"perfect JI"

Thanks everyone for the links and fundamental explanations.  I don't claim to
know the precise terminology - and my knowledge on the subject is limited - but
I'll do my best to convey what I was trying to say... 

It seemed to me - based upon performing basic calculations with harmonic ratios
-that no matter what I did, I always needed to adjust (tweak or compromise) a
little bit here and there in order for 3rds and 5th to "play nicely
together" while sounding reasonably decent for all 12 tones especially if there
would be key modulations.  In my calculations, I was intuitively accepting what
everyone is calling "rational intonation" as "just as good" in my mind as "just
intonation" and must confess that I don't yet understand why rational intonation
would not be equally as valid or acceptable to some as "pure just intonation". 

Oddly enough, before discovering and working some basic math with ratios of
pitch and harmony, the whole notion of temperment was something I'd never really
thought about.  I just played and listened to traditional western 12 tone
music - so this was quite a revelation to me. 

After trying to create my own "innovative" scales, I started learning that many
others over the years have worked very extensively on all of this.  19 tone
equal temperment immediately interested me in that it seems to add new harmonic
possibilities while retaining (for the most part) the traditional Western 12
tone harmonics. 

But then I joined this group and started reading posts about "perfect JI"
working equally well in "all keys" for "all songs" and kept "hitting a wall"...
I just have a fundamental lack of understanding how that can work. 

Michael basically summed up my JI question very well when he wrote:

<Isn't it fair enough to say temperaments can be explained as rounding between
fundamentals of JI IE...you are getting "more ratios near perfectly
Just...instead of less ratios that are exactly/perfectly Just?  How do you get
around this issue... without tempering?>

[Non-text portions of this message have been removed]

Hi Mark,

To answer your question.

First of all, what is the concept of "in tune"?
At first after a little experimenting it seems obvious.
A unison is in tune when it is in 1/1 ratio, an octave is in tune when it is in 2/1 ratio, 2 octaves is in tune when it is in 4/1 ratio, a fifth is in tune when it is in 3/2 ratio.
Now we all know that 12 fifths when reduced to a unison does not give 1/1, or reduced to an octave 2/1.
3 is a prime number, it can never become a 1 or a 2 by multiplying it by itself and then dividing that by 2.
But that's actually not a problem at all in practical music making, you just need more keys than 12 to play in different keys.
Pythagorean tuning works perfectly for all music, no real problems there.
But then.. that 81/64 major third does sound kind of dissonant. And we find the 5/4 major third.
We play a 1/1 5/4 3/2 major triad and go "yes! that sounds good and in tune, much better than the 81/64".
So people have logically said that 5/4 is the "justly intoned" major third.
However.. 3 major thirds of 5/4 don't make an octave. You can't multiply 5/4 by itself and get to 2/1.
And that IS a problem for practical music making.
And there are many many more problems the 5/4 causes like wolf fifths and drifting chord progressions etc.
But after tasting the sweet 5/4 major third we can no longer accept the 81/64 major third as in tune.
Coupled with a lot of evidence that choirs and trombone quartets etc naturally sing/play a major third as 5/4, the 5/4 has become THE just intoned major third.
Similarly, in classic 5-limit JI 6/5 has become THE minor third.

Now what I'm saying, is that this whole concept of 5/4 or 6/5 being THE major and minor thirds is wrong.
Not only does it not work mathematically in actual music, but it sounds wrong too - even in specific situations when there's nothing wrong with it mathematically.

Here 3 examples:

1/1 3/2 2/1 12/5 -> 3/2 15/8 9/4
If you play this chord progression with a stable electronic sound with enough overtones where you can hear the pitch well (listen carefully, it can be very subtle depending on your ears and speakers as well), you'll find that it doesn't sound right.
Now why wouldn't it? There's no mathematical impossibility here. It's a simple 1/1 6/5 3/2 minor followed by a 1/1 5/4 3/2 chord a fifth higher.
Also try it as 1/1 6/5 3/2 <-> 1/1 5/4 3/2 back and forth. Sounds terrible too.
Now play 1/1 3/2 2/1 64/27 -> 3/2 15/8 9/4. Yes that one does sound right. And so does 1/1 32/27 3/2 <-> 1/1 5/4 3/2.
And play 1/1 3/2 2/1 12/5 -> 3/2 256/135 9/4 -> 1/1 3/2 2/1 12/5. That one sounds right too.
And 5/4 3/2 15/8 -> 1/1 5/4 3/2 2/1 sounds right too.
So it's not the 1/1 6/5 3/2 in itself that sounds bad, nor the 1/1 5/4 3/2.
But certain combinations of 1/1 6/5 3/2 and 1/1 5/4 3/2 that sound bad and clearly call for other ratios.

Another example:
1/1 3/2 9/4 27/8 4/1 5/1 -> 27/16 5/2 27/8 4/1 5/1 (and hold the 5/1 during the progression)
Doesn't sound good does it.
1/1 3/2 9/4 27/8 4/1 81/16 -> 27/16 81/32 27/8 4/1 81/16 (hold the 81/16 during the progression)
This one does sound good.

Try the I-vi-ii-V7-I circle progression in the following scales:
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
The ii gets a wolf here. Doesn't sound good (but I long thought this was the best answer possible, how blind was I to the simple solution that comes next)
1/1 9/8 81/64 4/3 3/2 27/16 15/8 2/1 (for the final I chord in this progression one can make the 81/64 a 5/4)
This one sounds good.

So nothing is really impossible mathematically.
It's just that the original assumption that the major third should always be 5/4 and the minor always 6/5 was clearly wrong.
(and going to higher harmonic limits only makes the problems worse, I've explored that road fully)

Further experimentation/research eventually lead me to western music moving in a chain of fifths with one other chain of fifths a 5/4 parallel to it.
Fifths are always 3/2, octaves are always 2/1. To break these rules is to break "musical coherence" or "musical continuity" (there may be an exception for wolf fifths on passing notes, still experimenting with this, though likely the outcome will be that this is also not allowed)
Other rules I've found is that there are to be no comma shifts in held notes. And I've found rules on stepsizes.
Also found that (don't know how to really call it though) these rules collapse the 2 chains of fifths into these notes per octave available at any one time (it can shift from chord to chord)
1/1 135/128 9/8 32/27 5/4 4/3 45/32 3/2 405/256 5/3 16/9 15/8 2/1
(note, this is NOT a fixed scale for a key or something like that, this thing shifts around like crazy along the chain of fifths when one plays music.)
don't confuse the 1/1 point of the above "scale like thing" with the tonic. Any 1/1 5/4 3/2 or 1/1 6/5 3/2 in it can be the lowest resting point.

More to tell but that'll come on my website later.
I hope you get somewhat of an idea of how it works mathematically. Or of how it can work.
At it's basis lies a different concept of what's "in tune", one that actually sounds good :)
And in tune as it turns out is not captured at one one fixed time, but is relative to what came before and what comes after.

-Marcel

From: Mark Stephens
Sent: Sunday, February 27, 2011 10:51 PM
To: MakeMicroMusic@yahoogroups.com
Subject: [MMM] "perfect JI"

But then I joined this group and started reading posts about "perfect JI"
working equally well in "all keys" for "all songs" and kept "hitting a wall"...
I just have a fundamental lack of understanding how that can work.

