Yahoo Tuning Groups Ultimate Backup tuning The Contest

>
>
> I would include a referendum on ferret ownership in the state of California
> and the city of New York.
>
> :-)
>
>
> On Tue, Jan 12, 2010 at 1:12 PM, jonszanto <jszanto@...> wrote:
>
>>
>>
>> As long as the viability of tuning for a piece of music is be reduced to a
>> popularity contest, I hope the contestants will be asked their views on
>> same-sex marriage, so that we can settle a number of issues all at once.
>> When the contestant who has the aural equivalent of a boob job finally rises
>> to the top, we'll know - once and for all - what the very best way to tune a
>> piece really is.
>>
>> Come on, folks. Is this really being taken seriously?
>>
>> Sincerely,
>> Simon Cowell
>>
>>
Ah you guys are all crazy.

I've given several good reasons on why a non-blind test would be preferrable
to a blind test in this competition.
Yet nobody replied to these arguments.
Instead it seems to be turning into a shouting contest. Who can shout the
most overstated arguments the loudest while beeing deaf to reason.

You know it doesn't even matter to me much wether the files are blind on non
blind.
And I stand very open to turning it into a blind contest / random filenames.
Though having the files up for everybody to listen to for a week before
voting starts is important to me, as is beeing able to discuss the tunings
online. (I'm not turning this into a things where people need to be policed,
and people breaking these "rules" get flamed online for "ruining the
competition" or things like that (similar to what happened to Carl on the
competition a while back, yet everybody on list would be a judge here))
Which makes it not completely blind, which for other reasons it wouldn't be
anyhow to start with and would be impossible anyhow.

But it is my competition, and people can shove the shouting type of messages
on this subject up their *** I'm not listening to them.
If you have something meaningfull to say, give proper arguments and respond
to counterarguments in an intelligent and respectfull manner, and I will
listen.

Marcel

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Mike Battaglia <battaglia01@...>

Marcel: opinion on these forums is unanimous in that the test should
be double blind, if your goal with this is to really see which tuning
is "better".

You have heard plenty of well composed arguments as well as now some
humorous and sarcastic ones. At this point I think everything on the
matter has been said.

As you are the guy putting up the money here, it's obviously your say
what you want to do. If you would like to make it not be blind, then
just put your foot down and end the matter. But what more
"well-composed" arguments do you want? Everything about the issue has
been said already.

I recommend you make a final decision on it and just move on. If you
pick the non-blind choice, then know that so far the entire tuning
list has considered this to be a bad idea. However, ultimately it is
your money, and you make the decision that you think is most fair.

-Mike

On Tue, Jan 12, 2010 at 4:57 PM, Marcel de Velde <m.develde@...> wrote:
>
>
>>
>>
>>
>> I would include a referendum on ferret ownership in the state of California and the city of New York.
>>
>> :-)
>>
>> On Tue, Jan 12, 2010 at 1:12 PM, jonszanto <jszanto@...> wrote:
>>>
>>>
>>>
>>> As long as the viability of tuning for a piece of music is be reduced to a popularity contest, I hope the contestants will be asked their views on same-sex marriage, so that we can settle a number of issues all at once. When the contestant who has the aural equivalent of a boob job finally rises to the top, we'll know - once and for all - what the very best way to tune a piece really is.
>>>
>>> Come on, folks. Is this really being taken seriously?
>>>
>>> Sincerely,
>>> Simon Cowell
>>>
>
> Ah you guys are all crazy.
>
> I've given several good reasons on why a non-blind test would be preferrable to a blind test in this competition.
> Yet nobody replied to these arguments.
> Instead it seems to be turning into a shouting contest. Who can shout the most overstated arguments the loudest while beeing deaf to reason.
>
> You know it doesn't even matter to me much wether the files are blind on non blind.
> And I stand very open to turning it into a blind contest / random filenames. Though having the files up for everybody to listen to for a week before voting starts is important to me, as is beeing able to discuss the tunings online. (I'm not turning this into a things where people need to be policed, and people breaking these "rules" get flamed online for "ruining the competition" or things like that (similar to what happened to Carl on the competition a while back, yet everybody on list would be a judge here))
> Which makes it not completely blind, which for other reasons it wouldn't be anyhow to start with and would be impossible anyhow.
>
> But it is my competition, and people can shove the shouting type of messages on this subject up their *** I'm not listening to them.
> If you have something meaningfull to say, give proper arguments and respond to counterarguments in an intelligent and respectfull manner, and I will listen.
>
> Marcel
>
>

🔗Ozan Yarman <ozanyarman@...>

Alternatively, the competition could be arranged in two stages:

1. Voting entries and knowing contestants and chosen tunings

2. Voting randomized-incognito entries NOT knowing their tunings.

The votes which match for both stages would be administered as valid.
The rest would be discarded as invalid. This would satisfy both sides
of the argument.

Oz.

✩ ✩ ✩
www.ozanyarman.com

On Jan 13, 2010, at 12:22 AM, Mike Battaglia wrote:

> Marcel: opinion on these forums is unanimous in that the test should
> be double blind, if your goal with this is to really see which tuning
> is "better".
>
> You have heard plenty of well composed arguments as well as now some
> humorous and sarcastic ones. At this point I think everything on the
> matter has been said.
>
> As you are the guy putting up the money here, it's obviously your say
> what you want to do. If you would like to make it not be blind, then
> just put your foot down and end the matter. But what more
> "well-composed" arguments do you want? Everything about the issue has
> been said already.
>
> I recommend you make a final decision on it and just move on. If you
> pick the non-blind choice, then know that so far the entire tuning
> list has considered this to be a bad idea. However, ultimately it is
> your money, and you make the decision that you think is most fair.
>
> -Mike
>
>
> On Tue, Jan 12, 2010 at 4:57 PM, Marcel de Velde
> <m.develde@...> wrote:
>>
>>
>>>
>>>
>>>
>>> I would include a referendum on ferret ownership in the state of
>>> California and the city of New York.
>>>
>>> :-)
>>>
>>> On Tue, Jan 12, 2010 at 1:12 PM, jonszanto <jszanto@...> wrote:
>>>>
>>>>
>>>>
>>>> As long as the viability of tuning for a piece of music is be
>>>> reduced to a popularity contest, I hope the contestants will be
>>>> asked their views on same-sex marriage, so that we can settle a
>>>> number of issues all at once. When the contestant who has the
>>>> aural equivalent of a boob job finally rises to the top, we'll
>>>> know - once and for all - what the very best way to tune a piece
>>>> really is.
>>>>
>>>> Come on, folks. Is this really being taken seriously?
>>>>
>>>> Sincerely,
>>>> Simon Cowell
>>>>
>>
>> Ah you guys are all crazy.
>>
>> I've given several good reasons on why a non-blind test would be
>> preferrable to a blind test in this competition.
>> Yet nobody replied to these arguments.
>> Instead it seems to be turning into a shouting contest. Who can
>> shout the most overstated arguments the loudest while beeing deaf
>> to reason.
>>
>> You know it doesn't even matter to me much wether the files are
>> blind on non blind.
>> And I stand very open to turning it into a blind contest / random
>> filenames. Though having the files up for everybody to listen to
>> for a week before voting starts is important to me, as is beeing
>> able to discuss the tunings online. (I'm not turning this into a
>> things where people need to be policed, and people breaking these
>> "rules" get flamed online for "ruining the competition" or things
>> like that (similar to what happened to Carl on the competition a
>> while back, yet everybody on list would be a judge here))
>> Which makes it not completely blind, which for other reasons it
>> wouldn't be anyhow to start with and would be impossible anyhow.
>>
>> But it is my competition, and people can shove the shouting type of
>> messages on this subject up their *** I'm not listening to them.
>> If you have something meaningfull to say, give proper arguments and
>> respond to counterarguments in an intelligent and respectfull
>> manner, and I will listen.
>>
>> Marcel
>>
>>
>
>
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🔗jonszanto <jszanto@...>

🔗Daniel Forro <dan.for@...>

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

>"Why is a major triad more consonant than a minor one (even with sine waves)...an alternative explanation."

I have been fiddling around more and more with the same concept often taught in production workshops. That concept is minimizing the different between low and high points in volume in a music track (often done with compressors, maximizers...but, I'm am starting to believe, also possible at least in part by reducing beating/difference-tones even over tiny periods of time).

Attached are graphs of major and minor chords, which have the exact same intervals only in reverse.
So (as discussed before) you'd think that they would have the same roughness and consonance...but most people instantly sense the major triad is more relaxed sounding. But, when you look at the pictures, you'll notice a beautifully level part of the wave graph (highlighted in white) where the beating is minimized and no such "beat-less" rest in any part of the minor chord.

IMVHO...this all seems to say that we should actually consider things like compression and maximization on scales to help fine-tune them and see how they adjust certain frequencies to obtain cool "resting" areas where the beats level-out as they do in the major chord.

While it is true the human ear does prefer closer ratios at higher frequencies, the change in the curve over octaves in very slight and certainly not half as dramatic as the difference of the two intervals in the major vs. minor chord...which is why I'm asking the question "Do you think there's anything beyond the fact the human ear physiologically has a smaller critical band at higher frequencies that causes the preference for major vs. minor"?

🔗Daniel Forro <dan.for@...>

Just few points of amused distant observer who will not take part in:

- Competitions are possible in sports or in eating hamburgers. Not in the art, where result is based mainly on subjective opinion of jury. It's easy to judge quantity, not so easy to judge quality, and very difficult to judge artistic quality. There is some mechanistic, technical "craftsmanship" even in the art, but the rest (if there's some) is a pure magic. Somebody can like, somebody not.

- And I mean jury of well selected experts, not public voting (OK, here are also selected experts only)

- Voting - hm, participants shouldn't vote... But anyway if each of them votes for himself, result is the same...

- This "competition" is not primarily targeted on the artistic quality, to me it's not quite clear what will be measured - quantity or quality? By which method? Melody, harmony, consonance...?

- That Beethoven's work of course WAS written for 12ET. I'm not aware at all about any mention, or note, or consideration about tuning issues from the side of this particular composer. Also his works don't show anything like results of similar research or considerations. Maybe just "colors" of different keys... So maybe he was aware of tuning, but not so deeply to think about commas. Correct me if I'm wrong in this.

- I would understand if somebody offers money to support some talented person, research, institution, society or foundation as an independent decision of independent unbiased donor. But here a person offering money will take part in the competition, what more - even to change all works sent by participants. And anonymity of participants is not allowed.

- Nothing to say about the fact this person's target probably is only to show that his work is the best one...

- OK, money price, yes, why not. Some people will take part in just for money, we all have to pay our bills. But beg you pardon - all this rumour for 100 Euro? If 1000, 5000....

Take it easy, good luck to all participants.

And now back to work which have more sense. Sorry, I couldn't resist to send this. Erase, if you don't like it.

Daniel Forro

On 13 Jan 2010, at 1:22 PM, Carl Lumma wrote:

>
> --- In tuning@yahoogroups.com, "jonszanto" <jszanto@...> wrote:
>
> > Well, you see, that's how it appears to *me* (well, not ALL, just
> > some). The concept of a monetarily-driven, prize-oriented
> > "competition" for the Best Tuning is diametrically opposed to why
> > I'm involved in the arts, in music.
>
> I think prizes are a great way to encourage participation
> in projects like this, where every tuning, winner or not, is
> possibly of interest (at least to me).
> Economists have observed that people who offer prizes tend to
> get more than their money's worth of participation out.
> I won't interpret any winner as "best", though if there is one
> clear winner that would tell us something interesting too.
>
> -Carl
>

🔗Carl Lumma <carl@...>

Daniel wrote:
> - Voting - hm, participants shouldn't vote... But anyway if
> each of them votes for himself, result is the same...

The ballot can be set so each listener can vote for more than
one entry (or it can be set to allow one vote per listener only).
Either way, I am a voter who will not be submitting an entry, so
there will be at least one to break a tie.

> - This "competition" is not primarily targeted on the artistic
> quality, to me it's not quite clear what will be measured -
> quantity or quality? By which method? Melody, harmony,
> consonance...?

Only the tuning will differ. Melody and harmony should both
be considered.

> - That Beethoven's work of course WAS written for 12ET.

It was written for a trombone quartet.

> I'm not aware
> at all about any mention, or note, or consideration about tuning
> issues from the side of this particular composer. Also his works
> don't show anything like results of similar research or
> considerations. Maybe just "colors" of different keys... So maybe
> he was aware of tuning, but not so deeply to think about commas.

I'm aware of no evidence Beethoven thought about commas. He
left us the notes on the page to convey his intent; no tuning
is specified. Therefore we are free to use any tuning that
serves.

> But here a person offering money will take part in the
> competition, what more - even to change all works sent by
> participants. And anonymity of participants is not allowed.

It's Marcel's party. But I've said I think he would be
well advised to let Mike render the files, to randomize the
filenames, etc.

-Carl

🔗Mike Battaglia <battaglia01@...>

One interesting way to look at it is that there's no law of nature that says
that the brain has to look at three notes as being a single chord. A triad
can also be looked as three overlapping dyads: for C major you have C-E,
E-G, and C-G, for example. It can also be looked at as three individual
notes: C, E, and G, and it can be looked at as a fused triad: C-E-G.

For a minor chord, you have C-Eb-G. The C-Eb suggests a weak Ab fundamental,
the Eb-G suggests a slightly stronger Eb fundamental, and the C-G suggests a
very strong C fundamental. Looking at all of the notes separately, C Eb and
G suggest themselves as fundamentals. And, while trying to place the triad
as a whole, C-Eb-G suggests a very weak Ab fundamental, an octave below the
Ab fundamental from the C-Eb.

You are no doubt familiar with the C, Eb, and G suggesting themselves as
fundamentals -- that's why you can pick out the individual notes in the
chord. You are also no doubt familiar with the C-G suggesting a C an octave
below as the fundamental -- that's why the C-G in a minor chord seems so
strong and resonant. You are also no doubt familiar with the
second-strongest fundamental of the minor triad - the Eb-G dyad suggesting
an Eb -- which is why a Cm chord can also function, in a sense, as an Ebmaj6
chord.

You might not have thought of the C-Eb suggesting the Ab dyad, which is
possibly why Aeolian tends to be the minor scale of choice in western music
-- since it contains this bVI interval. You might also not have thought of
the C-Eb-G suggesting a low Ab, which is kind of like thinking of a Cm triad
as the upper partials of an Abmaj7 chord.

However, although you might not have thought of it, your brain certainly
has. It is my opinion that the simultaneous existing of these modes is
responsible for the characteristic "flavor" of the minor chord.

On the other hand, all of the fundamentals for all permutations of the C
major chord are the exact same thing - a C, two octaves below the root. So
there are only really two ways to see a C major chord: as three individual
notes, C, E and G, or as a rock-solid chunk of the harmonic series referring
to C two octaves below. If you think about your perception of the major
chord, this will probably ring true on some level for you. It certainly does
for me.

So it isn't a matter of that a minor chord is more "dissonant" than a major
chord -- it's that it contains more possible modes of consonance. If we want
to label this "dissonance," then fine by me... I've basically completely
given up on the belief that there is a single quantifiable dimension of
musical pleasantness at this point. This is certainly a different type of
beast than the kind of dissonance talked about by detuning notes, which
harmonic entropy models very well.

