Yahoo Tuning Groups Ultimate Backup tuning Devil's interval pt. 2

Neil Haverstick wrote:

> Yo...I was surprised that nobody posted info on why the tritone was
> considered devilish, so I thought I'd try again. I think it's an interesting
> subject, I've often heard it mentioned, but do not know just why it was
> considered evil...so if anybody does, maybe they could chat about it...HHH

I can't believe that the catholic church bothered to regulate
counterpoint, and the "diabolus in musica" was not the "tritone" in
that medieval adage either, but "mi contra fa". The context is singing
(and at the same time "analyzing" for what we would call accidentals)
in hexachords. When two parts sing a mi (say, in the naturalis
hexachord on C, so it's an E) and a fa (in the mollis hexachord on F;
Bb) at the same time or directly following each other, something must
be wrong and one of the parts has to parse their diatonics according
to a different hexachord. If the E is the bottom note, the higher part
has to switch to the durus (dürüm? gender?) hexachord on G and make
the note another mi, B natural; if Bb is the lower note, the E has to
become an Eb, the fa in a Bb hexachord.

I don't know enough about hexachord practice to tell you how "mi
contra fa" was differentiated from "fa contra mi" as in mi from the F hexachord (A) against fa from the C hexachord (F), so I don't recall
music where this had to be done, but I have read that "sometimes"
minor sixths also were amended to become major intervals. If they were
talking about penultimate notes on cadences, however, the obvious
solmisation of the minor sixths are mi-ut or la-fa (from the same
hexachord).

This probably won't satisfy you. Perhaps it helps if you bear in mind
that this is about two- and three-part music where "cadence" means an
approach to the final and its octave in contrary stepwise motion; the
tritone was "tamed" (put to use) only in four-part music when the
defining cadential movement was a v-i in the bass and the seventh was
introduced as a regular dissonance.

klaus

🔗monz <monz@tonalsoft.com>

Hi Neil and klaus,

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:

> I can't believe that the catholic church bothered to
> regulate counterpoint,

Really? It doesn't surprise me at all ... during the
800s-1500s counterpoint was an important part of every
Roman Catholic Mass. The church officials would regulate
their music as much as anything else of concern to the church.

> and the "diabolus in musica" was not the "tritone" in
> that medieval adage either, but "mi contra fa". The
> context is singing (and at the same time "analyzing" for
> what we would call accidentals) in hexachords. When two
> parts sing a mi (say, in the naturalis hexachord on C,
> so it's an E) and a fa (in the mollis hexachord on F;
> Bb) at the same time or directly following each other,
> something must be wrong and one of the parts has to parse
> their diatonics according to a different hexachord. If
> the E is the bottom note, the higher part has to switch
> to the durus (dürüm? gender?) hexachord on G and make
> the note another mi, B natural; if Bb is the lower note,
> the E has to become an Eb, the fa in a Bb hexachord.

It may make klaus's example more clear to illustrate
the hexachord system:

hexachord type ........ ut . re . mi . fa . sol . la
-----------------------------------------------------
naturalis [natural] ... C .. D .. E .. F .. G ... A
mollis [soft] ......... F .. G .. A .. Bb . C ... D
durus [hard] .......... G .. A .. B .. C .. D ... E

Your description comes from a later period, when mutation
allowed the existence of hexachords outside the Guidonian
3-hexachord system of c.1050 (thus, your "Bb hexachord").

The same procedure could be illustrated within the older
naturalis/mollis/durus system by saying this:

* if F-fa (naturalis hexachord) is the lower note
and B-mi (durus hexachord) the higher (i.e., an
augmented-4th or true "tritone"), the durus must
change to the mollis to transform B-mi (durus) into
Bb-fa (mollis) and thus change the augmented-4th into
a perfect-4th;

* if Bb-fa (mollis) is the higher note and E-mi (naturalis)
is the lower (i.e., a diminished-5th), the mollis must
change to the durus to transform Bb-fa (mollis) into
B-mi (durus) and thus change the diminished-5th into
a perfect-5th.

It seems to our modern eyes that this is not the same
as your illustration, but that's because it's difficult
for us to "look outside the box" of absolute pitch
nomenclature. In Guido's time, pitch nomenclature was
always relative, so my illustration demonstrates exactly
the same thing as yours ... i only put in the letter-names
to help the modern reader understand the pitch relationships.

But indeed, klaus's description does provide an exact
illustration of how the hexachord system evolved. Eb and
F# were the first new notes made available outside the
3-hexachord system of notes A Bb B C D E F G.

> This probably won't satisfy you. Perhaps it helps if
> you bear in mind that this is about two- and three-part
> music where "cadence" means an approach to the final
> and its octave in contrary stepwise motion;

I can't dig out any reference right now, but i'm certain
that the "diabolus in musica" concept existed during the
time of monophonic chant, and was employed in regard to
melodic steps of an augmented-4th or diminished-5th in
a chant melody.