Michael basically summed up my JI question very well when he wrote:

<Isn't it fair enough to say temperaments can be explained as rounding between
fundamentals of JI IE...you are getting "more ratios near perfectly
Just...instead of less ratios that are exactly/perfectly Just? How do you get
around this issue... without tempering?>

On Sun, Feb 27, 2011 at 6:13 PM, <m.develde@...> wrote:
>
> Here 3 examples:
>
> 1/1 3/2 2/1 12/5 -> 3/2 15/8 9/4
> If you play this chord progression with a stable electronic sound with
> enough overtones where you can hear the pitch well (listen carefully, it can
> be very subtle depending on your ears and speakers as well), you'll find
> that it doesn't sound right.
> Now why wouldn't it? There's no mathematical impossibility here. It's a
> simple 1/1 6/5 3/2 minor followed by a 1/1 5/4 3/2 chord a fifth higher.
> Also try it as 1/1 6/5 3/2 <-> 1/1 5/4 3/2 back and forth. Sounds terrible
> too.
> Now play 1/1 3/2 2/1 64/27 -> 3/2 15/8 9/4. Yes that one does sound right.
> And so does 1/1 32/27 3/2 <-> 1/1 5/4 3/2.

And play 1/1 3/2 2/1 19/8 -> 3/2 15/8 9/4, which also sounds right and
better than the last one.

> So nothing is really impossible mathematically.
> It's just that the original assumption that the major third should always be
> 5/4 and the minor always 6/5 was clearly wrong.
> (and going to higher harmonic limits only makes the problems worse, I've
> explored that road fully)

I guess I'll take the bait. Nobody really has much of a problem with
you experimenting with putting 81/64 where most people would put 5/4.
And nobody really has much of a problem with you trying to figure out
how to voice C-G-D-A-E in JI, or in experimenting with how to use wolf
fifths as stable sonorities in chords. There are plenty of times when
you use wolf fifths in ways that I think sound good, and plenty of
times when you use them in ways that I think just suck. Maybe it's
possible to set it up so that whenever a wolf fifth needs to get
involved, it sounds good and makes all of common practice work in JI.
I don't think you're quite there yet.

The problem is that none of the above actually matters. None of this
matters because it's not what you're known for in the community and
it's not really what your goal is. If your goal was just to do some
research to find the most pleasing way to expand meantone harmonies
out into JI, then you wouldn't have received a thousandth of the
negative reaction that you have.

The problem is that your attitude has effectively ruined the
reputation of whatever research it is that you're trying to do. You
have never once described your research as a "work in progress," or
said that your goals were to simply to find the best way to retune
meantone harmony to JI. Instead, you exploded onto the scene and
boldly proclaimed that you had the One True Tuning system, and said
that everything else besides your JI system du jour sounded like shit.
You decided you were going to arrogantly name it "Marcel-JI" after
yourself, which is terrible form. You posted enormous amounts of
messages per day like this, each time convinced that this was "the
right system" and anyone who disagreed was crazy, never stopping to
think that you'd probably change it again tomorrow.

You dismissed all of the tuning theory that had ever been developed
before you (have you actually read anything by Erv Wilson, ever?),
told composers that their music sounded like shit, decided you were
going to hold a competition to see "who had the best tuning system,"
said that Lassus' writing sucked because it didn't match your way of
thinking about JI, etc. Possibly the most cardinal sin of all is that
when you actually posted your results for people to see, and people
didn't like them, you humorously said that it's because they needed to
"learn how your system was superior" and to get used to it, which is
probably something you should get on with meantone harmonies. Or you
told them they needed to get their ears checked, which seems to imply
that your system doesn't work on human hearing. And I'm not even going
to get into the Drei Equale fiasco.

When people posted other lines of research, you were the first one
trolling their thread telling them how shitty it sounded and how
DeVelde-JI, your namesake system which will hopefully get you a statue
built some day, is the Only True Path. That is, until the day later,
when you realized that the only True Path turned out to have tons of
errors, and so you came up with a new true path. The latest is that
you've solved the comma shift problem by resorting to mostly 3-limit
JI, which I think is hilarious. And now you're saying how shitty the
Untwelve entries were because they all sound out of tune, which you
obviously did to get a rise out of people. This is the very definition
of what "trolling" means.

At some point, you actually had a decent line of research to work out,
which was to figure out some kind of optimal way to retune meantone to
JI. But that line of inquiry, which is a fairly interesting thing to
work out, has been completely buried by your penchant for
self-aggrandizement, which frankly comes off as arrogant and
repugnantly so. You have never posted an apology for any of the things
you have said, nor have you tried to make amends with anyone. And you
will continue to spin your wheels endlessly and never get a whit of
attention for any of the work that you're doing until you learn how to
be an adult and fit into an academic society with other researchers
and composers.

Figure it out.

-Mike

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Feb 27, 2011 at 6:13 PM, <m.develde@...> wrote:
> >
> > Here 3 examples:
> >
> > 1/1 3/2 2/1 12/5 -> 3/2 15/8 9/4
> > If you play this chord progression with a stable electronic sound with
> > enough overtones where you can hear the pitch well (listen carefully, it can
> > be very subtle depending on your ears and speakers as well), you'll find
> > that it doesn't sound right.
> > Now why wouldn't it? There's no mathematical impossibility here. It's a
> > simple 1/1 6/5 3/2 minor followed by a 1/1 5/4 3/2 chord a fifth higher.
> > Also try it as 1/1 6/5 3/2 <-> 1/1 5/4 3/2 back and forth. Sounds terrible
> > too.
> > Now play 1/1 3/2 2/1 64/27 -> 3/2 15/8 9/4. Yes that one does sound right.
> > And so does 1/1 32/27 3/2 <-> 1/1 5/4 3/2.
>
> And play 1/1 3/2 2/1 19/8 -> 3/2 15/8 9/4, which also sounds right and
> better than the last one.

I've done extensive research with the 19/16.
Several times.
But no, 19/16 does not sound better than 32/27.
I have a high end audio system, and have done very careful listening.
I could just make out (in several blind listening tests) that 19/16 was too high (posted that on this list back then too).
I could tell some days, other days I couldn't reliably tell which one I preferred.
But there's another problem with 19/16.
19/16 produces wolves!
You cannot use 19/16 in common practice music that uses somewhat big chords or certain connected major minor triads or you'll get drifting along the 19 axis (only way out are wolves like 256/171).
Trust me, I've been there (deep and several times) and 19/16 isn't the answer.
1/1 3/2 6/5 is the most consonant minor.
1/1 32/27 is the most consonant parallel minor.
1/1 1215/1024 is the minor with the most tension in common practice.

>
> > So nothing is really impossible mathematically.
> > It's just that the original assumption that the major third should always be
> > 5/4 and the minor always 6/5 was clearly wrong.
> > (and going to higher harmonic limits only makes the problems worse, I've
> > explored that road fully)
>
> I guess I'll take the bait. Nobody really has much of a problem with
> you experimenting with putting 81/64 where most people would put 5/4.
> And nobody really has much of a problem with you trying to figure out
> how to voice C-G-D-A-E in JI, or in experimenting with how to use wolf
> fifths as stable sonorities in chords. There are plenty of times when
> you use wolf fifths in ways that I think sound good, and plenty of
> times when you use them in ways that I think just suck. Maybe it's
> possible to set it up so that whenever a wolf fifth needs to get
> involved, it sounds good and makes all of common practice work in JI.
> I don't think you're quite there yet.

Just for clarity.
I no longer use wolf fifths.
I've done a lot of research in that area (abandoned it a few times, then picked it up again etc) as I thought it was the only acceptable solution and comme shifts and drifting were worse.
Sadly I was blind to the right way to integrate Pythagorean triads (had tried out a few wrong ways though).

>
> The problem is that none of the above actually matters. None of this
> matters because it's not what you're known for in the community and
> it's not really what your goal is. If your goal was just to do some
> research to find the most pleasing way to expand meantone harmonies
> out into JI, then you wouldn't have received a thousandth of the
> negative reaction that you have.

