Yahoo Tuning Groups Ultimate Backup tuning Re: The "bias" of a tuning -- also, caveats about 22 and 23 equal

Hello everybody! I'll pick throught this for bits I want to reply to.

> Once again, this approach represents the exact opposite of
> theory. Typically, theory involves a generalization about reality
> derived from observations of the world. Thus theory goes from
> specifics to generalities. In other words, theory involves primarily
> induction -- large general principles grow from small individual
> facts.

That's an acceptable definition of theory, and exactly what you do below!

> it is so incoherent and so ridiculously contrary to even the most
> basic elements of everyday musical experience. Viz., even a small
> child taking piano lessons knows that a musical interval's dissonance
> depends on its context, a fact which Schoenberg's so-called "theory"
> of music uttelry ignores.

I don't know of anything Schoenberg called "theory of music" but I did read
"Theory of Harmony" and it certainly does not ignore this.

> So on every front, Schoenberg's bizarre and laughable claims have
> been systemtically disproven. In every case, Schoenberg's kooky
> ideas audibly contradict the observable reality of actual music in
> the real world.

That's patently false, as Schoenberg's music itself exists in the real world.

> Of course much additional experimental evidence shows that JI
> tuning is not heard by most listeners as sounding optimal for
> standard Western music -- Terhardt and Ward's article "Psychaoucsitc
> Comparison of Just vs. Equal Tempered Tuning" from Acustica in 1974,
> Siegel & Siegel's article "Musicians Can't Tell Sharp from Flat" from
> 1986, etc.

That imples that *some* listeners do find JI optimal, which is fine by me.
What happened to Boomsliter and Creel?

> Unlike many other statements about microtonal tunings, the claim
> that each tuning has a bias either toward melody or toward harmony is
> not open to subjective interpretation. Ivor's and my definition is
> strict and simple, and produces reliably reproducible experimental
> confirmation by way of listening tests.

I had a hard time parsing that first sentence. Not open to subjective
interpretation? Is that what you meant to write? If so, what do listening
tests have to do with it?

> Second, because psycoacoustics tells us that only tertian triads
> whose thirds exceed the critical band in interval width can produce
> smooth functional harmonies on octave inversion, only tertian triads
> made up of thirds wider than the critical band can qualify as
> generally fucntional smooth harmonies (since only such tertian triads
> made up of thirds wider than about 280 cents remain smooth on octave
> inversion). This effect does NOT depend on warping the timbre, and
> cannot be changed by warping the timbre, since in this case the
> fundamental of at least one note of the triad will coexist in the
> same critical band with the root or the fifth of the triad on octave
> inversion, producing unacceptable acoustic roughness.

Now there's a generalization if ever I heard one! So what's wrong with
<http://x31eq.com/cadence.mp3>?

> But this is not possible. In most of these equal temperaments
> even today, in the year 2001, the only existing compositions are
> those produced by myself and Ivor Darreg. That is far far far too
> small an observational base upon which to build any kind of
> hypothesis. We would be buidling a castle on quicksand, as so many
> other microtonal so-caleld "theorists" have done before us.

Oh, come come. Why not draw the obvious conclusion? Real music in the real
world tells us these tunings are uninteresting. That doesn't bother me,
because I go by my ears.

> As a result, the time for theory has not yet arrived in
> microtonality. Idle speculations about various tunings are
> meaningless and unproductive until composers build up a sufficient
> repertory of music in each of the ETs and JI limits and NJ NET
> inharmonic series for listeners to judge the audibel regularities and
> discern musical patterns which transcend the individual style of the
> composer.

Well, it depends what you mean by "microtonality". We have enough significant
11-limit music from Harry Partch to construct a theory of Harry Partch's use of
11-limit harmony. What's wrong with that, or why isn't it "microtonal theory"?
Books are written on Palestrina's use of counterpoint, that's considered
respectable theory. An individual style is good enough.

> Without that repertory of music in ET and JI and NJ NET tuning,
> idle speculations are as useless and as worthless as guesses about
> the constituent elements which make up the sun prior to the invention
> of spectrometry, or wild fantasies about the interior structure of
> the atom prior to the discovery of the electron and the atomic
> nucleus.

Guesses needn't be worthless. You have to throw up a few crazy ideas before
you spot the good ones. Come on in, the water's lovely!

> To put it bluntly, we do not yet have remotely enough musical
> evidence in the form of actual compostions in each microtonal tuning
> for anyone to form meaningful hypotheses about the various ETs. This
> is why I don't do theory, and probably why Ivor didn't. Microtonality
> has not yet reached the stage where theory is even ready to begin.

