12 Equal vs. Just Tuning

Greetings,
Posting like the following always make me wonder at how many different
ways we listen to music:

>> The best argument agaisnt 12-ET, or any other kind of ET, is such scales
>are out of tune with the harmonic partials the notes in the intervals used
are made of.

and

>> In 12-ET E 400 is 14 cents large out of tune with the 5th partial E
386.314.
>The two pitches in any octave
>> beat strongly with each other!

>12-et as a fine tuning, indeed, and a vibrant one. Has a lot of energy
>in it - wakes one up!

12 ET may wake one up, at first, but there is an inuring effect that
comes with it. Ultimately, it begins to dull the senses at a particularly
organic level. Et can desensitize the nervous system in a sadly insidious
way.
When all like intervals are the same tempered size, the ear begins to
accept the dissonance as the standard harmonic quality, and stops listening
for the textural sensations that comes from juxtaposing tempered vs. Just
intervals. (We may liken this to weather. After a few weeks of perfect 70
degree, sunny weather in the South Pacific islands, I began to wish for the
excitement of a passing thunderstorm. Unchanging qualities dull our senses
in one way or another).
So it is with 12 ET. All thirds are the same and they are all busy, but
after a while, that busy-ness becomes less and less stimulative. We just
stop paying attention to the physical quality of the interval. Compare this
to a Kirnberger III and we find that the busy-ness of the A or Eb triad is
much more noticeable after the near purity of the C, G or F. Indeed, the
appreciation for either direction is enhanced by there being a contrast with
the other.

>(Though it may possibly be somewhat of a twentieth century aquired taste,
>otherwise why didn't the musicians of Bach's time go for it when they could
have easily retuned
>their harpsichords to match their lutes etc.).

(Half full/ half empty glasses sitting on the brow of my nose) I posit
that ET isn't an acquired taste so much as it is an entropic result of
convenience ( entrophy in the sense of the degradation of the matter and
energy in the universe to an ultimate state of inert uniformity). Great
music can be built with it, but it has its costs.
It is very difficult to get an ET by unison matching a keyboard to a
lute, but I don't think that is the reason for its rejection in the 18th
century. The well-tempered tunings are more complex than ET, and they
provide a greater degree of expression than those that were homogenious,(such
as the 1/4C or ET). The piano music of the Classical era made use of the
greater resources available when the keys had their own characters and the
loss of those characters is, imho, one reason that that music has fallen as
far from favor as it has.
So, I submit that the greatest shortcoming of ET is not that the keys are
lacking in consonance, but rather, that there is only one harmonic value for
any given class of intervals, the result of which is that in the listener,
the involuntary psycho-physiological-emotive processes are reduced, and that
much of the music's effect becomes based on intellectual response, rather
than the emotional/intellectual reaction that can make music such a magical
event.
I dunno, using ET to construct music is like using bricks to construct
buildings. They can create some major structures, but a brick building will
never create the same impression as one built of natural stone.
Playing Bach on ET is similar to building a replica of Notre Dame Cathedral
out of brick. Something is lost in the process, but only those that have seen
the original may notice what is missing.
Regards,
Ed Foote
Nashville, Tn.

Nice image below, Ed. Lately, I've been going with asking someone if they
would prefer to see Leonardo da Vinci's artworks with the actual colors he
chose to paint with? Or would the prefer view da Vinci's paintings with
colors that have altered over 500 years ago, some that have been "refreshed"
by a modern? So far everyone I've asked has preferred to see the original
colors. Johnny Reinhard

> .
> I dunno, using ET to construct music is like using bricks to construct
> buildings. They can create some major structures, but a brick building
> will
> never create the same impression as one built of natural stone.
> Playing Bach on ET is similar to building a replica of Notre Dame Cathedral
>
> out of brick. Something is lost in the process, but only those that have
> seen
> the original may notice what is missing.
> Regards,
> Ed Foote
> Nashville, Tn.
>
>

In a message dated 10/24/02 8:42:27 AM Central Daylight Time, a440a@aol.com
writes:

> using ET to construct music is like using bricks to construct
> buildings. They can create some major structures, but a brick building
> will
> never create the same impression as one built of natural stone.
> Playing Bach on ET is similar to building a replica of Notre Dame Cathedral
>
> out of brick. Something is lost in the process, but only those that have
> seen
> the original may notice what is missing.
> Regards,
> Ed Foote
>
Excellent post! ET was adopted so players could modulate to all keys, and
secondarily play in all keys. The crazy thing about this very serious
compromise is, that with a proper just-temperament scale with 19 notes per
ocatve one can still modulate to all keys and play in all keys. My Phillips
scale does this! No real compromises are necessary.

