'Tristan' chord

Dear all,

I have written an article about the first few bars of this opera (some
time ago).

http://everything2.com/index.pl?node_id=1393519

I assumed enharmonic equivalence, and came to a conclusion that the
chord had a particular symbolism within the opera. If you try to play
it in some kind of meantone, that conclusion is more or less
invalidated and the chord becomes just a funny dissonance.

This is without even getting into 7-limit chords, which as far as I
can hear do not belong within classical music (1600-1900) at all - at
least, all the attempts I have heard to use them sound incredibly
alien.

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:

> I assumed enharmonic equivalence, and came to a conclusion that the
> chord had a particular symbolism within the opera. If you try to play
> it in some kind of meantone, that conclusion is more or less
> invalidated and the chord becomes just a funny dissonance.

It is NOT a dissonance in anything which is close to 2/9 comma
meantone. It is, rather, a very well-known type of chord, a 7-limit
utonality. While utonalities may become dubious in higher prime
limits, tthey seem to work very well in the 5-limit (the minor triad)
and the 7-limit. Assuming Wagner

> This is without even getting into 7-limit chords, which as far as I
> can hear do not belong within classical music (1600-1900) at all - at
> least, all the attempts I have heard to use them sound incredibly
> alien.

The German sixth has a long and well-established place in classical
music, and in a meantone tuning it is impossible to hear C-E-G-A# as
anything other than septimal. It is not weird. It is not alien. It is
far from unknown. They still teach it in harmony class, they just
don't explain what it is or why it was used in common practice music.
The diminished triad is well-rooted in classical music, and in
meantone its natural to interpret that as a "magic" 1-6/5-10/7 chord.
Its enharmonic alteration to C-Eb-F# instead of C-Eb-Gb is even more
clearly a septimal chord, and that is more true yet of C-D#-F#.

Classical music is 5-limit music tuned to meantone with a flavoring of
the 7-limit; it no longer sounds like what people expect if 7-limit
chord relations are used everywhere, but if the basic structure is
triadic and diatonic, one can add flavorings such as the German sixth
to it and it will sound entirely natural and idiomatic. We know that,
because that is what composers *did*, and because we can listen to the
results. Wagner's hammering away with what looks to be a 7-limit
utonal chord was a new idea, but using the 7-limit resources of
meantone or of an irregular temperament related to meantone is not.

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:

> http://everything2.com/index.pl?node_id=1393519

I think it is absurd to describe F-B-D# as "highly dissonant" and then
call the dominant seventh chord as not very dissonant. If a dominant
seventh chord is not very dissonant, then F-B-D# is not very dissonant
also, and this is doubly true if we abandon the assumption that the
music is being played in 12-equal--and since this is the middle of the
nineteenth century, that is a good assumption to abandon.

The E-G#-D-A# chord following the Tristan chord might reasonably be
spelled E-G#-Cx-A# instead. In this case, it becomes a magic chord of
meantone; it can be regarded, once again, septimally; as
1-5/4-7/4-14/5, where the 5/4-14/5 interval, adjusted by 225/224, is
actually a 9/4. Hence the intervals in the chord are {5/4, 7/5, 8/5,
7/4, 9/4, 14/5} and it is a 9-limit consonant magic chord in meantone
(or miracle, for that matter.) This chord is clearly root at E, and
the Tristan chord contains a minor chord rooted at G#, a major third
above E. Hence the whole progression makes perfectly good sense as
dominant harmony: first A, F, E establishes A as tonic; then we get a
chord with a relation of a major third to the dominant E, progressing
to another chord with a strong E flavor, then to E7.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
(...)
> > If you try to play
> > it in some kind of meantone, that conclusion is more or less
> > invalidated and the chord becomes just a funny dissonance.
>
> It is NOT a dissonance in anything which is close to 2/9 comma
> meantone. It is, rather, a very well-known type of chord, a 7-limit
> utonality.

I find I am unable to understand the definition of 'utonality' in the
Encyclopedia. It seems to date from 1974. Also, I don't think
temperings stronger than 1/6 comma were used at all after the Baroque
period.

> While utonalities may become dubious in higher prime limits,
> they seem to work very well in the 5-limit (the minor triad)
> and the 7-limit.

It depends what you mean by 'work very well'. A minor triad is a
consonant chord which can, conventionally, be the first or the last
chord of a piece. A 7-limit chord or whatever approximates to it in
meantone is, I submit, heard by classical musicians as a dissonance
in need of resolution.

> > 7-limit chords, which as far as I
> > can hear do not belong within classical music (1600-1900) - at
> > least, all the attempts I have heard to use them sound incredibly
> > alien.
>
> The German sixth has a long and well-established place in classical
> music

You don't say! I do know what a German sixth is, and I also know what
it is used for, that is a quite strong dissonance resolving onto the
dominant. I also know that F-A-B-D# is a French sixth, not a German,
and is a more extreme dissonance, since it contains the augmented 4th
above the root.

> and in a meantone tuning it is impossible to hear C-E-G-A# as
> anything other than septimal.

How do I tell if I am hearing something as septimal or not? I hear a
dissonance, whereas if septimality were anything like 5-limit, I
would hear a consonance.

> The diminished triad is well-rooted in classical music

As a chord with a considerable degree of dissonance.

> in meantone its natural to interpret that as a "magic" 1-6/5-10/7
chord.

Why 'magic'?

> Its enharmonic alteration to C-Eb-F# instead of C-Eb-Gb is even more
> clearly a septimal chord, and that is more true yet of C-D#-F#.

Now this becomes confusing. When one plays a meantone 5th, it is
possible to tell that it is quite close to a pure consonance; with
the enharmonically altered meantone diminished 6th, it is not
possible and it sounds as a weird dissonance. Same with the meantone
diminished 4th versus the major 3rd. But you are saying that each of
these enharmonically altered tritone chords corresponds quite closely
to a just ratio in the 7-limit, so in this case the enharmonic
alteration does not turn a consonance into a dissonance or vice
versa. Does the 7-limit then erase the distinction between consonant
and dissonant triads? How can I hear if my septimal chord is in tune?

> Classical music is 5-limit music tuned to meantone with a flavoring
of
> the 7-limit; it no longer sounds like what people expect if 7-limit
> chord relations are used everywhere, but if the basic structure is
> triadic and diatonic, one can add flavorings such as the German
sixth
> to it and it will sound entirely natural and idiomatic. (...)

Well, we have several issues here. Is F-A-B-D# the utonal chord, or F-
G#-B-D#, or both? I don't mean that an aug 6th chord is weird or
alien, even in 1/6 comma. (Perhaps I do find it alien in 1/4
comma.) But I do claim that the chord F-B-D#-G# itself is, as a chord
in A minor, no matter what the tuning, alien to common practice,
since it superimposes the aug 4th pre-dominant function and the
leading-note dominant function, resulting in a consonance (D#-G#)
where a dissonance (D#-A) would be in a standard French 6th
progression. I also claim that the enharmonic reinterpretation of the
chord as E#-G#-B-D# is crucial to its effect as a mild dissonance in
the very remote key of D# minor, so any temperament that did not
allow this rehearing would not be appropriate.

