Yahoo Tuning Groups Ultimate Backup tuning Relevant psychoacoustics literature on the virtual fundamental phenomenon

On Mon, Jan 30, 2012 at 4:37 AM, lobawad <lobawad@...> wrote:
>
> >Consider a chord like
> > 3:12:16:20. The 12:16:20 is a 3:4:5 in its own right, which you >might
> > say has a VF at 4, but then there's a 3 in this chord too, so even if
> > I perceive 12:16:20 as partially being the harmonics of a timbre of
> > frequency "4," there's a "3" right next to it, which might imply a VF
> > of "1," but the "4" is weak, and then again I'm not even sure if the
> > nonlinear characteristics of what's going on here are such that the
> > explicit 3 might "interfere" with the virtual 4 in some sense, etc >etc
> > blah blah...
>
> Yes, but how can you say this after that whole rigamarole about the virtual fundamental popping out as it does with 5:4 when playing 400 cents instead? No the VF does NOT "pop" out, though you (and I!) can hear the "root" as plain as day- in our conditioned heads.

Yes, you're right. Actually, I'm not at all happy with my current
understanding of the role of this phenomenon in the perception music,
so this is worth talking about in more detail.

To be honest, I really hear a strong VF for a JI 5/4 either. And, to
get right down to it, I don't hear a strong VF for 3/2 either. It's
not this strong, obvious thing, but something more subtle that I have
to look for. There's a huge difference between "3/2" and "a harmonic
series minus 1/1" in my perception. I "can hear it if I try to look
for it," but there's a lot of looking needed. In fact, I "can hear it"
for 13/10 as well if I really try - I've been known to put it on in
the background for hours at a time while I work until I hear it fuse -
but it's not like that's just how I hear it if you play a piece of
music.

What makes it less obvious is if I hear a ton of 3/2's played in
parallel, using a really chilled out timbre, so I can hear all of the
partials moving together, in a high register. Then my brain gets the
cue that this is "a timbre" and fuses the whole thing together. That
doesn't really happen too much in music, though, even with parallel
fifths on a piano; something about that situation doesn't make it
fuse. Something about the onset of attack, maybe, or the complexity of
the timbre being used, just stops the magic from happening.

If some of you don't know at all what I'm talking about, just try this
experiment: go to a drawbar organ, like a Hammond B3, and put on only
the drawbars corresponding to the first and third harmonic. If you
don't have an organ like this, then load up a two-oscillator synth,
set the timbres to a sine wave, and set the two oscillators up so that
one is 3/1 higher than the other one. Make sure, when you do, that you
can hear this 3/1 clearly as an extra note. Then, play a really fast
line, and some chords, and go back to the note you started on and
listen to the sound now.

For me, I hear the whole thing as suddenly "fusing" significantly
after this point, and sounds like one note with a somewhat audible
"harmonic." Then play some quick melodic line and some chords and go
back to your original note and see if it sounds anything like that
anymore. There's something about hearing the partials all moving
together which makes the whole thing "fuse," and I find this is true
even for inharmonic timbres like marimba; I know that it's more
inharmonic but still hear it fuse into a single timbre or something.
So in this case the concept of all of the harmonics moving
synchronously as in a single auditory stream is more important than
how periodic they are as far as timbral fusion is concerned. YMMV.

-Mike

🔗Mike Battaglia <battaglia01@...>

Whoops, premature send, didn't link to the relevant literature.

The psychoacoustics literature has a ton to say on this. Within music,
there's some great research on this subject on David Huron's page -
these notes on voice leading, which many on XA have been reading (but
which I have yet to fully read myself), has some great notes on it:

http://www.music-cog.ohio-state.edu/Huron/Publications/huron.voice.leading.html

See here:

"The clarity of pitch perceptions has been simulated systematically in
a model of pitch formulated by Terhardt, Stoll and Seewann (1982a,
1982b). For both pure and complex tones, the model calculates a pitch
weight, which may be regarded as an index of the pitch's clarity, and
therefore, a measure of toneness. For pitches evoked by pure tones
(so-called "spectral pitches"), sensitivity is most acute in the
spectral dominance region -- a broad region centered near 700 Hz.
Pitches evoked by complex tones (so-called "virtual pitches")
typically show the greatest pitch weight when the evoked or actual
fundamental lies in a broad region centered near 300 Hz -- roughly D4
immediately above middle C (Terhardt, Stoll, Schermbach, & Parncutt,
1986)."

So for us, we should expect to hear the strongest VF for 5/4 if it's
played with the lower note about 2 octaves above middle C. That's
pretty consistent with my experience.

However, it should be noted that he uses this to refer to harmonic vs
inharmonic timbres! NOT for chords. The whole point here is to develop
some of these observations into an argument for the notion that
harmonic timbres are better for voice leading, for something like
polyphonic counterpoint, than inharmonic ones. He claims that it makes
it easiest to figure out what the actual pitches that are moving
around are.

---

So onto "Tonal fusion" - has this to say:

"Tonal fusion is the tendency for some concurrent sound combinations
to cohere into a single sound image. Tonal fusion arises most commonly
when the auditory system interprets certain frequency combinations as
comprising partials of a single complex tone (DeWitt & Crowder, 1987).
Two factors are known to affect tonal fusion: (1) the frequency ratio
of the component tones, and (2) their spectral content. Tonal fusion
is most probable when the combined spectral content conforms to a
single hypothetical harmonic series. This occurs most commonly when
the frequencies of the component tones are related by simple integer
ratios."

---

He then goes on and talks about tonal fusion and consonance:

"Following Stumpf, many music researchers have assumed that tonal
fusion and tonal consonance are the same phenomenon, and that both
arise from simple integer frequency ratios. However, the extant
psychoacoustic research does not support Stumpf's view. Bregman (1990)
has noted that the confusion arises from conflating "smooth sounding"
with "sounding as one." As we have seen, work by Greenwood (1961a,
1990, 1991), Plomp and Levelt (1965), Kameoka and Kuriyagawa (1969a,
1969b), and Iyer, Aarden, Hoglund and Huron (1999) implicates critical
band distances in the perception of tonal consonance or sensory
dissonance. This work shows that sensory dissonance is only indirectly
related to harmonicity or tonal fusion."

Well, that's interesting. Well, I'm not sure I necessarily agree that
critical band distances are the "magic bullet" either, or else mavila
would be intolerable, but to some extent I do agree with this -
because the intolerableness of mavila does somewhat correlate with the
harshness of the timbre that you use. Anyway, the "it's not VFs that
are important, it's beating!" line is just as played out to me as the
"it's not beating that's important, it's VFs!" line. But probably the
thing that's most relevant is here:

---

"Whether or not tonal fusion is a musically desirable phenomenon
depends on the music-perceptual goal. In Huron (1991b), it was shown
that in the polyphonic writing of J.S. Bach, tonally fused harmonic
intervals are avoided in proportion to the strength with which each
interval promotes tonal fusion. That is, unisons occur less frequently
than octaves, which occur less frequently than perfect fifths, which
occur less frequently than other intervals. Of course concurrent
octaves and concurrent fifths occur regularly in music, but
(remarkably) they occur less frequently in polyphonic music than they
would in a purely random juxtaposition of voices... **Note that this
observation is independent of the avoidance of parallel unisons,
fifths, or octaves. As simple static harmonic intervals, these
intervals are actively avoided in Bach's polyphonic works.**
Considering the importance of octaves and fifths in the formation of
common chords, their active avoidance is a remarkable feat (see Huron,
1991b)."

Well, that's really interesting. So he's saying that as a part of
Bach's desire to promote auditory stream segregation between the four
voices, he systematically avoids using the intervals most likely to
fuse. I think that's really interesting.

---

So finally, he says this:

"In light of the research on tonal fusion, we may formulate the
following principle:

4. Tonal Fusion Principle. The perceptual independence of concurrent
tones is weakened when their pitch relations promote tonal fusion.
Intervals that promote tonal fusion include (in decreasing order):
unisons, octaves, perfect fifths, ... Where the goal is the perceptual
independence of concurrent sounds, intervals ought to be shunned in
direct proportion to the degree to which they promote tonal fusion."

---

This is his conjecture, mind you, and I also suspect there's a lot
more to it than that. But, that's his conclusion from all of this. I
think it's rather interesting to think about, especially when we
consider the role of VFs in something like music. Is a VF different
from the tonal fusion of a set of harmonics into a VF? To what extent
does it really matter?

-Mike

On Mon, Jan 30, 2012 at 5:31 AM, Mike Battaglia <battaglia01@...> wrote:
>
> Yes, you're right. Actually, I'm not at all happy with my current
> understanding of the role of this phenomenon in the perception music,
> so this is worth talking about in more detail.

🔗Mike Battaglia <battaglia01@...>

On Mon, Jan 30, 2012 at 5:54 AM, Mike Battaglia <battaglia01@...> wrote:
>
> This is his conjecture, mind you, and I also suspect there's a lot
> more to it than that. But, that's his conclusion from all of this. I
> think it's rather interesting to think about, especially when we
> consider the role of VFs in something like music. Is a VF different
> from the tonal fusion of a set of harmonics into a VF? To what extent
> does it really matter?

Yikes, sorry for the triple post, but the last part of this got chopped off.

I think it may matter in the sound of larger chords, but more
importantly I STRONGLY BELIEVE that it matters in in -influencing- the
notes that you'll play underneath a chord. For instance, if I play
3:4:5, the bass note which "fits best" with that, e.g. forms the
overall most concordant sound, is something octave-equivalent to "1."
Same with 9/7: it sounds a lot more concordant if I play 4:7:9 or
1:7:9 than just 9/7 by itself. And once you "get used" to the sound of
a dyad as being a part of a larger chord, the difference it makes on
your perception could be huge. We have no tools at all to predict
what'll happen. That gets into things like habitually imagined
harmonic settings for a dyad, habitually imagined "roots," who knows.
It enters a realm that definitively does not involve the direct
activation of the missing fundamental phenomenon.

But I'm not sure that this particular psychoacoustic phenomenon is too
relevant for dyads played around middle C, outside of Terhardt's
region of dominance, in a tempered system, with a complex timbre,
really fast, in a setting that tends to promote melodic stream
segregation. And it doesn't happen at all for something like an
arpeggiated major chord, which doesn't destroy its consonance one bit.
Nor does it seem to matter that triadic harmony doesn't actually even
exist in something like a 2 part invention. So when we talk about VFs
in the context of =dyads= -- and we seem to talk about dyads a lot
these days -- we might want to be a little bit careful about how far
we take it.

That's all from me, must sleep...

