tune by the composer.
Eg if the composer likes the out of tune floating sound of 12tet then you
can argue it's ment that way.
But 12tet is out of tune no matter which chord you make except for unison
and octaves.

The fact that 4 equal divisions of the octave produces a dim7 that
> sounds identical in all keys is a feature, not a bug. The fact that
> you label it to be a malformation of 12-tet doesn't take away from its
> practicality. In this case, the fact that it is completely ambiguous
> and could resolve any which way is a property that has been exploited
> for years.
>

You can resolve any which way with the JI version too and can use it in
exactly thesame way as the 12tet one.
The difference is that if you take the JI version out of it's mode you
modulating to a different key.
If you play such a structure in 12tet you're doing thesame thing, just out
of tune.

>
> > Anything done in 12-et with the dim7 that sounds musical you can do in JI
> > better.
>
> Except sound the same in every inversion.
>

Yes which is not how the dim7 should really sound.

> > That it doesn't sound exactly thesame in all keys is a good thing and
> > doesn't take away musical possibilities.
>
> It takes away the possibility of having an unexpected resolution to a
> different chord than you would expect.
>

No it does not take away this possibility at all.
Why do you think such a thing??

> There are chords out there that have nothing to do with JI. Go look up
> some of the recent discussions on metastable ratios, for example. Such
> chords aren't against the law.
>

Those chords too have their basis in JI and are out of tune if you play them
any other way.

Marcel

🔗Marcel de Velde <m.develde@...>

🔗Mike Battaglia <battaglia01@...>

🔗Danny Wier <dawiertx@...>

On Thu, 2009-02-05 at 00:58 -0500, Ben Miller wrote:
> this is a super topic!! can you let me hear this stuff?

I'll need to make some MIDI (or low-quality MP3) files and upload them
to the Files section. I'll try to do files for the augmented sixth
chords, Scriabin's chord and other famous complex chords like Tristan
and Hendrix. They would be played in their 12-tone version, followed by
at least one 72-edo interpretation.

It might take me a while; I'm a horrible procrastinator.

~D.

> On Thu, Feb 5, 2009 at 12:48 AM, Danny Wier <dawiertx@...>
> wrote:
> On Thu, 2009-02-05 at 04:09 +0100, Marcel de Velde wrote:
> > Ah I'm sorry.
> > Gave it a bit more thought and I really can''t say yet what
> it should
> > be.
> > It's exactly in the area which I'm still working on.
> > Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
> > In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to
> me.
>
>
> I originally wanted 5/2 10/3 40/9 for the top three notes, but
> combined
> with 1/1 7/5 7/4 (I'll just use those for this reply), they
> produce a
> chord of 180:252:315:450:600:800. That's not something I'd
> want to
> resolve a progression with, if 1/1 is the root or key. If it's
> dissonance you want, or if you want to emphasize the 5/2 and
> up over all
> the other notes, then the chord would probably do fine.
>

🔗Danny Wier <dawiertx@...>

On Thu, 2009-02-05 at 19:11 +0100, Petr Parízek wrote:

> And then, have you ever, whether Danny or Marcel or anyone interested,
> heard Steve Reich's "The Desert Music" or "Sextet"? In many cases,
> there are lots of chords like "C#-F-B-E-A-D-G" with the C# being
> "doubled" in some lower octaves. And in some cases, particularly in
> the "Sextet", when this chord is used repeatedly to accompany other
> melodic voices, those melodic voices are sometimes constrained to an
> ordinary pentatonic scale which excludes the bass tone (like
> G-A-B-D-E). This means that the chord starts, counting from the lowest
> tone, with the diminished fourth followed by an augmented fourth (and
> even Scriabins Prometheus itself contains lots of these instances of
> the chord). When you play this thing in 12-equal, the diminished
> fourth has such a "tendency" to be used like a major third that you
> would immediately find the chord "out of tune" if you tried to tune
> this interval to a diminished fourth in, say, 5-limit JI. The only
> suggestion I can think of at the moment (should we really use JI) is
> to use 3-limit Pythagorean intonation. But again, a Pythag. dim.
> fourth is only about 2 cents away from a pure major third so I'm
> asking what's the point if real Pythag. major thirds don't sound so
> "synchronous" as dim. fourths. And anyway, the Pythag. F-B is much
> closer to 10/7 rather than 7/5, so the 7th won't work either.