The fundamental point here is that you seem to be writing of 7-limit
chords as consonances whereas I hear them as various kinds of
dissonance. How can we judge?

~~~Thomas~~~

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
> The fundamental point here is that you seem to be writing of
7-limit
> chords as consonances whereas I hear them as various kinds of
> dissonance. How can we judge?

Well, he is writing from a mathematical standpoint, and you are
writing from a musical one. I say, in the case of a piece of music,
you be the judge.

What baffles me about all this is what connection the link to
turducken (at the bottom of your Tristan page) has to all this. Not to
mention the link to incredible bassist, Tony Levin.

Wait: many people consider the Tristan chord as the birth of extended
jazz harmony - that is the only connection to Tony Levin I can come up
with...

Cheers,
Jon

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:

> I find I am unable to understand the definition of 'utonality' in the
> Encyclopedia. It seems to date from 1974.

A utonal chord is one which is octave equivalent to a certain fixed
tone divided by small integes; in other words it can be obtained by
taking the reciprocals of some portion of the "chord of nature" and
adjusting by octaves.

Also, I don't think
> temperings stronger than 1/6 comma were used at all after the Baroque
> period.

Jorgensen does not agree with this assessment. The 1797 Britannica
described a modified 1/5-comma (with the wolf distributed over two
sharp fifths) as "better adapted than any other for keyed
instruments", and Jorgensen seems to think that 1/5-comma or modified
versions thereof retained a large following well into the 19th
century. Hawkes in 1807 described his temperament as "substracting
one-fifth of a [syntonic] comma from a certain number of perfect
fifths...and to tune perfect, or in a small degree sharper, some of
the fifths. This seems to me the best principle for tempering our
present scale." Moreover even late into the 19th century some tuners
were still tuning meantone and calling the result equal. In fact,
tuners called a lot of different things equal. All of this, of course,
is just for keyboard instruments; orchestras or singers hardly needed
to be bound to that.

> > While utonalities may become dubious in higher prime limits,
> > they seem to work very well in the 5-limit (the minor triad)
> > and the 7-limit.
>
> It depends what you mean by 'work very well'. A minor triad is a
> consonant chord which can, conventionally, be the first or the last
> chord of a piece. A 7-limit chord or whatever approximates to it in
> meantone is, I submit, heard by classical musicians as a dissonance
> in need of resolution.

Except Wagner does not treat it that way, which undermines your whole
argument.

> > The German sixth has a long and well-established place in classical
> > music
>
> You don't say! I do know what a German sixth is, and I also know what
> it is used for, that is a quite strong dissonance resolving onto the
> dominant.

The meantone German sixth is far more consonant than the corresponding
dominant seventh, so this is
simply nonsense unless you are understanding "consonance" in some
sense other than its vertical sound. I don't think a tendency to
resolve in certain ways in a particular style can or should be used as
a definition of consonance if you are planning to modify the word with
adjectives like "extreme".

I also know that F-A-B-D# is a French sixth, not a German,
> and is a more extreme dissonance, since it contains the augmented 4th
> above the root.

I was talking about the German sixth, not any other species, and
calling the German sixth an extreme dissonance is simply absurd.
Audibly, it is more consonant than the dominant seventh, and it's been
a long time since people thought that was an extreme dissonance.

> > and in a meantone tuning it is impossible to hear C-E-G-A# as
> > anything other than septimal.

> How do I tell if I am hearing something as septimal or not?

*Listen* to it--it fuses into a single, smooth sounding chord, whereas
with the dominant seventh you can hear the subdominant degree, the
seventh of the chord, in splendid isolation from the rest of the
chord, not really merging with it. In the 12-et and 31-et versions of
Tristan you can hear that even for a utonal chord, there is much more
fusion of tones and less blurriness and beating in the 31-et version.

I hear a
> dissonance, whereas if septimality were anything like 5-limit, I
> would hear a consonance.

When, exactly, do you hear a dissonance? Do you often listen to German
sixths and the like in meantone?

> > The diminished triad is well-rooted in classical music
>
> As a chord with a considerable degree of dissonance.

Only by comparison with a triad. In modern terms, it hardly seems like
a very dissonant chord, and even less so when in a meantone tuning.

> > in meantone its natural to interpret that as a "magic" 1-6/5-10/7
> chord.
>
> Why 'magic'?

1-6/5 is a consonance, 1-10/7 is counted as a 7-limit consonance, and
6/5-10/7, in any system of tuning which is tempering out 126/125, is
the same as 1-6/5. While it isn't a chord with only just 7-limit
consonances for intervals in the strict sense, it is in the sense of
126/125 tempering, which means septimal meantone tempering. In
meantone, the chord is adjusted to be more consonant and the system of
harmony is such that its intervals can be considered to be septimal
consonances.

> > Its enharmonic alteration to C-Eb-F# instead of C-Eb-Gb is even more
> > clearly a septimal chord, and that is more true yet of C-D#-F#.
>
> Now this becomes confusing. When one plays a meantone 5th, it is
> possible to tell that it is quite close to a pure consonance; with
> the enharmonically altered meantone diminished 6th, it is not
> possible and it sounds as a weird dissonance.

In 31 equal it is a pretty good 26/17, but however you slice it, it's
the infamous wolf fifth.

Same with the meantone
> diminished 4th versus the major 3rd.

Not really. A diminished fourth can make an excellent 9/7 or 14/11,
depending on the exact tuning of the meantone in question.

But you are saying that each of
> these enharmonically altered tritone chords corresponds quite closely
> to a just ratio in the 7-limit...

That's right. In meantone they are *all* closer to being consonant
than 12-equal affords, but they are also all different. An augmented
second is not a minor third, but in meantone both the augmented second
and the minor third are more nearly consonant than the compromise
interval which munges them both together in 12-et. An augmented fourth
is not a diminished fifth, but both have moved to become closer to a
septimal consonance.

so in this case the enharmonic
> alteration does not turn a consonance into a dissonance or vice
> versa. Does the 7-limit then erase the distinction between consonant
> and dissonant triads? How can I hear if my septimal chord is in tune?

How can you hear if a major triad is in tune? You learn by listening,
paying attention to fusion and beating.

> > Classical music is 5-limit music tuned to meantone with a flavoring
> of
> > the 7-limit; it no longer sounds like what people expect if 7-limit
> > chord relations are used everywhere, but if the basic structure is
> > triadic and diatonic, one can add flavorings such as the German
> sixth
> > to it and it will sound entirely natural and idiomatic. (...)
>
> Well, we have several issues here. Is F-A-B-D# the utonal chord, or F-
> G#-B-D#, or both?

F-A-B-D# and F-G#-B-D# are different chords, so not both. F-A-B-D# is
a meantone tempering of 1-5/4-7/5-7/4, and F-G#-B-D# of 1-7/6-7/5-7/4,
the latter is a utonal tetrad, but not the former. The interval from
5/4 to 7/5 is, tempered by meantone, a tone, as A-B should be. The
result is "magic" in the 9-limit, especially if you put the A up an
octave.

I don't mean that an aug 6th chord is weird or
> alien, even in 1/6 comma. (Perhaps I do find it alien in 1/4
> comma.) But I do claim that the chord F-B-D#-G# itself is, as a chord
> in A minor, no matter what the tuning, alien to common practice,
> since it superimposes the aug 4th pre-dominant function and the
> leading-note dominant function, resulting in a consonance (D#-G#)
> where a dissonance (D#-A) would be in a standard French 6th
> progression.

That, I suppose, depends on whether you think Wagner is alien to
common practice or not, which in turn depends on how you define
"common practice". Certainly Wagner has been harmonically influential,
and is often used as an example in theory books.

I also claim that the enharmonic reinterpretation of the
> chord as E#-G#-B-D# is crucial to its effect as a mild dissonance in
> the very remote key of D# minor, so any temperament that did not
> allow this rehearing would not be appropriate.

The few notes I tuned seemed very appropriate to Wagner's music, and
clearly sounded better in 31 than in 12. How easily or successfully
the experiment could be continued could only be answered by trying it.

> The fundamental point here is that you seem to be writing of 7-limit
> chords as consonances whereas I hear them as various kinds of
> dissonance. How can we judge?

I'd start by becoming familiar with *just* seven limit harmony.