-Mike

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jan 30, 2012 at 4:37 AM, lobawad <lobawad@...> wrote:
> >
> > >Consider a chord like
> > > 3:12:16:20. The 12:16:20 is a 3:4:5 in its own right, which you >might
> > > say has a VF at 4, but then there's a 3 in this chord too, so even if
> > > I perceive 12:16:20 as partially being the harmonics of a timbre of
> > > frequency "4," there's a "3" right next to it, which might imply a VF
> > > of "1," but the "4" is weak, and then again I'm not even sure if the
> > > nonlinear characteristics of what's going on here are such that the
> > > explicit 3 might "interfere" with the virtual 4 in some sense, etc >etc
> > > blah blah...
> >
> > Yes, but how can you say this after that whole rigamarole about the virtual fundamental popping out as it does with 5:4 when playing 400 cents instead? No the VF does NOT "pop" out, though you (and I!) can hear the "root" as plain as day- in our conditioned heads.
>
> Yes, you're right. Actually, I'm not at all happy with my current
> understanding of the role of this phenomenon in the perception music,
> so this is worth talking about in more detail.
>
> To be honest, I really hear a strong VF for a JI 5/4 either. And, to
> get right down to it, I don't hear a strong VF for 3/2 either. It's
> not this strong, obvious thing, but something more subtle that I have
> to look for. There's a huge difference between "3/2" and "a harmonic
> series minus 1/1" in my perception. I "can hear it if I try to look
> for it," but there's a lot of looking needed. In fact, I "can hear it"
> for 13/10 as well if I really try - I've been known to put it on in
> the background for hours at a time while I work until I hear it fuse -
> but it's not like that's just how I hear it if you play a piece of
> music.

A friend of mine who is a professional audio engineer (and has turned into a really good one over the years) did not hear the "max bass" effect when we were checking out the famous Waves plugin. You are probably familiar with this- it emphasizes or synthesizes, via some kind of distortion I imagine, harmonic series in the bass such that the missing fundamental effect kicks in.

>
> What makes it less obvious is if I hear a ton of 3/2's played in
> parallel, using a really chilled out timbre, so I can hear all of the
> partials moving together, in a high register. Then my brain gets the
> cue that this is "a timbre" and fuses the whole thing together. That
> doesn't really happen too much in music, though, even with parallel
> fifths on a piano; something about that situation doesn't make it
> fuse. Something about the onset of attack, maybe, or the complexity of
> the timbre being used, just stops the magic from happening.
>
> If some of you don't know at all what I'm talking about, just try this
> experiment: go to a drawbar organ, like a Hammond B3, and put on only
> the drawbars corresponding to the first and third harmonic. If you
> don't have an organ like this, then load up a two-oscillator synth,
> set the timbres to a sine wave, and set the two oscillators up so that
> one is 3/1 higher than the other one. Make sure, when you do, that you
> can hear this 3/1 clearly as an extra note. Then, play a really fast
> line, and some chords, and go back to the note you started on and
> listen to the sound now.
>
> For me, I hear the whole thing as suddenly "fusing" significantly
> after this point, and sounds like one note with a somewhat audible
> "harmonic." Then play some quick melodic line and some chords and go
> back to your original note and see if it sounds anything like that
> anymore. There's something about hearing the partials all moving
> together which makes the whole thing "fuse," and I find this is true
> even for inharmonic timbres like marimba; I know that it's more
> inharmonic but still hear it fuse into a single timbre or something.
> So in this case the concept of all of the harmonics moving
> synchronously as in a single auditory stream is more important than
> how periodic they are as far as timbral fusion is concerned. YMMV.
>
> -Mike
>

That could be- at some point or in some ways harmonics become more like "masses" rather than discrete entities. This sounds obvious but what this actually translates to in real life is not so obvious or easy to understand.

I should mention that one of the sickest and golden-eared musicians I've ever worked with or even ever met (now a professor teaching Baroque music) sometimes did "brain-farts" about the identity and rootedness of octaves and fifths. She said the same thing I was thinking years ago in ear-training class- "but...I hear several tones as clear as day!"

🔗lobawad <lobawad@...>

Try this- created some pretty jarring dyad, play it mid-to high range. Now reckon the first-order difference tone and play that or an octave of that down low. I find it interesting that the effect here- I am sure you will hear it- of mitigating the "dissonance" of the original dyad works even if you don't play the new triad simultaneously. You can play the lower tone first, and the "dissonant" dyad following will still be mellower than it was in isolation.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jan 30, 2012 at 5:54 AM, Mike Battaglia <battaglia01@...> wrote:
> >
> > This is his conjecture, mind you, and I also suspect there's a lot
> > more to it than that. But, that's his conclusion from all of this. I
> > think it's rather interesting to think about, especially when we
> > consider the role of VFs in something like music. Is a VF different
> > from the tonal fusion of a set of harmonics into a VF? To what extent
> > does it really matter?
>
> Yikes, sorry for the triple post, but the last part of this got chopped off.
>
> I think it may matter in the sound of larger chords, but more
> importantly I STRONGLY BELIEVE that it matters in in -influencing- the
> notes that you'll play underneath a chord. For instance, if I play
> 3:4:5, the bass note which "fits best" with that, e.g. forms the
> overall most concordant sound, is something octave-equivalent to "1."
> Same with 9/7: it sounds a lot more concordant if I play 4:7:9 or
> 1:7:9 than just 9/7 by itself. And once you "get used" to the sound of
> a dyad as being a part of a larger chord, the difference it makes on
> your perception could be huge. We have no tools at all to predict
> what'll happen. That gets into things like habitually imagined
> harmonic settings for a dyad, habitually imagined "roots," who knows.
> It enters a realm that definitively does not involve the direct
> activation of the missing fundamental phenomenon.
>
> But I'm not sure that this particular psychoacoustic phenomenon is too
> relevant for dyads played around middle C, outside of Terhardt's
> region of dominance, in a tempered system, with a complex timbre,
> really fast, in a setting that tends to promote melodic stream
> segregation. And it doesn't happen at all for something like an
> arpeggiated major chord, which doesn't destroy its consonance one bit.
> Nor does it seem to matter that triadic harmony doesn't actually even
> exist in something like a 2 part invention. So when we talk about VFs
> in the context of =dyads= -- and we seem to talk about dyads a lot
> these days -- we might want to be a little bit careful about how far
> we take it.
>
> That's all from me, must sleep...
>
> -Mike
>

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

🔗clamengh <clamengh@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Thu, Feb 2, 2012 at 1:25 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> > I'd say this is half-true. But despite the fact that 3 and 5 limit harmony was what polyphony was developed in, I think they tend to fuse too much in terms of how easy it is to separate the voices for ideal polyphony. 7-limit is really better, or 11 for that ole xenharmonic feeling.
>
> This statement is fascinating to me. It makes sense, but I've never heard any examples of 7- or 11-limit polyphony where both the individual voices and the harmonies are as clear as in, say, a Bach fugue. (Or Guillaume de Machaut organum.)
>
> I'd be very interested to hear any examples that people think successfully take advantage of this supposed possibility for greater voice independence in higher-limit harmony.

My initial tendency is to think of 11-limit harmony as fusing more
than 5-limit harmony. However, I can imagine that one way that you
might make 7-limit harmony fuse less is by doing what Huron suggested
- systematically avoiding 2/1 and 3/2 as much as possible, while using
things like 5/4 more. In the 11-limit, you have even more intervals
which don't fuse readily, so you can use those intervals even more if
you want.*

Anyway, there is one real problem with this Huron study, in that it
may not be "timbral fusion" at all that we're concerned about: if it's
really true that in Bach's case, he avoided 2/1 first and 3/2 second -
not even in parallel but in general - it still may not make sense to
just jump from that to talking about timbral fusion as the antithesis
of voice leading. In this case, consider that octaves are also the
most common interval in the diatonic scale, and fifths the second-most
common, whereas thirds carry the most "information" in a certain
sense.

This statement can be formulated quite precisely, in fact: consider
the question, "what if I play a random type of fifth in the diatonic
scale?" This implies a probability distribution: you have a 6/7 chance
of playing a perfect fifth, and a 1/7 chance of playing a diminished
fifth. The Shannon entropy of this distribution is obviously much
lower than the entropy of the probability distribution of random types
of thirds, which is maximal in the diatonic scale. And if you're
working with a limited number of voices, you need to transmit as much
information as possible, yes? So that'd be another possible route to
explore this question, one which is related to the scales Bach
generally uses - and one which might be worth considering, as omitting
octaves and fifths as "less important" is common practice even if
we're not talking about counterpoint at all.

I'll post about this in more detail to tuning-math...

-Mike

*Important side question: if you're NOT playing these chords directly,
you're going to have to hear them being "implied" in arpeggiations and
other melodic figures, right? So you're not going to hear the magical
psychoacoustic effects that are supposedly what makes us love them so
much, right? In fact, that's what Huron's deliberately having us do
with all this. Well, it's a good thing this magical unspoken feature
exists, because it lets us recognize triadic harmony in 2 part
inventions. The central question thus is: for novel, xenharmonic
chords, do you have to have heard the whole chord at once, first, and
its harmonic/psychoacoustic/magical voodoo effects first, before being
able to "recognize" that chord being "implied" in an arpeggiation?

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 3, 2012 at 9:34 AM, Mike Battaglia <battaglia01@...> wrote:
>
> This statement can be formulated quite precisely, in fact: consider
> the question, "what if I play a random type of fifth in the diatonic
> scale?" This implies a probability distribution: you have a 6/7 chance
> of playing a perfect fifth, and a 1/7 chance of playing a diminished
> fifth. The Shannon entropy of this distribution is obviously much
> lower than the entropy of the probability distribution of random types
> of thirds, which is maximal in the diatonic scale. And if you're
> working with a limited number of voices, you need to transmit as much
> information as possible, yes? So that'd be another possible route to
> explore this question, one which is related to the scales Bach
> generally uses - and one which might be worth considering, as omitting
> octaves and fifths as "less important" is common practice even if
> we're not talking about counterpoint at all.

One last interesting thing to note: even if Huron's explanation is
correct and mine above is wrong, this whole thing about avoiding 3/2
and 5/4 is funny to me, because it's like saying to systematically
avoid the intervals with the strongest psychoacoustic effects. This
would seem to be the opposite of what we're all about here.

If Huron's study is right, then if I can translate slightly liberally
into the language we've been using, the idea is presumably to stop the
voices from blending and fusing - aka, to keep the "channel" of each
voice as clear as possible - to transmit melodic, scalar, tonal, and
other unknown information. I think that's a rather interesting
concept, because then our goal is to deliberately downplay many of the
psychoacoustic effects we consider the theory to be built on. On the
other hand, if my explanation is closer to correct, then that still
just says that purely scale-based considerations override concordance
in importance when discussing voice leading.

In short, if it really is true that composers in counterpoint used 2/1
and 3/2 less than other intervals, then if either of the above
explanations are correct, this either means that (many of) the
psychoacoustic effects associated with them are undesirable or of
secondary relevance. I think that's interesting.