Don't be silly, that's exactly the theory you indulged in above. Claiming it
isn't theory won't save it from being disproven when significant music gets
written using strong cadences that don't involve recognizable IV-V-I
progressions.

> To recap what every music historian and musicologist and
> competent musician already knows, throughout Western history music
> comes first and theory only later, afterwards. Musicians break rules
> and toss together musical structures ad hoc, by guessing, off the
> cuff. When these stabs in the dark prove msuically effective and
> enough composers start to use 'em, then theorists finally step in and
> try to explain things after the fact.

I'm totally dubious about this. It may be the definiton of "music theory" in
which case that isn't what I'm doing. But I'm sure theorizing went on. The
only difference between than and now is that we don't know who was doing the
theorizing back then because it didn't get written down until after.

> Moreover, we will continue stuck at the butterfly-collecting
> stage as long as the internet allows unproductive spasms of theory
> and meaningless bouts of idle speculation involving magic numbers and
> mystic fantasies like the harmonic series as the purported basis of
> music.
> In this regard the internet serves as a potent roadblock in the
> path of progress in microtonality. Right now we need more microtonal
> music -- more GOOD microtonal music...a LOT more good microtonal
> music...before the first theorist can even hope to step in and
> discern hidden patterns in the musical compositions in each tuning.

Blaming the Internet for the failure of your theories to catch on is as weak as
not calling them theories. Surely sex and drugs have a more powerful tendency
to distract the would be microtonalist.

For myself, I have an X5D sitting in front of me, and to my right a TX81Z and
a Capybara 320. All of these are capable of making real microtonal music, in
real time, and hence widen my knowledge of said. I wouldn't have known of
any of them but for the internet. And my computer wouldn't have Scala loaded
on it to help with the retuning. Nobody else would have midiconv or MIDI
Relay. I wouldn't have the cassettes of papers you (Brian) so kindly sent me.
Nor would I have the support and guidance of a microtonal community, leading me
towards new tunings and ideas, sometimes even giving me feedback on my music
(crucial if I'm going to mature as a composer).

The older generation of microtonalists really underestimate the value of the
Internet to those of us who would be isolated without it. By spreading
heretical ideas and music it is enormously useful in encouraging though and
experiment. That *will* lead to great music, give it time.

And I've got news for you. We're going to carry on with our theories and make
all our own mistakes. Maybe some of those will be mistakes you made yourself.
Keep up with the positive wisdom, what you've found works, what ideas helped
you with your composition. But you can't tell me what I hear is wrong.

> ---------
> Several more important addenda:
> Joe Monzo claimed that the wolf fifth in his Dowling tuning is
> 682 cents in width. This is not a wolf fifth. It is an entirely
> musically recognizable and musically function perfect fifth.

Redefining common words is bad enough, but attacking others for not second
guessing your definitions is cranky. The word "wolf" historically refers to
the unique fifth in a twelve note meantone. These "wolves" are much closer to
the just fifth than 682 cents, and it's not being just that makes them wolves.
The term is fully appropriate, by association, here.

> In another 4 days I'll post 2 fragments of pieces in 23 equal
> which show clearly and vividly that 23 equal can and does sound as
> though it has entirely functional p5ths. In another 4 days I'll
> delete all my current MP3 files from the files section. If you
> haven't downloaded 'em yet, get 'em in the next 4 days or they'll be
> gone to make room for other people's music.

I'll look forward to this. It'll be interesting to hear how you theory becomes
manifest. Did you ever post the end of that high-limit JI piece? It sounded
quite good, but it's difficult to tell where it's heading from the excerpt I
heard. I am behind on MP3 listening again, so perhaps I missed it.

Graham

"I toss therefore I am" -- Sartre

🔗monz <joemonz@...>

> From: Graham Breed <graham@...>
> To: <crazy_music@yahoogroups.com>
> Sent: Sunday, July 08, 2001 12:58 PM
> Subject: [crazy_music] Re: The "bias" of a tuning
-- also, caveats about 22 and 23 equal