Composing something in it would be excellent.

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> Well, he is writing from a mathematical standpoint, and you are
> writing from a musical one. I say, in the case of a piece of music,
> you be the judge.

No, Jon, I am writing from the point of view of someone with far more
*musical* experience both in composing in the 7-limit and in tning
things to meantone than you have.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> ... from the point of view of someone with far more
> *musical* experience ...

We'll leave _that_ emphasis to be judged, on it's merits, by the
masses. Or the oratorios. I was simply trying to clue Tom into the
approaches - differing ones - that the two of you take. One can see it
from reading your explanation of the 'Tristan' phenomenon alongside
his posted article.

No need to put any stock in my thoughts on this, though. I mainly find
it amusing to see a term like "utonal" used in conjunction with
Wagner. A real wrestling match.

Cheers,
Jon

Gene,

You need to understand that for many musicians the terms "consonant"
and "dissonant" have a meaning relative to how the chords are used in
a particular musical 'language'. This is partly a matter of convention
and is sometimes different from the more psycho-acoustic meaning you
or I would typically give it when we try to consider how chords sound,
as divorced from any particular tradition.

-- Dave

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> No need to put any stock in my thoughts on this, though. I mainly find
> it amusing to see a term like "utonal" used in conjunction with
> Wagner. A real wrestling match.

The only alternative I know of is "minor tetrad". Would that be less
confusing?

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> Gene,
>
> You need to understand that for many musicians the terms "consonant"
> and "dissonant" have a meaning relative to how the chords are used in
> a particular musical 'language'.

I'm aware of that. However, as I pointed out, you can't very well
continue to use this sort of language and then attach the adjective
"extreme" to the word "dissonance". You can call a fourth a dissonance
if you must, but please don't try to call it an "extreme dissonance"
or people will laugh at you. To say that the German sixth is a
dissonance may be true in the sense you relate, but it can't very well
be an "extreme dissonance" when the dominant seventh, a clearly more
dissonant *sounding* chord, is not called that. That is simply sowing
confusion and spreading misinformation.

In a message dated 4/25/2005 11:49:44 PM Eastern Standard Time,
gwsmith@svpal.org writes:
To say that the German sixth is a
dissonance may be true in the sense you relate, but it can't very well
be an "extreme dissonance" when the dominant seventh, a clearly more
dissonant *sounding* chord, is not called that. That is simply sowing
confusion and spreading misinformation.
It is the context of a German sixth as it relates to the key that makes it a
dissonant. It is not the chord itself but its use in a cadential pattern that
strikes up the band by its outsideness to the key. Its like talking
intervals instead of notes. The splash in the face of the augumented sixth chords --
of whatever intonation -- serve primarily to bring attention to the cadence in
no uncertain terms. They like to spend their time near Neapolitan six
chords, similarly dissonant in context to the other chords, but quite consonant (as
a major chord in first inversion) in any absolutist sense.

best, Johnny Reinhard

hi Dave and Gene,

--- In tuning@yahoogroups.com,
"Dave Keenan" <d.keenan@b...>
wrote:

>
> Gene,
>
> You need to understand that
> for many musicians the terms
> "consonant" and "dissonant"
> have a meaning relative to
> how the chords are used in
> a particular musical
> 'language'. This is partly
> a matter of convention and
> is sometimes different from
> the more psycho-acoustic
> meaning you or I would
> typically give it when we
> try to consider how chords
> sound, as divorced from any
> particular tradition.

just to remind all of you: this came up years ago, and is
precisely the reason why i separated the definitions of
sonance / consonance / dissonance from those of
accordance / concordance / discordance in the Encyclopedia.

i'm a strong advocate of using the "-cordance" terms to
describe the precise psycho-acoustical perceptions, and
leaving the "-sonance" terms for the ones dependent on
musical context.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> i'm a strong advocate of using the "-cordance" terms to
> describe the precise psycho-acoustical perceptions, and
> leaving the "-sonance" terms for the ones dependent on
> musical context.

In which case you could have an "extreme discordance", but an "extreme
dissonance" would be basically meaningless and a highly misleading
term to use about anything, and especially about anything which was
far from being highly discordant.

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> hi Dave and Gene,
>
>
> --- In tuning@yahoogroups.com,
> "Dave Keenan" <d.keenan@b...>
> wrote:
>
> >
> > Gene,
> >
> > You need to understand that
> > for many musicians the terms
> > "consonant" and "dissonant"
> > have a meaning relative to
> > how the chords are used in
> > a particular musical
> > 'language'. This is partly
> > a matter of convention and
> > is sometimes different from
> > the more psycho-acoustic
> > meaning you or I would
> > typically give it when we
> > try to consider how chords
> > sound, as divorced from any
> > particular tradition.
>
>
> just to remind all of you: this came up years ago, and is
> precisely the reason why i separated the definitions of
> sonance / consonance / dissonance from those of
> accordance / concordance / discordance in the Encyclopedia.
>
> i'm a strong advocate of using the "-cordance" terms to
> describe the precise psycho-acoustical perceptions, and
> leaving the "-sonance" terms for the ones dependent on
> musical context.

Hmm. Unfortunately the other way 'round makes more sense to me since
"-sonance" means "sound" while "-cordance" has a more general meaning
of "agreement". Perhaps better just to use an adjective as in "sensory
dissonance" versus "cadential dissonance" or some such. Also,
"unstable chord" has been used for the latter, where "unstable" means
"requiring resolution".

Tom, please note that on this list, the unqualified use of the terms
"consonant" or "dissonant" would usually be assumed to be indepenent
of traditional ideas of cadence, since this is after all a list
devoted to "alternate" tunings.

-- Dave Keenan

--- In tuning@yahoogroups.com,
"Tom Dent" <tdent@a...> wrote:
>
> I find I am unable to
> understand the definition of
> 'utonality' in the Encyclopedia.
> It seems to date from 1974.

'utonality' and 'utonal' are terms coined by Harry Partch.
the first edition of his book appeared in 1949, with this
definition in it. the copy i have is the 2nd edition, 1974.

> --- In tuning@yahoogroups.com,
> "Gene Ward Smith" <gwsmith@s...>
> wrote:
> >
> > While utonalities may become dubious in higher prime limits,
> > they seem to work very well in the 5-limit (the minor triad)
> > and the 7-limit.
>
> It depends what you mean by 'work very well'. A minor triad
> is a consonant chord which can, conventionally, be the first
> or the last chord of a piece. A 7-limit chord or whatever
> approximates to it in meantone is, I submit, heard by
> classical musicians as a dissonance in need of resolution.
>
> > > 7-limit chords, which as far as I can hear do not
> > > belong within classical music (1600-1900) - at
> > > least, all the attempts I have heard to use them sound
> > > incredibly alien.
> >
> > The German sixth has a long and well-established
> > place in classical music
>
> You don't say! I do know what a German sixth is, and I also
> know what it is used for, that is a quite strong dissonance
> resolving onto the dominant. I also know that F-A-B-D# is a
> French sixth, not a German, and is a more extreme dissonance,
> since it contains the augmented 4th above the root.
>
> > and in a meantone tuning it is impossible to hear C-E-G-A# as
> > anything other than septimal.
>
> How do I tell if I am hearing something as septimal or not?
> I hear a dissonance, whereas if septimality were anything
> like 5-limit, I would hear a consonance.

Tom, you and Gene are talking about two different things.

as i just mentioned in another post, we have terms for
both concepts -- "sonance / consonance / dissonance" deal
with perceptions that arise from a musical context in
an actual composition, while "accordance / concordance /
discordance" are reserved for psycho-acoustical perceptions
divorced from any musical context.

Gene is really saying that the meantone German 6th chord
is concordant, and you are saying that it is dissonant --
and you are both correct.

i have a mouse-over javascript pitch-height graph on
my "augmented 6th" page, which shows the error of various
meantone German 6th chords from a JI 4:5:6:7 tetrad.

http://tonalsoft.com/enc/augmented-6th.htm

-monz
http://tonalsoft.com
microtonal music software

hi Dave (and Tom and Gene),

--- In tuning@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > i'm a strong advocate of using the "-cordance" terms to