No that isn't my goal and never was.
Logic tells me that tuning is the basis of how the tonal side of music works.
An octave isn't an octave for nothing, it's 2/1.
And I belief that ones one "cracks the code" so to speak a whole new musical world will open up.
The reason I retune common practice music is only to discover how JI (and thus music) really works at a fundamental level.
I could think of no better way to find the laws of music then to theorise and test on common practice, then learn from my ears from the tests, theorise more with the new knowledge and try again.
And it worked!

>
> The problem is that your attitude has effectively ruined the
> reputation of whatever research it is that you're trying to do. You
> have never once described your research as a "work in progress," or
> said that your goals were to simply to find the best way to retune
> meantone harmony to JI. Instead, you exploded onto the scene and
> boldly proclaimed that you had the One True Tuning system, and said
> that everything else besides your JI system du jour sounded like shit.
> You decided you were going to arrogantly name it "Marcel-JI" after
> yourself, which is terrible form. You posted enormous amounts of

Yeah I did that on purpose because people were wining that I shouldn't call what I was doing JI.

> messages per day like this, each time convinced that this was "the
> right system" and anyone who disagreed was crazy, never stopping to
> think that you'd probably change it again tomorrow.

Yes, you're absolutely right!
I did have a bad tendensy there, absolutely true.
It came from passion, and somewhere I needed this belief that what I was doing was working.
It kept me in top concentration over and over again.
It's somehow how I work. But on the other side, I'm quick to admit if something is wrong somewhere.
I have appologised sincerely for this several times though.
And I'll do it again now.

My sincere apologies to the list for the times where I posted something too soon and was too sure of myself. I did not mean any harm by it, it was a state I often got in after days of nonstop work.
Shouldn't have bothered this list with it, but I'm an idiot sometimes.
I really mean what I say above, and I say it with shame.

>
> You dismissed all of the tuning theory that had ever been developed
> before you (have you actually read anything by Erv Wilson, ever?),

Yes I've read Erv Wilson and many many others.
In the case of Erv Wilson I did not dedicate considerable time to it because I saw early on that his theories do not solve the things I wish to see solved.
I still dismiss all of the tuning theory that has been developed, simply because it all leads to clearly out of tune results.
I have the good right to do so, and will continue to do so untill someone can show me a theory that can solve comma problems and actually tune something like Drei Equale successfully.

> told composers that their music sounded like shit, decided you were
> going to hold a competition to see "who had the best tuning system,"
> said that Lassus' writing sucked because it didn't match your way of
> thinking about JI, etc. Possibly the most cardinal sin of all is that
> when you actually posted your results for people to see, and people
> didn't like them, you humorously said that it's because they needed to
> "learn how your system was superior" and to get used to it, which is
> probably something you should get on with meantone harmonies. Or you
> told them they needed to get their ears checked, which seems to imply
> that your system doesn't work on human hearing. And I'm not even going
> to get into the Drei Equale fiasco.
>
> When people posted other lines of research, you were the first one
> trolling their thread telling them how shitty it sounded and how
> DeVelde-JI, your namesake system which will hopefully get you a statue
> built some day, is the Only True Path. That is, until the day later,
> when you realized that the only True Path turned out to have tons of
> errors, and so you came up with a new true path. The latest is that
> you've solved the comma shift problem by resorting to mostly 3-limit
> JI, which I think is hilarious. And now you're saying how shitty the
> Untwelve entries were because they all sound out of tune, which you
> obviously did to get a rise out of people. This is the very definition
> of what "trolling" means.

No I never did anything to troll.
The closest I've come to trolling was to do things like use the name "Marcel's JI", or recently call compositions "songs" because I think it's such nonsense that people find it reason to behave so negatively to Michael and wish to show him some support and at the same time sort of give the finger to all those whiners.
But it's more of a silent resistance things than trolling because I do not hope in any way that it provokes another response.

>
> At some point, you actually had a decent line of research to work out,
> which was to figure out some kind of optimal way to retune meantone to
> JI. But that line of inquiry, which is a fairly interesting thing to
> work out, has been completely buried by your penchant for
> self-aggrandizement, which frankly comes off as arrogant and
> repugnantly so. You have never posted an apology for any of the things
> you have said, nor have you tried to make amends with anyone. And you

Yes I have apologised several times, and I just about allways try to make ammends with people.
I usually start out with polite on topic posts, often trying to be helpfull. And I start out with a blanc sheet to just about anybody, even those who've been particularly nasty to me in the past.
But then the unprovoked negative personal attacks start again...
They tire me soo...
And you Mike are guilty of this too. I try to do normal to you every time again, yet you seem to have made up your mind about me a long time ago and when I do normal posts you're one of the people who comes at me with a negative personal attack.
You're not the worst, Carl, AKJ and Oz to name a few are truly terrible.
I've even tried to make amends with Carl several times. But he started again and again.
But even Carl and the others. I start with respectful posts, if they don't do personal attacks anymore then relations will be as normal in no time. I'm a very forgiving person.
And I mean personal attacks only, objective critisism no problem, even if it's harsh.

> will continue to spin your wheels endlessly and never get a whit of
> attention for any of the work that you're doing until you learn how to
> be an adult and fit into an academic society with other researchers
> and composers.
>
> Figure it out.
>
> -Mike
>

I don't wish to fit in any academic society :)
I see myself as an outsider of academic society.
I did not even finish highschool and have learned myself everything I've done in my life and am proud of that.
I'm very happy the way things are going with my work and the way I work.
Sure I wish there were less negative contacts on the list, but my work is the most important.

-Marcel

MikeB to Marcel>"The problem is that none of the above actually matters. None of this matters because it's not what you're known for in the community and it's not really what your goal is. If your goal was just to do some research to find the most pleasing way to expand meantone harmonies out into JI, then you wouldn't have received a thousandth of the negative reaction that you have."

   A real problem on this list now as I see it, is people telling each other what their supposed "goals" are and then framing them for it...EVEN after they make apparent deliberate efforts to change their way.
  Not to say Mike B/"you" intended it that way, but it sure sounds like it.

   Marcel finally "turned around" and started giving practical examples that basically the entire list had been begging him for (IE "either prove it or be quiet").  However instead of saying "ok, now we're getting somewhere, thank you...but I still see some problems with your theory which are...", you, Carl, and several others apparently are more interested in holding grudges against Marcel.  The only person on this entire thread I think has given an informative response to Marcel far as his theories (completely with criticism, but framed constructively)...is Igs.

>"Instead, you exploded onto the scene and boldly proclaimed that you had the One True Tuning system, and said that everything else besides your JI system du jour sounded like shit....Possibly the most cardinal sin of all is that when you actually posted your results for people to see, and people didn't like them, you humorously said that it's because they needed to "learn how your system was superior" and to get used to it"

    This is the one truly nasty thing I agree Marcel did and keeps doing.  But that doesn't automatically cancel his efforts either.  At the least, I suggest replying to him "I see some value in these efforts and that you're headed in a positive direction, but that certainly does not make your answer THE only answer or perfect".

>"You dismissed all of the tuning theory that had ever been developed before you (have you actually read anything by Erv Wilson, ever?),"

  Between this thread and the "Beatles" thread...I really wish this is one thing people would just drop.
  Just because someone is well known in music should not mean that you either have to agree with their artistry or be labeled an ignorant idiot.  Personally I haven't found any of Wilson's MOS's over 6 tones satisfactory to my ears...despite the mathematical elegance of his theories.  Same goes for Harry Partch and o-tonality and u-tonality...both of which I understand but neither of which I fully agree with (and o-tonality of which I agree with much more).. 

>"But that line of inquiry, which is a fairly interesting thing to work out, has been completely buried by your penchant for self-aggrandizement"

    I think Igs said it best:
essentially (as I understand it) that Marcel is coming up with a system of when to use more strict JI style chords and when to use pythagorean-style chords in order to introduce tension and resolve in places composers in common practice music use them most. 