> > [Brian McLaren]
> > Schoenberg claims that "the higher we go in
> > the harmonic series, the greater the dissonance of the intervals."
> > Even a small child realizes this is foolishly and laughably wrong, as
> > you can see by comparing the interval 11/9 with the interval 8/7.
> > Once again, compare the interval 641/512 to the interval 11/10. Once
> > again, compare a 4:5:6 just triad built on C# in the key of C to an
> > equal-tempered major 7th chord. The 12-equal major 7th chord sounds
> > far more musically consonant in the context of a C major I-IV-V-I
> > progression than does a final just triad based on C#.
> > All these simple and obvious examples show that Schoenberg's so-
> > called "theory" of dissonance as a degree of ehight in the overtone
> > theory was (in Heisenberg's words) "so bad it's not even wrong" since
> > it is so incoherent and so ridiculously contrary to even the most
> > basic elements of everyday musical experience. Viz., even a small
> > child taking piano lessons knows that a musical interval's dissonance
> > depends on its context, a fact which Schoenberg's so-called "theory"
> > of music uttelry ignores.
>
> I don't know of anything Schoenberg called "theory of music" but I did
read
> "Theory of Harmony" and it certainly does not ignore this.
>
> > So on every front, Schoenberg's bizarre and laughable claims have
> > been systemtically disproven. In every case, Schoenberg's kooky
> > ideas audibly contradict the observable reality of actual music in
> > the real world.
>
> That's patently false, as Schoenberg's music itself exists in the real
world.

Brian, you dismiss Schoenberg's theories without apparently having
taken the time to really grapple with his ideas and understand him
fully. And please, before you whip out your citations from Thomson's
_Schoenberg's Error_... I know that you're fond of backing up what
you say about Schoenberg by quoting Thomson, but in my work-in-progress
on the rational basis of Schoenberg's theory, I shred at least four
or five of the major foundation points upon which Thomson bases his work.
Chief among them is Thomson's insistence on treating consonance and
dissonance as clearly separable phenomena, whereas Schoenberg adamantly
maintained exactly the opposite. Thomson himself apparently has
misunderstood Schoenberg to a great extent, because he continually
finds fault with alleged aspects of Schoenberg's theory which
Schoenberg himself never believed in.

It's incorrect to state that 'Schoenberg claims that "the higher we
go in the harmonic series, the greater the dissonance of the intervals." '
He never said that. What he said was that the *comprehensibility*
of the ratios diminishes the higher up the overtone series one goes,
because the numbers become larger, and it therefore takes more thought
to determine the relationships, compared with, say, 2:1, 3:2, or 5:4.

And for another thing, he characterizes this whole aspect of his
work as "the possibly incorrect overtone theory", which he says
he is making use of simply because it is a paradigm which his ear
informs him is at least somewhat analagous to the way people perceive
and manipulate harmony. So he himself goes thru the trouble of
questioning the relevance of the overtone theory, and decides
to employ it after all only because he knows of no better analogy.
(And that was simply because he never took the time to learn
the basics about tuning math. OK, I know... tuning has nothing
to do with math...)

It's also necessary to view Schoenberg's _Harmonielehre_, especially
the original 1911 edition, for the polemical tract that it most
assuredly is. Schoenberg was lashing out against music-theory
stuck-in-the-muds like Riemann and Schenker who refused to admit
that prime-factors higher than 5 had anything to do with music.
Schoenberg was interested in assimilating the aesthetic effects
of ratios utilizing 7, 11, and 13, and he viewed the resources of
his new way of using the 12-tET chromatic scale as a way to do
exactly that.

Really, with the major exceptions of the tuning and instruments
they chose (not to mention the corporeal-vs-abstract business),
Schoenberg and Partch had very similar ideas about expanding
the possibilities of musical harmony.

So compare apples with apples instead of comparing your
"small child's" perception of "11/9 with the interval 8/7"
or "641/512 to the interval 11/10". Your perceptions of
these intervals is going to be vastly different from Schoenberg's,
because, for one thing, you've *used* and *heard* these
actual ratios and he never did. (Yes, so *that's* the point
you've been nailing on the head which *does* apply to Schoenberg.)

I also have to take exception to what you (Brian) say about
Schoenberg's compositions, as in this bit from
Sunday, July 01, 2001 8:11 AM:

> It doesn't take a rocket scientist to figure out that Arnold
> Schoenberg's music typically sounds like a combination of
> gang rape and vivisection sans anesthesia,

I don't know what Schoenberg pieces you've listened to, and
I will admit that some of his expressionistic stuff gets pretty
wild (and that's the stuff of his that I like best of all),
but really... the guy was a brilliant composer, and his music
covers quite a range of emotional expression. If you listen
to a good performance of _Erwartung_ (and make sure it's a
good one!), and try to put your perspective in line with what
any regular listener in 1909 was used to, you'll quickly realize
that Schoenberg was opening up tremendous new possibilities
for musical expression with this piece.