> > describe the precise psycho-acoustical perceptions, and
> > leaving the "-sonance" terms for the ones dependent on
> > musical context.
>
> Hmm. Unfortunately the other way 'round makes more sense
> to me since "-sonance" means "sound" while "-cordance"
> has a more general meaning of "agreement".

yes, i totally agree, and wrestled with this when i
first created the "-cordance" definitions. but i decided
to do it the way i did because it seemed to me that the
meanings of the "-sonance" terms with their "musical context"
connotations are already so firmly entrenched.

> Perhaps better just to use an adjective as in "sensory
> dissonance" versus "cadential dissonance" or some such.
> Also, "unstable chord" has been used for the latter,
> where "unstable" means "requiring resolution".

but i really do think that it's worthwhile to have single-word
terms for both concepts.

-monz
http://tonalsoft.com
microtonal music software

hi Tom,

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> --- In tuning@yahoogroups.com,
> "Tom Dent" <tdent@a...> wrote:
> >
> > I find I am unable to
> > understand the definition of
> > 'utonality' in the Encyclopedia.
> > It seems to date from 1974.
>
>
> 'utonality' and 'utonal' are terms coined by Harry Partch.
> the first edition of his book appeared in 1949, with this
> definition in it. the copy i have is the 2nd edition, 1974.

sorry ... i forgot to add: the simplest way to understand
"utonal" is that it describes a subharmonic series, exactly
the inverse of how "otonal" describes a harmonic series.

we have a shorthand way of writing this -- for example,
a complete 11-limit otonal hexad is 4:5:6:7:9:11, while
the utonal hexad is 1/(4:5:6:7:9:11). they represent the
following ratios:

4:5:6:7:9:11 otonal hexad:

11/4
9/4
7/4
3/2
5/4
1/1

1/(4:5:6:7:9:11) utonal hexad:

1/1
4/5
2/3
4/7
4/9
4/11

and Partch's theory assumed octave equivalence (or 2:1
equivalence, as he would prefer to state it), so all
exponents of 2 are interchangeable -- for these two
examples, the denominators of the otonal chord and
the numerators of the utonal chord (which form the
"numerary nexus") can be multipled or divided by any
power of 2 without changing the harmonic meaning.

-monz
http://tonalsoft.com
microtonal music software

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:

> Gene is really saying that the meantone German 6th chord
> is concordant, and you are saying that it is dissonant --
> and you are both correct.

There seems to be a general sense that I was operating under a naive
misunderstanding of what Tom could have meant by "dissonance", but I
wasn't. My point was that by calling the German sixth an "extreme
dissonance" you appear to be making the claim that it is discordant.
What else would it mean?

I notice that there are no entries for German sixth, French sixth or Neapolitan sixth in Tonalpedia. It should be great if these were added. Monz?

Cordially,
Ozan
----- Original Message -----
From: Afmmjr@aol.com
To: tuning@yahoogroups.com
Sent: 26 Nisan 2005 Salı 7:03
Subject: Re: [tuning] Re: 'Tristan' chord

In a message dated 4/25/2005 11:49:44 PM Eastern Standard Time, gwsmith@svpal.org writes:
To say that the German sixth is a
dissonance may be true in the sense you relate, but it can't very well
be an "extreme dissonance" when the dominant seventh, a clearly more
dissonant *sounding* chord, is not called that. That is simply sowing
confusion and spreading misinformation.
It is the context of a German sixth as it relates to the key that makes it a dissonant. It is not the chord itself but its use in a cadential pattern that strikes up the band by its outsideness to the key. Its like talking intervals instead of notes. The splash in the face of the augumented sixth chords -- of whatever intonation -- serve primarily to bring attention to the cadence in no uncertain terms. They like to spend their time near Neapolitan six chords, similarly dissonant in context to the other chords, but quite consonant (as a major chord in first inversion) in any absolutist sense.

best, Johnny Reinhard

Ah, I see that all the sixths I assumed was not included with the Tonal Encyclopedia is in the address Monz just gave.

Thank you Monz.
Ozan
----- Original Message -----
From: monz
To: tuning@yahoogroups.com
Sent: 26 Nisan 2005 Salı 18:51
Subject: [tuning] Re: 'Tristan' chord

i have a mouse-over javascript pitch-height graph on
my "augmented 6th" page, which shows the error of various
meantone German 6th chords from a JI 4:5:6:7 tetrad.

http://tonalsoft.com/enc/augmented-6th.htm

hi Ozan,

--- In tuning@yahoogroups.com,
"Ozan Yarman" <ozanyarman@s...>
wrote:

> I notice that there are no
> entries for German sixth,
> French sixth or Neapolitan
> sixth in Tonalpedia. It
> should be great if these
> were added. Monz?

yes, of course, all of those
should be in the Encyclopedia.
at this point, i need to finish
converting all the existing pages
to the new format ... so those new
pages will have to wait until after
that job is finished.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
>
> i have a mouse-over javascript pitch-height graph on
> my "augmented 6th" page, which shows the error of various
> meantone German 6th chords from a JI 4:5:6:7 tetrad.
>
> http://tonalsoft.com/enc/augmented-6th.htm
>

Very cute! However, I think there must be a slight mistake in the
table just above the mouseover graph, the row for 1/6 comma has
4.020747126 for the major 3rd. (Should be 5.02...)

It seems that in 1/6 comma or 55-edo, the supposed '7' is over half a
comma out of tune, which is probably a major factor in the neglect of
7-limit in post-1700 theory.

I think the linguistic convolutions of 'sonance' and 'cordance' are a
red herring - besides, the word 'concordance' already means something
else, for example a concordance to the Bible. I do not intend to
respect conventional speech-codes.

What I mean by 'dissonance', as is clear from context, is the music-
theory meaning of a chord conventionally requiring resolution by a
more stable chord. It is only in this context that there is any sharp
distinction between con- and dis-. If you consider chords as isolated
sonic phenomena then they lie on a continuous scale between the
unison and a random pitch cluster and there is no consistent way to
locate any dividing line.

Naturally, if you employ a musical style which is radically different
from the 'common practice', then this definition of dissonance does
not apply.

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:

> It seems that in 1/6 comma or 55-edo, the supposed '7' is over half a
> comma out of tune, which is probably a major factor in the neglect of
> 7-limit in post-1700 theory.

We have the following:

1/4 comma 1/7 comma flat
1/5 comma 1/3 (5/14) comma sharp
1/6 comma 2/3 (9/13) comma sharp

In 12-equal, the supposed '5' is 2/3 (7/11) comma sharp, and the
supposed '5/3' is 3/4 (8/11) cents sharp, so the 1/6 comma 7 is
comarable. However, note that 1/5 comma is very much better, and
despite your belief to the contrary, 1/6 comma was not the be-all and
end-all of tuning after the year 1700; I've cited Jorgensen to the
contrary. How we could find out what tuning the Munich Court Theatre
used for the premire I have no idea, but I see no reason to assume it
was equal temperament, or more like 1/6 comma than 1/5 comma. It's bad
enough trying to figure out what keyboardists actually did, but no
keyboards are in use here.

> What I mean by 'dissonance', as is clear from context, is the music-
> theory meaning of a chord conventionally requiring resolution by a
> more stable chord.

And an "extreme dissonance" is? It seems to me the chord either
requires resolution or it doesn't.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > Gene is really saying that the meantone German 6th chord
> > is concordant, and you are saying that it is dissonant --
> > and you are both correct.

Why is anyone talking about a 'German 6th'? Wagner has the following:

F - G# - B - D#
F - A - B - D#

neither of which is one. There is no reason for a German composer to
be obliged to use a German sixth...

> There seems to be a general sense that I was operating under a naive
> misunderstanding of what Tom could have meant by "dissonance", but I
> wasn't. My point was that by calling the German sixth an "extreme
> dissonance" you appear to be making the claim that it is discordant.
> What else would it mean?

I do find the second chord, the *French* sixth, quite harsh; music-
theoretically, it is objectively a dissonance. It contains two
tritones, a major 2nd and an aug 6th: compared to a dominant 7th
which only has a major 2nd and a tritone, or even to a German 6th, it
is more extreme.

I realise that people may offer an alternative analysis, but I think
it is reasonable to use standard mid-19th century harmonic analysis
(which can imply non-12-ET) to describe a mid-19th century piece. The
consensus at the time was that this beginning was really eccentric
and unprecedented, and the point of the analysis is to show why this
is the case. To our modern Schoenberg- or Partsch-acclimatized ears,
it may sound rather tame. However, I don't think it was Wagner's
intention to write tame or ordinary sonorities.