Thanks for the recommendation; I've never heard Steve Reich's music
until now. I also checked out your MIDI file; I like the chord
progressions definitely.

I'll need to listen to the compositions you named to comment any
further. ~D.

🔗chrisvaisvil@...

I would be glad to host your files. I think I'm just going to make an ftp directory with sub folders named for the submitter out if micro.soonlabel.com.

This offer is open to all on this list who need it.
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Danny Wier <dawiertx@sbcglobal.net>

Date: Fri, 06 Feb 2009 15:31:08
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] Scriabin's chord in JI

On Thu, 2009-02-05 at 00:58 -0500, Ben Miller wrote:
> this is a super topic!! can you let me hear this stuff?

It might take me a while; I'm a horrible procrastinator.

~D.

> On Thu, Feb 5, 2009 at 12:48 AM, Danny Wier <dawiertx@sbcglobal.net>
> wrote:
> On Thu, 2009-02-05 at 04:09 +0100, Marcel de Velde wrote:
> > Ah I'm sorry.
> > Gave it a bit more thought and I really can''t say yet what
> it should
> > be.
> > It's exactly in the area which I'm still working on.
> > Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
> > In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to
> me.
>
>
> I originally wanted 5/2 10/3 40/9 for the top three notes, but
> combined
> with 1/1 7/5 7/4 (I'll just use those for this reply), they
> produce a
> chord of 180:252:315:450:600:800. That's not something I'd
> want to
> resolve a progression with, if 1/1 is the root or key. If it's
> dissonance you want, or if you want to emphasize the 5/2 and
> up over all
> the other notes, then the chord would probably do fine.
>

🔗Danny Wier <dawiertx@...>

On Thu, 2009-02-05 at 18:31 -0500, Mike Battaglia wrote:

> As does Debussy. Debussy really nails it. I'm actually retuning his
> "Reverie" to be in 72tet now. There are a few instances in which the
> best overall tuning of a certain chord seems to line up with 12-tet,
> but sometimes JI chords really do sound like they nail what he was
> going for.

I've been thinking about "Clair de lune" a lot myself, specifically the
fast left-hand arpeggio second (measure 26 and after). The first two
beats have D flat major, the third F flat major. But I wonder if Fb and
Cb could be tuned as septimal minor third and seventh. In quarter-comma
meantone and 31-equal, the two pitches would map to Eh and Bh*, or
augmented second and sixth.

And you do have that climactic key change at m. 36 to E major (for
reasons of enharmonicity of course).

*'h' = my ad hoc symbol for natural.

> I don't know if you're familiar with that piece, but the beginning
> works very very well if the major thirds are tuned 9/7, for some
> reason I might never know.
>
> I think Stravinsky also approximates higher-limit JI in the Rite of
> Spring, especially 17/16 and 19/16, although I don't know if he was
> thinking in terms of the overtone series when he came up with some of
> his chords.

I'm not going to even touch /Le sacre du printemps/, haha. Not yet
anyway. But the thundering chord in "Les augurs" in part does seem to
fill out maqam Hijaz on E flat - and I've been contemplating how that
could be tuned in 72-edo. I have two versions of the lower jins
(tetrachord). {0, 7, 23, 30} approximates 1 16/15 5/4 4/3, which is
close to the Turkish method or raising the second note and lower the
third by a 53-tone comma. The other, {0, 8, 23, 30}, approximates the
harmonic chain 12:13:15:16 and is closer to the lower tetrachord of
Persian dastgahs Chahargah and Homayun (which would actually be {0, 8,
24, 30} in 72-edo and {0, 6, 18, 22} in 53).

I need to get to work on some sound files now. ~D.

🔗Carl Lumma <carl@...>

🔗Daniel Forro <dan.for@...>

🔗Daniel Forró <dan.for@...>

🔗Ben Miller <bencole.miller@...>

Thanks!! Get to it! :)