-Mike

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "clamengh" <clamengh@...> wrote:
>
> Hello Keenan,
> I am writing 7 limit contrapuntal music indeed.
> I'll need a while to achieve this, though.
> Meanwhile I have some examples to propose you (in some cases 7 limit extensions of ancient music, in my view a legitimate operation, but of course there could be different opinions about this):
>
> 1) My canon in A= 2 in 1 on a ground:
> http://www.youtube.com/watch?v=QAleDOjStQw
> 2) Bach's Jesu bleibet meine Freude, with septimal notes:
> http://www.youtube.com/watch?v=MORojdPLVPs
> 3) Bach's "G-string" air, with septimal C:
> http://www.youtube.com/watch?v=N77fi01JRHw
> 4) Pachelbel's Canon and Gigue, in some tunings, some of which with septimal C (in the canon only):
> http://www.youtube.com/watch?v=Pw3YHqd8nbA
> 5) Paradies' Toccata:
> http://www.youtube.com/watch?v=fLFwxn0AkJA
>
> In some cases, you'll need to peruse video descriptions to get more details.
> Also you could listen to Nicola Vicentino's fragment "Madonna il poco dolce" whose midi file you can find in Scala's archive.
> Best wishes,
> Claudi Meneghin

I really enjoy these, but I don't think any of them actually illustrate the "higher limit harmony allows voices to be more independent" idea under consideration.

Your canon is interesting, but it's not extraordinarily difficult to make three voices sound independent, and I could name plenty of pieces based on five-limit harmony (or even medieval three-limit harmony!) that do just as well. Remember you're competing with Bach here!

Keenan

🔗Keenan Pepper <keenanpepper@...>

🔗Carl Lumma <carl@...>

🔗Keenan Pepper <keenanpepper@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 3, 2012 at 7:07 PM, Keenan Pepper <keenanpepper@...> wrote:
>
> The problem here isn't with the voices being independent (I can always pick out all three of them easily), but with the harmony being intelligible. There are times in this piece when the voices sound like they're harmonically unrelated to me - I can't even tell that they're forming a rational chord at all, much less which chord it is specifically. Knowing Gene they must actually be a bunch of near-JI-accuracy 11- or 13-limit chords, but often they're too complex and go by too fast for my ear to notice this.

I hear tons of "implied" chords, but I know that if I was listening to
this before my 22-EDO guitar 11-limit brain explosion I'd just hear
crap and noise. I asked Gene about this on XA chat, and apparently his
goal was to try to "imply" larger, 11-limit chords (probably often
pentads) with 3 voices, just like a 2 part invention can imply triadic
harmony. However, if you can't figure out what the "implied" chords
are, can you make sense of what's going on at all? Do you need to hear
them explicitly first? This is why I'd love it if Gene released a
5-voice version with the chords explicitly spelled out, and then for
us to listen to that, and then go back to this and see if we hear all
of the implied chords a lot better. Or maybe just a 4-voice version
with bass notes added. It'd be like hearing a solo sax rendition of a
jazz tune without knowing the tune, vs hearing it after when you do
know the tune.

There's another thing going on, which is that the implied chords
change really really fast. I think the essence of "tonal" music is
that even if you're an idiot, you can still figure out what's going
on, because the information about what's being "implied" is compressed
in a neat sort of way which a guy named Schenker figured out. For
instance, if you're a musical idiot and you hear "Don't Worry, Be
Happy," then at the very least you can hear some sense of the tonic
the whole time. If you can tune in a bit more, then you can maybe
follow tonic, and periodic departures to the dominant or subdominant
which resolve back. If you can tune in even more, then you can follow
individual chords, like I, ii, IV and V. And if you tune in even more,
you might be able to track inversions of those chords. And if you tune
in even more, you can hear passing tones on the harmony in the chorus
implying the major II chord for all of an eighth note before abruptly
disappearing, which is what you caught and I missed.

But even if you're an idiot, then you can still follow it.

Gene's music, on the other hand, is more inspired by Renaissance music
- chords changing at rapid speed. But if you can't follow what's going
on - if you're an 11-limit idiot - then the whole thing falls apart.
If you're an 11-limit genius, though, it's probably exhilarating. I'm
like halfway between the two, so I can catch it coming in and out.

Most of us on here are probably halfway between total 11-limit idiot
and Gene, who actually wrote the piece and knows what all the chords
are. But the chord changes and harmonic rhythm aren't compressed in
that nice way; there's not a heirarchical structure of impliedness
which reveals finer discriminations as you tune in more.

Also, if you already know about Schenkerian analysis and want to model
it using lossy compression techniques and Huffman codes, I want to
have a conversation with you!

-Mike

🔗clamengh <clamengh@...>

Keenan Pepper> I really enjoy these, but I don't think any of them actually illustrate the "higher limit harmony allows voices to be more independent" idea under consideration.

Yes, you are definetely right. I hope the music I am writing now will do, but I am not sure about this: my style is rather traditional. Thanks for appreciation anyway!

Genewardsmith> I presumed Keenan did not think any of my music adequately demonstrated my point, but because that was the source of my observations, I'll give this:
>
> http://micro.soonlabel.com/gene_ward_smith/mine/trio-gorts.mp3
>

That's a very fine piece, many thanks. Would you mind to set up a harpsichord or chamber organ version, please? Or, I could do that myself, if you agree and if you pass me a scala .seq file of your piece. Then, if you agree, I could make a post of this at http://soonlabel.com/xenharmonic/ (of course duly stating your authorship!).

Best wishes to everybody!
Claudi Meneghin

> > 1) My canon in A= 2 in 1 on a ground:
> > http://www.youtube.com/watch?v=QAleDOjStQw
> > 2) Bach's Jesu bleibet meine Freude, with septimal notes:
> > http://www.youtube.com/watch?v=MORojdPLVPs
> > 3) Bach's "G-string" air, with septimal C:
> > http://www.youtube.com/watch?v=N77fi01JRHw
> > 4) Pachelbel's Canon and Gigue, in some tunings, some of which with septimal C (in the canon only):
> > http://www.youtube.com/watch?v=Pw3YHqd8nbA
> > 5) Paradies' Toccata:
> > http://www.youtube.com/watch?v=fLFwxn0AkJA
>

🔗gbreed@...

There are ways this music is very unlike renaissance polyphony. The voices are all together for most of the seven minutes. With a real motet, they'd drift in and out so the melodic lines can breathe, you get plenty of chances for subset chords, and sometimes they'll all play together for full harmony.

It's a shame there isn't a thriving school mixing these techniques with higher limit chords and timbres that make the chords fuse. But I know how much work it takes so I'm not stepping forward to volunteer.

Graham

------Original message------
From: Mike Battaglia <battaglia01@...>
To: <tuning@yahoogroups.com>
Date: Saturday, February 4, 2012 3:00:46 AM GMT-0500
Subject: Re: [tuning] Re: Relevant psychoacoustics literature on the virtual fundamental phenomenon

But even if you're an idiot, then you can still follow it.

Also, if you already know about Schenkerian analysis and want to model
it using lossy compression techniques and Huffman codes, I want to
have a conversation with you!

-Mike

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🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 4, 2012 at 8:36 AM, gbreed@... <gbreed@...> wrote:
>
> There are ways this music is very unlike renaissance polyphony. The voices are all together for most of the seven minutes. With a real motet, they'd drift in and out so the melodic lines can breathe, you get plenty of chances for subset chords, and sometimes they'll all play together for full harmony.

I heard it actually more similar to some medieval music, like Machaut,
for instance, which contains a dazzling array of triadic harmony that
flies in and out. Although the triadic harmony in Machaut is supposed
to be sort of dissonant, which isn't the case here.

> It's a shame there isn't a thriving school mixing these techniques with higher limit chords and timbres that make the chords fuse. But I know how much work it takes so I'm not stepping forward to volunteer.

Did you read what I just wrote about taking advantage of this concept
of "implied harmony" to make sure that there's a heirarchical
representation of impliedness, so that even people who can't catch all
of Gene's rapid-fire microtonal inflections can catch what's going on,
and how Schenkerian analysis will help us to usher in a glorious new
age which puts the "tonal" back in "microtonal?" I thought that was a
good way to start exploring the concept of chord progressions in
general, which we so far have not (save for Petr).

Which Renaissance composers did you have in mind, btw? I wonder how
that might look if put under a Schenkerian microscope.

-Mike

🔗Carl Lumma <carl@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > I'd say this is half-true. But despite the fact that 3 and 5 limit harmony was what polyphony was developed in, I think they tend to fuse too much in terms of how easy it is to separate the voices for ideal polyphony. 7-limit is really better, or 11 for that ole xenharmonic feeling.
>
> This statement is fascinating to me. It makes sense, but I've never heard any examples of 7- or 11-limit polyphony where both the individual voices and the harmonies are as clear as in, say, a Bach fugue. (Or Guillaume de Machaut organum.)
>
> I'd be very interested to hear any examples that people think successfully take advantage of this supposed possibility for greater voice independence in higher-limit harmony.
>
> Keenan
>

Hm, I feel that any real comparisons might not be possible. I think it is certain that if we use an 11/9 where "mi" would be in a diatonic scale, it is going to surely going to fuse less than 5/4 or 6/5, and probably be a more distinct voice than those two, but we're already talking apples and oranges as far as music. If we use 7/6 and 9/7 as our (sub/super)minor/major, we're going to have both less fusing and more contrast, so it seems obvious that the voices would be more distinct. But once again, that's no longer comparable music to the polyphonic music being mentioned here- not if it is written true to the materials, rather than a retuning of a historical piece (which is just going to sound out of tune, or altered into something else).

"Higher limits" in order to be comparable with historical musics would have to refer to the tuning of tall tertian chords. But once again, how can we compare distinction of voices between 2-4 voice textures and 4-? voice textures? If we do it like Gene did in his example, where the taller structures are either implied or are spelled out over a stretch of time rather than presented as simultaneities, we run into the problems Mike just brought up. It is "no fair", so to speak, that in "5-limit" we need only three voices to present a complete tertian sonority, and in higher "limits" at least four.

There are some things that I consider raw realities of more complex rational structures. In order to more or less literally use such tunings (i.e. non-trivial rational structures or accurate temperaments), concepts of commas and scales have to be very different than they are in standard musics. I made a brief example

http://www.mediafire.com/?u9ldabtnt3149nh

illustrating this. It may not sound like it, but it shares a very essential feature with Gene's tunes.

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Hm, I feel that any real comparisons might not be possible. I think it is certain that if we use an 11/9 where "mi" would be in a diatonic scale, it is going to surely going to fuse less than 5/4 or 6/5, and probably be a more distinct voice than those two, but we're already talking apples and oranges as far as music. If we use 7/6 and 9/7 as our (sub/super)minor/major, we're going to have both less fusing and more contrast, so it seems obvious that the voices would be more distinct. But once again, that's no longer comparable music to the polyphonic music being mentioned here- not if it is written true to the materials, rather than a retuning of a historical piece (which is just going to sound out of tune, or altered into something else).

