Tritone

On 2/13/02 9:55 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

>
> Message: 1
> Date: Wed, 13 Feb 2002 14:07:16 -0800
> From: "monz" <joemonz@yahoo.com>
> Subject: Re: tritone
>
>
> hi Jerry,
>
>> From: Gerald Eskelin <stg3music@earthlink.net>
>> To: <tuning@yahoogroups.com>
>> Sent: Wednesday, February 13, 2002 1:31 PM
>> Subject: [tuning] tritone (was: Digest Number 1891)
>>
>>
>> Me:
>>
>>> It's the ambiguous *keyboard* "tritone"
>>> that prompted its "three whole steps" nickname.
>>>
>> Monz:
>>>
>>> no it's not, Gerry.
>>>
>>> we've been thru this before, and my responses then
>>> were addressed directly to you.
>>
>> That doesn't mean the info stuck, Monz. Had I remembered
>> I would have added appropriate qualifiers.
>
>
> ok . . . upon reading my response to you again now,
> it seems a little harsh. hope you didn't take it that way.

Never a problem. I get a little "heady" once in a while too (as I'm sure
you've noticed) and appreciate a little latitude when I do.
>
>
>>> now of course i must acknowledge that the word "tritone"
>>> is used generically to mean *both* the "augmented 4th"
>>> *and* the "diminished 5th" -- and T H I S is probably
>>> more likely the result of keyboard-based thinking.
>>
>> You got it! *That's* the one I was talking about. The term
>> is handy when referring to either (or both) "inversions" as
>> they function (usually as dominant in common practice) in
>> musical contexts .
>
>
> ok . . . but it seems like you were describing the 12edo tritone
> (with the double meaning of aug4/dim5) as something special.

Actually, I was.
>
> i want to point out that in 12edo it's no more special than
> the double enharmonically-equivalent meanings of any of the
> other intervals. i.e., the aug1/min2, aug2/min3, maj3/dim4
> and their respective complements dim8/maj7, min7/aug6, min6/aug5.
>
Aha! There's the rub. My point was and is that the tritone is the only
*fifth* in the major key that is not perfect. That's why it's special. It
creates the "action" in the dominant seventh chord and, because there is
only *one*, it is the driving force in determining tonality. (Also see my
response below [#10 Digest 1895] to Margo. It relates to this point.)

The other enharmonic dissonances you listed are of course seeking
resolution, but only the tritone is unambiguous in its tonal destination,
provided (in 12edo) that the dominant root is sounding . In flexible tuning,
no root is needed when the larger (in my terms) tritone--augmented fourth
with leading tone on top--tends to expand; and the smaller
tritone--diminished fifth with the chord seventh on top--tends to contract.
The only basic thing not predetermined is whether the destination chord will
be major or minor. A "deceptive" cadence, of course, by its name, tends to
prove the point.

Incidentally, the "tritone" that results by flatting scale step 6 in the
minor mode is normally non-functional (in a modulatory sense) and that is
apparently why composers traditionally attempted to "hide" it by inverting
the diminished ii-chord to allow the strength of the subdominant pitch to
override any directional pull it might engender. In flexible tuning, the
flat-6 would likely tune differently--directly to 4 rather than to a
dominant root (implied or sounding).

So, fire away, Monz, whenever something I say sounds strange to you. That's
how I learn, and also how I find better ways of communicating my thoughts
and reporting my experience.

Gerald Eskelin

--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:

> Aha! There's the rub. My point was and is that the tritone is the
only
> *fifth* in the major key that is not perfect. That's why it's
special.

i agree completely. in my theory, i refer to this as
a 'characteristic dissonance' -- and the tritone is the _sole_
characteristic dissonance in the diatonic scale.

> It
> creates the "action" in the dominant seventh chord and, because
there is
> only *one*, it is the driving force in determining tonality.

again, agreed completely. the major/minor system arises from this
force.

> The other enharmonic dissonances you listed are of course seeking
> resolution, but only the tritone is unambiguous in its tonal
destination,
> provided (in 12edo) that the dominant root is sounding .

this is not necessary, for example the half-diminished chord built on
the leading tone of the major mode can work.
>
> Incidentally, the "tritone" that results by flatting scale step 6
in the
> minor mode is normally non-functional (in a modulatory sense) and
that is
> apparently why composers traditionally attempted to "hide" it by
inverting
> the diminished ii-chord to allow the strength of the subdominant
pitch to
> override any directional pull it might engender.

strange . . . i see it quite differently . . . i see the diminished
seventh chord as making powerful use of this tritone you see as non-
functional. and the minor mode won out over the other, similar pre-
tonal modes precisely because its native tritone is disjoint from the
tonic triad, in my opinion.

> In flexible tuning, the
> flat-6 would likely tune differently--directly to 4 rather than to a
> dominant root (implied or sounding).

i'd be happy to agree for the moment . . .