~~~T~~~

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> sorry ... i forgot to add: the simplest way to understand
> "utonal" is that it describes a subharmonic series, exactly
> the inverse of how "otonal" describes a harmonic series.
>
> we have a shorthand way of writing this -- for example,
> a complete 11-limit otonal hexad is 4:5:6:7:9:11, while
> the utonal hexad is 1/(4:5:6:7:9:11).

I prefer to write it 1/(11:9:7:6:5:4) since it is usual to list the
notes of a chord in order of increasing pitch and this is shorthand for
1/11 : 1/9 : 1/7 : 1/6 : 1/5 : 1/4

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > It seems that in 1/6 comma or 55-edo, the supposed '7' is over
> > half a comma out of tune,(...)
>
> We have the following:
>
> 1/4 comma 1/7 comma flat
> 1/5 comma 1/3 (5/14) comma sharp
> 1/6 comma 2/3 (9/13) comma sharp
>
> In 12-equal, the supposed '5' is 2/3 (7/11) comma sharp, and the
> supposed '5/3' is 3/4 (8/11) cents sharp, so the 1/6 comma 7 is
> comparable.

But we should compare like with like, in a given tuning, for
listeners in a given era. 20th century listeners only accept the very
sharp major third of 12-ET in keyboard music through long
familiarity. Temperaments through the mid-19th century delivered
better major 3rds (in common keys) than 12-ET did, and many in that
era found 12-ET thirds to be borderline unacceptable. Hence they
would find the 4:7 borderline unacceptable - even if they were
familiar with just 7-limit harmonies.

If you use 1/6 comma or 12-ET, or anything in between, or even 1/5
comma, the 4:5 is always better tuned than the 4:7. You don't mention
how out of tune the 4:7 is in 12-ET...

> despite your belief to the contrary, 1/6 comma was not the be-all
and
> end-all of tuning after the year 1700; I've cited Jorgensen to the
> contrary.

That is not my belief, so please do not misrepresent me. I know very
well that circulating unequal temperaments involving 1/6 Pythagorean
comma and weaker temperaments were used. I am quite confident that
the trend in the 18th century was towards weaker temperaments.

> How we could find out what tuning the Munich Court Theatre
> used for the premiere I have no idea, but I see no reason to assume
it
> was equal temperament, or more like 1/6 comma than 1/5 comma.

Right from the beginning of the 18th century, and continuing through
the time of Mozart, 1/6 comma was privileged over other meantone
tunings by theorists and practicioners. I don't know of any evidence
that orchestras intentionally used any stronger temperament after
1750.

> And an "extreme dissonance" is? It seems to me the chord either
> requires resolution or it doesn't.

An elementary point of standard music theory. A dissonance may
resolve, with the effect of reducing tension, onto a consonance, or
onto another *weaker* = *less extreme* dissonance. This does not
imply that the definition of a dissonance is in danger, since the
weaker dissonance still has to resolve itself.

Ab C D F# -> ddd

Ab C Eb F# -> dd

G B Fn G -> d

C C En G -> c

(Of course, it is possible to get much more extreme dissonances by
using minor 2nds, as in Bruckner 9 / III, but I restrict myself to
commonly known chords.)

At the risk of creating confusion, in conventional pieces, every
chord except the tonic chord in root position is an unstable one in
some sense, since the piece cannot end there. However, would require
one to look at the entire piece to determine context. Mostly one just
looks at the context of a progression of a few chords as above.

All of this is quite consistent with my article.

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:

> Why is anyone talking about a 'German 6th'?

Because you claimed it was a strong dissonance, though a French sixth
is "more extreme".

/tuning/topicId_58229.html#58235

> I do find the second chord, the *French* sixth, quite harsh; music-
> theoretically, it is objectively a dissonance. It contains two
> tritones, a major 2nd and an aug 6th: compared to a dominant 7th
> which only has a major 2nd and a tritone, or even to a German 6th, it
> is more extreme.

Only if a German sixth is extreme to start with, and it isn't.

> I realise that people may offer an alternative analysis, but I think
> it is reasonable to use standard mid-19th century harmonic analysis
> (which can imply non-12-ET) to describe a mid-19th century piece.

It is not, however, reasonable to assume 12-et, and yet that is how
analysis proceeds these days. It seems to me your point of view on the
Tristan chord is a 12-equal point of view.

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:

> But we should compare like with like, in a given tuning, for
> listeners in a given era. 20th century listeners only accept the very
> sharp major third of 12-ET in keyboard music through long
> familiarity. Temperaments through the mid-19th century delivered
> better major 3rds (in common keys) than 12-ET did, and many in that
> era found 12-ET thirds to be borderline unacceptable. Hence they
> would find the 4:7 borderline unacceptable - even if they were
> familiar with just 7-limit harmonies.

Considering the 4:7 is precisely and exactly in tune with a fifth of
56^(1/10), which is about 4/17 comma, this is hardly a reliable rule.
Anything close to this value will have a very acceptable 4:7, and in
fact 1/5-comma does reasonably well.

> If you use 1/6 comma or 12-ET, or anything in between, or even 1/5
> comma, the 4:5 is always better tuned than the 4:7. You don't mention
> how out of tune the 4:7 is in 12-ET...

Very, very out of tune: 31 cents sharp, or 13/9 comma. But of course,
that isn't very relevant if your tuning is closer to 1/5 comma.

> > despite your belief to the contrary, 1/6 comma was not the be-all
> and
> > end-all of tuning after the year 1700; I've cited Jorgensen to the
> > contrary.
>
> That is not my belief, so please do not misrepresent me. I know very
> well that circulating unequal temperaments involving 1/6 Pythagorean
> comma and weaker temperaments were used. I am quite confident that
> the trend in the 18th century was towards weaker temperaments.

Yet below you iterate the idea that 1/6 comma was "priveldged", which
is not a conclusion I would draw from the available evidence.

> > How we could find out what tuning the Munich Court Theatre
> > used for the premiere I have no idea, but I see no reason to assume
> it
> > was equal temperament, or more like 1/6 comma than 1/5 comma.
>
> Right from the beginning of the 18th century, and continuing through
> the time of Mozart, 1/6 comma was privileged over other meantone
> tunings by theorists and practicioners. I don't know of any evidence
> that orchestras intentionally used any stronger temperament after
> 1750.

I've *already* quoted stuff after 1750 which priveldges 1/5 comma, not
1/6 comma. You, on the other hand, have supplied no evidence that 1/6
comma was priviledged over all other meantone tunings--we know
Telemann and the Mozarts liked it, but that doesn't mean it had taken
over everywhere. If you look in Jorgensen you can find all sorts of
different tunings after 1750, and if you read theorists your case is
completely hopeless. Theorists were saying nice things about 31, 50 or
even 19.

In the New and Complete Dictionary of Arts and Science of 1764, we have:

"The fifth will be deficient by 1/4 comma. Which difference, although
it be sensible, yet experience shews, that fifths so diminished are
tolerable. This is what is called the common or vulger temperament...
There are also other temperaments proposed by different authors; as
that of 31 parts by Mr. Huygens, Mr. Sauver's of 43, Mr. Henfling's of
50, and that of 12."

This is not a ringing endorsement of 1/6 comma. Keller in 1707 and
Holden in 1170 proposed more or less 1/5 comma system. About Keller's
meantone, which is really between 1/4 and 1/5 comma (very nearly
5/23), John Robison in 1801 says it was "in great repute, and indeed
is generally practiced." This is hardly a ringing endorsement of 1/6
comma either, as it is basically saying 2/9 comma is what is taking
over everywhere, not 1/6 comma. If it really was being generally
practiced then the people generally practicing it had a very
acceptable 4:7.

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> >
> > i have a mouse-over javascript pitch-height graph on
> > my "augmented 6th" page, which shows the error of various
> > meantone German 6th chords from a JI 4:5:6:7 tetrad.
> >
> > http://tonalsoft.com/enc/augmented-6th.htm
> >
>
> Very cute! However, I think there must be a slight mistake
> in the table just above the mouseover graph, the row for
> 1/6 comma has 4.020747126 for the major 3rd. (Should be 5.02...)

yes, you're exactly right. thanks! it's been fixed, and
i also rearranged the order of the meantones in that table
so that now the pattern of rational approximations matches
those shown on the mouseover javascript graphic.