I'd bet that Boethius had something to say about this
... maybe i'll get a chance to take a look.

> the tritone was "tamed" (put to use) only in four-part
> music when the defining cadential movement was a v-i
> in the bass and the seventh was introduced as a regular
> dissonance.

That's true, and what's most interesting to me is that
not only did the augmented-4th and diminished-5th become
classified as "regular dissonance" -- they became the
*essential* dissonance of tonal music, the one that
*had* to be resolved, and in a particular way.

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

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗Mikal De Valia <chiptruth@excite.com>

finally a question i can respond to. this griup is WAY hardcore.

when the catholic church began included were people who hated the Truth and didn't want it promulgated. people seeing the holy Trinity as somewhat forbidding was a bonus to such early - period 'illuminaires' and so there was some devilish fear placed where it didn't belong, creating loathing for the Holy Trinity.

Music has always been where the heart and soul of cultures is -- devilishly those who sought rule @the time of Constantine and the hyper-militant Holy Roman Empire -- full of good people by the way -- don't get me wrong --

worked too, actually

it was the high secret clergy creating a need for their order. people -- the lies and Diabolical Sabotage in the early Church would blow your mind. and part of it I guess was creating intervals that later Carnosaur and other Satanic Rock bands would exploit for their cock rock.

chiptruth@excite.com
(punx.com blows)
--- On Thu 11/03, klaus schmirler < KSchmir@online.de > wrote:
From: klaus schmirler [mailto: KSchmir@online.de]
To: tuning@yahoogroups.com
Date: Fri, 04 Nov 2005 03:01:45 +0100
Subject: Re: [tuning] Devil's interval pt. 2

<tt>
Neil Haverstick wrote: 
 
> Yo...I was surprised that nobody posted info on why the tritone was 
> considered devilish, so I thought I'd try again. I think it's an interesting 
> subject, I've often heard it mentioned, but do not know just why it was 
> considered evil...so if anybody does, maybe they could chat about it...HHH 
 
I can't believe that the catholic church bothered to regulate 
counterpoint, and the "diabolus in musica" was not the "tritone" in 
that medieval adage either, but "mi contra fa". The context is singing 
(and at the same time "analyzing" for what we would call accidentals) 
in hexachords. When two parts sing a mi (say, in the naturalis 
hexachord on C, so it's an E) and a fa (in the mollis hexachord on F; 
Bb) at the same time or directly following each other, something must 
be wrong and one of the parts has to parse their diatonics according 
to a different hexachord. If the E is the bottom note, the higher part 
has to switch to the durus (d�r�m? gender?) hexachord on G and make 
the note another mi, B natural; if Bb is the lower note, the E has to 
become an Eb, the fa in a Bb hexachord. 
 
I don't know enough about hexachord practice to tell you how "mi 
contra fa" was differentiated from "fa contra mi" as in mi from the F 
hexachord (A) against fa from the C hexachord (F), so I don't recall 
music where this had to be done, but I have read that "sometimes" 
minor sixths also were amended to become major intervals. If they were 
talking about penultimate notes on cadences, however, the obvious 
solmisation of the minor sixths are mi-ut or la-fa (from the same 
hexachord). 
 
This probably won't satisfy you. Perhaps it helps if you bear in mind 
that this is about two- and three-part music where "cadence" means an 
approach to the final and its octave in contrary stepwise motion; the 
tritone was "tamed" (put to use) only in four-part music when the 
defining cadential movement was a v-i in the bass and the seventh was 
introduced as a regular dissonance. 
 
klaus 
 
</tt>

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🔗klaus schmirler <KSchmir@online.de>

monz wrote:

> > I can't dig out any reference right now, but i'm certain
> that the "diabolus in musica" concept existed during the
> time of monophonic chant, and was employed in regard to
> melodic steps of an augmented-4th or diminished-5th in
> a chant melody.

Reason tells me that the "contra" part is missing in monophonic music, but that doesn't really rule out much. Especially if it's true that the mi contra fa rule was only formulated in 1725, as the link in Hans' post says. And if it was formulated in Fux's counterpoint method Gradus ad Parnassum he was definitely interested in the "contra" aspect. But writers have written about hexachords, mi and fa for centuries before, and as far as I know they all acknowledged the tritone/altered octaves problem, even if their solutions differed.

By the way, for polyphonic music it is a safe bet that in the so-called Lydian mode the B would have been flattened most of the times :O).

klaus

🔗Jon Szanto <jszanto@cox.net>

--- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:
> And jazz with its tritones is good christian music while rock with its
> power chords is satanic?