I don't understand what you mean by "not comparable". I can compare any two things I want - they don't have to be similar in order for me to compare them.

The "apples and oranges" saying means that you shouldn't fault an apple for being a bad orange, not that apples and oranges must never be compared to each other.

I agree that retunings of existing pieces are not what we should be looking at here.

> "Higher limits" in order to be comparable with historical musics would have to refer to the tuning of tall tertian chords.

Why "tertian"? Tertian just means "made of thirds", and "third" just means "interval between 200 and 500 cents" (or whatever you want the boundaries to be). Why is that an important concept?

> But once again, how can we compare distinction of voices between 2-4 voice textures and 4-? voice textures? If we do it like Gene did in his example, where the taller structures are either implied or are spelled out over a stretch of time rather than presented as simultaneities, we run into the problems Mike just brought up. It is "no fair", so to speak, that in "5-limit" we need only three voices to present a complete tertian sonority, and in higher "limits" at least four.

Who's going to tell me that 10:12:15 is "complete" but 6:9:11 is "incomplete"? If I think of 6:9:11 as being "complete" and write music that reflects that, who are you to say "no, that's incomplete; you need at least four voices"?

They "have to be very different" in what ways, specifically?

> http://www.mediafire.com/?u9ldabtnt3149nh
>
> illustrating this. It may not sound like it, but it shares a very essential feature with Gene's tunes.

This sounds cool, even though I'm not sure what it's supposed to be illustrating.

Keenan

🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 4, 2012 at 4:41 PM, lobawad <lobawad@...> wrote:
>
> Hm, I feel that any real comparisons might not be possible. I think it is certain that if we use an 11/9 where "mi" would be in a diatonic scale, it is going to surely going to fuse less than 5/4 or 6/5, and probably be a more distinct voice than those two, but we're already talking apples and oranges as far as music.

I don't hear much actual fusion for either 5/4 or 6/5, in general.

> "Higher limits" in order to be comparable with historical musics would have to refer to the tuning of tall tertian chords. But once again, how can we compare distinction of voices between 2-4 voice textures and 4-? voice textures? If we do it like Gene did in his example, where the taller structures are either implied or are spelled out over a stretch of time rather than presented as simultaneities, we run into the problems Mike just brought up. It is "no fair", so to speak, that in "5-limit" we need only three voices to present a complete tertian sonority, and in higher "limits" at least four.

Keep in mind that we only need two voices to present a complete
tertian sonority, a la a Bach 2 part invention. The whole Schenker
thing I wrote about is, imo, pretty crucial to how it all works. Shame
that stuff's not sparking much interest, I feel like every time I
start writing these days I have so many random useful ideas that I'm
practically about to have a microtonal seizure.

> There are some things that I consider raw realities of more complex rational structures. In order to more or less literally use such tunings (i.e. non-trivial rational structures or accurate temperaments), concepts of commas and scales have to be very different than they are in standard musics. I made a brief example
>
> http://www.mediafire.com/?u9ldabtnt3149nh
>
> illustrating this. It may not sound like it, but it shares a very essential feature with Gene's tunes.

I don't get it - what features does it share? It sounds mostly like
5-limit harmony to me, but not tuned justly.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > Hm, I feel that any real comparisons might not be possible. I think it is certain that if we use an 11/9 where "mi" would be in a diatonic scale, it is going to surely going to fuse less than 5/4 or 6/5, and probably be a more distinct voice than those two, but we're already talking apples and oranges as far as music. If we use 7/6 and 9/7 as our (sub/super)minor/major, we're going to have both less fusing and more contrast, so it seems obvious that the voices would be more distinct. But once again, that's no longer comparable music to the polyphonic music being mentioned here- not if it is written true to the materials, rather than a retuning of a historical piece (which is just going to sound out of tune, or altered into something else).
>
> I don't understand what you mean by "not comparable". I can compare >any two things I want - they don't have to be similar in order for >me to compare them.

If someone makes scientific, or pseudo-scientific, claims about psychoacoustic effects and music, and we are to test these claims as such, "comparison" means blind testing, ABX comparison, using control groups, and so on.

>
> The "apples and oranges" saying means that you shouldn't fault an >apple for being a bad orange, not that apples and oranges must never >be compared to each other.

Yes. And faulting apples for being bad oranges is precisely what is going to happen when we try to test the original idea.

>
> I agree that retunings of existing pieces are not what we should be >looking at here.

We will get the apples and oranges syndrome if we do that. 9/7 is a bad 5/4.

>
> > "Higher limits" in order to be comparable with historical musics >would have to refer to the tuning of tall tertian chords.
>
> Why "tertian"? Tertian just means "made of thirds", and "third" >just means "interval between 200 and 500 cents" (or whatever you >want the boundaries to be). Why is that an important concept?

Tertian chords are a historical concept, that is why they are important "in order to be comparable with historical musics". Come on, higher limits being a "natural progression" in the tuning (and sheer existence for that matter) of ever taller tertian chords is a very old concept and it is silly to deny that a logical first place we to start testing the idea presenting is in a Just tuning of the seventh partial in a tertian seventh chord.

>
> > But once again, how can we compare distinction of voices between 2-4 voice textures and 4-? voice textures? If we do it like Gene did in his example, where the taller structures are either implied or are spelled out over a stretch of time rather than presented as simultaneities, we run into the problems Mike just brought up. It is "no fair", so to speak, that in "5-limit" we need only three voices to present a complete tertian sonority, and in higher "limits" at least four.
>
> Who's going to tell me that 10:12:15 is "complete" but 6:9:11 is "incomplete"? If I think of 6:9:11 as being "complete" and write music that reflects that, who are you to say "no, that's incomplete; you need at least four voices"?

And the vertical sonorities will fuse, in keeping with the original claims we are talking about? Remember that we are talking about the original claims, not about you, me, or music in general.

>
> > There are some things that I consider raw realities of more >complex rational structures. In order to more or less literally use >such tunings (i.e. non-trivial rational structures or accurate >temperaments), concepts of commas and scales have to be very >different than they are in standard musics. I made a brief example
>
> They "have to be very different" in what ways, specifically?
>
> > http://www.mediafire.com/?u9ldabtnt3149nh
> >
> > illustrating this. It may not sound like it, but it shares a very essential feature with Gene's tunes.
>
> This sounds cool, even though I'm not sure what it's supposed to be illustrating.
>
> Keenan
>

Simply put, using rational intervals, or accurate approximations thereof, while also using pitch classes, will result in pitch classes containing more than one pitch each, i.e. "commas will happen". You don't notice what is happening in the little piece I put up? Neither do I, not really, even though it is a very heavy-handed effect and I know it's there.

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Feb 4, 2012 at 4:41 PM, lobawad <lobawad@...> wrote:
> >
> > Hm, I feel that any real comparisons might not be possible. I think it is certain that if we use an 11/9 where "mi" would be in a diatonic scale, it is going to surely going to fuse less than 5/4 or 6/5, and probably be a more distinct voice than those two, but we're already talking apples and oranges as far as music.
>
> I don't hear much actual fusion for either 5/4 or 6/5, in general.
>
>
> > "Higher limits" in order to be comparable with historical musics would have to refer to the tuning of tall tertian chords. But once again, how can we compare distinction of voices between 2-4 voice textures and 4-? voice textures? If we do it like Gene did in his example, where the taller structures are either implied or are spelled out over a stretch of time rather than presented as simultaneities, we run into the problems Mike just brought up. It is "no fair", so to speak, that in "5-limit" we need only three voices to present a complete tertian sonority, and in higher "limits" at least four.
>
> Keep in mind that we only need two voices to present a complete
> tertian sonority, a la a Bach 2 part invention. The whole Schenker
> thing I wrote about is, imo, pretty crucial to how it all works. >Shame
> that stuff's not sparking much interest, I feel like every time I
> start writing these days I have so many random useful ideas that I'm
> practically about to have a microtonal seizure.

I'm sure I speak for more than one when saying that Schenkerian analysis is something we had to do in school years or decades ago and one of the reasons people have for doing microtonal music is to avoid such academic masturbations.

> >
> > http://www.mediafire.com/?u9ldabtnt3149nh
> >
> > illustrating this. It may not sound like it, but it shares a very essential feature with Gene's tunes.
>
> I don't get it - what features does it share? It sounds mostly like
> 5-limit harmony to me, but not tuned justly.

So 5, 7 and 11-limit chords in 41-equal does not sound Just to you? I'm going to wait and see if anyone spots the thing going on in the example before saying.

🔗lobawad <lobawad@...>

🔗Mike Battaglia <battaglia01@...>

🔗lobawad <lobawad@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> > I don't understand what you mean by "not comparable". I can compare >any two things I want - they don't have to be similar in order for >me to compare them.
>
> If someone makes scientific, or pseudo-scientific, claims about psychoacoustic effects and music, and we are to test these claims as such, "comparison" means blind testing, ABX comparison, using control groups, and so on.

Right, and my point is that you can use these techniques to compare anything you want to compare.

> > The "apples and oranges" saying means that you shouldn't fault an >apple for being a bad orange, not that apples and oranges must never >be compared to each other.
>
> Yes. And faulting apples for being bad oranges is precisely what is going to happen when we try to test the original idea.

I don't see why.

> > I agree that retunings of existing pieces are not what we should be >looking at here.
>
> We will get the apples and oranges syndrome if we do that. 9/7 is a bad 5/4.

Of course it is. But why are 9/7 and 5/4 the ones being compared here? Someone with a 12-equal background will think something like "sharp major third" and "in-tune major third" when they hear them, but that doesn't mean that "major third", or even "third", is a universal property intrinsic to both of them. 9/7 is also a bad 4/3 but for some reason that comparison is made much less often.

> > Why "tertian"? Tertian just means "made of thirds", and "third" >just means "interval between 200 and 500 cents" (or whatever you >want the boundaries to be). Why is that an important concept?
>
> Tertian chords are a historical concept, that is why they are important "in order to be comparable with historical musics". Come on, higher limits being a "natural progression" in the tuning (and sheer existence for that matter) of ever taller tertian chords is a very old concept and it is silly to deny that a logical first place we to start testing the idea presenting is in a Just tuning of the seventh partial in a tertian seventh chord.

I disagree; I think "tertian chord" is an irrelevant concept. 4:5:6:7 is "tertian" and 4:7:8:9:10 is "not tertian", but to me that seems like a useless thing to say.

> > Who's going to tell me that 10:12:15 is "complete" but 6:9:11 is "incomplete"? If I think of 6:9:11 as being "complete" and write music that reflects that, who are you to say "no, that's incomplete; you need at least four voices"?
>
> And the vertical sonorities will fuse, in keeping with the original claims we are talking about? Remember that we are talking about the original claims, not about you, me, or music in general.