   I figure we can either take paths of
A) Starting arguments based on pre-conceptions of each other's personalities (especially with reference to "deserved" personalities IE people famous in the world of microtonality)
B) Work on actual theories and not care who said them or try to guess why.  Granted, if there is a PROBLEM you see with a theory, go and point it out.  But do so saying something like "I need an example before I believe this, can you give me a specific example?" or "There is a problem with this theory I see in that it uses such high-numbered fractions despite being called JI...this needs to be explained if I am to take the theory
seriously."

     ATTACKS (on theories, not people) ARE WELCOME AND AT TIMES NEEDED FOR PROGRESS, BUT LET'S AT LEAST FOCUS ON CRITICIZING THE THEORIES RATHER THAN THE PEOPLE...I figure that would make things around here a whole lot more productive, not to mention more civilized.

--- In MakeMicroMusic@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> The only person on this entire thread I think has given an informative response to Marcel far as his theories (completely with criticism, but framed constructively)...is Igs.

Marcel agreed that his stuff could be done in a microtemperament, so I doubt I flamed him too hard.

>   Just because someone is well known in music should not mean that you either have to agree with their artistry or be labeled an ignorant idiot.  Personally I haven't found any of Wilson's MOS's over 6 tones satisfactory to my ears...despite the mathematical elegance of his theories. 

And what is the diatonic scale, chopped haggis?

Me> "Just because someone is well known in music should not mean that
you either have to agree with their artistry or be labeled an ignorant
idiot.  Personally I haven't found any of Wilson's MOS's over 6 tones
satisfactory to my ears...despite the mathematical elegance of his
theories. "

Gene>"And what is the diatonic scale, chopped haggis? "
     Hahaha....no...specifically when I said Wilson's MOS scales, I meant the ones on his old Golden Horagrams page.  Of course a diatonic scale IE with LLsLLLs is an MOS...then again, something like 7-tone diatonic JI with the additional "medium" step size making it "Hyper MOS" can also sound distinctively diatonic.

    How to say this as simply as possible...
A) People seem to prefer scales with as few very small steps as possible and, where they exist, for them to be maximally seperated.ALA the diatonic scale
B) People seem to prefer scales where rotations in chord progressions (and not just the intervals involved in making the chords themselves) are pure or at least near-pure fifths.

    Now you can make like I do and go a bit off the deep end and use weird intervals like 12/11 as "semitones" and the occasional resulting 22/15-like ratios as fifths...but, at least as I've found through listening practice,  people are still going to notice.

  Even my "flagship" hybrid scale, which has both 2 maximally spaced apart semitones and 2 maximally spaced apart "bad" 22/15 fifths (making in many way a diatonic-like formation)...a fair percentage of people who commented on the scale (I'd say, something around 20%) said the 22/15 still bit them the wrong way despite their "diatonic" positioning.
  And that contrasts to my "Arab" mode of the scale where the 2 22/15 "bad" fifths are not maximally spaced and more like half of people said "this sounds too weird".

   Lesson learned...people seem to insist on pure fifths and diatonic patterns in scales...which typically seems to point straight toward common practice music...even more so than my attempts to "blend between diatonic scales under Meantone and Mohajira scales".  And Marcel seems to be sticking to those diatonic restrictions pretty well so far as I can see...

[Non-text portions of this message have been removed]

On Sun, Feb 27, 2011 at 8:12 PM, Marcel <m.develde@...> wrote:
>
> And you Mike are guilty of this too. I try to do normal to you every time again, yet you seem to have made up your mind about me a long time ago and when I do normal posts you're one of the people who comes at me with a negative personal attack.

No. I respect what you're trying to do and I think you deserve as much
respect as anyone else. I am simply trying to show you how you come
off, and want to put out there that you'd receive more support if you
came across as more humble. That is all.

> You're not the worst, Carl, AKJ and Oz to name a few are truly terrible.

AKJ is "truly terrible" because, as I remember it, you told him that
his work was "out of tune shit" or something like that.

-Mike

--- In MakeMicroMusic@yahoogroups.com, <m.develde@...> wrote:

> Similarly, in classic 5-limit JI 6/5 has become THE minor third.
>
> Now what I'm saying, is that this whole concept of 5/4 or 6/5 being THE
> major and minor thirds is wrong.
> Not only does it not work mathematically in actual music, but it sounds
> wrong too - even in specific situations when there's nothing wrong with it
> mathematically.
>
> Here 3 examples:
>
> 1/1 3/2 2/1 12/5 -> 3/2 15/8 9/4
> If you play this chord progression with a stable electronic sound >with
> enough overtones where you can hear the pitch well (listen >carefully, it can
> be very subtle depending on your ears and speakers as well), you'll >find
> that it doesn't sound right.
> Now why wouldn't it? There's no mathematical impossibility here. >It's a
> simple 1/1 6/5 3/2 minor followed by a 1/1 5/4 3/2 chord a fifth >higher.
> Also try it as 1/1 6/5 3/2 <-> 1/1 5/4 3/2 back and forth. Sounds >terrible
> too.
> Now play 1/1 3/2 2/1 64/27 -> 3/2 15/8 9/4. Yes that one does sound >right.
> And so does 1/1 32/27 3/2 <-> 1/1 5/4 3/2.

This response is not about "taking the bait". It is about addressing tuning issues in a knowledgeble and thoughtful way.

Marcel, you are not really to be blamed for not knowing basic things about "common practice" music. But eventually you should learn. Let's call those chords c minor and G major. That's C-Eb-G and G-B-D as you probably know.

It's obvious what bothers you about the progression. Between Eb and B, no matter how you voice the chords, there is always going to be an augmented fifth (or a diminished fourth, if inverted). The fifth from Eb is Bb, not B, and the fourth from B is E, not Eb.

These are pretty strong "dissonant" intervals when thirds are tuned pure- the diminished fourth is 427 cents for example. There is no doubt that this is precisely what's bothering you, for this is the thing your solution "fixes".

By lowering the Eb to 32:27, rather than using 6:5, you are trying to change the augmented fifth to a minor sixth, or the diminished fourth to a major third. That is, you are trying to change an Eb to a D#, making them one interval, an identity that happens in strict 12-tET.

You could call this tempering out 128:125, or tempering out the lesser diesis, but most importantly, because "common practice" only has fixed intervals in theory, with a great variety of intonation possibilies in actual practice, it is "tempering out the difference between an augmented fifth and a minor sixth" (or dim 4th and M3).

What you are doing is a kind of temperament.

By the way, the above is an example of how those who claim that "5-limit JI" isn't microtonal are full of shit: the 128:125 distinction made when you tune common practice music with pure thirds and fifths is, at a bit smaller than a quartertone, a stellar example of a discernable and characteristic microtonal interval.

>
> Try the I-vi-ii-V7-I circle progression in the following scales:
> 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
> The ii gets a wolf here. Doesn't sound good (but I long thought >this was the
> best answer possible, how blind was I to the simple solution that >comes
> next)
> 1/1 9/8 81/64 4/3 3/2 27/16 15/8 2/1 (for the final I chord in this
> progression one can make the 81/64 a 5/4)
> This one sounds good.

Whether or not this sounds good depends on what kind of major thirds you want- for artistic purposes of course. For bright hard thirds this sounds good, and maybe 14:11 "thirds" would sound even better for some people, but for "beatless", or soft mellow thirds, it sounds simply wrong, and maybe for some people thirds even lower than 5:4, such as the thirds of 1/3 comma meantone, would be the best of all.

As far as the "making micro music" part, Marcel, you should take into consideration the fact that you can sell any kind of tuning- absolutely any- if you've can rig up an acoustic instrument to play it.