On 2/6/09, Danny Wier <dawiertx@...> wrote:
> On Thu, 2009-02-05 at 00:58 -0500, Ben Miller wrote:
>> this is a super topic!! can you let me hear this stuff?
>
> I'll need to make some MIDI (or low-quality MP3) files and upload them
> to the Files section. I'll try to do files for the augmented sixth
> chords, Scriabin's chord and other famous complex chords like Tristan
> and Hendrix. They would be played in their 12-tone version, followed by
> at least one 72-edo interpretation.
>
> It might take me a while; I'm a horrible procrastinator.
>
> ~D.
>
>> On Thu, Feb 5, 2009 at 12:48 AM, Danny Wier <dawiertx@...>
>> wrote:
>> On Thu, 2009-02-05 at 04:09 +0100, Marcel de Velde wrote:
>> > Ah I'm sorry.
>> > Gave it a bit more thought and I really can''t say yet what
>> it should
>> > be.
>> > It's exactly in the area which I'm still working on.
>> > Maybe it's 1/1 7/5 7/4 5/2 10/3 40/9
>> > In any case, the 1/1 5/2 10/3 40/9 seems allmost certain to
>> me.
>>
>>
>> I originally wanted 5/2 10/3 40/9 for the top three notes, but
>> combined
>> with 1/1 7/5 7/4 (I'll just use those for this reply), they
>> produce a
>> chord of 180:252:315:450:600:800. That's not something I'd
>> want to
>> resolve a progression with, if 1/1 is the root or key. If it's
>> dissonance you want, or if you want to emphasize the 5/2 and
>> up over all
>> the other notes, then the chord would probably do fine.
>>
>
>

--
Sent from my mobile device

🔗Petr Parízek <p.parizek@...>

🔗William Gard <billygard@...>

🔗Marcel de Velde <m.develde@...>

If you're playing something like C E G Bb D F# A in actual tonal music
you're most likely playing something like1/1 5/4 3/2 9/5 9/8 45/32 27/16
and not 1/1 5/4 3/2 7/4 9/4 11/4 13/4
sure the harmonic overtone version will sound ok played by itself as they're
harmonic overtones played as such.
But it would have no musical function. And you can't do anything with it.

Marcel

On Sat, Feb 7, 2009 at 8:33 PM, William Gard <billygard@...> wrote:

> This scale and chord is plainly based on the overtone series. You can
> hear it by just playing
> the first 7 odd harmonics. When I was first trying to justify the major
> scale on the basis of
> overtones, I was wondering why I didn't come up with a scale like this
> instead, with the raised
> 4th and flatted 7th.
>
> One things for sure about Debussy and Ravel, they do seem to have a strong
> affinity to the
> dominant 9th chord.
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Mike Battaglia
> <battaglia01@...> wrote:
> >
> > Debussy was the first person to use this chord, as far as I know. He
> > uses it in his work "Hommage a Rameau", for one. It's a dominant 7 #11
> > chord, which is "classically" derived from the Lydian Dominant scale:
> > C D E F# G A Bb C, which is the fourth mode of the melodic minor
> > scale.
>
>
>

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Debussy was the first person to use this chord, as far as I know. He
> uses it in his work "Hommage a Rameau", for one. It's a dominant 7
#11
> chord, which is "classically" derived from the Lydian Dominant
scale:
> C D E F# G A Bb C, which is the fourth mode of the melodic minor
> scale.
> -Mike
>
>
>
> On Thu, Feb 5, 2009 at 10:04 PM, Kraig Grady <kraiggrady@...> wrote:
> >
> > quite funny then cause i heard the chord in Gershwin without
> > mistake. Rhapsody in blue just before the last theme. I cannot off
> > hand think of an instance of this chord in either Stravinsky or
> > Bartok, but if you understand what they are doing you could surely
> > get this chord.
> >
> > There i s a Reich ensemble in L.A. where the leader has perfect
> > pitch, so good that someone did a piece where they would hit a
> > cluster of 11 notes and ask which note was left out. He nailed
> > every time without hesitation. I will ask him
> >
> > Posted by: "Petr Parízek"
> >
> > When I was in Slovakia in 2005, Reich came to have a presentation
there
> > and he said that he had found his inspiration for those chords
when
> > carefully studiing music of Stravinski and Bartók.
> > --
> >
> > /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> > Mesotonal Music from:
> > _'''''''_ ^North/Western Hemisphere:
> > North American Embassy of Anaphoria Island <http://anaphoria.com/>
> >
> > _'''''''_ ^South/Eastern Hemisphere:
> > Austronesian Outpost of Anaphoria
<http://anaphoriasouth.blogspot.com/>
> >
> > ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
> >
> >Well it is probably everywhere in Gershwin. In Jazz we call it the
7(b5), not the 7(#11) because it is at the expense of the fifth
whereas #11 appears with the maj 7 and still uncludes the fifth an
octave below. 7(b5) is one of the standard altered chords and, like
dim, is identical to the 7(b5) a flat-fifth away. This is handy
because we can substitute the five-one progression with b2-one so
that cycling becomes chromatic. On the other hand, #11 belongs to the
one maj chord group (lydian).