> It seems that in 1/6 comma or 55-edo, the supposed '7'
> is over half a comma out of tune, which is probably a
> major factor in the neglect of 7-limit in post-1700 theory.

not to mention the fact that post-1800 theory and practice
drifted towards 12-edo, where the '7' is *more* than a comma
sharp.

> I think the linguistic convolutions of 'sonance' and
> 'cordance' are a red herring - besides, the word
> 'concordance' already means something else, for example
> a concordance to the Bible. I do not intend to
> respect conventional speech-codes.

well ... we just have to disagree here. i started the
Encyclopedia years ago as a "Dictionary of Tuning Terms",
simply because it had been so much effort for me to spend
years among dusty university library shelves finding this
stuff, i wanted to make it easier for others interested
to find it online. if there's a way to make a conceptual
distinction clear by using a linguistic distinction,
i'm all for it.

to me, "concord" and "discord" clearly express the perceptions
of particular sonorities, without regard to any musical usage,
and "accordance" clearly expresses the concept of a continuum
of such perceptions.

as you say, "consonance" and "dissonance" are defined more
by a sense of musical progression, in that a dissonance sets
up a restlessness, a sense of having to resolve, and consonance
is that resolution. these are firmly established meanings for
these terms.

accordance deals instead with static sonorities.

> What I mean by 'dissonance', as is clear from context,
> is the music-theory meaning of a chord conventionally
> requiring resolution by a more stable chord. It is only
> in this context that there is any sharp distinction
> between con- and dis-. If you consider chords as isolated
> sonic phenomena then they lie on a continuous scale between
> the unison and a random pitch cluster and there is no
> consistent way to locate any dividing line.

aha! which is *precisely* the reason why i use the terms
"sonance" and "accordance", to refer to the whole continuum
in both cases.

that was precisely Schoenberg's theory.
sonance is a continuum which extends from consonant at one
extreme to dissonant at the other, with no clear division
between the two.

... but he didn't use the term "sonance", which IMO was
unfortunate, because it confused a lot of his readers so
much that they didn't really understand what he was saying.

> Naturally, if you employ a musical style which is
> radically different from the 'common practice', then
> this definition of dissonance does not apply.

echoes of Schoenberg again, who by 1908 *did*
"employ a musical style which is radically different
from the 'common practice'". :)

-monz
http://tonalsoft.com
microtonal music software

So you are not interested in talking about Wagner, only in picking
holes in what other people say, with the help of omission and
misrepresentation. I find this a very dull sport.

I said 'a quite strong dissonance', which in British English, my
native language, means 'somewhat strong'. Possibly it may mean
something else in American. In any case, it is correct, because the
German 6th may resolve onto a dominant 7th, which is itself a mild
dissonance. The fact that this *is* a resolution implies that we are
not in ET, since if we were, there would be no difference between a
dominant 7th and a German 6th.

Even so, I have yet to see any evidence that Wagner's piano or
orchestra were tuned in a way which diverged conspicuously from 12-
ET. The later 19th century was surely the era during which ET
gradually came to dominate. I realise this statement may be seen as
bad taste in this group, but it is standard music history.

~~~T~~~

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> >
> > Why is anyone talking about a 'German 6th'?
>
> Because you claimed it was a strong dissonance, though a French
sixth
> is "more extreme".
>
> /tuning/topicId_58229.html#58235
>
> > I do find the second chord, the *French* sixth, quite harsh;
music-
> > theoretically, it is objectively a dissonance. It contains two
> > tritones, a major 2nd and an aug 6th: compared to a dominant 7th
> > which only has a major 2nd and a tritone, or even to a German
6th, it
> > is more extreme.
>
> Only if a German sixth is extreme to start with, and it isn't.
>
> > I realise that people may offer an alternative analysis, but I
think
> > it is reasonable to use standard mid-19th century harmonic
analysis
> > (which can imply non-12-ET) to describe a mid-19th century piece.
>
> It is not, however, reasonable to assume 12-et, and yet that is how
> analysis proceeds these days. It seems to me your point of view on
the
> Tristan chord is a 12-equal point of view.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> Considering the 4:7 is precisely and exactly in tune with a fifth of
> 56^(1/10), which is about 4/17 comma, this is hardly a reliable
rule.
> Anything close to this value will have a very acceptable 4:7, and in
> fact 1/5-comma does reasonably well.

This would be relevant if 1/5 comma was used at all in the 19th
century by competent musicians. There are strong reasons why this
should not be the case: reasons provided by, for one, Haydn's piano
sonatas and piano trios, which remained classics and are unplayable
with any keyboard temperament which has a wolf or a large number of
badly-tuned tonalities. Beethoven's piano concertos likewise. And as
for Wagner, he learnt an awful lot from tht notorious pianist Liszt.
Find me a piano temperament which Liszt could have played that has
anything stronger than 1/6 comma.

> (...) 1/6 comma was privileged over other meantone
> > tunings by theorists and practicioners. I don't know of any
evidence
> > that orchestras intentionally used any stronger temperament after
> > 1750.
>
> I've *already* quoted stuff after 1750 which priveldges 1/5 comma,
not
> 1/6 comma. You, on the other hand, have supplied no evidence that
1/6
> comma was priviledged over all other meantone tunings--we know
> Telemann and the Mozarts liked it,

Exactly. It was privileged over other meantones by Telemann and
Mozart pere et fils, since they taught it systematically. I find them
sufficiently authoritative: *the* most eminent 18th century composers
who left any clear evidence about tuning. Who do you have to put
against them? Someone called John Robison, probably living in
England, the most musically backward country in Europe (which I say
as an Englishman myself), and an encyclopaedist who may never have
touched a keyboard in his life.

> over everywhere. If you look in Jorgensen you can find all sorts of
> different tunings after 1750, and if you read theorists your case is
> completely hopeless. Theorists were saying nice things about 31, 50
or
> even 19.

Who cares what theorists say if they have no practical experience?

When, and where, could have 2/9 comma have been 'taking over'? How
could CPE Bach and Haydn have used 2/9 comma fifths and played their
movements in D flat major and B major? What does any of this have to
do with Wagner's music, which habitually used enharmonic equivalences?

~~~T~~~

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
> Who cares what theorists say if they have no practical experience?

Brilliant. I'm going to come back to this statement somewhere down the
road, but I'm glad *someone* said it.

Bravo, Tom.

Cheers,
Jon (who fondly remembers his last visit to Dartington College down in
Totnes...)

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
>
>
> So you are not interested in talking about Wagner, only in picking
> holes in what other people say, with the help of omission and
> misrepresentation. I find this a very dull sport.

I don't know why you want to become personally insulting. Since you
seem bent on maintaining the misconceptions drilled into you by
teachers who themselves did not know much about tuning on a list
*devoted* to tuning, you are not in a very good position to start
throwing spitballs if that is what it is coming to. I suggest you
start by learning the tuning basics, such as what 7-limit chords are
and what they actually sound like, before dismissing the idea that a
septimal interpretation of some common practice chords, as well
apparently as some Wagner chords, makes a lot of sense.

> I said 'a quite strong dissonance', which in British English, my
> native language, means 'somewhat strong'. Possibly it may mean
> something else in American. In any case, it is correct, because the
> German 6th may resolve onto a dominant 7th, which is itself a mild
> dissonance. The fact that this *is* a resolution implies that we are
> not in ET, since if we were, there would be no difference between a
> dominant 7th and a German 6th.

Yes, we've covered this. I think your terminology is unfortunate and
confusing here, but obviously you like it, so why not move on?

> Even so, I have yet to see any evidence that Wagner's piano or
> orchestra were tuned in a way which diverged conspicuously from 12-
> ET.

That's the point: we don't *know*.

The later 19th century was surely the era during which ET
> gradually came to dominate.

Tristan is closer to the middle 19th century.

I realise this statement may be seen as
> bad taste in this group, but it is standard music history.

If orchestras really were playing with flatted fifths well into the
20th century, the history may need to be reassessed. I don't think
we've got a lot of evidence here, particularly since orchestras are
not keyboard instruments.

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:

> This would be relevant if 1/5 comma was used at all in the 19th
> century by competent musicians.

I've given quotes several times now saying that in fact it was.