-Cuthbert Lobawad (well I'm trying to restructure my online presence to avoid spam, redirect correspondance to specific appropriate addresses, etc. So I legally changed my name to one which well describes online communication in general. But you guys will recognize me by virtue of my very poor communication skills, ignorance, idiocy and so on. :-) )

--- In MakeMicroMusic@yahoogroups.com, "lobawad" <lobawad@...> wrote:

> But you guys will recognize me by virtue of my very poor communication skills, ignorance, idiocy and so on. :-) )

That makes you different from anyone else around here how, exactly?

>-Cuthbert Lobawad (well I'm trying to restructure my online presence
>to avoid spam, redirect correspondance to specific appropriate
>addresses, etc. So I legally changed my name to one which well
>describes online communication in general.

You legally changed your name to avoid spam? That's hardcore.

>But you guys will recognize
>me by virtue of my very poor communication skills, ignorance, idiocy
>and so on. :-) )

Actually we can't, so why don't you just tell us who you are?

-Carl

On Thu, Mar 3, 2011 at 2:44 PM, Carl Lumma <carl@...> wrote:
>
> >-Cuthbert Lobawad (well I'm trying to restructure my online presence
> >to avoid spam, redirect correspondance to specific appropriate
> >addresses, etc. So I legally changed my name to one which well
> >describes online communication in general.
>
> You legally changed your name to avoid spam? That's hardcore.
>
> >But you guys will recognize
> >me by virtue of my very poor communication skills, ignorance, idiocy
> >and so on. :-) )
>
> Actually we can't, so why don't you just tell us who you are?

MMM has sure been entertaining recently.

-Mike

Wait a minute. Use of a pseudonym, didactic tone

> Marcel, you are not really to be blamed for not knowing basic things
> about "common practice" music. But eventually you should learn.

mild condescension

> It's obvious what bothers you about the progression

actual understanding of music theory

> By lowering the Eb to 32:27, rather than using 6:5, you are trying to
> change the augmented fifth to a minor sixth,

minus one point for use of profanity

> By the way, the above is an example of how those who claim that
> "5-limit JI" isn't microtonal are full of shit:

emoticon

> :-)

It is none other than Paul Erlich. -Carl

Hi Lobawad,

Thanks for your serious response.

> This response is not about "taking the bait". It is about addressing tuning issues in a knowledgeble and thoughtful way.
>
> Marcel, you are not really to be blamed for not knowing basic things about "common practice" music. But eventually you should learn. Let's call those chords c minor and G major. That's C-Eb-G and G-B-D as you probably know.
>
> It's obvious what bothers you about the progression. Between Eb and B, no matter how you voice the chords, there is always going to be an augmented fifth (or a diminished fourth, if inverted). The fifth from Eb is Bb, not B, and the fourth from B is E, not Eb.
>

Thanks for explaining it.
But I already knew this :)

Btw, the diatonic system and our notation are actually not based on 5-limit JI but purely on Pythagorean.
If you follow our notation and diatonic theory exactly then you can simply follow the chain of fifths in our notation to get the corresponding Pythagorean tuning.
C major and A minor as a chain of fifths on:
F-C-G-D-A-E-B-F#-C#-G#-D#-A#

> These are pretty strong "dissonant" intervals when thirds are tuned pure- the diminished fourth is 427 cents for example. There is no doubt that this is precisely what's bothering you, for this is the thing your solution "fixes".
>

I prefer to call it tuning the thirds to 5/4 instead of saying that's tuning them "pure" as opinions differ on that :)

And yes, this is one of the things that's bothering me. Though there are many many other things that bother me and gets fixed in my solution.

> By lowering the Eb to 32:27, rather than using 6:5, you are trying to change the augmented fifth to a minor sixth, or the diminished fourth to a major third. That is, you are trying to change an Eb to a D#, making them one interval, an identity that happens in strict 12-tET.
>

No, the 32/27 is actually a normal Eb in our notation in normal music theory.
Follow the chain of fifths down from F 4/3 to come to Eb 32/27.

Btw in Drei Equale no1 the tuning is sometimes:
3/4 1/1 32/27 -> 3/4 15/16 9/8
and sometimes: 3/4 1/1 1215/1024 -> 3/4 15/16 9/8
It depends on certain things which I won't explain here now.

(btw I've had the right version of no1 up on this site for over 4 months, only last week I had a kink in my theory which made me do something stupid and make many chords 1/1 32/27 3/2, this one is wrong, just in case you had a look at the pdf past days)

> You could call this tempering out 128:125, or tempering out the lesser diesis, but most importantly, because "common practice" only has fixed intervals in theory, with a great variety of intonation possibilies in actual practice, it is "tempering out the difference between an augmented fifth and a minor sixth" (or dim 4th and M3).
>
> What you are doing is a kind of temperament.
>

I must disagree here.
In my opinion I'm not tempering anything.

> By the way, the above is an example of how those who claim that "5-limit JI" isn't microtonal are full of shit: the 128:125 distinction made when you tune common practice music with pure thirds and fifths is, at a bit smaller than a quartertone, a stellar example of a discernable and characteristic microtonal interval.
>
> >
> > Try the I-vi-ii-V7-I circle progression in the following scales:
> > 1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1
> > The ii gets a wolf here. Doesn't sound good (but I long thought >this was the
> > best answer possible, how blind was I to the simple solution that >comes
> > next)
> > 1/1 9/8 81/64 4/3 3/2 27/16 15/8 2/1 (for the final I chord in this
> > progression one can make the 81/64 a 5/4)
> > This one sounds good.
>
> Whether or not this sounds good depends on what kind of major thirds you want- for artistic purposes of course. For bright hard thirds this sounds good, and maybe 14:11 "thirds" would sound even better for some people, but for "beatless", or soft mellow thirds, it sounds simply wrong, and maybe for some people thirds even lower than 5:4, such as the thirds of 1/3 comma meantone, would be the best of all.
>

Music indicates itself in which position it wants mellow chords (for instance a final chord) or chords with more tension.
Also normal music theory says these things about tension and relaxation and the way they function in a composition.

-Marcel

On Thu, Mar 3, 2011 at 2:58 PM, Carl Lumma <carl@...> wrote:
>
> mild condescension
>
> > It's obvious what bothers you about the progression
>
> actual understanding of music theory
>
> > By lowering the Eb to 32:27, rather than using 6:5, you are trying to
> > change the augmented fifth to a minor sixth,

Yeah, but this isn't right, is it? In common practice harmony, 32/27
isn't an augmented second, it's still a minor third. Sinbad Cuthbar
has confused 128/125 with 81/80.

> It is none other than Paul Erlich. -Carl

I guessed Paul, but then I wasn't sure because of the above mixup.

-Mike

Lobawad>"But you guys will recognize me by virtue of my very poor communication skills, ignorance, idiocy and so on. :-) )"

Gene>"That makes you different from anyone else around here how, exactly? "

    It's always amusing how many generally smart people are on this list merrily ranting on about how each other (and often themselves) are idiots or make tons of mistakes.  I think it's kind of a side-effect of a culture here (and on many music sites) that seems to say by proclaiming yourself as having huge humility IE saying "I have a ton to learn", you are somehow indirectly showing how much you've read to find out just how much there is out there you don't know (IE that you are...an "experienced idiot"). :-D

   But hey, we could always try an alternative, like focusing on what we have done well and improving on it rather than impulsively saying "yeah, I'm don't know a whole lot about this" just because you aren't Erv Wilson or Harry Partch.  No wonder relatively few new ideas come out...we are so busy trying to "disprove the null hypothesis" (or call the person who came up with it dumb) to actually give ourselves fair credit for what we've done well.

[Non-text portions of this message have been removed]

Mike wrote:

>>> By lowering the Eb to 32:27, rather than using 6:5, you are trying to
>>> change the augmented fifth to a minor sixth,
>
>Yeah, but this isn't right, is it? In common practice harmony, 32/27
>isn't an augmented second, it's still a minor third. Sinbad Cuthbar
>has confused 128/125 with 81/80.