> From: paulerlich <paul@stretch-music.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, February 14, 2002 12:33 PM
> Subject: [tuning] Re: Tritone
>
>
> --- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:
>
> > Aha! There's the rub. My point was and is that the tritone
> > is the only *fifth* in the major key that is not perfect.
> > That's why it's special.
>
> i agree completely. in my theory, i refer to this as
> a 'characteristic dissonance' -- and the tritone is the _sole_
> characteristic dissonance in the diatonic scale.
>
> > It creates the "action" in the dominant seventh chord
> > and, because there is only *one*, it is the driving force
> > in determining tonality.
>
> again, agreed completely. the major/minor system arises from this
> force.

thanks, paul. i was going to agree with Jerry on this one,
but you've said essentially the same thing i was going to say.

-monz

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On 2/14/02 1:23 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com> wrote:

> Message: 18
> Date: Thu, 14 Feb 2002 20:33:59 -0000
> From: "paulerlich" <paul@stretch-music.com>
> Subject: Re: Tritone

Me:
>> The other enharmonic dissonances you listed are of course seeking
>> resolution, but only the tritone is unambiguous in its tonal
> destination,
>> provided (in 12edo) that the dominant root is sounding .

Paul:
> this is not necessary, for example the half-diminished chord built on
> the leading tone of the major mode can work.

Walter Piston calls this chord an "incomplete dominant ninth." That works
for me. My caution above is prompted by the fact that a 12edo tritone can be
interpreted two ways (B-F in C, or Cb-F in Gb). Flexible-tune it, of course,
and the ambiguity vanishes.
>>
>> Incidentally, the "tritone" that results by flatting scale step 6
> in the
>> minor mode is normally non-functional (in a modulatory sense) and
> that is
>> apparently why composers traditionally attempted to "hide" it by
> inverting
>> the diminished ii-chord to allow the strength of the subdominant
> pitch to
>> override any directional pull it might engender.
>
> strange . . . i see it quite differently . . . i see the diminished
> seventh chord as making powerful use of this tritone you see as non-
> functional. and the minor mode won out over the other, similar pre-
> tonal modes precisely because its native tritone is disjoint from the
> tonic triad, in my opinion.

Don't miss that the ii chord in both modes has a subdominant function. The
unfortunate "tritone" brought about by the minor mode's flat 6 simply gets
in the way.

Now, here we get into what I feel is a widely-held erroneous concept. The
Aeolian mode is *not* equal to the minor mode. That makes no sense. The
major/minor system is a *system* unto itself. The discovery of the
importance of the tritone was paramount in developing the *functional
harmony* that Rameou described (although I'm not sure he noticed the
importance of the tritone in the way we're discussing it). The difference
between the major and minor mode, in my opinion, centers on the major and/or
minor quality of tonic and subdominant chords. The dominant chord is major
in both modes to preserve the "action" of the tritone. That's the way I see
it.

>> In flexible tuning, the
>> flat-6 would likely tune differently--directly to 4 rather than to a
>> dominant root (implied or sounding).
>
> i'd be happy to agree for the moment . . .

"The moment" is all we have, my friend, for tomorrow we may change our
minds. :-)

Gerald Eskelin

> From: Gerald Eskelin <stg3music@earthlink.net>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, February 14, 2002 6:50 PM
> Subject: [tuning] Tritone
>
>
> On 2/14/02 1:23 PM, "tuning@yahoogroups.com" <tuning@yahoogroups.com>
wrote:
>
> > Message: 18
> > Date: Thu, 14 Feb 2002 20:33:59 -0000
> > From: "paulerlich" <paul@stretch-music.com>
> > Subject: Re: Tritone
>
> Me:
> > The other enharmonic dissonances you listed are of
> > course seeking resolution, but only the tritone is
> > unambiguous in its tonal destination, provided
> > (in 12edo) that the dominant root is sounding .
>
> Paul:
> > this is not necessary, for example the half-diminished
> > chord built on the leading tone of the major mode can work.
>
> Walter Piston calls this chord an "incomplete dominant ninth."
> That works for me. My caution above is prompted by the fact
> that a 12edo tritone can be interpreted two ways (B-F in C,
> or Cb-F in Gb). Flexible-tune it, of course, and the ambiguity
> vanishes.

i thought it worth pointing out that Schoenberg also taught
both of the concepts you describe above, Jerry.

the "incomplete dominant 9th-chord" is an idea that i believe
goes back to Schecter (mid-1800's, Bruckner's teacher),
possibly even earlier. it was pretty common currency among
German and Austrian theorists and composers of the later
1800s.

the "tritone substitution" you describe ((B-F in C, or
Cb-F in Gb) is something that Schoenberg talks about
explicitly in _Harmonielehre_ (1911), and i'm not sure
anyone else ever pointed it out before him. i hope someone
else can correct me if i'm wrong about that.

both of these ideas became a staple of jazz harmony
around the late 1930s-early 1940s (the late swing and
early bebop era), and thence ultimately found their way
into a lot of American pop music too, especially R&B.