Jazz useage isn't so much in terms of melodic material (though it must
exist) but uses the interval in altered chords and as a modulatory
tool, and basically as a _musical_ device. It seems like more current
popular music has exploited the alleged 'darker' nature of the
interval. From Wikipedia:

"The tritone retains its "Devil in Music" character in popular music,
specifically heavy metal. The opening of Black Sabbath's signature
song Black Sabbath makes heavy use of the tritone. Other metal songs
with prominent tritones in their main riffs are Diamond Head's Am I
Evil? and Metallica's For Whom the Bell Tolls and Enter Sandman.
Perhaps the single guitarist to have made the most extensive use of
the tritone is Robert Fripp of King Crimson, who used it repeatedly in
King Crimson albums like Larks' Tongues in Aspic, Starless and Bible
Black, and Red. Other examples are the beginning of Liszt's Dante
Sonata, Sibelius's Fourth Symphony and Jimi Hendrix's Purple Haze. The
tritone is also used throughout Benjamin Britten's War Requiem, as an
ironic "point of reference" despite the tone's inherent instability,
thereby offering subtle commentary on the nature of war itself. Slayer
has traditionally used the tritone extensively, and their 1998 album
titled "Diabolus in Musica", reflects that fact."

I got very tired of the interval when it was introduced in theory
classes, but I've always like the use of the tritone as an integral
part of Lutoslawski's "Funeral Music" for string orchestra.

Cheers,
Jon

🔗Brad Lehman <bpl@umich.edu>

> I can't dig out any reference right now, but i'm certain
> that the "diabolus in musica" concept existed during the
> time of monophonic chant, and was employed in regard to
> melodic steps of an augmented-4th or diminished-5th in
> a chant melody.

Indeed so: it was primarily a *melodic* thing being forbidden, and
having nothing to do one way or another with harmony.

A characteristically funny remark about it, in the _Webster's New
World Dictionary of Music_ (a remake expanding Nicolas Slonimsky's
_Lectionary of Music_):

"The earliest suggestion that the use of the tritone may not be a
_peccatum mortale_ was made by Ramos de Pareja in _Musica practica_
(1482), but his leniency received little approbation."

Slonimsky's own book didn't have that sentence about Ramos, or indeed
the half of the article that this is in. Instead, in his version he
went off to present Erik Satie's _Vexations_, where the piece is to be
played 840 times in succession and "is based entirely of tritones in
the right hand in parallel motion".

(Looking at the "tritone" article in both these books.)

The Webster's writer also pointed out: "It seems appropriate that the
stone rejected by medieval builders should become the cornerstone of
modern music, in all its principal aspects--polytonality, atonality,
and dodecaphony; the modern importance of the tritone derives from the
very quality that disenfranchised it before: its incompatibility with
the tonic-dominant complex."

Personally I'm especially fond of the falling tritone in Elgar's
violin concerto, main theme. And the tritone themes of Mahler 4
second movement, the Korngold violin concerto, Saint-Saens's "Danse
Macabre", and Strauss's "Metamorphosen". And the tritones and whole-
tone-scale business in Bernstein's "Mass", with some brutally obvious
religious connotations to the way he used them (including some irony).

Brad Lehman

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:

> ... It seems like more current popular music has exploited
> the alleged 'darker' nature of the interval. From Wikipedia:
>
> "The tritone retains its "Devil in Music" character in
> popular music, specifically heavy metal. The opening of
> Black Sabbath's signature song Black Sabbath makes heavy
> use of the tritone. Other metal songs with prominent
> tritones in their main riffs are Diamond Head's Am I Evil?
> and Metallica's For Whom the Bell Tolls and Enter Sandman.
> Perhaps the single guitarist to have made the most extensive
> use of the tritone is Robert Fripp of King Crimson, who
> used it repeatedly in King Crimson albums like Larks'
> Tongues in Aspic, Starless and Bible Black, and Red.
> Other examples are the beginning of Liszt's Dante Sonata,
> Sibelius's Fourth Symphony and Jimi Hendrix's Purple Haze.
> The tritone is also used throughout Benjamin Britten's
> War Requiem, as an ironic "point of reference" despite
> the tone's inherent instability, thereby offering subtle
> commentary on the nature of war itself. Slayer has
> traditionally used the tritone extensively, and their
> 1998 album titled "Diabolus in Musica", reflects that
> fact."

The Wikipedia article also ought to mention the use of
the tritone in hardcore rap from the 1980s, like
Public Enemy's _It Takes a Nation of Millions to Hold
Us Back_.

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

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "Jon Szanto" <jszanto@c...> wrote:
>
> --- In tuning@yahoogroups.com, klaus schmirler <KSchmir@o...> wrote:
> > And jazz with its tritones is good christian music while rock
with its
> > power chords is satanic?
>
> Jazz useage isn't so much in terms of melodic material (though it
must
> exist) but uses the interval in altered chords and as a modulatory
> tool, and basically as a _musical_ device.