12/5 - 15/8 = 32/25 and 32/25 - 5/4 = 128/125.

A dim4 is always -8, whereas an M3 is +4. In this case, that means
reinterpreting the interval from B-Eb as B-D#

-Carl

> A dim4 is always -8, whereas an M3 is +4. In this case, that means
> reinterpreting the interval from B-Eb as B-D#
>
> -Carl
>

Uhm..
A dim4 is -8. A M3 is +4 yes.
But why would that mean reinterpreting the interval from B-Eb as B-D#?
B-Eb being the diminished 4th nothing wrong with that.
In Pythagorean it is 3/2 2/1 32/27 -> 3/2 243/128 9/4
243/128 - 32/27 is the diminished fourth as B-Eb.
Making it a D# would mean raising the 32/27 by a Pythagorean comma.

Ah and all this Pythagorean logic breaks down when attaching 5-limit ratios to it anyhow..

-Marcel

Marcel wrote:
>A dim4 is -8. A M3 is +4 yes.
>But why would that mean reinterpreting the interval from B-Eb as B-D#?

Because B-Eb is a 4th and B-D# is a 3rd.

>B-Eb being the diminished 4th nothing wrong with that.

Correct. There is nothing "wrong" with it.

>Making it a D# would mean raising the 32/27 by a Pythagorean comma.

The ratio you get by specifying that it is a 3rd or a 4th or
anything else depends on the mapping.

-Carl

On Thu, Mar 3, 2011 at 4:02 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> >>> By lowering the Eb to 32:27, rather than using 6:5, you are trying to
> >>> change the augmented fifth to a minor sixth,
> >
> >Yeah, but this isn't right, is it? In common practice harmony, 32/27
> >isn't an augmented second, it's still a minor third. Sinbad Cuthbar
> >has confused 128/125 with 81/80.
>
> 12/5 - 15/8 = 32/25 and 32/25 - 5/4 = 128/125.
>
> A dim4 is always -8, whereas an M3 is +4. In this case, that means
> reinterpreting the interval from B-Eb as B-D#

He didn't say 32/25, he said 32/27. 32/27 is a pythagorean minor
third, not an augmented second.

-Mike

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:
>
>
> > A dim4 is always -8, whereas an M3 is +4. In this case, that means
> > reinterpreting the interval from B-Eb as B-D#
> >
> > -Carl
> >
>
>
> Uhm..
> A dim4 is -8. A M3 is +4 yes.
> But why would that mean reinterpreting the interval from B-Eb as B-D#?
> B-Eb being the diminished 4th nothing wrong with that.
> In Pythagorean it is 3/2 2/1 32/27 -> 3/2 243/128 9/4
> 243/128 - 32/27 is the diminished fourth as B-Eb.
> Making it a D# would mean raising the 32/27 by a Pythagorean comma.
>
> Ah and all this Pythagorean logic breaks down when attaching 5-limit ratios to it anyhow..
>
> -Marcel
>

Noone is confusing 128:125 with 81:80. Marcel's original example is in pure intonation, and the comma in question there is indeed 128:125, reckoned exactly as Carl just did.

In altering the Just chords the way he did, Marcel is tempering out, or altering, 128:125, not 81:80. The interval between 6/5 and 15/8 is 25/16, its inversion 32/25. However you voice c-G using pure thirds, there will be either an augmented fifth or a diminished fourth between the Eb and B. This is clearly what is bothering him (what else could be?), and what he is altering.

"Making the Eb a D#" does not mean raising or lowering any specific ratio by any other specific ratio. "Common practice" is based on no exact specific tuning. When the minor third above C is the same pitch as the major third above B, you are "making the Eb a D#"- I deliberately used the word "identity" here to indicate the, well, pitch identity of the intervals, to avoid misundertanding.

Happily my poor communication skills did not prevent Carl from recognizing exactly what was meant.

Anyway, Marcel stated the point: "Ah and all this Pythagorean logic breaks down when attaching 5-limit ratios to it anyhow..".

Isn't that what everyone keeps trying to tell you, Marcel? Didn't Gene just recently say that you are mixing Pythagorean and 5-limit Just?

Marcel, you answer here consisted of simply shifting the topic from the chords you presented (minor and major with pure thirds- they're called pure because they are beatless, that's just the way it is) to Pythagorean ratios, terminology, and commas.

This was not a glib ploy, though, it was the correct answer according to your system: when you percieve something as a problem with pure thirds, you shift to Pythagorean.

I don't like your results so far, but I respect them as they seem to have a consistent "Marcel" sound to them. Leaving taste aside, you have not eliminated commas, but created different commas. Some of them may be quite unusual.

Btw, 1215/1024 IS labeled as an augmented second in Scala.
But I take that to be complete nonsense. That's like pretending 5/3 is a 27/16 and simply continue counting from there on.
Doesn't work that way.
Also not the other way around.
The 5 limit intervals are PARALLEL to the Pythagorean ones, not a continuation of the Pythagorean chain.
So to come with normal music theory / notation arguments and then saying it relates 1 on 1 with how to tune 5-limit JI doesn't work at all.

-Marcel

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Mar 3, 2011 at 4:02 PM, Carl Lumma <carl@...> wrote:
> >
> > Mike wrote:
> >
> > >>> By lowering the Eb to 32:27, rather than using 6:5, you are trying to
> > >>> change the augmented fifth to a minor sixth,
> > >
> > >Yeah, but this isn't right, is it? In common practice harmony, 32/27
> > >isn't an augmented second, it's still a minor third. Sinbad Cuthbar
> > >has confused 128/125 with 81/80.
> >
> > 12/5 - 15/8 = 32/25 and 32/25 - 5/4 = 128/125.
> >
> > A dim4 is always -8, whereas an M3 is +4. In this case, that means
> > reinterpreting the interval from B-Eb as B-D#
>
> He didn't say 32/25, he said 32/27. 32/27 is a pythagorean minor
> third, not an augmented second.
>
> -Mike
>

You'd call the major third above B "Eb"? D# can be an augmented second- it can also be a major third. The point is that by lowering his minor third, Marcel is obviously attempting to alter the inevitable aug/dim found in a "5-limit" c-G, such that it "sounds like" some kind of maj/min. In a Pythagorean system, this kind of thing works. Obviously it works in 12-tET.

In Marcel's system, with a pure third in the major chord, he winds up with a 512/405, 405 cents, between the B and the Eb. This is obviously an attempt to turn the strong sound of the 427 cent 32/25 diminished fourth of a Just B-Eb into some kind of "major third". And the major third above B is D#.

(Depending on voicing, this could be about the aug5 being altered to pass as a minor sixth, of course.)

Hopefully this is clear now. As nightmarish as the maze of Marcel is, I believe that I haven't made any misteps here, and that the analysis is simply accurate.

More importantly, by listening to Marcel's examples, you can hear weird commas or what are clearly "temperings out".