What ET really accomplished was, it allowed most anyone to play an instrument
without taking music lessons. One could play by ear. And music quality and
performance went dowhill fast as a result! With MT or WM it took training and
skill to play an instrument correctly. The same is true of JI or JT.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

In a message dated 10/24/02 8:42:27 AM Central Daylight Time, a440a@aol.com
writes:

> using ET to construct music is like using bricks to construct
> buildings. They can create some major structures, but a brick building
> will
> never create the same impression as one built of natural stone.
> Playing Bach on ET is similar to building a replica of Notre Dame Cathedral
>
> out of brick. Something is lost in the process, but only those that have
> seen
> the original may notice what is missing.
> Regards,
> Ed Foote
>
Excellent post! ET was adopted so players could modulate to all keys, and
secondarily play in all keys. The crazy thing about this very serious
compromise is, that with a proper just-temperament scale, with 19 notes per oc
atve, with a scale for each key signature, one can still modulate to all keys
and play in all keys. My Phillips scale does this! No real compromises are
necessary.

What ET really accomplished was, it allowed most anyone to play an instrument
without taking hardly any, if any, music lessons. One could play by ear. And
music quality and performance went dowhill fast as a result! With MT or WM it
took training and skill to play an instrument correctly. The same is true of
JI or JT.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

--- In tuning@y..., prophecyspirit@a... wrote:

> My Phillips
> scale does this! No real compromises are necessary.

except of course the comma shift issues . . .

> What ET really accomplished was, it allowed most anyone to play an
> instrument
> without taking music lessons. One could play by ear.

i should hope one could play by ear in a better-tuned system, perhaps
even more so! i would argue that ET, if anything, promoted playing
with *too little* reliance on the ear.

i find that musicians who learned to play by ear often, if not
usually, play more musically than those who took music lessons.

In a message dated 10/24/02 1:43:18 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> i thought you said you needed 48 notes per octave to play in all keys.

You do, but they aren't all in one key signature.

> except of course the comma shift issues

1-2 cents off the theoretical value isn't any comma!

> i should hope one could play by ear in a better-tuned system, perhaps
> even more so! i would argue that ET, if anything, promoted playing
> with *too little* reliance on the ear.

Those who used or use MT, WM, JI, or JT have to be careful how they play.
Whereas ET allows one to play most any interval or chord with no particular
difference. The miserable drawbar Hammond has so few harmonics, one hardly
even could notice when oneself or someone else made a mistake in playing! A
great hindrance to real teaching or learning.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:

> > except of course the comma shift issues
>
> 1-2 cents off the theoretical value isn't any comma!

no, i'm talking about the 16 cents shifts, for example what happens
to the note e when going from c major to a minor, as i understood
your partial reply to that query. the various forms of adaptive ji
and adaptive tuning do much better.

> > i should hope one could play by ear in a better-tuned system,
perhaps
> > even more so! i would argue that ET, if anything, promoted
playing
> > with *too little* reliance on the ear.
>
> Those who used or use MT, WM, JI, or JT have to be careful how they
play.
> Whereas ET allows one to play most any interval or chord with no
particular
> difference.

compared with a 12-tone WT? if you want an unmusical result, sure.
otherwise, it seems you have to work even harder to get
any "character of the keys" across.

> The miserable drawbar Hammond has so few harmonics, one hardly
> even could notice when oneself or someone else made a mistake in
>playing!

i don't know where you're from, but on my planet, the hammond is one
of the most wonderful instruments, has plenty of harmonics (tuned to
12-equal) which can be manipulated to lead to an infinite timbral
variety, and mistakes are clearly and immediately audible (my leslie
speaker was destroyed in a fire, unfortunately) . . .

> A
> great hindrance to real teaching or learning.

let me take a wild guess -- you think all popular music is garbage?

In a message dated 10/24/02 4:18:58 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> i'm talking about the 16 cents shifts, for example what happens
> to the note e when going from c major to a minor, as i understood
> your partial reply to that query. the various forms of adaptive ji
> and adaptive tuning do much better.

The E in a minor, the C relative minor, is the same pitch it is in C
major--384 cents.as the a-minor scale is the tertian minor of F, which is the
C IV. So there's no root-pitch shifts in such closely-related keys.

In other words E major and E septimal minor use 400 cents as their root.
Whereas tertian e minor, the relative minor of G the C V, uses E 384 cents as
its root.

> compared with a 12-tone WT? if you want an unmusical result, sure.
> otherwise, it seems you have to work even harder to get
> any "character of the keys" across.

The Johannus organ I play has MT and WM tuning, as well as ET. and both MT
and WM have plenty of character.
>
> i don't know where you're from, but on my planet, the hammond is one
> of the most wonderful instruments, has plenty of harmonics (tuned to
> 12-equal) which can be manipulated to lead to an infinite timbral
> variety,

The drawbar Hammond as originally made only had 7 harmonics for an 8' stop.
Many years later three more drawbars were added, but still not enough to
create a proper Principal stop! As a true Pricipal has 16 audible
harmonics--1-16--witn none mising.