-monz

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--- In tuning@y..., Gerald Eskelin <stg3music@e...> wrote:

> > strange . . . i see it quite differently . . . i see the
diminished
> > seventh chord as making powerful use of this tritone you see as
non-
> > functional. and the minor mode won out over the other, similar
pre-
> > tonal modes precisely because its native tritone is disjoint from
the
> > tonic triad, in my opinion.
>
> Don't miss that the ii chord in both modes has a subdominant
function. The
> unfortunate "tritone" brought about by the minor mode's flat 6
simply gets
> in the way.

hmm . . . i see it as setting up a resolution which is delayed, very
functional, not "in the way" whatsoever. but this whole discussion
really isn't about tuning, so i'm going to avoid getting into it here.

--- In tuning@y..., "monz" <joemonz@y...> wrote:

> the "incomplete dominant 9th-chord" is an idea that i believe
> goes back to Schecter (mid-1800's, Bruckner's teacher),
> possibly even earlier. it was pretty common currency among
> German and Austrian theorists and composers of the later
> 1800s.

you'll find it in bach, although back then it probably wasn't thought
of as an "incomplete dominant 9th-chord".

Monz's mention of the once dreaded tritone got me to realize that, although I am aware that this interval was banned by the church at one time (correct?), I really don't know why. What reason was given, and is there an official proclamation about it? And, of course the 7th harmonic was long viewed with suspicion as well, and I'm also interested to know some reasons why. In Danielou's "Music and the Power of Sound," he says Indian musicians avoid the 7th harmonic for spiritual reasons, but I also know European musicians/theorists did the same. It's also very interesting to me that, in the harmonic series, Bb (the 7th harmonic) appears before the major 7th B, which is the 15th harmonic...and yet, because of the predominance of the major scale in Western music, the first chord constructed in the harmonized major scale, is the major 7th chord. Maybe that's why blues related musics are so popular, as the dom 7th is much more predominant than the maj 7. When I teach my students to improvise, we talk about the major scale, cause it's so pervasive, but I tend to start them improvising on the mixolydian mode first, as it applies to most all of American popular music styles (and the blues scale is very important as well)...best...HHH
microstick.net

Soliman the Magnificent is known to have decreed the burning of instruments of a Baroque ensemble after a concert by European musicians in Topkapi Palace, worrying that this music was a threat to social and religious morals of his empire.

Cordially,
Ozan

----- Original Message -----
From: Neil Haverstick
To: tuning@yahoogroups.com
Sent: 01 Kasım 2005 Salı 18:38
Subject: [tuning] Tritone

Monz's mention of the once dreaded tritone got me to realize that,
although I am aware that this interval was banned by the church at one time
(correct?), I really don't know why. What reason was given, and is there an
official proclamation about it? And, of course the 7th harmonic was long
viewed with suspicion as well, and I'm also interested to know some reasons
why. In Danielou's "Music and the Power of Sound," he says Indian musicians
avoid the 7th harmonic for spiritual reasons, but I also know European
musicians/theorists did the same. It's also very interesting to me that, in
the harmonic series, Bb (the 7th harmonic) appears before the major 7th B,
which is the 15th harmonic...and yet, because of the predominance of the
major scale in Western music, the first chord constructed in the harmonized
major scale, is the major 7th chord. Maybe that's why blues related musics
are so popular, as the dom 7th is much more predominant than the maj 7. When
I teach my students to improvise, we talk about the major scale, cause it's
so pervasive, but I tend to start them improvising on the mixolydian mode
first, as it applies to most all of American popular music styles (and the
blues scale is very important as well)...best...HHH
microstick.net

Plato is known to have thought that various modes effected the moral fiber of
humans; i.e. certain modes were lusty, others good for the military, others
contemplative, etc.

-Aaron.

On Tuesday 01 November 2005 11:36 am, Ozan Yarman wrote:
> Soliman the Magnificent is known to have decreed the burning of instruments
> of a Baroque ensemble after a concert by European musicians in Topkapi
> Palace, worrying that this music was a threat to social and religious
> morals of his empire.
>
> Cordially,
> Ozan
>
> ----- Original Message -----
> From: Neil Haverstick
> To: tuning@yahoogroups.com
> Sent: 01 Kasım 2005 Salı 18:38
> Subject: [tuning] Tritone
>
>
> Monz's mention of the once dreaded tritone got me to realize that,
> although I am aware that this interval was banned by the church at one
> time (correct?), I really don't know why. What reason was given, and is
> there an official proclamation about it? And, of course the 7th harmonic
> was long viewed with suspicion as well, and I'm also interested to know
> some reasons why. In Danielou's "Music and the Power of Sound," he says
> Indian musicians avoid the 7th harmonic for spiritual reasons, but I also
> know European musicians/theorists did the same. It's also very interesting
> to me that, in the harmonic series, Bb (the 7th harmonic) appears before
> the major 7th B, which is the 15th harmonic...and yet, because of the
> predominance of the major scale in Western music, the first chord
> constructed in the harmonized major scale, is the major 7th chord. Maybe
> that's why blues related musics are so popular, as the dom 7th is much more
> predominant than the maj 7. When I teach my students to improvise, we talk
> about the major scale, cause it's so pervasive, but I tend to start them
> improvising on the mixolydian mode first, as it applies to most all of
> American popular music styles (and the blues scale is very important as
> well)...best...HHH
> microstick.net