--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Mar 3, 2011 at 4:02 PM, Carl Lumma <carl@...> wrote:
> >
> > Mike wrote:
> >
> > >>> By lowering the Eb to 32:27, rather than using 6:5, you are trying to
> > >>> change the augmented fifth to a minor sixth,
> > >
> > >Yeah, but this isn't right, is it? In common practice harmony, 32/27
> > >isn't an augmented second, it's still a minor third. Sinbad Cuthbar
> > >has confused 128/125 with 81/80.
> >
> > 12/5 - 15/8 = 32/25 and 32/25 - 5/4 = 128/125.
> >
> > A dim4 is always -8, whereas an M3 is +4. In this case, that means
> > reinterpreting the interval from B-Eb as B-D#
>
> He didn't say 32/25, he said 32/27. 32/27 is a pythagorean minor
> third, not an augmented second.
>
> -Mike
>

> Noone is confusing 128:125 with 81:80. Marcel's original example is in pure intonation, and the comma in question there is indeed 128:125, reckoned exactly as Carl just did.
>
> In altering the Just chords the way he did, Marcel is tempering out, or altering, 128:125, not 81:80. The interval between 6/5 and 15/8 is 25/16, its inversion 32/25. However you voice c-G using pure thirds, there will be either an augmented fifth or a diminished fourth between the Eb and B. This is clearly what is bothering him (what else could be?), and what he is altering.
>

B 15/16 - Eb 32/27 is not a normal pure major third, it is 512/405.
A Pythagorean major third would be 81/64 as in B 15/16 - Eb 1215/1024
A regular 5-limit major third would be 5/4 as in B 15/16 - Eb 75/64 (now here you have an argument for D# perhaps) but this is actually out of tune. Good would also be B 243/256 - Eb 1215/1024 (perhaps also labeled as D#)

And perhaps I should make a list of things that bother me in classic 5-limit "JI" as there's a LOT :)
But anyhow, the method you describe of stacking 5/4 fifths is a method that doesn't work and sounds very out of tune.
One can't practice common practice music with it, period.

> "Making the Eb a D#" does not mean raising or lowering any specific ratio by any other specific ratio. "Common practice" is based on no exact specific tuning. When the minor third above C is the same pitch as the major third above B, you are "making the Eb a D#"- I deliberately used the word "identity" here to indicate the, well, pitch identity of the intervals, to avoid misundertanding.
>

There are very specific rules for notation.
And they are based on Pythagorean.

> Happily my poor communication skills did not prevent Carl from recognizing exactly what was meant.
>
> Anyway, Marcel stated the point: "Ah and all this Pythagorean logic breaks down when attaching 5-limit ratios to it anyhow..".
>
> Isn't that what everyone keeps trying to tell you, Marcel? Didn't Gene just recently say that you are mixing Pythagorean and 5-limit Just?
>

And you think I'm using Pythagorean chords in places because of notation reasons??

> Marcel, you answer here consisted of simply shifting the topic from the chords you presented (minor and major with pure thirds- they're called pure because they are beatless, that's just the way it is) to Pythagorean ratios, terminology, and commas.
>

No ratios is beatless except the unison of 1/1.
5/4 beats less than 81/64 yes, but both are just.
81/64 however isn't just in places where the 5/4 should be.
5/4 isn't just in places where the 81/64 should be.
Music indicates where which one goes.

> This was not a glib ploy, though, it was the correct answer according to your system: when you percieve something as a problem with pure thirds, you shift to Pythagorean.
>

There's a lot more to it than that.

> I don't like your results so far, but I respect them as they seem to have a consistent "Marcel" sound to them. Leaving taste aside, you have not eliminated commas, but created different commas. Some of them may be quite unusual.
>

No unusual commas are used at all.
All fifths are 3/2, fourths 4/3.
And there are 3 major thirds, 5/4, 81/64 and 512/405.
corresponding minors, and sixths.
And all tritones are 45/32 or it's inversion.

-Marcel

--- In MakeMicroMusic@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> More importantly, by listening to Marcel's examples, you can hear weird commas or what are clearly "temperings out".
>

No weird commas or tempering.
Are you listening to the right examples?

/makemicromusic/files/Marcel/Beethoven_Drei_Equale_no1_%28MJI_2010-10-22%29.mid

/makemicromusic/files/Marcel/Lassus_comma-pump_JI_%2820110302_MdV%29.mid

I won't include Drei Equale no2 as it doesn't have many comma problems (for classic 5-limit "ji" that is..) and is mostly straight 5/4 majors (and also I have to put up the old version as this one has 2 notes off by a schisma)

Also didn't include no3 as I'm redoing it. Did it yesterday with the Schisma error with big consequences throughout the piece.

So these 2 examples I posted are good examples of my theory.
Yes, they sound boring and "normal", but I consider that a good thing as nobody in the general public will take any offense to them, yet they are strongly more emotional and clear than 12tet.

-Marcel

lobawad wrote:

>Noone

Noone! Are you sure you're Paul Erlich?

>This is clearly what is bothering him (what else could be?),
>and what he is altering.

I wouldn't give him too much credit for consistency in his
preferences or motives.

>D# can be an augmented second-

B-D# is never a second where I'm from.

Petr then. -Carl

Mike wrote:

>>>> By lowering the Eb to 32:27, rather than using 6:5, you are trying
>>>> to change the augmented fifth to a minor sixth,
>>>
>>> Yeah, but this isn't right, is it? In common practice harmony, 32/27
>>> isn't an augmented second, it's still a minor third. Sinbad Cuthbar
>>> has confused 128/125 with 81/80.
>>
>> 12/5 - 15/8 = 32/25 and 32/25 - 5/4 = 128/125.
>>
>> A dim4 is always -8, whereas an M3 is +4. In this case, that means
>> reinterpreting the interval from B-Eb as B-D#
>
> He didn't say 32/25, he said 32/27.

Hopefully subsequent messages have cleared this up (?).

-Carl

Oooh could it be? :)
I've missed Petr!
We almost never agreed but he has the right "tuning head" so to say in my opinion :)

-Marcel

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> lobawad wrote:
>
> >Noone
>
> Noone! Are you sure you're Paul Erlich?
>
> >This is clearly what is bothering him (what else could be?),
> >and what he is altering.
>
> I wouldn't give him too much credit for consistency in his
> preferences or motives.
>
> >D# can be an augmented second-
>
> B-D# is never a second where I'm from.
>
> Petr then. -Carl
>

Please Carl, read. D# certainly can be an augmented second... from C! A major third from B, a major sixth from... etc.

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> lobawad wrote:
>
> >Noone
>
> Noone! Are you sure you're Paul Erlich?
>
> >This is clearly what is bothering him (what else could be?),
> >and what he is altering.
>
> I wouldn't give him too much credit for consistency in his
> preferences or motives.
>
> >D# can be an augmented second-
>
> B-D# is never a second where I'm from.
>
> Petr then. -Carl
>

--- In MakeMicroMusic@yahoogroups.com, "Marcel" <m.develde@...> wrote:

>
> B 15/16 - Eb 32/27 is not a normal pure major third, it is 512/405.
> A Pythagorean major third would be 81/64 as in B 15/16 - Eb >1215/1024
> A regular 5-limit major third would be 5/4 as in B 15/16 - Eb 75/64 >(now here you have an argument for D# perhaps) but this is actually >out of tune. Good would also be B 243/256 - Eb 1215/1024 (perhaps >also labeled as D#)

So, you do conceive of B-Eb as a major third. The major third above B is D#, however. In your c-G example, you have created three different "major thirds". (Let's address the intervals in terms of thirds, we could use the sixths as well of course).

The first is the 81:64 found in the Pythagorean minor chord as the complement of the Pythagorean 32:27, the second is the 512:405 occuring between the chords, the third is the 5:4 in the major chord.

Really, you've tuned the aug5/dim4 to Pythagorean maj/min. The comma between 81:64 and 512:405 is less than two cents. There is perhaps
some music so microtonal that two cents could be percieved as a distinct, I don't know. But, it is safe to say that the diminished fourth and the ditone will be equated in the ear- even the finest ear would hear them as slightly varied versions of the "same thing".

The ditone is, in the minor chord, clearly functioning as a major third. The 5:4 is, in the major chord, clearly functioning as a major third. As a fifth an 81:80 sharp of pure moving to a pure fifth will reveal a commatic "wolf", so will a major third an 81:80 sharp moving to a pure third.

>
> No unusual commas are used at all.
> All fifths are 3/2, fourths 4/3.
> And there are 3 major thirds, 5/4, 81/64 and 512/405.
> corresponding minors, and sixths.
> And all tritones are 45/32 or it's inversion.