-Mike

On Wed, Jan 13, 2010 at 12:54 AM, Michael <djtrancendance@yahoo.com> wrote:

>
> [Attachment(s) <#126263f7e1f76754_TopText> from Michael included below]
>
> >"Why is a major triad more consonant than a minor one (even with sine
> waves)...an alternative explanation."
>
> I have been fiddling around more and more with the same concept often
> taught in production workshops. That concept is minimizing the different
> between low and high points in volume in a music track (often done with
> compressors, maximizers...but, I'm am starting to believe, also possible at
> least in part by reducing beating/difference-tones even over tiny periods of
> time).
>
>
> Attached are graphs of major and minor chords, which have the exact
> same intervals only in reverse.
> So (as discussed before) you'd think that they would have the same
> roughness and consonance...but most people instantly sense the major triad
> is more relaxed sounding. But, when you look at the pictures, you'll notice
> a beautifully level part of the wave graph (highlighted in white) where the
> beating is minimized and no such "beat-less" rest in any part of the minor
> chord.
>
>
>
> IMVHO...this all seems to say that we should actually consider things
> like compression and maximization on scales to help fine-tune them and see
> how they adjust certain frequencies to obtain cool "resting" areas where the
> beats level-out as they do in the major chord.
>
> While it is true the human ear does prefer closer ratios at higher
> frequencies, the change in the curve over octaves in very slight and
> certainly not half as dramatic as the difference of the two intervals in the
> major vs. minor chord...which is why I'm asking the question "Do you think
> there's anything beyond the fact the human ear physiologically has a smaller
> critical band at higher frequencies that causes the preference for major vs.
> minor"?
>
>

🔗Mike Battaglia <battaglia01@...>

Carl: If you're not going to submit an entry, then perhaps you should do the
rendering. I plan on submitting an entry, and if mine wins, the last thing I
want to hear about is that I didn't render them properly and rigged it in my
favor.

Marcel's ZynAddSubFX plugin sounded like an easy way to get it all going. If
you want to be a trusted third party to handle the randomizing of the
filenames and all of that, that would be fine by my vote.

Of course, this is all assuming that Marcel decides in the end to make it
blind, which I am hoping for.

-Mike

On Wed, Jan 13, 2010 at 1:29 AM, Carl Lumma <carl@...> wrote:

>
>
> Daniel wrote:
> > - Voting - hm, participants shouldn't vote... But anyway if
> > each of them votes for himself, result is the same...
>
> The ballot can be set so each listener can vote for more than
> one entry (or it can be set to allow one vote per listener only).
> Either way, I am a voter who will not be submitting an entry, so
> there will be at least one to break a tie.
>
>
> > - This "competition" is not primarily targeted on the artistic
> > quality, to me it's not quite clear what will be measured -
> > quantity or quality? By which method? Melody, harmony,
> > consonance...?
>
> Only the tuning will differ. Melody and harmony should both
> be considered.
>
>
> > - That Beethoven's work of course WAS written for 12ET.
>
> It was written for a trombone quartet.
>
>
> > I'm not aware
> > at all about any mention, or note, or consideration about tuning
> > issues from the side of this particular composer. Also his works
> > don't show anything like results of similar research or
> > considerations. Maybe just "colors" of different keys... So maybe
> > he was aware of tuning, but not so deeply to think about commas.
>
> I'm aware of no evidence Beethoven thought about commas. He
> left us the notes on the page to convey his intent; no tuning
> is specified. Therefore we are free to use any tuning that
> serves.
>
>
> > But here a person offering money will take part in the
> > competition, what more - even to change all works sent by
> > participants. And anonymity of participants is not allowed.
>
> It's Marcel's party. But I've said I think he would be
> well advised to let Mike render the files, to randomize the
> filenames, etc.
>
> -Carl
>
>
>

🔗Daniel Forró <dan.for@...>

On 13 Jan 2010, at 5:59 PM, Mike Battaglia wrote:

>
> One interesting way to look at it is that there's no law of nature > that says that the brain has to look at three notes as being a > single chord.
>

But if they sound together and their structure is similar or the same as the structure of harmonic series or some of its segments, brain probably understands it as a chord. Otherwise we will not be able to listen to and enjoy and analyse harmonic progressions of Western music (which means it's dependent on the cultural context).
> A triad can also be looked as three overlapping dyads: for C major > you have C-E, E-G, and C-G, for example. It can also be looked at > as three individual notes: C, E, and G, and it can be looked at as > a fused triad: C-E-G.
>
It's questionable if brain does such sorting, I doubt it, it would be time consuming, opposite to the synthesis process which can bring some result on higher levels of music reception. But who knows how it is.
>
> For a minor chord, you have C-Eb-G. The C-Eb suggests a weak Ab > fundamental, the Eb-G suggests a slightly stronger Eb fundamental, > and the C-G suggests a very strong C fundamental. Looking at all of > the notes separately, C Eb and G suggest themselves as > fundamentals. And, while trying to place the triad as a whole, C-Eb-> G suggests a very weak Ab fundamental, an octave below the Ab > fundamental from the C-Eb.
>
> You are no doubt familiar with the C, Eb, and G suggesting > themselves as fundamentals -- that's why you can pick out the > individual notes in the chord. You are also no doubt familiar with > the C-G suggesting a C an octave below as the fundamental -- that's > why the C-G in a minor chord seems so strong and resonant. You are > also no doubt familiar with the second-strongest fundamental of the > minor triad - the Eb-G dyad suggesting an Eb -- which is why a Cm > chord can also function, in a sense, as an Ebmaj6 chord.
>
> You might not have thought of the C-Eb suggesting the Ab dyad, > which is possibly why Aeolian tends to be the minor scale of choice > in western music -- since it contains this bVI interval.
>
Sorry to destroy this construction of yours so brutally - bVI is also to find in Phrygian and Locrian, harmonic minor, melodic minor downwards, whole tone :-0 and many other scales. Besides - western music doesn't use only diatonic system based on 7-tone scales.

> You might also not have thought of the C-Eb-G suggesting a low Ab, > which is kind of like thinking of a Cm triad as the upper partials > of an Abmaj7 chord.
>
> However, although you might not have thought of it, your brain > certainly has. It is my opinion that the simultaneous existing of > these modes is responsible for the characteristic "flavor" of the > minor chord.
>
>
Exactly this can be the reason why minor chord can be felt as more dissonant than major - fight between the notes Ab x G (in your previous example).

> On the other hand, all of the fundamentals for all permutations of > the C major chord are the exact same thing - a C, two octaves below > the root. So there are only really two ways to see a C major chord: > as three individual notes, C, E and G, or as a rock-solid chunk of > the harmonic series referring to C two octaves below. If you think > about your perception of the major chord, this will probably ring > true on some level for you. It certainly does for me.
>

Exactly, it's more simple, more near to the base of the sound - harmonic series. If we see major/minor contrast this way, then it's based on laws of nature. But let's not forget about cultural bias as well.

Daniel Forro

> So it isn't a matter of that a minor chord is more "dissonant" than > a major chord -- it's that it contains more possible modes of > consonance. If we want to label this "dissonance," then fine by > me... I've basically completely given up on the belief that there > is a single quantifiable dimension of musical pleasantness at this > point. This is certainly a different type of beast than the kind of > dissonance talked about by detuning notes, which harmonic entropy > models very well.
>
> -Mike
>

🔗Mike Battaglia <battaglia01@...>

> > One interesting way to look at it is that there's no law of nature
> > that says that the brain has to look at three notes as being a
> > single chord.
> But if they sound together and their structure is similar or the same
> as the structure of harmonic series or some of its segments, brain
> probably understands it as a chord. Otherwise we will not be able to
> listen to and enjoy and analyse harmonic progressions of Western
> music (which means it's dependent on the cultural context).

They always sound together. Two people can also be speaking at the
same time, and the brain has no trouble placing them as two separate
harmonic spectra just fine.

> It's questionable if brain does such sorting, I doubt it, it would be
> time consuming, opposite to the synthesis process which can bring
> some result on higher levels of music reception. But who knows how it
> is.

What sorting is involved? The brain has no idea that the huge wash of
sound coming in is what we call a "chord." It just autonomously finds
all possible harmonic relationships. Obviously each note will itself
have its own harmonic series, and the brain will certainly pick that
up. Other than that, it will also hear the relationship between C and
Eb, between Eb and G, and between C and G. It might hear the
relationship between C, Eb and G (10:12:15) directly, but it won't be
anywhere near as strong as C-G.

> > You might not have thought of the C-Eb suggesting the Ab dyad,
> > which is possibly why Aeolian tends to be the minor scale of choice
> > in western music -- since it contains this bVI interval.
> >
> Sorry to destroy this construction of yours so brutally - bVI is also
> to find in Phrygian and Locrian, harmonic minor, melodic minor
> downwards, whole tone :-0 and many other scales.

When did I say that it wasn't? The point is that although Ab is not an
actual note in the Cm chord, it certainly exists in the "neighborhood"
of that chord, expressed both in the above analysis of the dyads of
the chord as well as the scale that we have tended to use to flesh the
chord out.

> Besides - western music doesn't use only diatonic system based on 7-tone scales.

What is your point?

> Exactly this can be the reason why minor chord can be felt as more
> dissonant than major - fight between the notes Ab x G (in your
> previous example).

So why is an Abmaj7 such an extremely consonant chord then?

-Mike

🔗Daniel Forró <dan.for@...>

On 13 Jan 2010, at 7:08 PM, Mike Battaglia wrote:

> They always sound together. Two people can also be speaking at the
> same time, and the brain has no trouble placing them as two separate
> harmonic spectra just fine.
>

I don't think simple sounding harmonic tones and complex speech as a semantic signal can be compared in this context. Besides speech is not only harmonic spectre.

> What sorting is involved? The brain has no idea that the huge wash of
> sound coming in is what we call a "chord." It just autonomously finds
> all possible harmonic relationships. Obviously each note will itself
> have its own harmonic series, and the brain will certainly pick that
> up. Other than that, it will also hear the relationship between C and
> Eb, between Eb and G, and between C and G. It might hear the
> relationship between C, Eb and G (10:12:15) directly, but it won't be
> anywhere near as strong as C-G.
>

There are more theories how we hear, and as far as I know until now none of them was accepted as the universal and valid one. Process of hearing has probably two phases - one is in ear, another one in the brain. We have to learn since the birth how to understand the signals we hear, be it language, natural sounds or structure of the musical sound and music as a language.

> > > You might not have thought of the C-Eb suggesting the Ab dyad,
> > > which is possibly why Aeolian tends to be the minor scale of > choice
> > > in western music -- since it contains this bVI interval.
> > >
> > Sorry to destroy this construction of yours so brutally - bVI is > also
> > to find in Phrygian and Locrian, harmonic minor, melodic minor
> > downwards, whole tone :-0 and many other scales.
>
> When did I say that it wasn't? The point is that although Ab is not an
> actual note in the Cm chord, it certainly exists in the "neighborhood"
> of that chord, expressed both in the above analysis of the dyads of
> the chord as well as the scale that we have tended to use to flesh the
> chord out.
>

I have another original construction why Ionian was taken as basic major and Aeolian as basic minor scale, it's based on historical development of music. Besides you need for this only one sharp and one flat, and it can be also called theory of the golden rule of middle way. Let's take 7 possible scales: Locrian is out of the game because of its diminished fifth which doesn't create stable Tonic. Three major scales: Lydian is too much major, Ionian major, Mixolydian little bit minor. Three minor scales: Dorian is little bit major, Aeolian minor, Phrygian too much minor. Now let's take Bb, the first flat which was used. Original all-white-keys (AWK) Dorian on D will be changed with it into Aeolian, original AWK Lydian on F will become Ionian. And with the first used sharp - F#, original AWK Phrygian on E will be turned into Aeolian, finally original AWK Mixolydian on G gives Ionian. It's highly possible this process happened this way. But maybe in some parallel world they have selected both extremes - Lydian as a main major and Phrygian as a main minor. It would give increased contrast between major and minor. Maybe George Russell came from such world...

>
> > Besides - western music doesn't use only diatonic system based on > 7-tone scales.
>
> What is your point?
>
Just to widen your sentence which looks like western music is based only on Aeolian scale :-)

> So why is an Abmaj7 such an extremely consonant chord then?
>
> -Mike
I wouldn't call it extremely consonant by itself, it depends on the context. Meanwhile in the Baroque music it was still considered dissonant, in jazz or contemporary music it can sound consonantly in the comparison with more dissonant chords. Also tuning, voicing, inversion and instrumentation is important for resulting impact.

Daniel Forro

🔗Michael <djtrancendance@...>

>"So major triad is more "natural", like a base, of whole
physics of the sound. Which even is culturally independent, as it's a
law of nature."

This part makes perfect sense. Again, what I'm looking at is the parts that seem to represent laws of nature rather than cultural subjectivity (which really does not go anywhere, IMVHO, because it will always be so subjective).

>"But if it's true, hasn't it something to do with the fact that major chord can be found in the beginning of harmonic series?"

I believe so, yes...but I don't believe that's the only physiological reason.
If it were, would not the quest to create a consonant scale be solved with simply finding a scale that can create the most triads the lowest in the series IE x/12 or lower (IE very strict JI, 5 or 7-limit)? If that were the case...you'd think we'd have already "solved" the quest for the most consonant 7-tone scale, for example.

________________________________
From: Daniel Forró <dan.for@...>
To: tuning@yahoogroups.com
Sent: Wed, January 13, 2010 3:38:54 AM
Subject: Re: [tuning] Why is a major triad more consonant than a minor one (even with sine waves)...an alternative explanation.

On 13 Jan 2010, at 2:54 PM, Michael wrote:

>
> [Attachment( s) from Michael included below]
>
> >"Why is a major triad more consonant than a minor one (even with
> sine waves)...an alternative explanation. "
>

And why it should be so? Resulting sound depends on the frequency,
inversions, tuning, voicing, instrumentation, maybe even cultural
differences, listener's music experience.. .

But if it's true, hasn't it something to do with the fact that major
chord can be found in the beginning of harmonic series? Differential
tones are also here which is not the case of minor chord if I'm not
wrong. So major triad is more "natural", like a base, of whole
physics of the sound. Which even is culturally independent, as it's a
law of nature.

Daniel Forro

🔗Petr Pařízek <p.parizek@...>

🔗Daniel Forró <dan.for@...>

On 14 Jan 2010, at 12:24 AM, Michael wrote:
>
> >"But if it's true, hasn't it something to do with the fact that > major chord can be found in the beginning of harmonic series?"
>
> I believe so, yes...but I don't believe that's the only > physiological reason.
> If it were, would not the quest to create a consonant scale be > solved with simply finding a scale that can create the most triads > the lowest in the series IE x/12 or lower (IE very strict JI, 5 or > 7-limit)? If that were the case...you'd think we'd have already > "solved" the quest for the most consonant 7-tone scale, for example.

Maybe, for the melodies which are one voice only, and created from 7-note scale...

But music is not so simple, we have chords (and not only those of triadic structure), then relations between them, and chromatic system, and leading notes and tendencies in the melody. It looks like a universal system of tuning or scale for the music created until now is not possible. More and more I believe that the best way would be some flexible adaptive system based on the context of flowing music. There's also no reason to have only one type of tuning in one composition, this also can change during the work. Besides different tunings can be used in different layers of the composition. I see also better future for unequal tuning systems...

And always is questionable why there's a quest for consonance only, it's limited view in my opinion. We need as well dissonances, at least for the contrast. There should be some research in the direction what a perfect dissonance is, not only perfect consonance. I think definition of perfect consonance is easier, let's suppose everything what's JI sounds perfectly. But again all this can be analysed theoretically on individual intervals and chords, but then in the musical context it can work differentlly.

Daniel Forro

🔗Michael <djtrancendance@...>

>"I wouldn't call it extremely consonant by itself, it depends on the
context. Meanwhile in the Baroque music it was still considered
dissonant, in jazz or contemporary music it can sound consonantly in
the comparison with more dissonant chords. Also tuning, voicing,
inversion and instrumentation is important for resulting impact."

Oh man....I was kind of hoping this thread would stick on the subject of possible or existing physiological psycho-acoustic phenomena, but I guess not. This discussion seems now to be more about cultural differences and use of different modes than psycho-acoustics directly applicable to micro-tonal.
What does voicing matter when someone is creating a scale? I'm pretty convinced we are now talking more about compositional techniques than tuning itself.