There are strong reasons why this
> should not be the case: reasons provided by, for one, Haydn's piano
> sonatas and piano trios, which remained classics and are unplayable
> with any keyboard temperament which has a wolf or a large number of
> badly-tuned tonalities.

Beethoven's piano concertos likewise. And as
> for Wagner, he learnt an awful lot from tht notorious pianist Liszt.
> Find me a piano temperament which Liszt could have played that has
> anything stronger than 1/6 comma.

1/6 comma is fine for my argument. Moving from equal to 1/6 comma
makes a huge difference in the septimal interpretation of chords, and
possibly the Tristan chord on Wagner's piano was tuned so as to give
it a distinctly different and more concordant quality than it would
have in equal temperament.

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
> > Who cares what theorists say if they have no practical experience?
>
> Brilliant. I'm going to come back to this statement somewhere down the
> road, but I'm glad *someone* said it.

Then again, who cares what PhDs in music theory think if they have no
practical experience *and* can't hack the math?

Jon Szanto wrote:

>--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
> >
>>Who cares what theorists say if they have no practical experience?
>> >>
>
>Brilliant. I'm going to come back to this statement somewhere down the
>road, but I'm glad *someone* said it.
>
>Bravo, Tom.
> >
ditto! ;)

hehe...

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

As Kant pointed out, beyond a certain point little can be known for certain.
Little good i believe is done by speculating too far pass this point.
Possibly it might be good to impose such limits upon ourselves

> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

>The German sixth has a long and well-established place in classical
>music, and in a meantone tuning it is impossible to hear C-E-G-A# as
>anything other than septimal. It is not weird. It is not alien. It is
>far from unknown. They still teach it in harmony class, they just
>don't explain what it is or why it was used in common practice music.
>The diminished triad is well-rooted in classical music, and in
>meantone its natural to interpret that as a "magic" 1-6/5-10/7 chord.
>Its enharmonic alteration to C-Eb-F# instead of C-Eb-Gb is even more
>clearly a septimal chord, and that is more true yet of C-D#-F#.
>
>Classical music is 5-limit music tuned to meantone with a flavoring of
>the 7-limit; it no longer sounds like what people expect if 7-limit
>chord relations are used everywhere, but if the basic structure is
>triadic and diatonic, one can add flavorings such as the German sixth
>to it and it will sound entirely natural and idiomatic. We know that,
>because that is what composers *did*,

What did they do, exactly? The evidence for composers of this
period using/intending meantone is, it seems to me, a mere fantasy.

-Carl

>How do I tell if I am hearing something as septimal or not? I hear a
>dissonance, whereas if septimality were anything like 5-limit, I
>would hear a consonance.

It's an acquired taste. While orchestral intonation is far less
accurate/consistent than the current thread implies, near-septimal
chords do appear in the wild. But they do not appear with any
great degree of consistency.

>> Its enharmonic alteration to C-Eb-F# instead of C-Eb-Gb is even more
>> clearly a septimal chord, and that is more true yet of C-D#-F#.
>
>Now this becomes confusing. When one plays a meantone 5th, it is
>possible to tell that it is quite close to a pure consonance; with
>the enharmonically altered meantone diminished 6th, it is not
>possible and it sounds as a weird dissonance. Same with the meantone
>diminished 4th versus the major 3rd. But you are saying that each of
>these enharmonically altered tritone chords corresponds quite closely
>to a just ratio in the 7-limit, so in this case the enharmonic
>alteration does not turn a consonance into a dissonance or vice
>versa. Does the 7-limit then erase the distinction between consonant
>and dissonant triads?

Consonance/dissonance is, properly speaking, the domain of
functional harmony, and only indirectly of psychoacoustics.

Concordance/discordance is the terminology suggested by Easley
Blackwood for the pyschoacoustic part. As such, many listeners
report septimal chords of the kind Gene is talking about as
concordant. Many do not. In the context of Barbershop music,
I did, from the age of 5 or so. In the context of acoustic piano
music (Michael Harrison) when I first heard it at age 19, I
did not. In a few months, though, I recognized them as the
same sound, and now I find them supremely consonant.

This kind of experience indicates (to me) the power of the new
sounds of extended JI for a new music. Their place in the common
practice repertoire is much more dubious.

-Carl

>> The fundamental point here is that you seem to be writing of
>> 7-limit chords as consonances whereas I hear them as various
>> kinds of dissonance. How can we judge?
>
>Well, he is writing from a mathematical standpoint, and you are
>writing from a musical one.

Oh yes, Jon, it's all down to math vs. music. Put a sock in it,
will you?

-Carl

>> This would be relevant if 1/5 comma was used at all in the 19th
>> century by competent musicians.
>
>I've given quotes several times now saying that in fact it was.

Huh?

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> What did they do, exactly? The evidence for composers of this
> period using/intending meantone is, it seems to me, a mere fantasy.

Eh? Since when was meantone never used in the 18th century?

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> > [Jon] Well, he is writing from a mathematical standpoint, and
> > you are writing from a musical one.
>
> Oh yes, Jon, it's all down to math vs. music. Put a sock in it,
> will you?

Carl! It's so good to have you back!

Of course, I was trying to make a distinction in how our backgrounds
affect our perceptions, and pointing out that Gene was having a hard
time with the "extreme dissonance" phrase, coming from a background
that values clear, precise terms (not to mention the psycho-acoustic
matters), whereas Tom's background was clearly in music and utilizing
terms as any (well, any learned) musician would see those same
progressions vis a vis consonance/dissonance.

A number of other people noticed this as well.

But I've been too wordy, I imagine, and once again am sock-worthy...

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:

> Of course, I was trying to make a distinction in how our backgrounds
> affect our perceptions, and pointing out that Gene was having a hard
> time with the "extreme dissonance" phrase, coming from a background
> that values clear, precise terms (not to mention the psycho-acoustic
> matters), whereas Tom's background was clearly in music and utilizing
> terms as any (well, any learned) musician would see those same
> progressions vis a vis consonance/dissonance.

But we weren't talking about progressions; rather a chord in
isolation. What to someone with training in music does "hearing" an
isolated dissonance mean if dissonance is defined only in functional
terms? You can't hear what a chord is functionally very well in
isolation from other chords or even melody.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> But we weren't talking about progressions; rather a chord in
> isolation.

I disagree. In musical terms, the relative dissonance of a chord (or
interval, I suppose) is contextual, and you chose to complain about
"extreme dissonance".

Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > But we weren't talking about progressions; rather a chord in
> > isolation.
>
> I disagree. In musical terms, the relative dissonance of a chord (or
> interval, I suppose) is contextual, and you chose to complain about
> "extreme dissonance".

The idea that intervals differ in terms of relative agreeableness or
concordance is by no means so recent as Helmholtz, and reading older
literature will show that. Can anyone find clear citations earlier
than the 20th century for dissonance as a purely contextual notion?
I'm skeptical any such notion was clearly put forward until much more
recently than the time when the agreeableness distinction was widely
understood.

>> What did they do, exactly? The evidence for composers of this
>> period using/intending meantone is, it seems to me, a mere fantasy.
>
>Eh? Since when was meantone never used in the 18th century?

Didn't "this period" refer to the 19th century here?

-Carl

At 10:38 PM 4/29/2005, you wrote:
>--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>> > [Jon] Well, he is writing from a mathematical standpoint, and
>> > you are writing from a musical one.
>>
>> Oh yes, Jon, it's all down to math vs. music. Put a sock in it,
>> will you?
>
>Carl! It's so good to have you back!
>
>Of course, I was trying to make a distinction in how our backgrounds
>affect our perceptions, and pointing out that Gene was having a hard
>time with the "extreme dissonance" phrase, coming from a background
>that values clear, precise terms (not to mention the psycho-acoustic
>matters), whereas Tom's background was clearly in music and utilizing
>terms as any (well, any learned) musician would see those same
>progressions vis a vis consonance/dissonance.

I agree that Gene's nitpicking on "extreme dissonance" was excessive,
but I don't think any such mathematician/musician generalization is
true, or serves discourse here.