It depends what you mean by "fuse", but I can't think of a way in which the "fusion" of 10:12:15 is significantly different from that of 6:9:11. (It's hard to tell because 10:12:15 sounds so familiar and 6:9:11 so unfamiliar, but psychoacoustically they're very similar.)

> Simply put, using rational intervals, or accurate approximations thereof, while also using pitch classes, will result in pitch classes containing more than one pitch each, i.e. "commas will happen". You don't notice what is happening in the little piece I put up? Neither do I, not really, even though it is a very heavy-handed effect and I know it's there.

First of all, I don't know what you mean when you say "pitch class". I know of two meanings - the first is simply an equivalence class of octave-equivalent pitches, which can't be what you're talking about, and the second is based on 12-equal categories, like "Bb" is a pitch class. If that's what you mean by "pitch class" then you're taking a very pessimistic attitude toward xenharmonic music, because you're implying it will only ever be heard as variations or colorations of 12-equal and never as totally new, independent categories.

If I intentionally try to stay in "gamelan mode" (where there are pretty much only 5 "pitch classes" rather than 12), and listen to some chromatic Western music, the 12-equal music sounds like it's full of all these little comma shifts too. It's quite difficult to do this, of course, because I've been exposed to the chromatic scale my whole life and gamelan music only 6 years, but sometimes I can keep from switching into 12-equal mode for a second and then it's like "whoa, these white people have like 2 or 3 versions of every note". Clearly that's not something intrinsic to the music, but instead a result of mismatched/inappropriate categories.

So no, I don't agree that "commas will happen". When is a comma not a comma?

Keenan

🔗Mike Battaglia <battaglia01@...>

🔗gbreed@...

I don't have the facility to go through responding to each paragraph. I don't know much about Schenkerian analysis. There's something to be said for assigning roots to microtonal chords.

I studied Gesualdo a lot in the sense of counting how many notes he was using and writing code to verify his spelling. He's late for renaissance but follows the same style. He got a lot of grief from theorists who analysed his music in tonal terms and found it didn't add up. If you apply the rules of his time it makes a lot more sense.

I based my Magic music on chord progressions rather than counterpoint. I think that's the best way for lead/accompaniment music and that's a good way of structuring mainstream music where temperament matters. Counterpoint is a different effect and it works with independent lines moving in harmony rather than chords progressing.

Graham

------Original message------
From: Mike Battaglia <battaglia01@...>
To: <tuning@yahoogroups.com>
Date: Saturday, February 4, 2012 11:31:03 AM GMT-0500
Subject: Re: Re: [tuning] Re: Relevant psychoacoustics literature on the virtual fundamental phenomenon

Which Renaissance composers did you have in mind, btw? I wonder how
that might look if put under a Schenkerian microscope.

-Mike

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

🔗Mike Battaglia <battaglia01@...>

On Sun, Feb 5, 2012 at 5:35 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I'd hope that people have more reason for doing microtonal music than
> > to get away from music theory homework they didn't like or understand.
>
> ...and I suggest that you read Schenker, in German not just in the bowdlerized versions you get in American universities. Perhaps you will see why it is that is those who do understand his schtick who are most opposed to it, not those who don't.

I'm well aware that Schenkerian analysis is a bit overblown in some
respects, and in historical retrospect it's kind of creepy how he his
raison d'etre for all this stuff was rooted in German nationalism in
immediately pre-Nazi Germany. It's also kind of lame that this was
going on while my favorite genre of classical music was being invented
over in France. Also, I'm really not the biggest Schenkerian analysis
buff; I know the basic concepts and how they're applied in some simple
concepts and that's really it, I know there are some strange
interpretations of it that I disagree with, like that a piece of music
is one long drawn out I-V-I or something.

But you can't throw the baby out with the bathwater. There's an
insight here which really does have relevance, which is that not only
can chords be "implied" by a fragment of music, but that it's also
possible to create a heirarchy of such layers. This is a pretty useful
concept in jazz too, where if I'm going to solo over a piece of music
I need to be able to distinguish the underlying "skeleton" of the
chord progression, which communicates the real essence of what's going
on, from the idiomatic stuff being thrown on top of it. Not being able
to distinguish between the two is a good way to sound like you're
stuck in 1950 without any hope of ever getting out.

Note that "skeleton" in this case doesn't imply like an absolute,
stupidly dumbed down version where everything is just I and V or
whatever - you can do that too but the results tend to sound
amateurish. It just refers to some sense of going up that heirarchy a
little bit.

So maybe you don't want to call that Schenkerian, and if Schenkerian
analysis has some kind of negative connotation these days then maybe I
also don't want to call it that either. But whatever it's called, I
happen to think that concept applies here, and that it also ties in a
bit with Krumhansl's research, which shows that the perception of a
"tonic" has to do in some meaningful sense with how often it's played
- probably a much coarser insight than what we're talking about here.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
>
> > > Would you consider extending this to a longer piece?
> > >
> >
> > I'd wind up needing most of 41-equal to do so. You can use huge sets of intervals in your setup, I cannot- sets or subsets of 24 tones are is about the limit. So probably not.
>
> Well, hell. Of course, there are all these nifty things like Miracle[21] (Blackjack), Wizard[22], etc, which you might try, and vast quantities of other scales.
>

You don't use these scales much, or at all, do you? Unless I am mistaken, you use the pitches you need from a large set of possible pitches, so you really are using the temperament and not "a scale". If the pitches you use were reduced and fit into an MOS interval scheme, I'm sure the "scale" would usually be much larger than 22. And this approach, I have found, is what works in achieving the stated goal of "higher limit just".

I have tried Blackjack and many other scales. They are not very able to implement tall chords based on higher partials. One problem, which you probably don't run into in your microtemperaments, is that it is not sufficient to have a decent 9/8 and 11/8 in a tuning in order to create a "natural" eleventh chord. These must be tempered such that a
decent 11/9 remains between them.

🔗Mike Battaglia <battaglia01@...>

On Mon, Feb 6, 2012 at 1:07 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> >
> > Well, hell. Of course, there are all these nifty things like Miracle[21] (Blackjack), Wizard[22], etc, which you might try, and vast quantities of other scales.
>
> You don't use these scales much, or at all, do you? Unless I am mistaken, you use the pitches you need from a large set of possible pitches, so you really are using the temperament and not "a scale". If the pitches you use were reduced and fit into an MOS interval scheme, I'm sure the "scale" would usually be much larger than 22. And this approach, I have found, is what works in achieving the stated goal of "higher limit just".

??? Do you know how to read temperament[xx] notation? All of the
scales mentioned above are MOS's, and their cardinality is xx, so all
of the scales mentioned are <= 22 notes by definition.

For example, Miracle[21] means 21 notes of Miracle temperament,
meaning 21 miracle generators stacked on top of one another and
reduced within an octave. Also, these numbers inside the [ ] brackets
aren't usually just picked at random, but are picked to yield an MOS.
So in this case, miracle[21] and wizard[22] are both MOS's of size <=
22, which have 11-limit chords in them. Gene's one of the only people
I know of to really embrace using those scales too.

> I have tried Blackjack and many other scales. They are not very able to implement tall chords based on higher partials. One problem, which you probably don't run into in your microtemperaments, is that it is not sufficient to have a decent 9/8 and 11/8 in a tuning in order to create a "natural" eleventh chord. These must be tempered such that a
> decent 11/9 remains between them.

Sure, that's fine in all of the above cases. These are regular
temperaments, so the mapping for 11/9 is just the mapping for 11 - the
mapping for 9. Things like TE and TOP end up minimizing weighted
damage over all of the intervals in the prime limit. So it's set up
that the most accurate tuning isn't just the thing which gives you a
good 11 and a good 9, but also a good 11/9. Not just a good 5 and a
good 3, but a good 5/3 and a good 6/5 and so on.

In this case, Miracle and Wizard are about as accurate as it gets in
the 11-limit. But you can always just use those scales as subsets of
41-EDO, so the tuning won't get any worse than 41-EDO already is.

-Mike

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Feb 6, 2012 at 1:07 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > >
> > > Well, hell. Of course, there are all these nifty things like Miracle[21] (Blackjack), Wizard[22], etc, which you might try, and vast quantities of other scales.
> >
> > You don't use these scales much, or at all, do you? Unless I am mistaken, you use the pitches you need from a large set of possible pitches, so you really are using the temperament and not "a scale". If the pitches you use were reduced and fit into an MOS interval scheme, I'm sure the "scale" would usually be much larger than 22. And this approach, I have found, is what works in achieving the stated goal of "higher limit just".
>
> ??? Do you know how to read temperament[xx] notation? All of the
> scales mentioned above are MOS's, and their cardinality is xx, so all
> of the scales mentioned are <= 22 notes by definition.

Mike, please carefully read what I write before responding, okay? "21 or 22 pitches in MOS format does not suffice".

>
> For example, Miracle[21] means 21 notes of Miracle temperament,
> meaning 21 miracle generators stacked on top of one another and
> reduced within an octave. Also, these numbers inside the [ ] brackets
> aren't usually just picked at random, but are picked to yield an MOS.
> So in this case, miracle[21] and wizard[22] are both MOS's of size <=
> 22, which have 11-limit chords in them. Gene's one of the only people
> I know of to really embrace using those scales too.

Neither blackjack not wizard offer decent 11-limit chords. I think that Gene is using much larger structures, but he'll have to say.

>
> > I have tried Blackjack and many other scales. They are not very able to implement tall chords based on higher partials. One problem, which you probably don't run into in your microtemperaments, is that it is not sufficient to have a decent 9/8 and 11/8 in a tuning in order to create a "natural" eleventh chord. These must be tempered such that a
> > decent 11/9 remains between them.
>
> Sure, that's fine in all of the above cases. These are regular
> temperaments, so the mapping for 11/9 is just the mapping for 11 - the
> mapping for 9. Things like TE and TOP end up minimizing weighted
> damage over all of the intervals in the prime limit. So it's set up
> that the most accurate tuning isn't just the thing which gives you a
> good 11 and a good 9, but also a good 11/9. Not just a good 5 and a
> good 3, but a good 5/3 and a good 6/5 and so on.

This does not address the fact that you can't make a decent sound natural eleventh chord.
>
> In this case, Miracle and Wizard are about as accurate as it gets in
> the 11-limit. But you can always just use those scales as subsets of
> 41-EDO, so the tuning won't get any worse than 41-EDO already is.

These subsets fail because they temper out, in practice, more than the temperament is meant to.