As a challenge on the topic of periodicity, look at the following scale

1/1
7/6
5/4
4/3
3/2
5/3
7/4
2/1

(next octave is)
7/3
5/2
8/3
6/2

You get the fairly pure (IMVHO) just/harmonic-series triads

1/1 5/4 3/2 (AKA 4:5:6)
7/6 4/3 3/2 (AKA 7:8:9)
5/4 3/2 7/4 (AKA 5:6:7)
4/3 5/3 2/1 (AKA 4:5:6)
3/2 7/4 2/1 (AKA 6:7:8)
5/3 2/1 7/3 (AKA 5:6:7)

And the OK, but not as pretty...
7/4 2/1 5/2 (7:8:10)

Yet I haven't heard of such a scale mentioned anywhere (yet)....what's the catch (and or, how can a scale be made to produce all very pure triads)?

I'm just wondering....what scale supposedly makes the high number of just major triads (NOT including the harmonic series itself or so-called "dynamic JI" scales).
And, if there's an answer...why is said scale not considered the Holy Grail so far as periodicity-based consonance?

🔗Michael <djtrancendance@...>

Petr> "AFAIK, there’s no precise
definition of what „consonant“ means."

That is true...though I believe firmly that most people's definitions of consonance tend toward a limited number of things (IE roughness and periodicity/"single-tonality"). Although people weigh the balue of each one of those differently, I think it's fair to say both have to be there to a good extent to even be considered by most people.

>"A few years ago,
I’ve read a webpage where someone was calling the triad of 0-350-700 cents „more
consonant“ than frequency factors of 4:6:7. The problem here is that something
like 3:5:7:9:11 sounds to me perfectly in tune, while 0-350-700 cents sounds to
me almost like chaos so I can’t call it „consonant“."

Odd...my guess is they were using sine-wave to test the triads (IE with no overtones) and likely had the perception that roughness is more important than periodicity of overtones.

'''---------------------------------------------------------------------------------------------------------------------------------------------------------------------

One thing seems clear to me though: periodicity (and JI, for that matter) is the way to go for those who relate consonance to having all notes point to a root tone.

However, of course, there are people (myself included) who actually think too much harmonic distortion from closely-space periodic notes sounds mechnical and grating to the senses and are willing to sacrifice some periodicity to limit harmonic distortion. This leads me to believe, for example, that JI is not the answer to everything and that there must be new unexplored scales that can do a better job for those who dislike excessive harmonic distortion but want more chords available in scales, for example.

🔗Chris <chrisvaisvil@...>

Please define haronic distortion in your contex.

Thanks.

Chris
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Michael <djtrancendance@yahoo.com>
Date: Wed, 13 Jan 2010 08:46:47
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] Why is a major triad more consonant than a minor one (even with sine waves)...an alternative explanation.

Petr> "AFAIK, there’s no precise
definition of what „consonant“ means."

Odd...my guess is they were using sine-wave to test the triads (IE with no overtones) and likely had the perception that roughness is more important than periodicity of overtones.

'''---------------------------------------------------------------------------------------------------------------------------------------------------------------------

One thing seems clear to me though: periodicity (and JI, for that matter) is the way to go for those who relate consonance to having all notes point to a root tone.

🔗Michael <djtrancendance@...>

Daniel>"More and more I believe that the best way would be
some flexible adaptive system based on the context of flowing music."

Seems like a good idea...the problems I have seen so far (IE with things like existing Adaptive JI software) is that

A) It seems to only purify existing well-known types of chords and types of chords that lie straight on the harmonic series (rather than accommodate to new ones)
B) They seem to gravitate toward maintaining periodicity, but do not consider roughness as much (IE I haven't seen any systems, say, with a parameter to help space notes wider to a similar sounding new chord in the case of too much harmonic distortion).
C) At times the notes change by over 10 cents due to the algorithm suddenly to "perfect" the intervals, giving a kind of drunken "old-West" feel to the resulting music that partly offsets/defeats the gain made by the increase in purity.

The idea that some people may be annoyed by too much harmonic distortion (to the point it sounds like a huge amplitude modulator is run over the entire chord) and/or want to, say, make a chord using lots of intervals not too far from major-seconds seems to evade to minds of adaptive scale software programmers...so, IMVHO, sadly you often end up with compositions that sound/feel almost exactly the same as 12TET ones, but are simply purer sounding: rarely I've found very new-sounding chords possible due to adaptive JI software.

That being said, do you know any adaptive tuning software which addresses these issues?

>"Besides different tunings can be used in different layers of the composition.
True, for an absolutely brilliant composer. For the rest of us, though, I wonder if there's a solution to the extreme difficulty level involved in matching different scales in ways overtones don't clash terribly when "cross-scale" chords are played. Same goes with things like 53-TET...it takes a huge learning curve and amount of thinking to quickly find the notes to "perfect" a chord when there are so many near-answers.

>"And always is questionable why there's a quest for consonance only, it's limited view in my opinion. We need as well dissonances, at
least for the contrast."

To me, dissonance just seems so easy to add. Simply adding noise, notes about a 1.05 ratio from each other, many notes close together at the same time, notes with bizarre timbres, faster tempo....can all create dissonance. IMVHO, solving for dissonance is like saying for what values of x does is 14<x<18...where virtually everything not calculated adds to dissonance (what are the chances of a number hitting or nearing 16 out of all numbers?).

Of course, there should be a contrast between the most consonant and dissonant chords in a scale, for example....but, unless you are using the harmonic series as your scale it's almost certain that there is a significant range between the highest consonance and dissonance in it.

🔗Petr Pařízek <p.parizek@...>

🔗Michael <djtrancendance@...>

Petr>"#1. Closely spaced? Have you ever
tried something like 4:7:10:13? Or 3:7:11:15? Do you find something „wrong“
about the periodicity in these chords?"

Probably not...actually such chords simply seem to have less periodicity where my issue is the tackling the problem of roughness (though less important than the issue of periodicity) is far too often not taken into account enough.

I was talking more about things like 9:12:13 where you have a close ratio like 13/12 which causes you to ask the question "should I sacrifice some periodicity for the sake of reducing roughness"? The problem here is that such ratios are so rough, people almost never use them in chords, and thus that limits the number of chords people can/want-to make within a scale.

Another way to state the problem: it would be really nice if someone could find a way to make a major second (or even something between a major and minor second) work smoothly within a single octave so that more chords could be considered thesible for use in non-avant-garde composition.

----------------------------------------------------------------------------------

For example, at least for pure sine waves, something like more 9 : 11.7 : 13 would have less roughness because the 13/11.7 is further-spaced than 13/12. Another way to say this is a way to temper a scale very carefully off just intervals.

A real problem I see is people almost always go for either low-numbered fractions for periodicity or completely high-numbered fraction (or even irrational numbered) scales for limiting roughness...but don't consider compromising between both of them in their optimizations (either they optimize for one or the other but rarely both).

>"#2. If you’re not aiming for an
imaginary root pitch, then what are you aiming for?"
Maybe the pitch is a tad imaginary/"off a single common tone" due to imperfect periodicity, but the goal is to find chords that create virtual pitches fairly close and/or periodically related to the nearest periodic chord's root tone(s) that the mind considers it mostly pure while having a substantial amount less roughness.

________________________________
From: Petr Pařízek <p.parizek@...>
To: tuning@yahoogroups.com
Sent: Wed, January 13, 2010 11:34:04 AM
Subject: Re: [tuning] Why is a major triad more consonant than a minor one (even with sine waves)...an alternative explanation.

Michael
wrote:
>
However, of course, there are people (myself included)
> who
actually think too much harmonic distortion from closely-space periodic notes
sounds mechnical and grating to the senses.
#1. Closely spaced? Have you ever
tried something like 4:7:10:13? Or 3:7:11:15? Do you find something „wrong“
about the periodicity in these chords?
#2. If you’re not aiming for an
imaginary root pitch, then what are you aiming for?
Petr

🔗Michael <djtrancendance@...>

Note....the above scale can also be summarized as a simple 7-tone subset over the 12th-23rd partials of the harmonic series.

However, the fact it can be reduced to so many different types of chords with different feel due to the common denominators of both 2 and 3 (and not simply only 3 or 2 individually) I think makes it worth at least wondering about.

________________________________
From: Michael <djtrancendance@...>
To: tuning@yahoogroups.com
Sent: Wed, January 13, 2010 10:28:44 AM
Subject: Major vs. Minor triads...a scale with a ton of perfect triads and/or which 6-8 tone scales have the most of these?

As a challenge on the topic of periodicity, look at the following scale

1/1
7/6
5/4
4/3
3/2
5/3
7/4
2/1

(next octave is)
7/3
5/2
8/3
6/2

You get the fairly pure (IMVHO) just/harmonic-series triads

1/1 5/4 3/2 (AKA 4:5:6)
7/6 4/3 3/2 (AKA 7:8:9)
5/4 3/2 7/4 (AKA 5:6:7)
4/3 5/3 2/1 (AKA 4:5:6)
3/2 7/4 2/1 (AKA 6:7:8)
5/3 2/1 7/3 (AKA 5:6:7)

And the OK, but not as pretty...
7/4 2/1 5/2 (7:8:10)

Yet I haven't heard of such a scale mentioned anywhere (yet)....what's the catch (and or, how can a scale be made to produce all very pure triads)?

🔗Chris Vaisvil <chrisvaisvil@...>

Michael - I want to know what harmonic distortion means to you so that I
might add to this conversation because I have a feeling you mean something
different than the distortion of the harmonic spectra of a tone....

http://en.wikipedia.org/wiki/Total_harmonic_distortion

I think any "theory of consonance in tuning" has to take register into
account. A lot of what goes on here in [tuning] makes the assumption that
everything is octave equivalent - however, may I point out that the critical
band phenomenon is evidence to the contrary.

Also, you may find this interesting

http://en.wikipedia.org/wiki/Symphony_of_Psalms
http://en.wikipedia.org/wiki/Psalms_chord

Specifically

On Wed, Jan 13, 2010 at 11:55 AM, Chris <chrisvaisvil@...> wrote:

> Please define haronic distortion in your contex.
>
> Thanks.
>
> Chris
>
> Sent via BlackBerry from T-Mobile
> ------------------------------
> *From: * Michael <djtrancendance@...>
> *Date: *Wed, 13 Jan 2010 08:46:47 -0800 (PST)
> *To: *<tuning@yahoogroups.com>
> *Subject: *Re: [tuning] Why is a major triad more consonant than a minor
> one (even with sine waves)...an alternative explanation.
>
>
>
> Petr> "AFAIK, there’s no precise definition of what „consonant“ means."
>
>
> That is true...though I believe firmly that most people's definitions
> of consonance tend toward a limited number of things (IE roughness and
> periodicity/"single-tonality"). Although people weigh the balue of each one
> of those differently, I think it's fair to say both have to be there to a
> good extent to even be considered by most people.
>
>
> >"A few years ago, I’ve read a webpage where someone was calling the triad
> of 0-350-700 cents „more consonant“ than frequency factors of 4:6:7. The
> problem here is that something like 3:5:7:9:11 sounds to me perfectly in
> tune, while 0-350-700 cents sounds to me almost like chaos so I can’t call
> it „consonant“."
>
> Odd...my guess is they were using sine-wave to test the triads (IE with
> no overtones) and likely had the perception that roughness is more important
> than periodicity of overtones.
>
>
>
> '''---------------------------------------------------------------------------------------------------------------------------------------------------------------------
>
> One thing seems clear to me though: periodicity (and JI, for that matter)
> is the way to go for those who relate consonance to having all notes point
> to a root tone.
>
> However, of course, there are people (myself included) who actually
> think too much harmonic distortion from closely-space periodic notes sounds
> mechnical and grating to the senses and are willing to sacrifice some
> periodicity to limit harmonic distortion. This leads me to believe, for
> example, that JI is not the answer to everything and that there must be new
> unexplored scales that can do a better job for those who dislike excessive
> harmonic distortion but want more chords available in scales, for example.
>
>
>
>

🔗Carl Lumma <carl@...>

🔗monz <joemonz@...>

Hi Daniel,

--- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:

> - That Beethoven's work of course WAS written for 12ET.
> I'm not aware at all about any mention, or note, or
> consideration about tuning issues from the side of
> this particular composer. Also his works don't show
> anything like results of similar research or considerations.
> Maybe just "colors" of different keys... So maybe he
> was aware of tuning, but not so deeply to think about commas.
> Correct me if I'm wrong in this.

Beethoven certainly did think about commas.

There's no documentary proof that i know of to support
this statement, but it is absolutely certain that the
prevailing tunings in use during the late 1700s were
12-tone well-temperaments for keyboards and something
along the lines of a 31-tone subset of 1/6-comma meantone
(or 55-edo) for orchestral playing.

This is important in the case of Beethoven because
by the time 12-edo really started to become prominent
in practice, during the early decades of the 1800s,
Beethoven was deaf. So the tunings which he would have
had in his "inner ear" from his younger days would have
been well-temperament for keyboards and non-12-edo
meantone for other instruments.

The key characteristics only happen in a subset of
one of these tunings, for example a 12-tone well-temperament
or a 12-tone subset of meantone. They don't happen in 12-edo.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

🔗Michael <djtrancendance@...>

Chris>"Michael - I want to know what harmonic distortion means to you so that
I might add to this conversation because I have a feeling you mean
something different than the distortion of the harmonic spectra of a
tone...."

Actually, this sounds like a related phenomenon, although it is in a different context IE I'm not saying the reason I'm against it is because it will cause your speakers to less accurately reproduce sounds due to distortion.

I'm talking about the distortion your ears, and not the speaker,
recognize when they hear beating compounded on a single fundamental,

If you play the entire harmonic series with 20hz as the root note all the way up to 20480hz or so (IE the 10th octave or so) as a single chord, note just how violent the vibration is. Of course, this does murder to loud speakers (which hate quickly attacking frequencies b/c they often can't respond quickly enough)...but, even at a low volume your speakers can easily handle it sounds dramatic and very overly repetitive (at least to me).

The effect is like taking an amplitude modulator set to the frequency of the fundamental of the harmonic series and pushing it on the entire sound.
Try it for yourself: play even just 100hz 200hz 300hz 400hz 500hz 600hz sine waves at once and notice how mechanical the beating sounds. Now try so shift some of those tones around a little and note how, even though the "tonality/focus on the root tone" is take away a bit that the beating is on more than just one frequency and doesn't create such a pounding sound.

>"I think any "theory of consonance in tuning" has to take register into
account. A lot of what goes on here in [tuning] makes the assumption
that everything is octave equivalent - however, may I point out that
the critical band phenomenon is evidence to the contrary."

Right, but the question then becomes how do you follow that curve without completely sacrificing all periodicity? I'm not saying it's impossible, but I have no clue even vaguely where to start on that one.
One easy way to take advantage of it that I do know where to start with...is to simply add more notes in between notes on higher octaves IE you could make a scale with 7 notes around 200hz which adds 2 more notes at 1600hz and pushes the notes around it up and down a tad to make space for it.

An easy candidate for this is, for example, adding a c# between the large C and D (and the large A and B) intervals in the basic just-intonation diatonic scale ALA going from

1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 to
1/1 (17/16) 5/4 4/3 3/2 (19/12) 5/3 15/8 at 1600hz to take advantage of the closer gaps allowed at higher frequencies via the curve of critical band.

>"http://en.wikipedia.org/wiki/Psalms_chord"

Now that is one interesting chord...on one hand it sounds beautifully different...on the other hand it is a charged example IMVHO of why close intervals aren't used much in chords (roughness, not lack of periodicity: even if you play a JI-perfect version of the chord it will still "bark" at you).
Especially (if I got it right) the minor second "hurts": to my ears anything closer than about a minor second plus an extra 1/4 tone space sounds too rough to be held as a dominant chord in a piece of music (sadly). Hence why I'm so gung-ho on the idea of searching for a hack to allow such chords (and several new ones) to "bark" enough less so they become much more useable.