> > To recap what every music historian and musicologist and
> > competent musician already knows, throughout Western history music
> > comes first and theory only later, afterwards. Musicians break rules
> > and toss together musical structures ad hoc, by guessing, off the
> > cuff. When these stabs in the dark prove msuically effective and
> > enough composers start to use 'em, then theorists finally step in and
> > try to explain things after the fact.
>
> I'm totally dubious about this. It may be the definiton of "music theory"
in
> which case that isn't what I'm doing. But I'm sure theorizing went on.
The
> only difference between than and now is that we don't know who was doing
the
> theorizing back then because it didn't get written down until after.

Throughout the history of music-theory, there are examples of both
prescriptive and descriptive theory. Whether or not one believes
in the equal validity of both types, one cannot simply ignore
the vast body of work written in the prescriptive tradition
and pretend it doesn't exist.

> > Joe Monzo claimed that the wolf fifth in his Dowling tuning is
> > 682 cents in width. This is not a wolf fifth. It is an entirely
> > musically recognizable and musically function perfect fifth.
>
> Redefining common words is bad enough, but attacking others for not second
> guessing your definitions is cranky. The word "wolf" historically refers
to
> the unique fifth in a twelve note meantone. These "wolves" are much
closer to
> the just fifth than 682 cents, and it's not being just that makes them
wolves.
> The term is fully appropriate, by association, here.

Thanks for jumping to my defense, Graham. Brian, I quote here for
you something from my Dowland webpage, and if you visit the page
and listen to the mp3 of Dowland's _Lachrimae_ *in his tuning*,
I'm sure you'll agree that "there be wolves here":
http://www.ixpres.com/interval/monzo/fngrbds/dowland/dowland.htm

> One glaring example of these unusual intervals is the Eb chord
> which appears on the first beat of the 2nd measure. The score
> calls for a high Bb on the last beat of the 1st measure which
> is 15 5/9 cents flatter than 12-tET Bb. Then on the first beat
> of the next measure comes an Eb-Bb-Eb trine with pitches deviating
> from 12-tET by +10 1/6, +12 1/6, and -17 1/2 cents, respectively.
> So we have:
>
>
> frequency ratios
>
> Bb -15.6 ï¿½ | 372 |
> | Eb +10.2 ï¿½ | 252
> | Bb +12.2 ï¿½ | 189
> | Eb -17.5 ï¿½ | 124
>
>
> The top Bb forms a 3:1 ratio with the bottom Eb, and
> the middle Eb:Bb is a 4:3, so there are a Pythagorean
> "12th" ("8ve"+"5th") on the outside and "4th" on the
> inside. But the "4th" on the inside is made of different
> pitches from the "12th" on the outside. The higher Eb
> forms a 31:21 ratio with the top Bb, and the lower Bb
> forms a 189:124 ratio with the bottom Eb.

And if that's not crystal clear, try this notation:

Bb = 2 8ves + ~284 cents
Eb = 1 8ve + ~810 cents
Bb = 1 8ve + ~312 cents
Eb = ~782 cents

The "octaves" here are ~1172.299664 cents for the Bb's
and ~1227.700336 cents for the Eb's!

So I'm not talking here about any "implied functional 5th" etc.

I'm talking about one Eb:Bb "5th" that's ~674.2546651 cents,
and a different Eb:Bb "5th" that's ~729.6553366 cents,
BOTH BEING USED AT THE SAME TIME!!

If *that's* not wolves, then please tell me what is.

-monz
http://www.monz.org
"All roads lead to n^0"

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🔗David J. Finnamore <daeron@...>

Brian,

The snippet of your piece in 37-limit JI is really beautiful. The marimba patterns are
intriguing. I agree with you that it has moxy and swing. It roils with warm, raw
humanity.

You know, not everyone has to go through MIDI hell to make music. There are such things
as multi-port MIDI interfaces that simplify matters greatly. You can make music every
day, and go months without touching a MIDI cable. Or to get even simpler, you can plug an
adapter into a typical Windows soundcard, play your controller keyboard through MIDI Relay
or Fractal Tune Smithy into a softsynth or wavetable synth, and switch tunings in the
blink of an eye - all for less than the cost of a 486 and a stack of 10 to 20 year old
sample playback synths. Though I must admit, I got a huge kick out of Monz's suggestion
that you make a MIDI-fied Partchian performance piece out of your man-vs.-machine
struggles!

xed@... wrote:

Fifths? Who said anything about fifths? "Harmony" she wrote. Harmony vs. melody, not
fifths vs. melody.

> And any kind of I-IV-V-I cadence in the ETs 6 or 8 or
> 11 or 13 or 16 or 18 or 23 cannot and will not sound like a
> functional or musically conclusive cadence in these ETs.