🔗Mike Battaglia <battaglia01@...>

On Mon, Feb 6, 2012 at 1:34 AM, lobawad <lobawad@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > On Mon, Feb 6, 2012 at 1:07 AM, lobawad <lobawad@...> wrote:
>
> > > You don't use these scales much, or at all, do you? Unless I am mistaken, you use the pitches you need from a large set of possible pitches, so you really are using the temperament and not "a scale". If the pitches you use were reduced and fit into an MOS interval scheme, I'm sure the "scale" would usually be much larger than 22. And this approach, I have found, is what works in achieving the stated goal of "higher limit just".
> >
> > ??? Do you know how to read temperament[xx] notation? All of the
> > scales mentioned above are MOS's, and their cardinality is xx, so all
> > of the scales mentioned are <= 22 notes by definition.
>
> Mike, please carefully read what I write before responding, okay? "21 or 22 pitches in MOS format does not suffice".

I don't see where you said the phrase that you put in quotes.

> Neither blackjack not wizard offer decent 11-limit chords. I think that Gene is using much larger structures, but he'll have to say.

Wizard has two 4:5:6:7:9:11's.

> > > I have tried Blackjack and many other scales. They are not very able to implement tall chords based on higher partials. One problem, which you probably don't run into in your microtemperaments, is that it is not sufficient to have a decent 9/8 and 11/8 in a tuning in order to create a "natural" eleventh chord. These must be tempered such that a
> > > decent 11/9 remains between them.
> >
> > Sure, that's fine in all of the above cases. These are regular
> > temperaments, so the mapping for 11/9 is just the mapping for 11 - the
> > mapping for 9. Things like TE and TOP end up minimizing weighted
> > damage over all of the intervals in the prime limit. So it's set up
> > that the most accurate tuning isn't just the thing which gives you a
> > good 11 and a good 9, but also a good 11/9. Not just a good 5 and a
> > good 3, but a good 5/3 and a good 6/5 and so on.
>
> This does not address the fact that you can't make a decent sound natural eleventh chord.

Yes it does. If you think that 41-EDO gives good 11-limit hexads, then
POTE wizard is more accurate and give you better ones. This is because
POTE was designed in a non-stupid way, which doesn't give you good
11's and good 9's but messes up 11/9.

> > In this case, Miracle and Wizard are about as accurate as it gets in
> > the 11-limit. But you can always just use those scales as subsets of
> > 41-EDO, so the tuning won't get any worse than 41-EDO already is.
>
> These subsets fail because they temper out, in practice, more than the temperament is meant to.

Can you give an example?

-Mike

🔗Keenan Pepper <keenanpepper@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > I don't understand what you mean by "not comparable". I can compare >any two things I want - they don't have to be similar in order for >me to compare them.
> >
> > If someone makes scientific, or pseudo-scientific, claims about psychoacoustic effects and music, and we are to test these claims as such, "comparison" means blind testing, ABX comparison, using control groups, and so on.
>
> Right, and my point is that you can use these techniques to compare anything you want to compare.

Well then let's have some tests which allow us to test whether or not more complex ratios make voices in polyphonic music more distinct than less complex ratios do.

I'd love to have my doubts about the testability of this put to rest- assuage, man!

>
> > > I agree that retunings of existing pieces are not what we should be >looking at here.
> >
> > We will get the apples and oranges syndrome if we do that. 9/7 is a bad 5/4.
>
> Of course it is. But why are 9/7 and 5/4 the ones being compared here? Someone with a 12-equal background will think something like "sharp major third" and "in-tune major third" when they hear them, but that doesn't mean that "major third", or even "third", is a universal property intrinsic to both of them.

Yes, I have said this very same thing a number of times here. I'm glad to see not everyone is bamboozled by the "field of attraction" jive.

>9/7 is also a bad 4/3 but for some reason that comparison is made >much less often.

I have discussed this here, specifically with Igliashon. My point was specifically not to conflate "fa" and "4/3".

>
> > > Why "tertian"? Tertian just means "made of thirds", and "third" >just means "interval between 200 and 500 cents" (or whatever you >want the boundaries to be). Why is that an important concept?
> >
> > Tertian chords are a historical concept, that is why they are important "in order to be comparable with historical musics". Come on, higher limits being a "natural progression" in the tuning (and sheer existence for that matter) of ever taller tertian chords is a very old concept and it is silly to deny that a logical first place we to start testing the idea presenting is in a Just tuning of the seventh partial in a tertian seventh chord.
>
> I disagree; I think "tertian chord" is an irrelevant concept. 4:5:6:7 is "tertian" and 4:7:8:9:10 is "not tertian", but to me that seems like a useless thing to say.
>
> > > Who's going to tell me that 10:12:15 is "complete" but 6:9:11 is "incomplete"? If I think of 6:9:11 as being "complete" and write music that reflects that, who are you to say "no, that's incomplete; you need at least four voices"?
> >
> > And the vertical sonorities will fuse, in keeping with the original claims we are talking about? Remember that we are talking about the original claims, not about you, me, or music in general.
>
> It depends what you mean by "fuse", but I can't think of a way in which the "fusion" of 10:12:15 is significantly different from that of 6:9:11. (It's hard to tell because 10:12:15 sounds so familiar and 6:9:11 so unfamiliar, but psychoacoustically they're very similar.)
>
> > Simply put, using rational intervals, or accurate approximations thereof, while also using pitch classes, will result in pitch classes containing more than one pitch each, i.e. "commas will happen". You don't notice what is happening in the little piece I put up? Neither do I, not really, even though it is a very heavy-handed effect and I know it's there.
>
> First of all, I don't know what you mean when you say "pitch class". I know of two meanings - the first is simply an equivalence class of octave-equivalent pitches, which can't be what you're talking about, and the second is based on 12-equal categories, like "Bb" is a pitch class. If that's what you mean by "pitch class" then you're taking a very pessimistic attitude toward xenharmonic music, because you're implying it will only ever be heard as variations or colorations of 12-equal and never as totally new, independent categories.
>
> If I intentionally try to stay in "gamelan mode" (where there are pretty much only 5 "pitch classes" rather than 12), and listen to some chromatic Western music, the 12-equal music sounds like it's full of all these little comma shifts too. It's quite difficult to do this, of course, because I've been exposed to the chromatic scale my whole life and gamelan music only 6 years, but sometimes I can keep from switching into 12-equal mode for a second and then it's like "whoa, these white people have like 2 or 3 versions of every note". Clearly that's not something intrinsic to the music, but instead a result of mismatched/inappropriate categories.
>
> So no, I don't agree that "commas will happen". When is a comma not a comma?
>
> Keenan
>

???? Do you really read what I write? Your gamelan example is a perfect example of what I said!

Look, it is very simple, even trivial. When your "pitch grid" or "note grid", let's say gamelan scale for example (doesn't matter) is cruder than the grid to which actual sounding pitches adhere, you get commas. My point was that when creating tall ("higher limit") rational structures, you can simply embrace them. The perceptual grid of pitch class, scale, do-re-mi, whatever, doesn't necessarily have a problem with them (not in accurate and micro- temperaments)

When is a comma not a comma? When it is a step size.

🔗lobawad <lobawad@...>

Gotta run, back later!

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Feb 6, 2012 at 1:34 AM, lobawad <lobawad@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > On Mon, Feb 6, 2012 at 1:07 AM, lobawad <lobawad@> wrote:
> >
> > > > You don't use these scales much, or at all, do you? Unless I am mistaken, you use the pitches you need from a large set of possible pitches, so you really are using the temperament and not "a scale". If the pitches you use were reduced and fit into an MOS interval scheme, I'm sure the "scale" would usually be much larger than 22. And this approach, I have found, is what works in achieving the stated goal of "higher limit just".
> > >
> > > ??? Do you know how to read temperament[xx] notation? All of the
> > > scales mentioned above are MOS's, and their cardinality is xx, so all
> > > of the scales mentioned are <= 22 notes by definition.
> >
> > Mike, please carefully read what I write before responding, okay? "21 or 22 pitches in MOS format does not suffice".
>
> I don't see where you said the phrase that you put in quotes.
>
> > Neither blackjack not wizard offer decent 11-limit chords. I think that Gene is using much larger structures, but he'll have to say.
>
> Wizard has two 4:5:6:7:9:11's.
>
> > > > I have tried Blackjack and many other scales. They are not very able to implement tall chords based on higher partials. One problem, which you probably don't run into in your microtemperaments, is that it is not sufficient to have a decent 9/8 and 11/8 in a tuning in order to create a "natural" eleventh chord. These must be tempered such that a
> > > > decent 11/9 remains between them.
> > >
> > > Sure, that's fine in all of the above cases. These are regular
> > > temperaments, so the mapping for 11/9 is just the mapping for 11 - the
> > > mapping for 9. Things like TE and TOP end up minimizing weighted
> > > damage over all of the intervals in the prime limit. So it's set up
> > > that the most accurate tuning isn't just the thing which gives you a
> > > good 11 and a good 9, but also a good 11/9. Not just a good 5 and a
> > > good 3, but a good 5/3 and a good 6/5 and so on.
> >
> > This does not address the fact that you can't make a decent sound natural eleventh chord.
>
> Yes it does. If you think that 41-EDO gives good 11-limit hexads, then
> POTE wizard is more accurate and give you better ones. This is because
> POTE was designed in a non-stupid way, which doesn't give you good
> 11's and good 9's but messes up 11/9.
>
> > > In this case, Miracle and Wizard are about as accurate as it gets in
> > > the 11-limit. But you can always just use those scales as subsets of
> > > 41-EDO, so the tuning won't get any worse than 41-EDO already is.
> >
> > These subsets fail because they temper out, in practice, more than the temperament is meant to.
>
> Can you give an example?
>
> -Mike
>

🔗Mike Battaglia <battaglia01@...>

🔗lobawad <lobawad@...>

It's in the content. If you didn't get it from there, well now you have it.

>
> > Neither blackjack not wizard offer decent 11-limit chords. I think that Gene is using much larger structures, but he'll have to say.
>
> Wizard has two 4:5:6:7:9:11's.

How can you say this if you do not hear 4:5:6 (in conventional roots-doubled voicing!) in 41-tET as Just? Even if you do accept the approximations in Wizard as sufficiently Just, two 4:5:6:7:9:11's does not anything near "11-limit" make.

>
> > > > I have tried Blackjack and many other scales. They are not very able to implement tall chords based on higher partials. One problem, which you probably don't run into in your microtemperaments, is that it is not sufficient to have a decent 9/8 and 11/8 in a tuning in order to create a "natural" eleventh chord. These must be tempered such that a
> > > > decent 11/9 remains between them.
> > >
> > > Sure, that's fine in all of the above cases.

That particular example is fine in Blackjack, but Blackjack already has problems incorporating the seventh partial, if we approach Just Intonation not as Rational Tunings, a la Partch, but as Just Intonation in a historical sense.