________________________________
From: Chris Vaisvil <chrisvaisvil@gmail.com>
To: tuning@yahoogroups.com
Sent: Wed, January 13, 2010 12:28:07 PM
Subject: Re: [tuning] Why is a major triad more consonant than a minor one (even with sine waves)...an alternative explanation.

Michael - I want to know what harmonic distortion means to you so that I might add to this conversation because I have a feeling you mean something different than the distortion of the harmonic spectra of a tone....

http://en.wikipedia.org/wiki/Total_harmonic_distortion

I think any "theory of consonance in tuning" has to take register into account. A lot of what goes on here in [tuning] makes the assumption that everything is octave equivalent - however, may I point out that the critical band phenomenon is evidence to the contrary.

Also, you may find this interesting

http://en.wikipedia.org/wiki/Symphony_of_Psalms
http://en.wikipedia.org/wiki/Psalms_chord

Specifically

In music, the Psalms chord is "the famous opening chord"[1] of Igor Stravinsky's Symphony of Psalms, a "barking E minor triad - characteristically spaced",[2] "like no E-minor triad that was ever known before".[3] It is common to both the octatonic scale and the Phrygian scale on E, and the contrasting sections of the first movement based on the scales are linked by statements of the Psalms chord.[1]

On Wed, Jan 13, 2010 at 11:55 AM, Chris <chrisvaisvil@ gmail.com> wrote:

>
>
>
>
>
>
>
>
>
>
>
>
>
>
>Please define haronic distortion in your contex.
>
>Thanks.
>
>Chris
>Sent via BlackBerry from T-Mobile
________________________________

>From: Michael <djtrancendance@ yahoo.com>
>
>Date: Wed, 13 Jan 2010 08:46:47 -0800 (PST)
>To: <tuning@yahoogroups. com>
>Subject: Re: [tuning] Why is a major triad more consonant than a minor one (even with sine waves)...an alternative explanation.
>
> >
>
>>
>
>>
>
>Petr> "AFAIK, there’s no precise
>definition of what „consonant“ means."
>
>
> That is true...though I believe firmly that most people's definitions of consonance tend toward a limited number of things (IE roughness and periodicity/"single-tonality"). Although people weigh the balue of each one of those differently, I think it's fair to say both have to be there to a good extent to even be considered by most people.
>
>
>
>>"A few years ago,
>I’ve read a webpage where someone was calling the triad of 0-350-700 cents „more
>consonant“ than frequency factors of 4:6:7. The problem here is that something
>like 3:5:7:9:11 sounds to me perfectly in tune, while 0-350-700 cents sounds to
>me almost like chaos so I can’t call it „consonant“."
>
> Odd...my guess is they were using sine-wave to test the triads (IE with no overtones) and likely had the perception that roughness is more important than periodicity of overtones.
>
>
>'''------------ --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- --------- ---------
>
> One thing seems clear to me though: periodicity (and JI, for that matter) is the way to go for those who relate consonance to having all notes point to a root tone.
>
> However, of course, there are people (myself included) who actually think too much harmonic distortion from closely-space periodic notes sounds mechnical and grating to the senses and are willing to sacrifice some periodicity to limit harmonic distortion. This leads me to believe, for example, that JI
> is not the answer to everything and that there must be new unexplored scales that can do a better job for those who dislike excessive harmonic distortion but want more chords available in scales, for example.
>
>
>
>>
>
>

🔗Mike Battaglia <battaglia01@...>

On Wed, Jan 13, 2010 at 6:19 AM, Daniel Forró <dan.for@...> wrote:
> I don't think simple sounding harmonic tones and complex speech as a
> semantic signal can be compared in this context. Besides speech is
> not only harmonic spectre.

The idea is that two voices talking at the same time are really two
sets of harmonic spectra going at the same time. But in reality, the
sum total of every single sound hitting your ear drum might as well be
a single sound source, as far as your brain is concerned. The
differentiation we make between one person talking and another is
entirely a cognitive construct -- without that you just have the whole
of existence making sound all at once, in an unbroken whole.

Your brain's job is to make sense of this and split this whole up into
individual parts, which are then assigned to different objects. So
when two voices are talking, after all is said and done, your brain
realizes that there are two distinct spectra going on - one for each
voice. It does not try to combine the two into one larger, super-voice
-- likely because of tracking/envelope differences -- which just
serves as a proof of a concept that yes, the brain can simultaneously
track more than one fundamental at the same time, or fuse more than
one series at the same time, or however you'd like to call it.

That being said, when a triad is played, your ear again has no idea
that cognitively speaking, we conceptualize of it as a triad. For a
triad it will come up with 7 distinct spectra: one for each of the
individual notes being played, one corresponding to the fundamental of
the whole chord, and one corresponding for the fundamental of each
dyad. For a major triad, the dyads C-E and E-G, as well as the triad
C-E-G, will be the same, and the C-G dyad will be one octave up. So in
reality you will have 5 different spectra, three of which are the same
chroma - C.

If you just take a second to think about it, you will find that this
makes perfect sense: our experience of a major chord is just this,
three individual notes that on a more subconscious level fuse to
create the virtual C an octave and 2 octaves below. I'm not sure yet
if your brain flips between all of the possible fundamentals, though
-- as in an auditory version of the Necker Cube -- or hears them all
simultaneously.

> I have another original construction why Ionian was taken as basic
> major and Aeolian as basic minor scale, it's based on historical
> development of music. Besides you need for this only one sharp and
> one flat, and it can be also called theory of the golden rule of
> middle way. Let's take 7 possible scales: Locrian is out of the game
> because of its diminished fifth which doesn't create stable Tonic.
> Three major scales: Lydian is too much major, Ionian major,
> Mixolydian little bit minor. Three minor scales: Dorian is little bit
> major, Aeolian minor, Phrygian too much minor.

Well let's put it this way: assuming that the maj 2nd was picked over
the min 2nd just because of its closer harmonic proximity to the root
-- why was the min 6th picked over the maj 6th? My hypothesis is that
it has something to do with the fact that spectrally speaking, it's
already in the chord.

> Now let's take Bb, the
> first flat which was used. Original all-white-keys (AWK) Dorian on D
> will be changed with it into Aeolian, original AWK Lydian on F will
> become Ionian. And with the first used sharp - F#, original AWK
> Phrygian on E will be turned into Aeolian, finally original AWK
> Mixolydian on G gives Ionian. It's highly possible this process
> happened this way. But maybe in some parallel world they have
> selected both extremes - Lydian as a main major and Phrygian as a
> main minor. It would give increased contrast between major and minor.
> Maybe George Russell came from such world...

> I wouldn't call it extremely consonant by itself, it depends on the
> context. Meanwhile in the Baroque music it was still considered
> dissonant, in jazz or contemporary music it can sound consonantly in
> the comparison with more dissonant chords. Also tuning, voicing,
> inversion and instrumentation is important for resulting impact.

It certainly sounds pleasant to me.

-Mike

🔗Cox Franklin <franklincox@...>

FYI,
I am hosting a colloquium in March at which I hope some of these issues will be discussed
by scholars. The era from ca. 1750 to 1900 is not well understood in terms of tuning practices. Owen Jorgensen's books gave us a start on understanding keyboard tuning practices, which according to him could not have been modern 12-tone edo. Abbe Vogler was an influential teacher in the late 1700's who introduced some of the most influential chromatic progressions used by the early Romantics; one would think that these would have required 12-tone edo, but the tuning system he proposed was not edu (he died in the 18-teens, I believe. There are string manuals from this period that clearly distinguish finger positions for sharps and flats (C# lower than Db), such as Romberg's, who played the early Beethoven cello sonatas. So the standard belief that Beethoven's music was performed with 12-tone edo is probably wrong. But we don't have enough solid research yet to be certain what systems players were using.
Franklin Cox

Dr. Franklin Cox

1107 Xenia Ave.

Yellow Springs, OH 45387

(937) 767-1165

franklincox@...

--- On Wed, 1/13/10, monz <joemonz@...> wrote:

From: monz <joemonz@...>
Subject: [tuning] Beethoven tunings (was: The Contest)
To: tuning@yahoogroups.com
Date: Wednesday, January 13, 2010, 8:00 PM

Hi Daniel,

--- In tuning@yahoogroups. com, Daniel Forro <dan.for@... > wrote:

> - That Beethoven's work of course WAS written for 12ET.

> I'm not aware at all about any mention, or note, or

> consideration about tuning issues from the side of

> this particular composer. Also his works don't show

> anything like results of similar research or considerations.

> Maybe just "colors" of different keys... So maybe he

> was aware of tuning, but not so deeply to think about commas.

> Correct me if I'm wrong in this.

Beethoven certainly did think about commas.

There's no documentary proof that i know of to support

this statement, but it is absolutely certain that the

prevailing tunings in use during the late 1700s were

12-tone well-temperaments for keyboards and something

along the lines of a 31-tone subset of 1/6-comma meantone

(or 55-edo) for orchestral playing.

This is important in the case of Beethoven because

by the time 12-edo really started to become prominent

in practice, during the early decades of the 1800s,

Beethoven was deaf. So the tunings which he would have

had in his "inner ear" from his younger days would have

been well-temperament for keyboards and non-12-edo

meantone for other instruments.

The key characteristics only happen in a subset of

one of these tunings, for example a 12-tone well-temperament

or a 12-tone subset of meantone. They don't happen in 12-edo.

-monz

http://tonalsoft. com/tonescape. aspx

Tonescape microtonal music software

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

Mike>"It does not try to combine the two into one larger, super-voice"

True and....some things to think about: put two sounds closely together and they fluctuate and mangle each other via beating.

However each over-tone of the human voice is not a single sine wave but a bunch of very closely spaced ones...so even if the main/center sine wave of each voice cancels the other due to phase-cancellation, chances are another one (that's so close your brain can't hear the difference) will stick out.
The other thing of course, is no two voices are exactly the same far as either root pitch, timbre, or phasing. Even if two people say the same thing at the same time, timing will produce at least an obvious chorus effect due to slight timing error (IE even the exact same voice spoken over a recording of itself saying the same thing at the same pitches)...and that's certainly not a perfect "super voice", far from it. Also if anything more is different two voices will be very easily heard as separate.

>"That being said, when a triad is played, your ear again has no idea that cognitively speaking, we conceptualize of it as a triad."

Psycho-acoustically much of the effect low-numbered fractions create is simply quick beating due to shorter periodicity. The beating (per frequency) is often almost so quick you can't tell it's there. IMVHO much the reason the mind "likes" periodic harmonics is that it has an easier time calculating when they will repeat: even when graphing a wave file you'll see a simple fraction like 7/6 is simpler to look at then, say 121/107.
I can swear that's where both concepts of roughness/beating and periodicity come together: they both give the brain an idea of a pattern it can summarize quickly and easily rather than keep "recalculating" where it may go. If it repeats over a short period (IE periodicity), you know where it will go...if it beats less within the period, the curves within the period become easier to summarize and have less "edges" to trace to hear the "picture".

Anything that can be both easily summarized by the brain and contains a lot of information, I believe, gets its attention.

And something like

reward = amount-of-information-conveyed/trickiness-of-pattern-finding

I am guessing summarizes what makes certain music effective, at least mathematically. Emotionally...that's a whole other ballgame: otherwise we would likely all gravitate toward very orchestral & motif-based classical music (Debussy anyone?), the rhythmic equivalent (African poly-rhythmic music), or maybe even something with easy-to-track notes but lots of information conveyed via timbre (often trance music or distorted/overtone-intensive rock music). :-D

🔗Marcel de Velde <m.develde@...>

🔗Mike Battaglia <battaglia01@...>

🔗monz <joemonz@...>

Hi Carl,

Those are all good points you make.

However, i still wish to point out that for
non-keyboard music during the period when
Beethoven could still hear (up to c.1810),
the most likely tuning paradigm used by good
players was probably something resembling a
20-to-31-tone subset of 1/6-comma meantone.

This would still cause different keys to have
different sets of intervals, and therefore,
different audible characteristics. Using a
meantone tempering of about 1/6 comma, a
chain-of-5ths of 55 notes would be required
to eliminate the discrepancies in interval
sizes between different keys, and musical
notation itself proves that virtually no
composer during the "common-practice" period
ever used more than 31 different notes --
that is, the meantone chain from Gbb to Ax.

The only example i know of in the standard
repertoire, of the use of a note outside this
range, is an F#x (F triple-sharp) in a piano piece
by Alkan: 3rd movement of _Concerto for Solo Piano_,
Op. 39, No. 10 - left-hand staff of the top system
on page 24 of this file:

http://imslp.org/images/f/fb/Alkan_-_Concerto_from_12_etudes_Mvt3.pdf.

The practice of restricting the use of notation
to this 31-tone range probably is a result of
the common use of 1/4-comma meantone in the early part
of the "tonal" period (c.1500-1750), because
that tuning resembles 31-edo and thus essentially
"closes" with a 31-tone pitch set.

But by Beethoven's time something more like 55-edo
was the norm in practice, and so by restricting
the notation to this 31-tone subset, the key
characteristics would again be in evidence.

Anyway, i have discovered thru the use of Tonescape
that Beethoven almost always limited himself to
a _15_-tone set of pitches, which always has
the same lattice structure regardless of which
key he used as his tonic. Rather than say more
about it here right now, I think i'll prepare
a presentation on this for Franklin Cox's colloquium,
because for me this was a major discovery.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <joemonz@> wrote:
>
> > The key characteristics only happen in a subset of
> > one of these tunings, for example a 12-tone well-temperament
> > or a 12-tone subset of meantone. They don't happen in 12-edo.
>
> Evidence is shaky that the key characteristics discussed in the
> Baroque and classical periods pertained to the varying errors
> of well temperaments. Most extant discussions (that I've seen)
> refer to instrumental ensemble music, not solo keyboard music.
> And they seem to be about absolute pitch qualities of the root
> pitch of the key, not harmonic purity. (Identifying the key of
> a piece is one of the first things that friends of mine with
> weak absolute pitch can do, and they've described this as a
> pitch color judgment.) On the other hand, this interpretation
> runs into the lack of concert pitch standards at the time.
> I should check Claudio Di Veroli's book to see if he has a
> position on this...
>
> -Carl
>

🔗monz <joemonz@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
>
> Hi Carl,
>
> Those are all good points you make.
>
> However, i still wish to point out that for
> non-keyboard music during the period when
> Beethoven could still hear (up to c.1810),
> the most likely tuning paradigm used by good
> players was probably something resembling a
> 20-to-31-tone subset of 1/6-comma meantone.
>
> This would still cause different keys to have
> different sets of intervals, and therefore,
> different audible characteristics.

But there would only be wolves or good keys!

> Using a
> meantone tempering of about 1/6 comma, a
> chain-of-5ths of 55 notes would be required
> to eliminate the discrepancies in interval
> sizes between different keys, and musical
> notation itself proves that virtually no
> composer during the "common-practice" period
> ever used more than 31 different notes --
> that is, the meantone chain from Gbb to Ax.

Of course most pieces use much less.

> The practice of restricting the use of notation
> to this 31-tone range probably is a result of
> the common use of 1/4-comma meantone in the early part
> of the "tonal" period (c.1500-1750), because
> that tuning resembles 31-edo and thus essentially
> "closes" with a 31-tone pitch set.

The notation is clearly set up to work best when
accidentals aren't piled up excessively. That keeps
us in the range you mention. You can call that an
artifact of 1/4-comma meantone, but I think it's
just the nature of songs not to modulate too far.

-Carl

🔗Marcel de Velde <m.develde@...>

🔗Mike Battaglia <battaglia01@...>

🔗Marcel de Velde <m.develde@...>

🔗Petr Parízek <p.parizek@...>

Marcel wrote:

> But I'm talking about big wolves :)
> Like 1/1 32/27 40/27 (D F A in C) and 1/1 75/64 3/2 minor chords,
> 1/1 5/4 40/27 and 1/1 32/25 3/2 major chords.