-Carl

>> > But we weren't talking about progressions; rather a chord in
>> > isolation.
>>
>> I disagree. In musical terms, the relative dissonance of a chord (or
>> interval, I suppose) is contextual, and you chose to complain about
>> "extreme dissonance".
>
>The idea that intervals differ in terms of relative agreeableness or
>concordance is by no means so recent as Helmholtz, and reading older
>literature will show that. Can anyone find clear citations earlier
>than the 20th century for dissonance as a purely contextual notion?
>I'm skeptical any such notion was clearly put forward until much more
>recently than the time when the agreeableness distinction was widely
>understood.

We're arguing about the order in which these two different types of
distinctions were first made? Count me out.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
> >> What did they do, exactly? The evidence for composers of this
> >> period using/intending meantone is, it seems to me, a mere fantasy.
> >
> >Eh? Since when was meantone never used in the 18th century?
>
> Didn't "this period" refer to the 19th century here?

I thought we were talking about the German sixth--are we back to the
Tristan chord? My suggestion was by no means that Wagner's piano or
orchestra used meantone, just that it might not be equal temperament.
This is, after all, the middle of the 19th century.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> I agree that Gene's nitpicking on "extreme dissonance" was excessive,
> but I don't think any such mathematician/musician generalization is
> true, or serves discourse here.

It came in response to suggestions I was an ignorant boob. It seems to
me I had some reason because of that to explain why I took the
comments the way I did, and good reason to so take them, given the
"extreme" and the "listening".

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >> The fundamental point here is that you seem to be writing of
> >> 7-limit chords as consonances whereas I hear them as various
> >> kinds of dissonance. How can we judge?
> >
> >Well, he is writing from a mathematical standpoint, and you are
> >writing from a musical one.
>
> Oh yes, Jon, it's all down to math vs. music. Put a sock in it,
> will you?

i say we just combine the math and music and forget about
any dichotomy. i'm happy to report that i'm just home from
the first public presentation of Tonalsoft Muzika microtonal
music software. it took place at the Sonic Arts Gallery on
Friday evening, April 29, as part of the South Park "Walkabout",
a neighborhood event which occurs about 3 times a year.

i did 7 demonstrations of Muzika, as various groups of
interested people wandered in, and Jonathan, Brink and i
did some jam sessions, with them playing keyboards and me
playing ("noodling" with the mouse) the Muzika lattice,
using it as an instrument.

the full commercial release of the software is still scheduled
for summer 2005.

-monz
http://tonalsoft.com
microtonal music software

--- In tuning@yahoogroups.com,
"Gene Ward Smith" <gwsmith@s...>
wrote:

> The idea that intervals differ
> in terms of relative
> agreeableness or concordance
> is by no means so recent as
> Helmholtz, and reading older
> literature will show that.

the ancient Greeks specifically
cited the 3:2 and 4:3 intervals
as "_symphoniae_", which we would
now translate as "consonances".
it was widely felt that only
epimoric ratios ( i.e., (n=1)/n )
should be admitted into a tuning
system, and in the proportional
progression 1:2:3:4:5:... etc.,
1:2 is the ratio of the octave
and does not produce any new notes,
then 2:3 and 3:4 both do produce
new notes, from which an entire
scale can be created. 5 was not
admitted as a consonance by the
most ancient authors, thus, there
was a recognition of a connection
between numerical complexity of the
ratio and the music perception of
consonance.

> Can anyone find clear citations
> earlier than the 20th century
> for dissonance as a purely
> contextual notion? I'm
> skeptical any such notion was
> clearly put forward until much
> more recently than the time
> when the agreeableness distinction
> was widely understood.

did you see my post talking about the recognition of differing
musical styles? i think it was not possible for anyone to
notice a contextual meaning for "dissonance" until the
variability of musical styles was consciously discerned.
this only happened after the invention of long-playing record,
early 1950s. i would not be surprised if Blackwood was
the first to discuss it in depth.

-monz
http://tonalsoft.com
microtonal music software

>i say we just combine the math and music and forget about
>any dichotomy. i'm happy to report that i'm just home from
>the first public presentation of Tonalsoft Muzika microtonal
>music software. it took place at the Sonic Arts Gallery on
>Friday evening, April 29, as part of the South Park "Walkabout",
>a neighborhood event which occurs about 3 times a year.
>
>i did 7 demonstrations of Muzika, as various groups of
>interested people wandered in, and Jonathan, Brink and i
>did some jam sessions, with them playing keyboards and me
>playing ("noodling" with the mouse) the Muzika lattice,
>using it as an instrument.

Awesome!

When did it change from Musica to Muzika?

-Carl

>i think it was not possible for anyone to
>notice a contextual meaning for "dissonance" until the
>variability of musical styles was consciously discerned.

Are you sure about that, monz?

-Carl

In a message dated 4/30/2005 6:12:38 AM Eastern Standard Time,
monz@tonalsoft.com writes:
i think it was not possible for anyone to
notice a contextual meaning for "dissonance" until the
variability of musical styles was consciously discerned.
this only happened after the invention of long-playing record,
early 1950s. i would not be surprised if Blackwood was
the first to discuss it in depth.
Nope. Johann Philipp Kirnberger spoke of differences in dissonance in 1776
regarding the dominant 7th chord and its context. I'll try to find the proper
reference.

Re Easley Blackwood: I had ocassion to interview him on WKCR Radio in New
York back in the day. At the time I was playing regularly in 31-tone tuning with
Jon Catler's band. In a very genuine manner he explained that he had only
theorized about 31 ET but had never heard it. My responses to him were at odds
with his theorizing and I feel confident he looked further into the matter.

best, Johnny Reinhard

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> Awesome!
>
> When did it change from Musica to Muzika?

yesterday.
:)

we got a trademark on Muzika ... i still like
the old spelling, but that's how it goes ...

-monz

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > i think it was not possible for anyone to
> > notice a contextual meaning for "dissonance" until the
> > variability of musical styles was consciously discerned.
>
> Are you sure about that, monz?

no ... that's why i wrote "i think ...". ;-)

i'd have to do some research to make a confident statement
about this, and as you all know, i have absolutely no time
for research right now.

but based on the absurd amount of research i've already
done in this field, i think there's at least some weight
to what i wrote.

-monz
http://tonalsoft.com
microtonal music software

Congratulations Monz!

Cordially,
Ozan

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

i say we just combine the math and music and forget about
any dichotomy. i'm happy to report that i'm just home from
the first public presentation of Tonalsoft Muzika microtonal
music software. it took place at the Sonic Arts Gallery on
Friday evening, April 29, as part of the South Park "Walkabout",
a neighborhood event which occurs about 3 times a year.

i did 7 demonstrations of Muzika, as various groups of
interested people wandered in, and Jonathan, Brink and i
did some jam sessions, with them playing keyboards and me
playing ("noodling" with the mouse) the Muzika lattice,
using it as an instrument.

the full commercial release of the software is still scheduled
for summer 2005.

-monz
http://tonalsoft.com
microtonal music software

Muzika??? That reminds me of "Muzika-yı Humayun", or the Imperial Band of the Ottoman Army founded after the 1826 revolution in place of the Janissary band "Mehteran". Maybe Monz will be interested in considering "Royal" and "Imperial" versions of Muzika for the consumers.

Coridally,
Ozan

----- Original Message -----
From: Carl Lumma
To: tuning@yahoogroups.com
Sent: 30 Nisan 2005 Cumartesi 19:45
Subject: Re: [tuning] first public presentation of Tonalsoft Muzika

>i say we just combine the math and music and forget about
>any dichotomy. i'm happy to report that i'm just home from
>the first public presentation of Tonalsoft Muzika microtonal
>music software. it took place at the Sonic Arts Gallery on
>Friday evening, April 29, as part of the South Park "Walkabout",
>a neighborhood event which occurs about 3 times a year.
>
>i did 7 demonstrations of Muzika, as various groups of
>interested people wandered in, and Jonathan, Brink and i
>did some jam sessions, with them playing keyboards and me
>playing ("noodling" with the mouse) the Muzika lattice,
>using it as an instrument.

Awesome!

When did it change from Musica to Muzika?

-Carl