I'm going to appeal not only to authority (Tartini in this case), but to general consensus in discussions which have appeared on this tuning list, as well as my own perception, in saying that a dominant seventh chord and a natural seventh chord are not the same thing, and if you make them the same thing, you're in some particular xenharmonic world, which is fine but it is not keeping with the concept of extending, rather than completely revamping (or misinterpreting, knowingly or otherwise) Western tonality.

In short, if we are working within the context of extending Western tonality via Just Intonation, a tuning which is "7-limit" must include, and not replace, the "5-limit". Look at 22-equal as a whole for an example of a tuning that does not fail in this particular (natural vs. dominant 7th) aspect (does a good job actually).

In the case of practical sets of pitches derived from temperaments, it doesn't matter if the temperament or "master" tuning distinguishes properly, if the actual pitches you are using do not. Maintaining the distinction between 7/6 and 6/5 in a couple of places in a set of pitches is simply not enough, for example.

🔗Mike Battaglia <battaglia01@...>

On Mon, Feb 6, 2012 at 4:55 AM, lobawad <lobawad@...> wrote:
>
> > > Neither blackjack not wizard offer decent 11-limit chords. I think that Gene is using much larger structures, but he'll have to say.
> >
> > Wizard has two 4:5:6:7:9:11's.
>
> How can you say this if you do not hear 4:5:6 (in conventional roots-doubled voicing!) in 41-tET as Just? Even if you do accept the approximations in Wizard as sufficiently Just, two 4:5:6:7:9:11's does not anything near "11-limit" make.

The second point is fair enough, but I hear 4:5:6 as being pretty
just-ish in 41-EDO. The 5/4 is a bit flat but the net effect of 4:5:6,
and definitely 4:5:6:7:9:11, is pretty "just" to me. And if this were
a real performance with real instruments I doubt I'd even notice much
was different unless you deliberately contrasted it to a pure JI
4:5:6:7:9:11 and flipped back and forth a bunch of times.

> > > > Sure, that's fine in all of the above cases.
>
> That particular example is fine in Blackjack, but Blackjack already has problems incorporating the seventh partial, if we approach Just Intonation not as Rational Tunings, a la Partch, but as Just Intonation in a historical sense.

What?! The 7/4 of 72-EDO is 3 cents flat! What is your compass of
acceptable tuning error?

> I'm going to appeal not only to authority (Tartini in this case), but to general consensus in discussions which have appeared on this tuning list, as well as my own perception, in saying that a dominant seventh chord and a natural seventh chord are not the same thing, and if you make them the same thing, you're in some particular xenharmonic world, which is fine but it is not keeping with the concept of extending, rather than completely revamping (or misinterpreting, knowingly or otherwise) Western tonality.

What is a natural seventh chord? Is it 4:5:6:7 (intonationally) or
4:5:6:7 (categorically/scalarly) or what?

But in this case, the thing we're talking about in blackjack has a 5/4
that's ~3 cents flat, a 3/2 that's 2 cents flat, and a 7/4 which is 3
cents flat, so that's definitely close enough to make me happy. A
slight octave stretch can make it even closer. I wouldn't say that's a
"dominant 7 chord" in the western sense at all.

> In short, if we are working within the context of extending Western tonality via Just Intonation, a tuning which is "7-limit" must include, and not replace, the "5-limit". Look at 22-equal as a whole for an example of a tuning that does not fail in this particular (natural vs. dominant 7th) aspect (does a good job actually).

Does "dominant 7" to you mean "two stacked perfect fourths" and
"natural 7" mean "the pattern of intonational activity associated with
7/4?" Then yes, I agree. Intoning dominant 7's as 7/4 is magical, just
like intoning major thirds as 5/4 is magical.

> In the case of practical sets of pitches derived from temperaments, it doesn't matter if the temperament or "master" tuning distinguishes properly, if the actual pitches you are using do not. Maintaining the distinction between 7/6 and 6/5 in a couple of places in a set of pitches is simply not enough, for example.

Again, do you mean intonationally here or categorically? I can think
of a certain sense in which it does matter: the 327 cent interval in
22-EDO is tempered between 6/5 and 11/9. It functions well enough
intonationally for government work as 11/9 in 4:5:6:7:9:11 to please
my ears, and also in 6/5. So those two contexts bias me into hearing
the "root" of some particular interval like that differently, which
totally changes its sound in every way possible.

For me, an interval like 11/9 is like tofu: if you play it in
4:5:6:7:9:11 a lot, it "soaks up the presence" of that chord so that I
hear a tiny bit of it in just the dyad. 327 cents in 22-EDO can be
tofu in two ways, so it soaks up both presences. This is obviously
related to learning, but how does it work exactly? I dunno, but it
seems there's some ratio component to it, because even though 5/4 by
itself generates a weak VF, 4:5:6:7:9:11 definitely doesn't and buzzes
quite nicely for me even in 22-EDO. Am I soaking up these nice
psychoacoustic effects and projecting them onto 327 cents, for
instance?

I think you're talking about scale steps: it makes no sense to
distinguish between 7/6 and 6/5 if they're tuned to be like 7 cents
apart. I agree, but I'd apply this realization more to categories like
"major third." A tuning for meantone which has a generator of a really
flat fifth, such that the major thirds and minor thirds are really
close, makes it hard to tell them apart. This principle was put in
action a few months ago; you should have seen us fail miserably in
figuring out what mode of mavila someone was playing because the
thirds were too close in size.

But why should that apply to ratios? I think it only applies for their
beating effects and not from potential "derived-from-psychoacoustic"
effects like the tofu one. I don't know what's going on but why make
the assumption that such distinctions don't apply in any sense?

-Mike

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

>
> What?! The 7/4 of 72-EDO is 3 cents flat! What is your compass of
> acceptable tuning error?

41-tET is acceptable tuning error. I am not talking about the tuning error of a single interval, but integration of higher harmonics as a whole.

>
> > I'm going to appeal not only to authority (Tartini in this case), but to general consensus in discussions which have appeared on this tuning list, as well as my own perception, in saying that a dominant seventh chord and a natural seventh chord are not the same thing, and if you make them the same thing, you're in some particular xenharmonic world, which is fine but it is not keeping with the concept of extending, rather than completely revamping (or misinterpreting, knowingly or otherwise) Western tonality.
>
> What is a natural seventh chord? Is it 4:5:6:7 (intonationally) or
> 4:5:6:7 (categorically/scalarly) or what?

Outside of this tuning list, no one in my experience would think I am talking about anything other than the pure 4:5:6:7, so, intonationally. In the case of rational musics, which are mistakenly called JI, of course the two would be distinguished by calling one 5-limit and the other 7-limit.

>
> But in this case, the thing we're talking about in blackjack has a >5/4
> that's ~3 cents flat, a 3/2 that's 2 cents flat, and a 7/4 which is 3
> cents flat, so that's definitely close enough to make me happy. A
> slight octave stretch can make it even closer. I wouldn't say >that's a
> "dominant 7 chord" in the western sense at all.

Nor would I. Nor writers of old, nor others on this list. Which means that if we want a dominant chord as well as a natural seventh chord, we need both "5 and 7 limit", and to not conflate them, right?

>
> > In short, if we are working within the context of extending Western tonality via Just Intonation, a tuning which is "7-limit" must include, and not replace, the "5-limit". Look at 22-equal as a whole for an example of a tuning that does not fail in this particular (natural vs. dominant 7th) aspect (does a good job actually).

>
> Does "dominant 7" to you mean "two stacked perfect fourths"

That is yet another thing- a Pythagorean or 3-limit seventh chord.

>and
> "natural 7" mean "the pattern of intonational activity associated with
> 7/4?"

4:5:6:7, yeah.

>Then yes, I agree. Intoning dominant 7's as 7/4 is magical, just
> like intoning major thirds as 5/4 is magical.

"Dominant" is a function. Intoning dominant chords with 7/4s causes them to longer be "dominant", not in a traditional sense. AFAIK there is a pretty good consensus on this. This distinction is certainly important to me when making music that is a continuation of Western tradition, rather than breaking with it as per usual.

>
> > In the case of practical sets of pitches derived from temperaments, it doesn't matter if the temperament or "master" tuning distinguishes properly, if the actual pitches you are using do not. Maintaining the distinction between 7/6 and 6/5 in a couple of places in a set of pitches is simply not enough, for example.
>
> Again, do you mean intonationally here or categorically? I can think
> of a certain sense in which it does matter: the 327 cent interval in
> 22-EDO is tempered between 6/5 and 11/9. It functions well enough
> intonationally for government work as 11/9 in 4:5:6:7:9:11 to please
> my ears, and also in 6/5. So those two contexts bias me into hearing
> the "root" of some particular interval like that differently, which
> totally changes its sound in every way possible.
>
> For me, an interval like 11/9 is like tofu: if you play it in
> 4:5:6:7:9:11 a lot, it "soaks up the presence" of that chord so that I
> hear a tiny bit of it in just the dyad. 327 cents in 22-EDO can be
> tofu in two ways, so it soaks up both presences. This is obviously
> related to learning, but how does it work exactly? I dunno, but it
> seems there's some ratio component to it, because even though 5/4 by
> itself generates a weak VF, 4:5:6:7:9:11 definitely doesn't and buzzes
> quite nicely for me even in 22-EDO. Am I soaking up these nice
> psychoacoustic effects and projecting them onto 327 cents, for
> instance?
>
> I think you're talking about scale steps: it makes no sense to
> distinguish between 7/6 and 6/5 if they're tuned to be like 7 cents
> apart. I agree, but I'd apply this realization more to categories like
> "major third." A tuning for meantone which has a generator of a really
> flat fifth, such that the major thirds and minor thirds are really
> close, makes it hard to tell them apart. This principle was put in
> action a few months ago; you should have seen us fail miserably in
> figuring out what mode of mavila someone was playing because the
> thirds were too close in size.
>
> But why should that apply to ratios? I think it only applies for their
> beating effects and not from potential "derived-from-psychoacoustic"
> effects like the tofu one. I don't know what's going on but why make
> the assumption that such distinctions don't apply in any sense?
>
> -Mike
>

11/9 is anything but "tofu" to me- without 11/9 being distinctly different from 6/5, "11-limit" simply doesn't happen for me, same as how I don't feel "7-limit" if minor and subminor are equated (except with certain complex "funky" timbres).

🔗Keenan Pepper <keenanpepper@...>

🔗lobawad <lobawad@...>

🔗Carl Lumma <carl@...>

🔗lobawad <lobawad@...>

🔗Kalle Aho <kalleaho@...>

And how do orchestras and choirs actually (ideally) intone dominant seventh chords? Is it à la Rameau 20:25:30:36 or is it 36:45:54:64?