Are you joking???

Hey, this is really too much. 75/64 is an augmented second, not a minor third, And 32/25 is a diminished fourth, not a major third. It's a bit like if you said that 8192/6561 is a Pythagorean major third. But it's not, because you have to rise by 5 octaves and fall by 8 fifths to get there, so it's a diminished fourth. Instead, 81/64 is a major third, because you rise by 4 fifths and fall by 2 octaves to get there. And the 5-limit question is similar. If you do 5/4 squared and fall by one octave, you get a falling diminished fourth (25/32), which is the same as going from C4 to E4, then to G#4, and then G#3. If you then claim that 32/25 is a major third, you're doing exactly the same thing that Janácek was doing, when he claimed it was actually not very important whether one wrote C-Eb or C-D# (because both sounded the same on the piano). But if there's a particular harmonic progression which is clearly calling for an Eb, then there's no point in using D#. Unfortunately, Janácek was probably considering this to be an "outdated way of thinking" and was happily using chords like C#-F-G# in situations where Db-F-Ab should be used (in context of the preceding intervals and chords), which eventually made his piano scores extremely difficult to read for a lot of people including myself.

Petr

🔗Daniel Forró <dan.for@...>

Hi, Peter,

I know every note in Janacek piano works, so I'm quite sure there are
not such problems you indicate. Could you show some example?
Sometimes it's difficult to read because of his using of whole tone
and diminished scales which always goes against traditional tonality,
or his quick modulations, and jumps from sharps to flats, maybe
sometimes too much double accidentals and using for example flats for
chord in the left hand and sharps for melody... But it's always
compositionally logical, he had a reason for his way of writing.

Besides recent Faltus and Stedron critical edition changed lot of
this and simplified. Five years ago I accompanied Violin Sonata from
the new edition and it was incomparable with older editions.

I will go thru Janacek's theoretical works once more to find a statement where he claimed that enharmonic writing is not so
important. Yes, he was very original composer and personality, doing
often crazy and unusual things, but I doubt he would do things
against his own theories. Where have you found this quotation?

Daniel Forro

On 15 Jan 2010, at 5:44 PM, Petr Parízek wrote:

>
>
> Marcel wrote:
>
> > But I'm talking about big wolves :)
> > Like 1/1 32/27 40/27 (D F A in C) and 1/1 75/64 3/2 minor chords,
> > 1/1 5/4 40/27 and 1/1 32/25 3/2 major chords.
>
> Are you joking???
>
> Hey, this is really too much. 75/64 is an augmented second, not a
> minor third, And 32/25 is a diminished fourth, not a major third.
> It’s a bit like if you said that 8192/6561 is a Pythagorean major
> third. But it’s not, because you have to rise by 5 octaves and
> fall by 8 fifths to get there, so it’s a diminished fourth.
> Instead, 81/64 is a major third, because you rise by 4 fifths and
> fall by 2 octaves to get there. And the 5-limit question is
> similar. If you do 5/4 squared and fall by one octave, you get a
> falling diminished fourth (25/32), which is the same as going from
> C4 to E4, then to G#4, and then G#3. If you then claim that 32/25
> is a major third, you’re doing exactly the same thing that
> Janáček was doing, when he claimed it was actually not very
> important whether one wrote C-Eb or C-D# (because both sounded the
> same on the piano). But if there’s a particular harmonic
> progression which is clearly calling for an Eb, then there’s no
> point in using D#. Unfortunately, Janáček was probably considering
> this to be an „outdated way of thinking“ and was happily using
> chords like C#-F-G# in situations where Db-F-Ab should be used (in
> context of the preceding intervals and chords), which eventually
> made his piano scores extremely difficult to read for a lot of
> people including myself.
>
> Petr
>

🔗Petr Pařízek <p.parizek@...>

🔗Daniel Forró <dan.for@...>

On 15 Jan 2010, at 7:45 PM, Petr Pařízek wrote:

> Hi Daniel.
> #1. I could probably find other examples as well but a good one may
> be the third part of "In the mists" where he often uses a B minor
> triad in places where I would go for Cb,
>

If you mean the beginning of the 3rd movement, the chord is Bmi,
which is more easy to read then Cbmi. Here he probably prefered
readability and changed from flats to sharps. But of course he could
have sharps since the beginning - 6# is the same like 6b as for
readability.

> or he keeps alternating between C# and Db for no particular reason.
>

Reason is key jump, which is typical for his "pattern", repetitive
style. Sometimes he is in C# minor, sometimes Db major...

> #2. Faltus himself talked about Janáček's concept of (don't know > the English translation) "intervaly formální" (being the written
> ones) and "intervaly věcné" (being the sounding ones). He had
> ellegedly stated that even if you wrote C-G#, you could still use > it as if it were a minor sixth because both G# and Ab sounded the
> same.
>
> Petr
>

I will check, that's interesting. It wouldn't cause problems in
keyboard works (just to complicate reading), but Janacek has also
string quartets and other chamber, orchestral and vocal works, I'm
sure he had to be aware of tuning issues and enharmonicity.

Daniel F

🔗Marcel de Velde <m.develde@...>

Hi Petr!

> But I'm talking about big wolves :)
> > Like 1/1 32/27 40/27 (D F A in C) and 1/1 75/64 3/2 minor chords,
> > 1/1 5/4 40/27 and 1/1 32/25 3/2 major chords.
>
> Are you joking???
>
> Hey, this is really too much. 75/64 is an augmented second, not a minor
> third, And 32/25 is a diminished fourth, not a major third. It’s a bit like
> if you said that 8192/6561 is a Pythagorean major third. But it’s not,
> because you have to rise by 5 octaves and fall by 8 fifths to get there, so
> it’s a diminished fourth. Instead, 81/64 is a major third, because you rise
> by 4 fifths and fall by 2 octaves to get there. And the 5-limit question is
> similar. If you do 5/4 squared and fall by one octave, you get a falling
> diminished fourth (25/32), which is the same as going from C4 to E4, then to
> G#4, and then G#3. If you then claim that 32/25 is a major third, you’re
> doing exactly the same thing that Janáček was doing, when he claimed it was
> actually not very important whether one wrote C-Eb or C-D# (because both
> sounded the same on the piano). But if there’s a particular harmonic
> progression which is clearly calling for an Eb, then there’s no point in
> using D#. Unfortunately, Janáček was probably considering this to be an
> „outdated way of thinking“ and was happily using chords like C#-F-G# in
> situations where Db-F-Ab should be used (in context of the preceding
> intervals and chords), which eventually made his piano scores extremely
> difficult to read for a lot of people including myself.
>
> Petr
>

I'm not joking :)
I do agree with you that something like 1/1 32/25 3/2 should in a perfect
world not be called a major triad / chord.
However, I'm dealing with translating music written in enharmonic spelling
to JI.
I don't trust one little bit of spelling of any composer. No matter how he
wrote the notes, as he didn't write them for JI.
So I think it will often be the case that a chord written as a major chord
wil end up beeing for instance a 1/1 32/25 3/2 chord.

Proof of this is in for instance Beethoven's Drei Equale No1.
Beethoven wrote it as if it's in the tonic of F (or D minor).
Yet I analyse it as beeing in the tonic of C.
The first 2 chords are:
D - A - D - F
A - A - C# - E

In the tonic of C this makes:
D (9/8) - A (5/3) - D (9/4) - F (8/3)
A (5/3) - A (5/3) - C# (32/15) - E (5/4) This is a 1/1 32/25 3/2 chord
spelled as a major chord by none other than Beethoven himself.

But you allready give another example of Janacek, who spells like this
intentionally.
And I must agree with him, it doesn't matter for 12tet piano (though too bad
he apparently did it in a way that's hard to read for you, as the opposite
should be his goal it seems to me)
But besides this, again, I don't trust any composers spelling of notes when
dealing with JI. So they may have just as well written it in any other way.

Marcel

🔗Petr Pařízek <p.parizek@...>

Marcel wrote:

> I don't trust one little bit of spelling of any composer.
> No matter how he wrote the notes, as he didn't write them for JI.

Marcel, this is really becoming unbelievable. What you’ve just said is nothing else than a superficial and self-conseated statement which only shows your closed-minded attitude. If you had been reading previous posts carefully, you would surely have understood that Beethoven knew about meantone and about the difference in meanings of C# and Db even though music was often performed in non-meantone tunings in his times. Even though he didn’t write the piece for JI, he DID write the piece using standard notation. You see the difference? He didn’t record it with a 1-dimmensional 12-tone keyboard, he wrote it down in a notation systém which is 2-dimmensional and is nothing else than a written representation of meantone. And this was in the era when classical harmony was already at a very high level. So saying that the „proper“ spelling might be different is simply unappropriate in this case.

> So I think it will often be the case that a chord written as a major chord wil end up
> beeing for instance a 1/1 32/25 3/2 chord.

I’ve already explained many times why this is impossible and you still seem to resist.

> A (5/3) - A (5/3) - C# (32/15) - E (5/4) This is a 1/1 32/25 3/2 chord
> spelled as a major chord by none other than Beethoven himself.

My goodness, how can you say this on one hand and, on the other, claim that you might know more about enharmonic spelling than Beethoven did? How many times do I have to repeat myself? The standard notation is a result of past usage of meantone, which means that what you’ve just said would be almost impossible to defend. I would rather say that this A major triad is understood as 1/1-32/25-3/2 by noone else than you. There’s absolutely no way to defend such an utterly consonant and complex chord right at the beginning of the piece. Do you think that a late 18-century trombone quartet would find it okay to play such a chord just a few seconds after the piece starts, had they been its authors? They wouldn’t, obviously, because the triadic harmony comes from the „systematic“ 5-limit JI concept which I was explaining earlier.

> But you allready give another example of Janacek, who spells like this intentionally.

Saying that Janáček’s spelling might be incorrect is not as simplistic as saying that Beethoven’s spelling might be incorrect for one simple reason. In the 18th century, classical harmony had to obey very strict rules which had a lot of things in common with Baroque harmony. The composers got so used to it that they just took it for granted. In contrast, Janáček was very rebelious about music theory in many ways and made lots of very specific oppinions about voice leading, interval names, rhythm, harmony, musical forms and other stuff -- I mean, oppinions which didn’t make much sense in context of the preceding development of European music. His theoretical publications were often viewed as single-minded and were pretty unsuccessful, for a number of reasons. And I’m not surprised at all. After reading the entire „In the mists“ during 2003, I just felt as if I’d read a book full of phrases like „thear wozza nies gurltheir“ instead of „there was a nice girl there“. You see, it was really terribly difficult to read

Petr

🔗Marcel de Velde <m.develde@...>

Petr,

Marcel, this is really becoming unbelievable. What you’ve just said is
> nothing else than a superficial and self-conseated statement which only
> shows your closed-minded attitude.
>

I do not have a close minded attitude.
I have quite the opposite, a very openminded attitude, with which I seek to
find the truth about how JI really works.

> If you had been reading previous posts carefully, you would surely have
> understood that Beethoven knew about meantone and about the difference in
> meanings of C# and Db even though music was often performed in non-meantone
> tunings in his times. Even though he didn’t write the piece for JI, he DID
> write the piece using standard notation. You see the difference? He didn’t
> record it with a 1-dimmensional 12-tone keyboard, he wrote it down in a
> notation systém which is 2-dimmensional and is nothing else than a written
> representation of meantone. And this was in the era when classical harmony
> was already at a very high level. So saying that the „proper“ spelling might
> be different is simply unappropriate in this case.
>
> > So I think it will often be the case that a chord written as a major
> chord wil end up
> > beeing for instance a 1/1 32/25 3/2 chord.
>
> I’ve already explained many times why this is impossible and you still seem
> to resist.
>
> > A (5/3) - A (5/3) - C# (32/15) - E (5/4) This is a 1/1 32/25 3/2 chord
> > spelled as a major chord by none other than Beethoven himself.
>
> My goodness, how can you say this on one hand and, on the other, claim that
> you might know more about enharmonic spelling than Beethoven did? How many
> times do I have to repeat myself? The standard notation is a result of past
> usage of meantone, which means that what you’ve just said would be almost
> impossible to defend. I would rather say that this A major triad is
> understood as 1/1-32/25-3/2 by noone else than you. There’s absolutely no
> way to defend such an utterly consonant and complex chord right at the
> beginning of the piece. Do you think that a late 18-century trombone quartet
> would find it okay to play such a chord just a few seconds after the piece
> starts, had they been its authors? They wouldn’t, obviously, because the
> triadic harmony comes from the „systematic“ 5-limit JI concept which I was
> explaining earlier.
>
> > But you allready give another example of Janacek, who spells like this
> intentionally.
>
> Saying that Janáček’s spelling might be incorrect is not as simplistic as
> saying that Beethoven’s spelling might be incorrect for one simple reason.
> In the 18th century, classical harmony had to obey very strict rules which
> had a lot of things in common with Baroque harmony. The composers got so
> used to it that they just took it for granted. In contrast, Janáček was very
> rebelious about music theory in many ways and made lots of very specific
> oppinions about voice leading, interval names, rhythm, harmony, musical
> forms and other stuff -- I mean, oppinions which didn’t make much sense in
> context of the preceding development of European music. His theoretical
> publications were often viewed as single-minded and were pretty
> unsuccessful, for a number of reasons. And I’m not surprised at all. After
> reading the entire „In the mists“ during 2003, I just felt as if I’d read a
> book full of phrases like „thear wozza nies gurltheir“ instead of „there was
> a nice girl there“. You see, it was really terribly difficult to read
>
> Petr
>

Petr, we have a difference of opinion.
If I'm following your thoughts correctly then it becomes clear that you
allways see a major chord spelled as a major chord as 1/1 5/4 3/2, and a
minor chord spelled as a minor chord as 1/1 6/5 3/2?
Yet you've also said that sometimes such a chord is not 1/1 5/4 3/2 but 1/1
81/64 3/2? (which is more dissonant than any of my chords in my opinion)
And a D F A chord in C, what is it? going to have a comma shift with certain
progressions? or gets a different tuning with different chord progressions?
JI is not directly one on one related to enharmonic spelling. And why do you
insist everybody spells their notes correctly? (except janacek)
I belief JI is the highest form of note spelling.

And one more thing. Why does it matter how Beethoven starts the drei equale?
A starting chord can just as well be dissonant as any other chord.
The starting chord is a ii minor chord, then a VI major (1/1 32/25 3/2 from
VI), then I - V - I progression, etc. All in tonic C.

Marcel

🔗Daniel Forró <dan.for@...>

On 16 Jan 2010, at 6:14 AM, Marcel de Velde wrote:
>
> Proof of this is in for instance Beethoven's Drei Equale No1.
> Beethoven wrote it as if it's in the tonic of F (or D minor).

D minor.

> Yet I analyse it as beeing in the tonic of C.
> The first 2 chords are:
> D - A - D - F
> A - A - C# - E
>
> In the tonic of C this makes:
> D (9/8) - A (5/3) - D (9/4) - F (8/3)
> A (5/3) - A (5/3) - C# (32/15) - E (5/4) This is a 1/1 32/25 3/2 > chord spelled as a major chord by none other than Beethoven himself.
>

Of course it is written in D minor, with some old modal progressions there and here, secondaty dominants and VII chords and Picardy third major ending and final chord. Anybody with a basic knowledge of functional harmony theory can see it clearly.

> But you allready give another example of Janacek, who spells like > this intentionally.

He was not so stupid. All his unusual spellings have reason. And believe or not, one of them was to make a score better readable.

Daniel Forro

> And I must agree with him, it doesn't matter for 12tet piano > (though too bad he apparently did it in a way that's hard to read > for you, as the opposite should be his goal it seems to me)
> But besides this, again, I don't trust any composers spelling of > notes when dealing with JI. So they may have just as well written > it in any other way.
>
> Marcel

🔗Daniel Forró <dan.for@...>

🔗Marcel de Velde <m.develde@...>

🔗Petr Parízek <p.parizek@...>

🔗Petr Pařízek <p.parizek@...>

Marcel wrote:

> If I'm following your thoughts correctly then it becomes clear that you allways see
> a major chord spelled as a major chord as 1/1 5/4 3/2, and a minor chord spelled as
> a minor chord as 1/1 6/5 3/2?