I've practiced organ on five different Hammonds, and the organ I now play has
a digital-sampled Hammond stop and a digital-sampled theater-organ fluty
stop. So I know firsthand what they're like and sound like..

> let me take a wild guess -- you think all popular music is garbage?
>
Popular music has nothing special to do with this discussion. I'm dealing
with Western music generally. Each type in it could benefit from a JT scale.
Incluiding jazz. In fact, I think jazz would even sound better to those who
like it, due to the kinds of chords used.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/24/02 4:18:58 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > i'm talking about the 16 cents shifts, for example what happens
> > to the note e when going from c major to a minor, as i understood
> > your partial reply to that query. the various forms of adaptive
ji
> > and adaptive tuning do much better.
>
> The E in a minor, the C relative minor, is the same pitch it is in
C
> major--384 cents.as the a-minor scale is the tertian minor of F,
which is the
> C IV. So there's no root-pitch shifts in such closely-related keys.

what about (again) the progressions I-vi-ii-V-I and I-IV-ii-V-I?
didn't you say you would use 900-0-400 for the a minor chord?

> > compared with a 12-tone WT? if you want an unmusical result,
sure.
> > otherwise, it seems you have to work even harder to get
> > any "character of the keys" across.
>
> The Johannus organ I play has MT and WM tuning, as well as ET. and
both MT
> and WM have plenty of character.

yes, of course!! thus my statement.

> Each type in it could benefit from a JT scale.
> Incluiding jazz. In fact, I think jazz would even sound better to
those who
> like it, due to the kinds of chords used.

jazz . . . how would you render a C6/9 chord (C-E-G-A-D) in JT? how
about G13#11 (G-B-C#-D-E-F-A)?

Hi Pauline,

> While ET was known and used in Bach's day, it took till 1800 for it to catch on
> "universially" in Germany,and till 1850 for it to catch on in England, and eve
> later in America. that speaks volumes in itself about its iinadequacies, despite its convenience!

Well, makes it an aquired taste anyway. Whether that also makes it a poor scale, I'm not
sure. I think it is a fine one if one takes it in its own terms - but if you compare
it with historical temperaemnts, of course you won't find the variety you like in those,
and ditto, if you compare it with just intonation you won't find the pure j.i. intervals
either... I just think those who like 12-et are to be respected, and many like it
and don't like j.i. - well whether you call it habit or aquired taste, it's the same
thing really. I like 12-et on many occasions, but maybe not so much if I hear it immediately after
some other tuning with pure j.i. intervals. But, I don't hear these things very analytically
anyway. Maybe that applies to others too...

> While percussion instruments have a different partial series than other instruments,
> the partials are still in harmony with each other within just temperament limitations.
> For example in the regular harmonic partials the 11th harmonid at 551 cents, while it
> doesn't form part of a harmonious chord, is nonetheless beat free when played with a chord.
> The 13th at 841 cents is the same.

Yes, that's an interesting point. So the fifth and seventh harmonics are the ones
that will beat.

However, the eleventh and thirteenth harmonics can also seem "out of tune" to a musician
thoroughly trained to 12-et too I gather. At times I can hear them that way too,
especially if I have been listening to a lot of 12-et music.

The thought was that if one listened carefully to the timbre of a string
instrument one would hear that all these notes actually get played anyway,
all of them, as the hidden partials within the timbre, so how can one
really say that they are "out of tune" in 12-et?

Once one has made that step, I think one is perhaps on ones way to understanding
the point of just intonation - well one possible way in anyway.

I have found out that I can easily make a clip of a 'cello voice
using FFT synthesis in FTS, then fade one of the partials in and out.

So, here it is:
http://tunesmithy.netfirms.com/tunes/tunes.htm#Newbie_notes

I know it doesn't sound that much like a 'cello after you take
the partials apart and put them together like that, but
perhaps it gives an idea.

My hope of course is that it might help 12-et habituated newbie
microtonalist listeners to hear the 7th, 11th and 13th harmonics
as in tune :-), or potentially so anyway, or at least understand
why some might find them so - rather than to learn to
hear 'cello concertos etc. as populated with
annoying out of tune notes :-(.

But you have to listen quite hard to hear them anyway so don't suppose that
would happen.

Robert

In a message dated 10/24/02 9:05:07 PM Central Daylight Time,
robertwalker@ntlworld.com writes:

> So the fifth and seventh harmonics are the ones
> that will beat.
>
My point was, when the just 4th, 5th, 6th, 7th, 9th, 11th, and 13th harmonics
are played together as a chord, they are beat free with each other. By beat
free I mean no noticable beat unless listened for very carefully.

Pauline

HI Pauline,

> My point was, when the just 4th, 5th, 6th, 7th, 9th, 11th, and 13th harmonics
> are played together as a chord, they are beat free with each other. By beat free
> I mean no noticable beat unless listened for very carefully.

Sorry, hadn't quite understood what you wwre saying. Thanks for the correction.

Robert