The effect is that of some pure thirds, when in motion continually darting back toward 12-tET whenever they get more than about 10 cents away. Something like a poorly-done version of Hermode tuning.

Well, Marcel, good luck in your endeavors.

When did you say from C? And why would you say that, since it
doesn't have fuck-all to do with this example?

In case it wasn't blindingly obvious, I think people who use
pseudonyms online are full of shit. That goes double when they're
obviously known to the community already.

-Carl

Wad wrote:

>Please Carl, read. D# certainly can be an augmented second... from C!
>A major third from B, a major sixth from... etc.
>
>--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>>
>> lobawad wrote:
>>
>> >Noone
>>
>> Noone! Are you sure you're Paul Erlich?
>>
>>> This is clearly what is bothering him (what else could be?),
>>> and what he is altering.
>>
>> I wouldn't give him too much credit for consistency in his
>> preferences or motives.
>>
>>> D# can be an augmented second-
>>
>> B-D# is never a second where I'm from.
>>
>> Petr then. -Carl
>>

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:

> In case it wasn't blindingly obvious, I think people who use
> pseudonyms online are full of shit. That goes double when they're
> obviously known to the community already.

Carl Carl Carl. He noticed I am writing soul music, which means he's got to be a good guy. And it proves he's not McLaren.

Gene wrote:

>Carl Carl Carl. He noticed I am writing soul music, which means he's
>got to be a good guy. And it proves he's not McLaren.

It was never gonna be McLaren. Petr or Cameron are more likely.

Balance and fairness in human socializations can be achieved when
everyone has the same costs/payoffs. Here, somebody is showing up
with information on us but not bringing anything of their own to
the table. That's why I think it's a shyster move.

-Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Gene wrote:
>
> >Carl Carl Carl. He noticed I am writing soul music, which means he's
> >got to be a good guy. And it proves he's not McLaren.
>
> It was never gonna be McLaren. Petr or Cameron are more likely.

Not Petr. Might be Mr. Bobro.

>> It was never gonna be McLaren. Petr or Cameron are more likely.
>
>Not Petr. Might be Mr. Bobro.

Ding ding I think we have a winner. For the record, I like Cameron
quite a lot. Also, before people had the ability to make anonymous
thingamabobs twice daily, there was something called forgiveness.
It got tied up with religion and I wonder if it hasn't suffered
along with that unfortunate art. -Carl

--- In MakeMicroMusic@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> >> It was never gonna be McLaren. Petr or Cameron are more likely.
> >
> >Not Petr. Might be Mr. Bobro.
>
> Ding ding I think we have a winner. For the record, I like Cameron
> quite a lot. Also, before people had the ability to make anonymous
> thingamabobs twice daily, there was something called forgiveness.
> It got tied up with religion and I wonder if it hasn't suffered
> along with that unfortunate art. -Carl
>

Nope, it's not Cameron.
I know who it is :)

And I owe this person an apology.
This person ones told me that all fifths must be pure in JI and that a wolf fifth is not correct.
This person even told me that a Pythagorean triad is preferable over a wolf.
I strongly protested back then.
And now look what I'm doing :)
It took me a long time to see the light.
But now that I do, hereby I say: Yes you were right about these things all along! Please forgive my blindness back then :)

-Marcel

>Nope, it's not Cameron.
>I know who it is :)
>
>And I owe this person an apology.
>This person ones told me that all fifths must be pure in JI and that a
>wolf fifth is not correct.
>This person even told me that a Pythagorean triad is preferable over a wolf.
>I strongly protested back then.

Mark? Mark is a minor genius and I bow before him. -Carl

> So, you do conceive of B-Eb as a major third. The major third above B is D#, however. In your c-G example, you have created three different "major thirds". (Let's address the intervals in terms of thirds, we could use the sixths as well of course).
>

Yes, I conceive every diminished fourth to be usable as a major third In for instance a major triad (even when it's not written as as major third in normal music theory).
However I do not conceive every major third to be suitable as a relaxing major third suitable in for instance a final chord ending a piece.

> The first is the 81:64 found in the Pythagorean minor chord as the complement of the Pythagorean 32:27, the second is the 512:405 occuring between the chords, the third is the 5:4 in the major chord.
>
> Really, you've tuned the aug5/dim4 to Pythagorean maj/min. The comma between 81:64 and 512:405 is less than two cents. There is perhaps
> some music so microtonal that two cents could be percieved as a distinct, I don't know. But, it is safe to say that the diminished fourth and the ditone will be equated in the ear- even the finest ear would hear them as slightly varied versions of the "same thing".
>

Yes, the difference of a Schisma is barely audible with minor chords.
The difference becomes much more audible with major chords though.

But it's not just about the audible difference of the Schisma.
Since in my theory the Schisma leads to a difference of a Syntonic comma at for instance the tritone.
And a 1215/1024 makes pure 3/2 fifths with different tones than 32/27.
A wolf is never allowed, even if it's a Schisma wolf.

Here is the Scale I work with for common practice music:
1/1 135/128 9/8 1215/1024 5/4 4/3 45/32 3/2 405/256 27/16 16/9 15/8 2/1

The step sizes of the scale are this:

1/1 does not correspond to a fixed tonic or anything, also this scale is not a fixed scale for a single key or anything like that, it moves constantly along an infinite chain of fifths with the music.
It is more like a collapsed "harmonic and step potential" scale.

Here is the same thing in 7-limit:
1/1 135/128 567/512 9/8 1215/1024 5/4 21/16 4/3 45/32 189/128 3/2 405/256 1701/1024 27/16 7/4 16/9 15/8 63/32 2/1

Step sizes:
135/128 21/20 64/63 135/128 256/243 21/20 64/63 135/128 21/20 64/63 135/128 21/20 64/63 28/27 64/63 135/128 21/20 64/63

64/63 is actually a real step size.
Therefore 21/16 and even 63/32 are not wolves! :)

> The ditone is, in the minor chord, clearly functioning as a major third. The 5:4 is, in the major chord, clearly functioning as a major third. As a fifth an 81:80 sharp of pure moving to a pure fifth will reveal a commatic "wolf", so will a major third an 81:80 sharp moving to a pure third.
>

What do you base this on?
I see moving from for instance 1/1 4/3 27/16 to 1/1 5/4 3/2 as perfectly OK. No "wolf" like things going on there.
If one were to first drop the 4/3 to 5/4 while holding the 27/16 then it would become a different progression all together and make a 81/64 instead of a 5/4, but because it is a different progression one would also change the function of the chord and it is in this case reflected in a different tuning.

Or do you mean going from 1/1 81/64 to 1/1 5/4?
That is not allowed no (well under a specific circumstance where the 81/64 voice moves elsewhere and another voice comes in at 5/4 it may be allowed, not sure yet, and gives a somewhat jumpy progression).

>
> >
> > No unusual commas are used at all.
> > All fifths are 3/2, fourths 4/3.
> > And there are 3 major thirds, 5/4, 81/64 and 512/405.
> > corresponding minors, and sixths.
> > And all tritones are 45/32 or it's inversion.
>
> The effect is that of some pure thirds, when in motion continually darting back toward 12-tET whenever they get more than about 10 cents away. Something like a poorly-done version of Hermode tuning.
>

Yes, in certain progressions one will get for instance 135/128 4/3 405/256 major chords etc. But the thing is I've found this to be correct.
It depends on the "phrase" and it's ending / resting points for instance and what the relations of the chords in the progression are, what the function is of these chords and therefore how they are tuned.
As it turns out, this works 100% perfectly for common practice music.

> Well, Marcel, good luck in your endeavors.
>

Thank you :)

And it's very good to have you back!
Hope you will stick around this time and not be chased off by people like me ;)

-Marcel