If the music is strictly based on 5-limit triads (like Renaissance or early Baroque music, for example), then, yes, you’re right. Some differences may occur in cases of polyphonic music or music which doesn’t care about chords.

> Yet you've also said that sometimes such a chord is not 1/1 5/4 3/2
> but 1/1 81/64 3/2? (which is more dissonant than any of my chords in my opinion)

In cases where you are primarily interested in the melodic steps of the individual voices and don’t care about chords (like some middle-age polyphonic pieces), then Pythagorean tuning is appropriate because it perfectly preserves the important characteristics of the melodic steps -- i.e. a major second of C-Db being smaller than the „chroma“ of C-C#, C# being higher than Db, and so on. And you also have really only two step sizes in a Pythagorean diatonic scale, a major second of 9/8 and a minor second of 256/243. But when you start thinking about chords and about the way the voices sound together (which is what happened towards the end of the 15th century), then the prime 5 comes in, thirds and sixths become as „stable“ as fifths and fourths, and the difference in intonation of a „chroma“ and a minor second turns the other way round (i.e. C-Db is larger than C-C# and C# is lower than Db, not higher). Although there’s a remarcable difference in the sound of 64:81:96 (meaning 1/1-81/64-3/2) and 4:5:6 (meaning 1/1-5/4-3/2), there’s no difference in how these two are notated because Renaissance music was mostly played in meantone (if not rarely in 5-limit JI) where 81/80 is tempered out. BUT (and there’s the big but) the important thing to know here is that this is the one and only interval which is tempered out in meantone, which means that the diesis of 128/125 (the distance from 5/4 to 32/25) is not tempered out, nor is the Pythagorean comma, nor the 5-limit schisma (although the schisma is only about 2 cents in size). For this reason, a chord which is notated as A-C#-E should always come out as 4:5:6 in the case of strictly „chordal“ 5-limit music, or 64:81:96 in the case of strictly „melodic“ 3-limit music. Obviously, when you’re doing something which is „melodic“ and which is 5-limit, then some new possibilities may occur. One of them, for example, might be a situation where you would have to use a major third of 100/81 or some such. But none of them is to render A-C#-E as 1/1-32/25-3/2, because if 1/1 is A, then 32/25 is Db and not C#, which is perfectly preserved in our standard notation -- i.e. in meantone. 32/25 is away from 5/4 by a diesis of 128/125, which is not an integer multiple of the syntonic comma size, which means that you can’t get this diesis by stacking syntonic commas one above another, which means that the diesis isn’t tempered out in meantone, which means that a notated minor third can’t come out as 32/25 in 5-limit JI -- because nothing else than the syntonic comma vanishes in meantone.

> And a D F A chord in C, what is it? going to have a comma shift with certain progressions?
> or gets a different tuning with different chord progressions?

Maybe you’ll be surprised, but both of these solutions are possible and both of them were even sometimes applied during the 16th century prior to finally settling on meantone. There were theorists and instrument builders who were designing keyboards with more than 12 keys or who were using two 12-tone keyboards at once to get a 24-tone set (Fogliano, Zarlino, Salinas, Vicentino, Mersenne and maybe others).

> JI is not directly one on one related to enharmonic spelling.

It isn’t in the 5-limit field, but it is in the 3-limit field. When you start with 3-limit JI which is 2-dimmensional, the intervals can be perfectly preserved. When you then add the prime 5, you get a 3-dimmensional systém. Of course, you can turn any 3-dimmensional systém into a 2-dimmensional one by choosing one interval which you’re going to ignore in your new systém. This is the same as if you temper it out. So if standard notation doesn’t distinguish two pitches which would originally (i.e. in 5-limit JI) differ by a syntonic comma, it’s the same as if meantone doesn’t distinguish two pitches originally differing by a syntonic comma. But now that you have made a 2D systém out of a 3D one by ignoring the syntonic comma, you have to keep in mind that only the size of the syntonic comma (and its integer multiples) vanishes in it, which means that you can render A-C# as either 81/64 or 5/4 or maybe rarely 100/81, but not 32/25.

> And why do you insist everybody spells their notes correctly? (except janacek)

Until about the mid-1800s, the rules of classical-romantic harmony were so tight and precise that everyone who went against them would simply „stick out“. Obviously, there were a handful of composers who „sticked out“ this way and there’s still some debate on why they were doing so, AFAIK.

> I belief JI is the highest form of note spelling.

Sure, because 5-limit JI is a 3D systém and both standard notation and meantone are 2D systems. But when converting a „model“ piece of music (based primarily on some old chord relations coming from 5-limit JI) from 5-limit JI to notes or to meantone, one needs to remember what is lost after the conversion and what is preserved. You seem to only care about the data which is lost in the conversion without considering the data which stays preserved.

> And one more thing. Why does it matter how Beethoven starts the drei equale?
> A starting chord can just as well be dissonant as any other chord.

Maybe it can but in a different way than you describe. There were obviously composers who used dense clusters even in the 17th century, but anyway, they stayed within certain boundaries. A diminished fourth could either be resolved to a minor third (like C#_F-C#_E or C#_F-D_F) or included in a dense cluster (like A-Bb-C#-D-E-F-G-A) but not in a triad which is not resolved to something else. Using 32/25 in a triad where nothing gets resolved is against the rules of common classical harmony.

Petr

🔗Petr Pařízek <p.parizek@...>

🔗Daniel Forró <dan.for@...>

On 16 Jan 2010, at 9:19 PM, Petr Parízek wrote:

> Daniel Forró wrote:
>
> > He was not so stupid. All his unusual spellings have reason. And
> > believe or not, one of them was to make a score better readable.
>
> He was not stupid, he was just very stubborn and thought that lots
> of people around him had an „old-fashioned“ way of thinking.
> Unfortunately, he promoted his ideas in such a way that he threw
> away some things in music theory which had fairly clear reasons why
> they were there.
>
Yes, great souls among us are sometimes like him and stay unfollowed.
Fortunately his music is better than his theories, but so typical
that it can't be followed. He represents an original mix of
traditional and modern thinking.

> It’s similar to the event which probably you know more about than I
> do -- when some people thought the standard notation was too
> complicated and they invented something called Klavierscribo. The
> fact it hadn’t eventually succeeded has some very clear reasons and
> I can honestly say that it looks to me almost like nonsense because
> it’s essentially a 1-dimmensional systém based on 12-EDO and
> therefore strips out many things which are important in non-12-EDO
> context. Obviously, the inventors of Klavierscribo weren’t stupid,
> but they probably didn’t think about the broader meaning of
> harmony, or they thought that it was not as important for musicians
> as it actually was, otherwise they would probably have come up with
> a „more-dimmensional“ system.
>
> Petr
>
It looks you didn't get it right if you are talking about
Klavarskribo. You should understand better what it is and what not.
It's quite clear just from its name. It has nothing to do with
universal standard music notation, it's just a kind of tablature for
keyboard instruments. It didn't show notes, but keys.
In this sense it's similar to the other tablatures, like those for
fretted stringed instruments (they also don't show notes, but
fingerings - which finger should be used in which place on the
fingerboard) or tablature for Japanese koto (which show number of
string to be played, finger, rhythm, dynamics, articulation and the
way of playing, plus pitch bend or other specialties - glissandos,
arpeggios, tremolos, vibratos, beats, harmonics, damping, sul tasto,
sul ponticello, left from the bridge etc.).

For tablature is not important tuning (it's written extra} or
enharmonic spelling, it's only a graphical description of tactile
action on the instrument.

Daniel Forro

🔗Petr Parízek <p.parizek@...>

🔗Daniel Forró <dan.for@...>

🔗Cox Franklin <franklincox@...>

The piece is not in C major. That's just the second phrase of the piece. You can't pick out the second phrase of a piece and claim the piece is in that key when all other evidence--the closing key, the opening key, the key signature, the other cadences, and so forth--undercuts that key.

Dr. Franklin Cox

1107 Xenia Ave.

Yellow Springs, OH 45387

(937) 767-1165

franklincox@...

--- On Sat, 1/16/10, Marcel de Velde <m.develde@gmail.com> wrote:

From: Marcel de Velde <m.develde@...>
Subject: Re: [tuning] Re: Beethoven tunings (was: The Contest)
To: tuning@yahoogroups.com
Date: Saturday, January 16, 2010, 2:09 AM

Of course it is written in D minor, with some old modal progressions

there and here, secondaty dominants and VII chords and Picardy third

major ending and final chord. Anybody with a basic knowledge of

functional harmony theory can see it clearly.

Well I think it's not rightly so written in D minor.
And it's not a true Picardy third major ending / final chord.

The tonic is set as C in the first few chords:

D - A - D - F
A - A - C# - E
This could still be anything.
But then comes:
E - C - E - G ( I )
G - B - D - F ( V7 )
C - G - C - E ( I )
Now this establishes clearly the tonic as beeing C!!

You can listen to the Drei Equali in JI in the tonic of C at www.develde. net

Marcel

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Marcel de Velde <m.develde@...>

> The piece is not in C major. That's just the second phrase of the piece.
> You can't pick out the second phrase of a piece and claim the piece is in
> that key when all other evidence--the closing key, the opening key, the key
> signature, the other cadences, and so forth--undercuts that key.

I did not say C major. That's a scale in my opinion.
I'm not into major / minor.
I said the tonic is C. The piece uses several modal scales from the tonic of
C (aswell as C major sometimes).

The second phrase does in this instance create a strong sense of tonic.
You can't get more clear than with I - V7 - I. Especially when before that
there were only 2 chords of which one is very easy to see as ii.
Furthermore the tonic of C is often reinforced throughout the piece.
After the first 3 phrases, the 4 melodies all go down and end in C major
chord. After which the diminished chord, and it resolves again to C major,
after which diminished again, then more sadness like phrase 1 and 3, then
phrase 1 again then again the I - V7 - I, etc

And lets change one single note as a test.
The C# to C.
It still sounds right, only changes a great deal the emotion of the chord
(not from happy to sad as would be the case with changing a dominant major
to a minor, but because this is not a dominant chord but a very emotional
1/1 32/25 3/2 chord, it changes to a less emotionally charged chord)
Now we have ii - vi - I - V7 - I chord progression in C.

As for the starting and ending D chords. They have a very different
character / feel to me than tonic chords.
Sure, often in many sompositions the starting and ending chords are tonic
chords. But not in this piece.
They are so tragic / they wring. Now when the piece is in C they finally do
so in tuning aswell.
This piece is not about tonic chord consonance, it's about the dissonant
chords that have a sad and painfull emotion.

As for the key signature, I've allready explained previously this holds no
value to me. Why should I trust this when dealing with JI.

Marcel
www.develde.net

🔗Marcel de Velde <m.develde@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Marcel,

Isn't the point to render all historic music as it was intended to be heard
by the composer?

I'm confused as to why you insist that JI is to be rendered differently (and
in your mind better) than what the composer intended - it sounds totally...
well conceited.
Especially with a composer of Beethoven's stature. With all due respect I
have great difficulty thinking you know Ludwig's music better than him.

Chris

On Sat, Jan 16, 2010 at 2:59 PM, Marcel de Velde <m.develde@...>wrote:

>
>
>
> The piece is not in C major. That's just the second phrase of the piece.
>> You can't pick out the second phrase of a piece and claim the piece is in
>> that key when all other evidence--the closing key, the opening key, the key
>> signature, the other cadences, and so forth--undercuts that key.
>
>
> I did not say C major. That's a scale in my opinion.
> I'm not into major / minor.
> I said the tonic is C. The piece uses several modal scales from the tonic
> of C (aswell as C major sometimes).
>
> The second phrase does in this instance create a strong sense of tonic.
> You can't get more clear than with I - V7 - I. Especially when before that
> there were only 2 chords of which one is very easy to see as ii.
> Furthermore the tonic of C is often reinforced throughout the piece.
> After the first 3 phrases, the 4 melodies all go down and end in C major
> chord. After which the diminished chord, and it resolves again to C major,
> after which diminished again, then more sadness like phrase 1 and 3, then
> phrase 1 again then again the I - V7 - I, etc
>
>

🔗Marcel de Velde <m.develde@...>

🔗Daniel Forró <dan.for@...>

Back to the school, man.

Daniel Forro

On 17 Jan 2010, at 4:59 AM, Marcel de Velde wrote:

>
>
>
> The piece is not in C major. That's just the second phrase of the > piece. You can't pick out the second phrase of a piece and claim > the piece is in that key when all other evidence--the closing key, > the opening key, the key signature, the other cadences, and so > forth--undercuts that key.
> I did not say C major. That's a scale in my opinion.
> I'm not into major / minor.
> I said the tonic is C. The piece uses several modal scales from the > tonic of C (aswell as C major sometimes).
>
> The second phrase does in this instance create a strong sense of > tonic.
> You can't get more clear than with I - V7 - I. Especially when > before that there were only 2 chords of which one is very easy to > see as ii.
> Furthermore the tonic of C is often reinforced throughout the piece.
> After the first 3 phrases, the 4 melodies all go down and end in C > major chord. After which the diminished chord, and it resolves > again to C major, after which diminished again, then more sadness > like phrase 1 and 3, then phrase 1 again then again the I - V7 - I, > etc
>
> And lets change one single note as a test.
> The C# to C.
> It still sounds right, only changes a great deal the emotion of the > chord (not from happy to sad as would be the case with changing a > dominant major to a minor, but because this is not a dominant chord > but a very emotional 1/1 32/25 3/2 chord, it changes to a less > emotionally charged chord)
> Now we have ii - vi - I - V7 - I chord progression in C.
>
> As for the starting and ending D chords. They have a very different > character / feel to me than tonic chords.
> Sure, often in many sompositions the starting and ending chords are > tonic chords. But not in this piece.
> They are so tragic / they wring. Now when the piece is in C they > finally do so in tuning aswell.
> This piece is not about tonic chord consonance, it's about the > dissonant chords that have a sad and painfull emotion.
>
> As for the key signature, I've allready explained previously this > holds no value to me. Why should I trust this when dealing with JI.
>
> Marcel
> www.develde.net

🔗Marcel de Velde <m.develde@...>

🔗christopherv <chrisvaisvil@...>

I was very curious as to what was going on in this piece.

Today having some time while waiting for my daughter I assigned chords to sheet music printed out from Marcel's midi file of Drei Equali. (Please understand Sonar is not smart assigning accidentals).

http://clones.soonlabel.com/public/classical-music/drei-equali-chords.jpg

While I've only assigned chord names the over arching tonal center progression seems to me to be from D minor to G - frankly that G does not sound minor nor major to my ears - just G unison. (I added that G as the end just to satisfy my anticipation.)

Does anyone know from what period in Beethoven's life this piece is from? I can't say I've studied a lot of Beethoven and the original 50 measures is really interesting.

In any case in my opinion there are two very definite cadences in D minor and then a tonal center shift to G at the end. My impression is that this piece sets up for a piece to follow.

I'm only a two year theory student so I'm sure many of you can do better than this - I've yet to put in the harmonic analysis. On the other hand I think the tonal center is pretty apparent - anyone agree / disagree?