-Rick
>

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Another specific feature of 12-et is that it's allways out of
tune, and
> > every interval sounds thesame, and it puts a boring gray haze
over all music
> > played in it.
>
> First off, your reasoning is circular. It's out of tune relative to
> the chord you specified above. It's perfectly "in tune" if that's
what
> it's meant to be.
>
> The fact that 4 equal divisions of the octave produces a dim7 that
> sounds identical in all keys is a feature, not a bug. The fact that
> you label it to be a malformation of 12-tet doesn't take away from
its
> practicality. In this case, the fact that it is completely ambiguous
> and could resolve any which way is a property that has been
exploited
> for years.
>
> > Anything done in 12-et with the dim7 that sounds musical you can
do in JI
> > better.
>
> Except sound the same in every inversion.
>
> > That it doesn't sound exactly thesame in all keys is a good thing
and
> > doesn't take away musical possibilities.
>
> It takes away the possibility of having an unexpected resolution to
a
> different chord than you would expect.
>
> There are chords out there that have nothing to do with JI. Go look
up
> some of the recent discussions on metastable ratios, for example.
Such
> chords aren't against the law.
>
> -Mike
>
Mike's absolutely right about this. Dim chords are not 'out-of-tune'
but represent one of THE most important discoveries in all of musical
harmony. For whatever tuning system you might wish to adopt, octave
equivalence will always exist outside as a fact of nature and the
diminished 5 (tritone) is the ONLY interval which is the square root
of 2 i.e. when multiplied by itself gives the octave. That 1: sqr2 =
sqr2: 2 shows that both notes share precisely the same harmonic
function simultaneously (a C and F# will be both 1 and sqr2 at the
same time) so that it is impossible to determine the tonic.
Similarly, the dim chord is the only 4 note chord which is the 4th
root of 2, the augmented the only triad, etc...These symmetries
supply us with harmonic ambiguities which allow us to modulate
smoothly. If we lower each note in a dim chord by a semitone we get a
dom 7 chord, each one a min 3rd apart. So if we replace any dom 7
chord with a diminished a semitone above we can come out in any key a
min 3rd, b5 or maj 6 away. Most common is resolving to relative maj
from min or vice-versa eg G# dim = G7(b9) = E7(b9) groups, so we can
resolve to both C maj or A min. J.S. Bach uses this all the time. So
do Jazz musicians.

Rick

🔗Mike Battaglia <battaglia01@...>

Marcel: Why do you insist that the only valid harmonies are 5-limit ones?

-Mike

On Sat, Feb 7, 2009 at 3:30 PM, Marcel de Velde <m.develde@...> wrote:
> If you're playing something like C E G Bb D F# A in actual tonal music
> you're most likely playing something like
>
> 1/1 5/4 3/2 9/5 9/8 45/32 27/16
> and not 1/1 5/4 3/2 7/4 9/4 11/4 13/4
> sure the harmonic overtone version will sound ok played by itself as they're
> harmonic overtones played as such.
> But it would have no musical function. And you can't do anything with it.
> Marcel
>
> On Sat, Feb 7, 2009 at 8:33 PM, William Gard <billygard@...> wrote:
>>
>> This scale and chord is plainly based on the overtone series. You can hear
>> it by just playing
>> the first 7 odd harmonics. When I was first trying to justify the major
>> scale on the basis of
>> overtones, I was wondering why I didn't come up with a scale like this
>> instead, with the raised
>> 4th and flatted 7th.
>>
>> One things for sure about Debussy and Ravel, they do seem to have a strong
>> affinity to the
>> dominant 9th chord.
>>
>> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>> >
>> > Debussy was the first person to use this chord, as far as I know. He
>> > uses it in his work "Hommage a Rameau", for one. It's a dominant 7 #11
>> > chord, which is "classically" derived from the Lydian Dominant scale:
>> > C D E F# G A Bb C, which is the fourth mode of the melodic minor
>> > scale.
>>
>
>