In a sense this is true of classical music as well. I hear the
tritone a bit more as part of the normal harmonic texture in jazz
than in classical music. In classical music, the tritone occurs as
part of the dominant seventh (and half-diminshed seventh, and
diminished seventh) chord, serves as the characteristic dissonance
and sets up a strong resolution (which the composer may thwart, of
course) to a (possibly fleeting) tonic triad (thus defining tonality
itself and restricting the possible choices of mode relative to the
pre-tritone practice). Resolution doesn't occur until one arrives at
a sonority without a tritone. In jazz, however, chords are commonly
extended to 5, 6, or 7 notes, and typical chord voicings include
stacks of (mixed perfect and augmented) fourths. It's even common to
have chords with *two* tritones; for example a G13#9 chord or G(-D)-B-
F-A#-E. Some jazz chords contain a tritone over the *root*,
designated a #11 or b5 -- maybe this is specifically what Jon was
thinking about. And bluesy jazz often resolves on "tonics" which
would be considered "dominant sevenths" or "dominant ninths"
classically speaking, thus still containing a tritone. Still, much
jazz does seem to have some classical harmonic/tonal forces at its
core and departs from and settles down on chords with no tritone, for
example like Cmaj13 (C(-G)-B-E-A-D), Cminmaj9 (C(-G)-Eb-B-D), and
Cm11 (C(-G)-Eb-F-Bb-D). Then again, extension of these chords which
*do* contain a tritone, like Cmaj13#11 (C(-G)-B-E-A-D-F#) and Cm13 (C
(-G)-Bb-Eb-F-A-D), are often used as jazz piece endings, again
flouting the classical conventions in a beautiful way.

🔗monz <monz@tonalsoft.com>

Hi Paul,

Apologies for snipping out so many selective parts of
what i quoted from you, but i did it to make the lead-in
to my response clearer. Hopefully i didn't alter the
context of what you wrote too much.

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> ... In classical music, the tritone occurs as part of the
> ... seventh ... chord[s], serves as the characteristic
> dissonance and sets up a strong resolution ... to a ...
> tonic triad ... . Resolution doesn't occur until one
> arrives at a sonority without a tritone. In jazz, however,
> chords are commonly extended to 5, 6, or 7 notes, and
> typical chord voicings include stacks of (mixed perfect
> and augmented) fourths. ... And bluesy jazz often resolves
> on "tonics" which would be considered "dominant sevenths"
> or "dominant ninths" classically speaking, thus still
> containing a tritone. Still, much jazz does seem to have
> some classical harmonic/tonal forces at its core and
> departs from and settles down on chords with no tritone
> ... . Then again, extension of these chords which
> *do* contain a tritone ... are often used as jazz piece
> endings, again flouting the classical conventions in a
> beautiful way.

You mentioned blues, and we discussed 7th-chords and
septimal intervals in blues harmony here recently.
I wanted to point out again that typical blues harmony
is an endless succession of "dominant-7th" chords,
every one of which contains a tritone. So there's
*never* any resolution of the tritone in blues. That's
one of the things that makes it so different from other
genres of Western music ... perhaps even the main thing.

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

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Mikal De Valia" <chiptruth@e...> wrote:

> it was the high secret clergy creating a need for their order.

Don't know about that, but there's an old idea that the Trinity is
symbolized in the triad. Here's a quote I found from Delsarte:

''Sound contains three sounds: That of the _tonic_, the _dominant_, and
the _mediant_. The tonic (Father) necessarily generates the dominant
(Son), and the mediant (Holy Ghost) proceeds necessarily from the first
two.''

http://www.fullbooks.com/Delsarte-System-of-Oratoryx15767.html

I think however the idea is older than this. In any case, note the
corollary: septimal harmony intrudes on the Trinity. It is, perhaps,
satanic, or at least not divine. It would be interesting to trace the
history of these ideas, the tritone as diabolic and the triad as
divine, and see how far back they go and if there is any relationship.

Devil's interval pt. 2

🔗Neil Haverstick <microstick@msn.com>

🔗klaus schmirler <KSchmir@online.de>

🔗monz <monz@tonalsoft.com>

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗hstraub64 <hstraub64@telesonique.net>

🔗Mikal De Valia <chiptruth@excite.com>

🔗klaus schmirler <KSchmir@online.de>

🔗klaus schmirler <KSchmir@online.de>

🔗Jon Szanto <jszanto@cox.net>

🔗Brad Lehman <bpl@umich.edu>

🔗monz <monz@tonalsoft.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗monz <monz@tonalsoft.com>

🔗Gene Ward Smith <gwsmith@svpal.org>