Chris

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
>
> > It's up on my website now.
> > Ok some parts are a bit off, but for the large part it's very close to JI
> > in tonic of C.
> > And some very clearly identifying notes are played thesame in both.
> >
>
> Upon closer listening.
> The real trombones play the first 3 phrases as if they're in the tonic of
> Ab.
> D (9/8) - A (5/3) - D (9/4) - F (8/3)
> A (5/3) - A (5/3) - C# (25/12) - E (5/2) making this chord 1/1 5/4 3/2
>
> Then instead of I - V - I, it's VI - III - VI, same consonant tuning.
>
> Then phrase 3 again with 9/8 4/3 5/3 -> 5/3 25/24 5/4 etc
>
> 2 notes difference from tonic of C in this case.
> 16/15 becomes 25/24, and 8/5 becomes 25/16
>
> It's a real possibility, and more consonant.
> But it does mean that other parts of the piece must modulate.
> I'll go investigate further.
> But no way this piece is in D, really noo waay.
>
> Marcel
>

🔗Chris Vaisvil <chrisvaisvil@...>

Interesting

In this real performance - the last chords are D minor?

http://www.youtube.com/watch?v=fJPm5GBXjvs

On Mon, Jan 18, 2010 at 9:26 PM, christopherv <chrisvaisvil@...>wrote:

>
>
> I was very curious as to what was going on in this piece.
>
> Today having some time while waiting for my daughter I assigned chords to
> sheet music printed out from Marcel's midi file of Drei Equali. (Please
> understand Sonar is not smart assigning accidentals).
>
> http://clones.soonlabel.com/public/classical-music/drei-equali-chords.jpg
>
> While I've only assigned chord names the over arching tonal center
> progression seems to me to be from D minor to G - frankly that G does not
> sound minor nor major to my ears - just G unison. (I added that G as the end
> just to satisfy my anticipation.)
>
> Does anyone know from what period in Beethoven's life this piece is from? I
> can't say I've studied a lot of Beethoven and the original 50 measures is
> really interesting.
>
> In any case in my opinion there are two very definite cadences in D minor
> and then a tonal center shift to G at the end. My impression is that this
> piece sets up for a piece to follow.
>
> I'm only a two year theory student so I'm sure many of you can do better
> than this - I've yet to put in the harmonic analysis. On the other hand I
> think the tonal center is pretty apparent - anyone agree / disagree?
>
> Chris
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Marcel de Velde
> <m.develde@...> wrote:
> >
> > > It's up on my website now.
> > > Ok some parts are a bit off, but for the large part it's very close to
> JI
> > > in tonic of C.
> > > And some very clearly identifying notes are played thesame in both.
> > >
> >
> > Upon closer listening.
> > The real trombones play the first 3 phrases as if they're in the tonic of
> > Ab.
> > D (9/8) - A (5/3) - D (9/4) - F (8/3)
> > A (5/3) - A (5/3) - C# (25/12) - E (5/2) making this chord 1/1 5/4 3/2
> >
> > Then instead of I - V - I, it's VI - III - VI, same consonant tuning.
> >
> > Then phrase 3 again with 9/8 4/3 5/3 -> 5/3 25/24 5/4 etc
> >
> > 2 notes difference from tonic of C in this case.
> > 16/15 becomes 25/24, and 8/5 becomes 25/16
> >
> > It's a real possibility, and more consonant.
> > But it does mean that other parts of the piece must modulate.
> > I'll go investigate further.
> > But no way this piece is in D, really noo waay.
> >
> > Marcel
> >
>
>
>

🔗Daniel Forró <dan.for@...>

Your score is full of enharmonic mistakes and strange voice crossings. How do you want to analyse it from such bad material? Why not to use original score? You can download it from IMSLP pages:

http://imslp.org/wiki/3_Equali,_WoO_30_(Beethoven,_Ludwig_van)

Be prepared to read alt and tenor clefs :-)

On 19 Jan 2010, at 11:26 AM, christopherv wrote:

> I was very curious as to what was going on in this piece.
>
> Today having some time while waiting for my daughter I assigned > chords to sheet music printed out from Marcel's midi file of Drei > Equali.
>
> (Please understand Sonar is not smart assigning accidentals).
>

Then you should use some better software for scores, this way is not the best one how to learn music theory properly.
>
> http://clones.soonlabel.com/public/classical-music/drei-equali-> chords.jpg
>
> While I've only assigned chord names the over arching tonal center > progression seems to me to be from D minor to G - frankly that G > does not sound minor nor major to my ears - just G unison. (I added > that G as the end just to satisfy my anticipation.)
>
> Does anyone know from what period in Beethoven's life this piece is > from?
>
November 2nd, 1812, composed in Linz. But it doesn't tell anything, as in my opinion it's rather atypical piece for Beethoven, for this period of his life and generally for the mainstream music of those times. The reason can be it's a ceremonial, funeral music (it was even performed at his own funeral) so he used some elements of older, pre-Classicism music to give it this character, how it was still used those times in the liturgical, church music (which conservatively used modal scales and harmonic progressions as well as polyphony). He could hear also such progressions in folk music (Moravian - not so far from Vienna, and he visited it, also Hungarian, Romanian...) played somewhere in Viennese restaurant by foreign musicians (Gypsies), but that's just my hypothesis based on very rare elements of folk music reflected in his works (csardas etc.).
Sudden jump to C major in bar 5 would be difficult to explain in functional harmony. Of course it's possible, but it can be explained quite easily as a Renaissance modal harmony progression, and ending deviation to major tonic confirmed by plagal progression to minor subdominant was typical for Baroque era.

> I can't say I've studied a lot of Beethoven and the original 50 > measures is really interesting.
>
> In any case in my opinion there are two very definite cadences in D > minor and then a tonal center shift to G at the end.
>
In no case. It's just minor subdominant confirming in a plagal way final D major. See how relatively long this part is - 7 bars, to have enough time to establish and support that major ending chord, which is even repeated three times. This was usual way in Baroque music (often supported by sustained bass note) and generally in church music which prefers plagal endings (T-S-T), not authentic (T-D-T).
BTW some composers of 19th and 20th century - mainly Slavonic - preferred also plagal cadences - Dvorak, Janacek, Martinu for example. It's interesting to divide composers by their cadences.

Daniel Forro

> My impression is that this piece sets up for a piece to follow.
>
> I'm only a two year theory student so I'm sure many of you can do > better than this - I've yet to put in the harmonic analysis. On the > other hand I think the tonal center is pretty apparent - anyone > agree / disagree?
>
> Chris
>

🔗Daniel Forró <dan.for@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Daniel, I noted Sonar has poor accidental assignments.
Analyzing in alto or tenor clefs will not change what I did.

I did find the original - I thought it was best to use Marcel's midi file.

And besides it is simply is easier to real on the grand staff and I don't
care about voice crossing.....

Chris

On Mon, Jan 18, 2010 at 10:38 PM, Daniel Forró <dan.for@...> wrote:

>
>
> Your score is full of enharmonic mistakes and strange voice
> crossings. How do you want to analyse it from such bad material? Why
> not to use original score? You can download it from IMSLP pages:
>
> http://imslp.org/wiki/3_Equali,_WoO_30_(Beethoven,_Ludwig_van)
>
> Be prepared to read alt and tenor clefs :-)
>
>
> On 19 Jan 2010, at 11:26 AM, christopherv wrote:
>
> > I was very curious as to what was going on in this piece.
> >
> > Today having some time while waiting for my daughter I assigned
> > chords to sheet music printed out from Marcel's midi file of Drei
> > Equali.
> >
> > (Please understand Sonar is not smart assigning accidentals).
> >
>
> Then you should use some better software for scores, this way is not
> the best one how to learn music theory properly.
>
> >
> > http://clones.soonlabel.com/public/classical-music/drei-equali-
> > chords.jpg
> >
> > While I've only assigned chord names the over arching tonal center
> > progression seems to me to be from D minor to G - frankly that G
> > does not sound minor nor major to my ears - just G unison. (I added
> > that G as the end just to satisfy my anticipation.)
> >
> > Does anyone know from what period in Beethoven's life this piece is
> > from?
> >
> November 2nd, 1812, composed in Linz. But it doesn't tell anything,
> as in my opinion it's rather atypical piece for Beethoven, for this
> period of his life and generally for the mainstream music of those
> times. The reason can be it's a ceremonial, funeral music (it was
> even performed at his own funeral) so he used some elements of older,
> pre-Classicism music to give it this character, how it was still used
> those times in the liturgical, church music (which conservatively
> used modal scales and harmonic progressions as well as polyphony). He
> could hear also such progressions in folk music (Moravian - not so
> far from Vienna, and he visited it, also Hungarian, Romanian...)
> played somewhere in Viennese restaurant by foreign musicians
> (Gypsies), but that's just my hypothesis based on very rare elements
> of folk music reflected in his works (csardas etc.).
> Sudden jump to C major in bar 5 would be difficult to explain in
> functional harmony. Of course it's possible, but it can be explained
> quite easily as a Renaissance modal harmony progression, and ending
> deviation to major tonic confirmed by plagal progression to minor
> subdominant was typical for Baroque era.
>
>
> > I can't say I've studied a lot of Beethoven and the original 50
> > measures is really interesting.
> >
> > In any case in my opinion there are two very definite cadences in D
> > minor and then a tonal center shift to G at the end.
> >
> In no case. It's just minor subdominant confirming in a plagal way
> final D major. See how relatively long this part is - 7 bars, to have
> enough time to establish and support that major ending chord, which
> is even repeated three times. This was usual way in Baroque music
> (often supported by sustained bass note) and generally in church
> music which prefers plagal endings (T-S-T), not authentic (T-D-T).
> BTW some composers of 19th and 20th century - mainly Slavonic -
> preferred also plagal cadences - Dvorak, Janacek, Martinu for
> example. It's interesting to divide composers by their cadences.
>
> Daniel Forro
>
>
> > My impression is that this piece sets up for a piece to follow.
> >
> > I'm only a two year theory student so I'm sure many of you can do
> > better than this - I've yet to put in the harmonic analysis. On the
> > other hand I think the tonal center is pretty apparent - anyone
> > agree / disagree?
> >
> > Chris
> >
>
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Daniel Forró <dan.for@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Daniel Forró <dan.for@...>

🔗Marcel de Velde <m.develde@...>

> Sudden jump to C major in bar 5 would be difficult to explain in
> functional harmony. Of course it's possible, but it can be explained
> quite easily as a Renaissance modal harmony progression, and ending
> deviation to major tonic confirmed by plagal progression to minor
> subdominant was typical for Baroque era.
>

Yes I too thought bar 5 would be C major.
But I now think this is in the tonic of E !!
The whole beginning is in E I think.
And it is the main melody that indicates the tonic!

It goes like this:
f, f, f, E - restpoint for melody
e, f, g, g, g, f, f, E - again E is is the restpoint for the melody
f, g, a, a, a, g, g, f, e, f, f, E - and again resting on E.

The high melody with E as it's restpoint is the main thing in the beginning.
It's only that it's not harmonized in a normal way.
But then again, how do you harmonize such a modal scale in a "normal" way.
It seems like the high melody is in Phrygian mode.

But anyhow, I put the whole beginning in E in JI.
And it sounds perfect this way.
You can hear it on www.develde.net

> I can't say I've studied a lot of Beethoven and the original 50
> > measures is really interesting.
> >
> > In any case in my opinion there are two very definite cadences in D
> > minor and then a tonal center shift to G at the end.
> >
> In no case. It's just minor subdominant confirming in a plagal way
> final D major. See how relatively long this part is - 7 bars, to have
> enough time to establish and support that major ending chord, which
> is even repeated three times. This was usual way in Baroque music
> (often supported by sustained bass note) and generally in church
> music which prefers plagal endings (T-S-T), not authentic (T-D-T).
> BTW some composers of 19th and 20th century - mainly Slavonic -
> preferred also plagal cadences - Dvorak, Janacek, Martinu for
> example. It's interesting to divide composers by their cadences.
>

It seems to me too that the ending may be in G indeed. I was looking at that
myself too.
Repeating the chord 3 times may be very needed to make a dominant chord
sound semi-final.
If you play a G minor after the D major ending chord, the G minor
immediately takes over the "ending feel".

Lots more to tell about this piece, indeed it's very very interesting, but
I'll do that later when I'm a bit further with my new JI analysis.
But it's going very well I'm glad to say! :)

Btw one more piece of info, Drei Equale No.1 sounds to me like it has
several similarities with Beethoven's 7th in A major, Op.92- II allegretto.
Which is a piece of which Beethoven himself said it's one of his best works
ever.

Marcel

🔗Marcel de Velde <m.develde@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗a_sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:
> --- In tuning@yahoogroups.com, Daniel Forro <dan.for@> wrote:
>
> > - That Beethoven's work of course WAS written for 12ET.
> > I'm not aware at all about any mention, or note, or
> > consideration about tuning issues from the side of
> > this particular composer.
>
> This is important in the case of Beethoven because
> by the time 12-edo really started to become prominent
> in practice, during the early decades of the 1800s,
> Beethoven was deaf.

Hi Daniel & Monz,
for Beethoven's tuning attend the reference:

http://www.google.de/url?sa=t&source=web&ct=res&cd=2&ved=0CAsQFjAB&url=http%3A%2F%2Fwww.sim.spk-berlin.de%2Fuploads%2F04-publikationen%2Fsimpk_kub02_inhalt.pdf&rct=j&q=mark-lindley+beethoven+stimmung&ei=nhJWS8_wLIa5_Qb45NWdCg&usg=AFQjCNF-kQdxuygXYO59diPemiU_sbKoOQ

Quotation from there on p.12
"
Here we would like to refer the reader to an additional source. During the final revisions
of this volume for publication, our attention was drawn to a recent discovery
in Beethoven research that is significant in the context of Mark Lindleyâs basic hypothesis.
In his article, âEin verlorener Registerklang. Beethovens Imitation der Aeolsharfeâ
(Musik & Ãsthetik #9 [2005], pp. 83-92), Hans-Werner KÃ¼then considers a
Beethoven sketchleaf he discovered which contains excerpts from the Allgemeine
musikalische Zeitung from February to September 1801. Among these excerpts, there is
an entry by Beethoven which refers to an anouncement for, as well as a review of,
a Tuning Book, or Even More Precisely: Instructions how Every Music Lover Can Repair and
Thus Also Tune His Keyboard Instrument, Incidentally, Whether It Has Strings or Pipework.
The book was written by Joseph BÃ¼ttner and Ernst Nachersberg and published in
Breslau in 1801(!).
This written entry attests first of all to Beethovenâs active interest in the question
of piano tuning. Beyond this, BÃ¼ttnerâs work offers concrete evidence that equal temperament
tuning can by no means be taken for granted as a universal practice around 1800. Although the basic premise for proper tuning as stated in BÃ¼ttnerâs book is that
it should allow one âto play equally âpureâ in all twelve hard and soft keysâ, BÃ¼ttner
subsequently claims: âThe only true tuning can be given to an instrument, if one
bases it upon unequal temperament.â To be sure, equal temperament was employed
nonetheless. It was, however, somewhat modified to compromise for certain disadvantages
in comparison with the older unequally tempered system: âThe n ew style
of tuning weakens all fifths equally, that is, each one only by a twelfth of a comma
(ï±ï²ï°th of a whole tone); of course all major thirds are tuned larger than pure and,
necessarily, offend the ear. That is why the new system does not really meet with the
approval of many [listeners]; they find it too harsh and less harmonious than the old
[one].â The reviewer for the AmZ promptly criticizes the tuning book for not advocating
resolutely enough the one and only appropriate equal temperament tuning.
Whether it was this particular alleged deficit of the piano tuning book that attracted
Beethovenâs attention, or even provoked his opposition, must, of course, remain
speculation. Such criticisms did not, however, diminish his interest in the subject.
The significance of BÃ¼ttnerâs writing with regard to the basic hypothesis of the
present volume is obvious: there is little question that it implies the existence of ideas
about a subtly unequal temperament at the beginning of the nineteenth century. Yet
even the question as to whether this would support specific details of Mark Lindleyâs
âstyle of tuningâ, such as he sees in BÃ¼ttnerâs instructions for the rate of beating for
certain thirds, must be discussed at a later point....