Harmony = I-IV-V-I? It ain't necessarily so. There are many kinds of vertical
progressions; not all of them require so much as even the concept of thirds and fifths.

> Bereft of musically conclusive tertian triads and standard
> tertian triadic progressions, the ETs without recognizable perfect
> fifths cannot establish a tonal center through standard Western tonic-
> dominant and tonic-subdominant harmonic progressions. This leaves
> the composer with only 2 alternativces -- use weaker harmonic
> progressions such as I-III or I-VI to try to establish tonality, or
> use melody to establish tonality.
> Hands-on experience composing and listening to the ETs without
> recognizable perfect fifths (6, 8, 11, 13, 16, 18, 23) shows that the
> weaker harmonic progressions like I-III-I and I-VI-I do not work
> effectively to establish final-sounding cadences, and do not work
> well to establish a sense of tonality, compared to traditional I-IV-V-
> I cadences in 12 equal.

You speak as if the term "harmony" were restricted to Western tonality. Perhaps it would
be better to substitute "Western tonality" for "harmony" to avoid confusion.

> Ivor's and my claim about bias therefore represents nothing more
> than a much simpler statement that "some ETs do not have musically
> recognizable and functional perfect fifths."

That statement is as uncontrovertible as it is obvious, but it is not equivalent to the
statement that some ETs are not suitable for harmony. I'm gonna get my psuedo-13 equal
guitar out soon and upload some mp3s to show what I mean.

-----

> Joe Monzo claimed that the wolf fifth in his Dowling tuning is
> 682 cents in width. This is not a wolf fifth. It is an entirely
> musically recognizable and musically function perfect fifth.

I thought the wolf fifth was historically defined as the fifth that one finds "across the
break" on a keyboard tuned to a series of fifths. In Pythagorean tuning, the wolf is 3:2
less a Pythagorean comma, or about 678 cents - very close to 682. And in the context of
all those perfectly pure fifths, 678 sounds shockingly out of tune, even though it might
sound perfectly acceptable when surrounded by fifths of similar size. In twelve tone QC
meantone, the standard keyboard tuning of Dowland's time, the wolf would be a sharp fifth,
not a flat one, at about 738 cents, I think. (Did I get that right?) Of course, Dowland
composed for the lute, not the keyboard, so his wolf might have been a modified
Pythagorean type.

> This points up why
> it's so important to get experience not just in one JI limit, or a
> bunch of different JI limits, but also in a variety of different
> ETs. Unless you do, your understanding of how such basic things as
> perfect fifths work in various ETs will be incorrect and very badly
> crippled.

That's a true statement, taken by itself. But Joe wasn't talking about various ETs, he
was talking about Dowland, who composed for lute during the late Renaissance period.
Surely, musical context should play some role in determining the tuning of a wolf? The
sizes of the thirds influence the perception of the consonance of the fifth in a tertian
triad. As you said:

> Although mathematically the perfect fifths of 9 equal should nto
> be musically functional, in reality they are. I can't explain why.
> But listeners agree: 9 equal's 666.666-cent perfect fifths function
> and sound, in the context of the 9 equal tuning, as musically
> effective perfect fifths.
> You want weird?
> In the context of the 18-equal tuning, 18's exact same 666.666-
> cent perfect fitghts DO NOT sound and DO NOT fucntion as musically
> effective p5ths. Unless -- 18 equal is used as 2 offset susbcales of
> 9 equal.

You said you can't explain why, and I can't offer a doctoral thesis on it, but it's
obvious from hands-on experience that there's a synergy that goes into play with triads
that causes their constituent intervals to be perceived differently than the same sizes of
intervals heard as bare dyads. That's at least the vague beginnings of an explanation.

-----

> When
> math comes in, the music goes out the window.

Say rather, "when math leads the way in, or imposes itself rigidly, music goes out." But
when music comes in, math always comes sneaking in behind in its shadow. As long as it
stays in its shadow, all is well. If math is forbidden to enter at all, music collapses
into the chaos of indecipherable noise, or meaningless blathering.

--
David J. Finnamore
Nashville, TN, USA
http://www.elvenminstrel.com
--
"Always take skeptics with a grain of salt." - Kris Peck

Re: The "bias" of a tuning -- also, caveats about 22 and 23 equal

🔗Graham Breed <graham@...>

🔗monz <joemonz@...>

🔗David J. Finnamore <daeron@...>

🔗Jon Szanto <JSZANTO@...>

🔗David J. Finnamore <daeron@...>

🔗Jon Szanto <JSZANTO@...>

🔗David J. Finnamore <daeron@...>