[page 14]

...The selection of Beethovenâs Opus 34 as the chief example for such a
demonstration was perhaps not stringent, but suggested itself for several reasons.
The variations are suitable in range, catchiness and musical diversity for
a comparative tuning project of this nature. Planned as a cycle of keys, they
were also continuously drawn upon as an example in the inevitable question
regarding key characteristics....
"

My conclusion:
I personally agree with that hypothesis of my old friend Mark Lindley,
that Beethoven expected at least for his opus 34 an tuning near to
Joseph Buettner's and Ernst Nacherberg's above mentioned 1801
remarkable unequal tuning instructions.

bye
A.S.

🔗Marcel de Velde <m.develde@...>

Hi Chris!

Marcel,
>
> With all due respect I believe you are not talking about tonality.
> The piece is clearly in Dm and this is not in doubt at all.
>
> Perhaps your JI system is in C, Ab, or E, - but this piece is not in C,
> Ab, or E.
>
> I suspect there is a terminology gap in your communication somewhere.
>
> Thanks,
>
> Chris
>

Yes you're atleast partly right.
I must admit I'm not an expert in the way tonality is described in classic
harmony / music schools.
I understand normal music theory sais this piece is in D minor.

But, I found that normally with most pieces Just Intonation agrees with
normal music theory as to what is the tonic.
I've investigated a few simple pieces by Bach recently and they transfer
very easy to JI in the tonic that is stated for the piece.

My own harmonic permutation JI theory gives the following scale for the
tonic of 1/1
1/1 16/15 9/8 6/5 5/4 4/3 45/32 3/2 8/5 5/3 9/5 15/8 2/1

A simple piece that is for instance in C major will normally play perfect
when the 1/1 of the above scale is placed on C.
This is offcourse only if one accepts minor chords like 9/8 4/3 5/3, but I
see those chords as correct.

So basically a short version of my meaning of tonality is that the 12tone JI
scale produces an in tune result, and this meaning of tonality also gives me
an audible tonal feel.

I've experimented a lot with different JI concepts of tonality with both the
drei equale and several Bach pieces, and think I now have a pretty good
working method.

In the case of the drei equale, normal music theory may say it is in D
minor, but in this specific case putting 1/1 of the 12tone JI scale on D
clearly gives terribly out of tune results.
I don't think this is the mistake of the JI concept of tonality. I think
this is the mistake of the very limited concept of tonality in normal music
theory.
I think it's absolutely nonsense to see everything as major/minor.
If i'm correct there is no clear theory for modal scales and tonality and
functional harmony.
I see this as an obvious shortcomming in normal music theory.
And something that JI makes very clear that such an expanded theory of
tonality is clearly needed.

Therefore I think that my use of the word tonic and tonality are valid and
make sense, but are perhaps confusing simply because they sometimes disagree
with normal music theory.
I'll use the words JI tonic, and JI tonality from now on.

In any case, I've finished analysing the drei equale in full with what I've
learned about JI tonality.
The result is this:
bars 1 to 15 are in JI tonic E
bars 15 to 27 are in JI tonic A
bars 28 to 35 are in JI tonic E
bars 35 to end are in JI tonic A

You can hear the result at www.develde.net

You can very clearly hear the JI tonics and changes in JI tonics.
It's now as if the piece is divided into 4 sections.
I found it very interesting to hear this effect so clearly, highly
recomended listen!
I think it's my best version yet :)

Marcel

🔗Marcel de Velde <m.develde@...>

🔗Michael <djtrancendance@...>

I am wondering what some of you periodicity block buffs think and would like to add about this IMVHO highly simplified way of explaining JI, possible implications of it, and improvement.
*********************************************************************************************

I've been experimenting with how to get more tonal color from within (even) strict JI.
Take the basic JI diatonic scale of
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1

...of course, the greatest common denominator is 24 and the scale can be written as
24/24 27/24 30/24 32/24 36/24 40/24 45/24 48/24
AKA 24:27:30:32:36:40:45:48

I noticed that common multiples include the numbers (which, of course, all divide perfectly into 24)
3,4, and 8 (directly from the denominators)
12 (from denominator sets of 3 and 4 used for chords)
24 (from denominator sets of 8 and 3 used for chords)

So my theory (no clue if the same thing has already been accomplished) is that since
A) Each possible chord involves a straight harmonic set involving the above common factors IE x/3, x/4, x/8, x/12....IE the notes 5/4 3/2 15/8 form the chord 10:12:15 (over 8).
....then it follows that.........
B) The common multiple is a way to determine the tonal "color" of the chord. So in A) the chord has the colors of the multiples 2,4 and 8.
And in the "odd" chord 5/4, 4/3, 5/3 (15:16:20...over 12)...for example, you get the colors of the multiples 3,4 and 12.

C) The quickest way to get quite varied color is to aim for least and second-to-least common multiples that are factors of different prime numbers.
So in the second chord (15:16:20...over 12), you get additional tonal color because the LCM is 3 and the second to least is 4 (which "factors down" to a prime at 2).
.....whereas the 10:12:15 chord has the LCM at 2 and the second at 4 and these BOTH "factor down" to the prime of 2.

Hence...the 15:16:20 chord has more tonality...and, IMVHO, a major the reason diatonic JI, which its denominator of 3, has more color than the harmonic series (IE x/16, which "factors down" to the common multiple of 2).

Furthermore, some denominators beside 3 that can be used to add color b/c they factor down to primes are
5 (prime)
7 (prime)
6 and 9 (factors down to 3)
12 (factors down to 3 or 2)
15 (factors down to 3 or 5)
18 (factors down to 3 or 2)...my personal favorite as it contains many factors with primes of 2 and 3 IE 2,3,6,9 and is still lower than the "JI standard" common multiple of 24.
24 (factors down to 3 or 2)

One easy application is to change JI diatonic to x/12 form IE
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 becomes

1/1 13/12 5/4 4/3 3/2 5/3 11/6 2/1
.........in order to allow more chords with both x/3 and x/2 factors.

********************************************************************************
Now here's where IMVHO it gets really interesting...

Once you make a scale involving many of, say, the above factors to add color, you can mess around with things that aren't as strict.
Like tempering to your own discretion by up to around 7 cents to help eliminate roughness IE the root tones being too close and causing beating (though experimentation I've found anything closer than about 12/11 begins to sound quite rough) or even, for example, throwing in denominators that make LCM's for certain chords higher than 24 to add color (IE using 6/5 instead of 5/4 in diatonic JI would make the LCM 40 IE x/8*x/5).

Then you can experiment with things like maximizing the amount of tonal color, eliminating roughness, and keeping a low LCM (24 or less between all notes the entire scale) to enhance periodicity. So that's one approach to handling periodicity + roughness + tonal color all at once.

-Michael

🔗Michael <djtrancendance@...>

Have any of you worked with the Ptolemy Homalon scales and/or variations of them?

I talked to Jacques Dudon about a scale I came across via experimentation and, for the second time, it came from that series. Also, I found it while trying to figure out an ideal scale for a new song and apparently it's also one of Jacques' favorite live scales.
Note the scale can be easily doubled from x/18 to x/36 format (thus enabling a massive 14 notes instead of 7 while keeping the 7-tone intervals perfectly in both "modes").

The best basic form of the scale (IMVHO) I've found so far is
1. (1/1)
2. 10/9 = 1.1111111
3. 11/9 1.2222222
4. (4/3) 1.3333333
5. (3/2) 1.5
6. (5/3) 1.66666666
7. (11/6) 1.8333333

18:20:22:24:27:30:33:36

...which can be expanded with new tones in () into the 14-tone monster below (where the new tones are the exact same 7 tone scale duplicated)

36:(38):40:(42):44:(46):48:(51):54:(57):60:(63):66:(69):72

1. (1/1)
1b. (19/18) = 1.05555555
2. 10/9 = 1.1111111
2b. (21/18) = 1.16666666
3. 11/9 1.2222222
3b. (23/18) = 1.277777777
4. (4/3) 1.3333333
4b. (17/12) = 1.416666666
5. (3/2) 1.5
5b. (19/12) = 1.5833333333
6. (5/3) 1.66666666
6b. (21/12) = 1.75
7. (11/6) 1.8333333
7b. (23/12) = 1.916666666

I am shocked that I hear so little (on this list and elsewhere) about this scale system and so rarely seen it used. It (in 7-tone form) seems to keep the purity of JI diatonic, keeping very low denominators for the most part...all the while improving on root-tone roughness (thus merging upon 7TET)...avoiding the nasty 15/14 JI diatonic half-step interval and, instead, only having 12/11 as the smallest/"highest-beating" interval.

Any ideas on best uses of/improvement for this scale system?

🔗Danny Wier <dawiertx@...>

Glad you posted this, Michael, since I did some experimentation on how to think of scales as series of overtones. (I also like to think of "minor" tonalities as the inverse, a series of pitches with a common overtone, i.e. a series of undertones.)

I've found it's best to construct trichords, tetrachords and pentachords as a sequence of overtones, using as small a GCF as reasonably possible, and building scales using those, as is done with maqams and ragas, and the first note in each polychord being a "dominant", from which the bass is derived. The 8:9:10 trichord on a I-IV-V progression would give you the Ptolemy/Zarlino major plus an alternative major sixth, 27/16.

And I've had someone tell me that 12:13:15:16 would make a great Hijaz tetrachord.

~D.

--- On Wed, 1/20/10, Michael <djtrancendance@...> wrote:

From: Michael <djtrancendance@...>
Subject: [tuning] GCD and one possible way to explain (and fine tune) tonal color in JI
To: tuning@yahoogroups.com
Date: Wednesday, January 20, 2010, 9:41 AM

I am wondering what some of you periodicity block buffs think and would like to add about this IMVHO highly simplified way of explaining JI, possible implications of it, and improvement.
************ ********* ********* ********* ********* ********* ********* ********* ********* *********

I've been experimenting with how to get more tonal color from within (even) strict JI.
Take the basic JI diatonic scale of
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1

...of course, the greatest common denominator is 24 and the scale can be written as
24/24 27/24 30/24 32/24 36/24 40/24 45/24 48/24

AKA 24:27:30:32: 36:40:45: 48

So my theory (no clue if the same thing has already been accomplished) is that since
A) Each possible chord involves a straight
harmonic set involving the above common factors IE x/3, x/4, x/8, x/12....IE the notes 5/4 3/2 15/8 form the chord 10:12:15 (over 8).
....then it follows that........ .
B) The common multiple is a way to determine the tonal "color" of the chord. So in A) the chord has the colors of the multiples 2,4 and 8.
And in the "odd" chord 5/4, 4/3, 5/3 (15:16:20... over 12)...for example, you get the colors of the multiples 3,4 and 12.

C) The quickest way to get quite varied color is to aim for least and second-to-least common multiples that are factors of different prime numbers.
So in the second chord (15:16:20... over 12), you get additional tonal color because the LCM is 3 and the second to least is 4 (which "factors down" to a prime at 2).
.....whereas the 10:12:15 chord has the LCM at 2 and the second at 4 and these BOTH "factor down" to the prime of 2.

Hence...the 15:16:20
chord has more tonality...and, IMVHO, a major the reason diatonic JI, which its denominator of 3, has more color than the harmonic series (IE x/16, which "factors down" to the common multiple of 2).

One easy application is to change JI diatonic to x/12 form IE
1/1 9/8 5/4 4/3 3/2 5/3 15/8 2/1 becomes

1/1 13/12 5/4 4/3 3/2 5/3 11/6 2/1
.........in order to allow more chords with both x/3 and x/2
factors.

************ ********* ********* ********* ********* ********* ********* ********* *****
Now here's where IMVHO it gets really interesting. ..

Then you can experiment with things like maximizing the amount of tonal color, eliminating roughness, and keeping a low LCM (24 or less between all notes the entire scale) to enhance
periodicity. So that's one approach to handling periodicity + roughness + tonal color all at once.

-Michael

🔗cameron <misterbobro@...>

Sure- tunings based on the 11th partial are what most "sings" on my erhu. 11/9 and 11/6 are the sweetest and strongest thirds and sixths.

The two strings of the erhu are traditionally tuned a pure fifth apart, so that a droning sympathetic fifth is part of the sound- so, 12/11 is better than 10/9 on the instrument. It is very cool that the pure intervals are universal, I was able to communicate with the Chnese musician who sold me the erhu in Nantong by singing different intervals, so we could discuss tunings and scales without spoken language.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Have any of you worked with the Ptolemy Homalon scales and/or variations of them?
>
> I talked to Jacques Dudon about a scale I came across via experimentation and, for the second time, it came from that series. Also, I found it while trying to figure out an ideal scale for a new song and apparently it's also one of Jacques' favorite live scales.
> Note the scale can be easily doubled from x/18 to x/36 format (thus enabling a massive 14 notes instead of 7 while keeping the 7-tone intervals perfectly in both "modes").
>
> The best basic form of the scale (IMVHO) I've found so far is
> 1. (1/1)
> 2. 10/9 = 1.1111111
> 3. 11/9 1.2222222
> 4. (4/3) 1.3333333
> 5. (3/2) 1.5
> 6. (5/3) 1.66666666
> 7. (11/6) 1.8333333
>
> OR
>
> 18:20:22:24:27:30:33:36
>
> ...which can be expanded with new tones in () into the 14-tone monster below (where the new tones are the exact same 7 tone scale duplicated)
>
> 36:(38):40:(42):44:(46):48:(51):54:(57):60:(63):66:(69):72
>
> or
>
> 1. (1/1)
> 1b. (19/18) = 1.05555555
> 2. 10/9 = 1.1111111
> 2b. (21/18) = 1.16666666
> 3. 11/9 1.2222222
> 3b. (23/18) = 1.277777777
> 4. (4/3) 1.3333333
> 4b. (17/12) = 1.416666666
> 5. (3/2) 1.5
> 5b. (19/12) = 1.5833333333
> 6. (5/3) 1.66666666
> 6b. (21/12) = 1.75
> 7. (11/6) 1.8333333
> 7b. (23/12) = 1.916666666
>
>
>
>
> I am shocked that I hear so little (on this list and elsewhere) about this scale system and so rarely seen it used. It (in 7-tone form) seems to keep the purity of JI diatonic, keeping very low denominators for the most part...all the while improving on root-tone roughness (thus merging upon 7TET)...avoiding the nasty 15/14 JI diatonic half-step interval and, instead, only having 12/11 as the smallest/"highest-beating" interval.
>
>
> Any ideas on best uses of/improvement for this scale system?
>

🔗Graham Breed <gbreed@...>

🔗cameron <misterbobro@...>

I got a registered instrument, with a card (like a credit card) and embossed number. It is a little more expensive, but conforms to international import/export laws. Studying the card later I was able to determine what kind of snakeskin it uses- it is a more primitive relative of the boa, and is farmed. The wood is not mentioned, but wood being my long family tradition (I can still cut piston-fit dovetails by hand), I'm pretty sure it is acacia, either from Australia or China, and plantation wood.

Nantong is wonderful, great food and sub-tropical climate. Sang at the old pagoda- "Microtonal" would be an understatement, my Theremin player went off on a tangent mid-song on one tune, but somehow a harmonically related tangent, and we made it miraculously back, hahaha! I heard lots of really microtonal music in China, there seems to be a great gap between commercial cheese and the musics of the
actual many different peoples.

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> "cameron" <misterbobro@...> wrote:
>
> > The two strings of the erhu are traditionally tuned a
> > pure fifth apart, so that a droning sympathetic fifth is
> > part of the sound- so, 12/11 is better than 10/9 on the
> > instrument. It is very cool that the pure intervals are
> > universal, I was able to communicate with the Chnese
> > musician who sold me the erhu in Nantong by singing
> > different intervals, so we could discuss tunings and
> > scales without spoken language.
>
> Nantong, you say! That's a cool city, I used to live
> there. I don't know anything about the erhu scene though.
> Let us know what you conclude about the tuning.
>
> Did you get yours exported? The ones I see in the
> shops involve endangered species and can't be taken
> outside China.
>
> Graham
>