Kalle

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > >Then yes, I agree. Intoning dominant 7's as 7/4 is magical, just
> > > > like intoning major thirds as 5/4 is magical.
> > >
> > > "Dominant" is a function. Intoning dominant chords with 7/4s causes them to longer be "dominant", not in a traditional sense. AFAIK there is a pretty good consensus on this. This distinction is certainly important to me when making music that is a continuation of Western tradition, rather than breaking with it as per usual.
> >
> > There's consensus about something?? There's never consensus about anything.
> >
> > I strongly disagree with the above. Barbershop quartets intone dominant seventh chords as 4:5:6:7 all the time and they're still dominant sevent chords. Nothing about the intonation "causes them to no longer be 'dominant'".
> >
> > Speak up if you agree with me.
> >
> > Keenan
> >
>
> Come on Keenan, the whole world can see the cheap sophistry you're trying to pull here. I did not say "causes them to no longer be 'dominant'", I said no longer dominant in a traditional sense.
>
> There is a huge difference, anyone listening to barbershop in comparison with orchestras and choirs can hear it.
>

🔗genewardsmith <genewardsmith@...>

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

> > Well, hell. Of course, there are all these nifty things like Miracle[21] (Blackjack), Wizard[22], etc, which you might try, and vast quantities of other scales.
> >
>
> You don't use these scales much, or at all, do you?

I actually do.

Unless I am mistaken, you use the pitches you need from a large set of possible pitches, so you really are using the temperament and not "a scale".

Sometimes that too.

>If the pitches you use were reduced and fit into an MOS interval scheme, I'm sure the "scale" would usually be much larger than 22. And this approach, I have found, is what works in achieving the stated goal of "higher limit just".

Well, there's Choraled, in a 26 note scale of hemifamity, Rachmaninoff Plays Blackjack, in Miracle[21], the 21 notes of Blackjack, Pianodactyl, in Rodan[26], and the piece I just linked to, which is in Guanyin(22), the 22-note hobbit of guanyin.

11/9 has a complexity of 3 in miracle, so miracle has 11/9's up the wazoo: it's a neutral triads/tetrads temperament, tempering out 243/242. In 72 equal, 9/8 is 3.91 cents flat, 11/8 is 1.32 cents flat and 11/9 is 2.59 cents sharp.

🔗genewardsmith <genewardsmith@...>

🔗gbreed@...

No true Scotsman

Graham

------Original message------
From: lobawad <lobawad@...>
To: <tuning@yahoogroups.com>
Date: Monday, February 6, 2012 7:37:58 PM GMT-0000
Subject: [tuning] Re: Relevant psychoacoustics literature on the virtual fundamental phenomenon

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > >Then yes, I agree. Intoning dominant 7's as 7/4 is magical, just
> > > like intoning major thirds as 5/4 is magical.
> >
> > "Dominant" is a function. Intoning dominant chords with 7/4s causes them to longer be "dominant", not in a traditional sense. AFAIK there is a pretty good consensus on this. This distinction is certainly important to me when making music that is a continuation of Western tradition, rather than breaking with it as per usual.
>
> There's consensus about something?? There's never consensus about anything.
>
> I strongly disagree with the above. Barbershop quartets intone dominant seventh chords as 4:5:6:7 all the time and they're still dominant sevent chords. Nothing about the intonation "causes them to no longer be 'dominant'".
>
> Speak up if you agree with me.
>
> Keenan
>

Come on Keenan, the whole world can see the cheap sophistry you're trying to pull here. I did not say "causes them to no longer be 'dominant'", I said no longer dominant in a traditional sense.

There is a huge difference, anyone listening to barbershop in comparison with orchestras and choirs can hear it.

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

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Feb 6, 2012 at 2:37 PM, lobawad <lobawad@...> wrote:
>
> Come on Keenan, the whole world can see the cheap sophistry you're trying to pull here. I did not say "causes them to no longer be 'dominant'", I said no longer dominant in a traditional sense.

I'll speak up in defense of Keenan that it seemed like you were saying
that there was a huge difference in function between the two. To that
effect, I'll speak in Keenan's defense with a musical example in
porcupine in 22-EDO, where the V-I resolutions to my ears sound both
"dominant" and intonationally like "4:5:6:7," much more so than those
in 12-EDO do:

http://soundcloud.com/mikebattagliamusic/functionalporcupineexcerpt

A slower example:

http://soundcloud.com/mikebattagliamusic/functional-porcupine-with-7

If that's not the claim that you were making then OK, but it seemed
like you were. You even just reiterated that dominant sevenths and
natural sevenths have different "functional" and "tonal" uses in your
latest response. Your concept of a "natural seventh" seems to me to be
similar to your concept of a thing like "fa," which you're equating
with 4:5:6:7. Or, to be honest, I have no idea what you're saying, but
I know that I can take a dominant 7 chord and intone it as 4:5:6:7 in
certain circumstances and still have it retain the same tonal
function.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗gbreed@...

Note that cassandra also supports 41 with an 11-limit complexity of 20

Graham

------Original message------
From: Mike Battaglia <battaglia01@gmail.com>
To: <tuning@yahoogroups.com>
Date: Monday, February 6, 2012 4:32:49 PM GMT-0500
Subject: Re: [tuning] Re: Relevant psychoacoustics literature on the virtual fundamental phenomenon

On Mon, Feb 6, 2012 at 3:29 PM, genewardsmith
<genewardsmith@...> wrote:
>
> Both of them, but especially miracle, have gazillions of 11-limit chords:
>
> http://xenharmonic.wikispaces.com/Chords+of+miracle
>
> http://xenharmonic.wikispaces.com/Chords+of+wizard
>
> Just go up the list of triads, tetrads, etc and include only those whose complexity is less than 21 or 22 as the case may be.

I think Cameron was talking specifically about full 11-limit otonal
hexads. This suggests a useful thing to do with EDO's, which is to
find the rank-2 regular temperament that it supports with the lowest
complexity. The MOS's of temperament will in a certain sense be
"maximally useful" for that EDO for people who don't want to use the
full thing, but only subsets. In this case, I found that magic[22] did
the trick a little better than miracle[21] in 41-EDO.

A generalization of this would also be useful when considering
higher-rank temperaments that lower-rank ones support in general, but
then I think the answer is always going to be JI, unfortunately...

-Mike

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

🔗genewardsmith <genewardsmith@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> And how do orchestras and choirs actually (ideally) intone dominant seventh chords? Is it à la Rameau 20:25:30:36 or is it 36:45:54:64?

Differently, depending on piece, style, etc. And I don't think that the options are so limited- why assume that intonation is always taken from the root? I don't think in practice, or in the ideal (which is subjective), this is always the case.

>
> Kalle
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > > >Then yes, I agree. Intoning dominant 7's as 7/4 is magical, just
> > > > > like intoning major thirds as 5/4 is magical.
> > > >
> > > > "Dominant" is a function. Intoning dominant chords with 7/4s causes them to longer be "dominant", not in a traditional sense. AFAIK there is a pretty good consensus on this. This distinction is certainly important to me when making music that is a continuation of Western tradition, rather than breaking with it as per usual.
> > >
> > > There's consensus about something?? There's never consensus about anything.
> > >
> > > I strongly disagree with the above. Barbershop quartets intone dominant seventh chords as 4:5:6:7 all the time and they're still dominant sevent chords. Nothing about the intonation "causes them to no longer be 'dominant'".
> > >
> > > Speak up if you agree with me.
> > >
> > > Keenan
> > >
> >
> > Come on Keenan, the whole world can see the cheap sophistry you're trying to pull here. I did not say "causes them to no longer be 'dominant'", I said no longer dominant in a traditional sense.
> >
> > There is a huge difference, anyone listening to barbershop in comparison with orchestras and choirs can hear it.
> >
>

🔗lobawad <lobawad@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
> Come on Keenan, the whole world can see the cheap sophistry you're trying to pull here. I did not say "causes them to no longer be 'dominant'", I said no longer dominant in a traditional sense.
>
> There is a huge difference, anyone listening to barbershop in comparison with orchestras and choirs can hear it.

Yeah, of course it sounds different. It sounds like a different kind of dominant seventh chord.

If you had said "4:5:6:7 is not a traditional intonation of dominant seventh chords" then I'd have accepted that as obviously true and moved on, but it seemed like you were trying to say something different.

Here, I'll quote the entire paragraph you wrote:

> "Dominant" is a function. Intoning dominant chords with 7/4s causes them to
> longer be "dominant", not in a traditional sense. AFAIK there is a pretty
> good consensus on this. This distinction is certainly important to me when
> making music that is a continuation of Western tradition, rather than
> breaking with it as per usual.

This doesn't seem like you're simply saying "dominant seventh chords are not traditionally intoned as 4:5:6:7". It seems like you're saying there's some more important difference in "function" between the two things - that you perceive, or that you expect your listeners to perceive, the two chords as "different things" rather than differently-tuned versions of "the same thing".

If all you were trying to say was that 4:5:6:7 is not the traditional intonation, then I apologize for the confusion.

Keenan

🔗Keenan Pepper <keenanpepper@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Feb 6, 2012 at 2:37 PM, lobawad <lobawad@...> wrote:
> >
> > Come on Keenan, the whole world can see the cheap sophistry you're trying to pull here. I did not say "causes them to no longer be 'dominant'", I said no longer dominant in a traditional sense.
>
> I'll speak up in defense of Keenan that it seemed like you were saying
> that there was a huge difference in function between the two. To that
> effect, I'll speak in Keenan's defense with a musical example in
> porcupine in 22-EDO, where the V-I resolutions to my ears sound both
> "dominant" and intonationally like "4:5:6:7," much more so than those
> in 12-EDO do:
>
> http://soundcloud.com/mikebattagliamusic/functionalporcupineexcerpt
>

Although it is softer than what would usually be the case in Western music, the dominant function is clear. The physical sound of it reminds me of the very swing-era orchestras I mentioned earlier.

> A slower example:
>
> http://soundcloud.com/mikebattagliamusic/functional-porcupine-with-7
>

... and in this one I hear no concrete dominant functions at all, LOL.

> If that's not the claim that you were making then OK, but it seemed
> like you were. You even just reiterated that dominant sevenths and
> natural sevenths have different "functional" and "tonal" uses in your
> latest response. Your concept of a "natural seventh" seems to me to be
> similar to your concept of a thing like "fa," which you're equating
> with 4:5:6:7. Or, to be honest, I have no idea what you're saying, but
> I know that I can take a dominant 7 chord and intone it as 4:5:6:7 in
> certain circumstances and still have it retain the same tonal
> function.

But I never said you couldn't. You can, and do. I do, too. I was specifically talking about approaching rational harmony via evolution (or pseudo-evolution perhaps) of traditional Western harmonic music.
I took care to bring up Tartini for crying out loud! Read Tartini and his contemporaries on the seventh partial, it is very interesting.

🔗genewardsmith <genewardsmith@...>

🔗Kalle Aho <kalleaho@...>

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > Come on Keenan, the whole world can see the cheap sophistry you're trying to pull here. I did not say "causes them to no longer be 'dominant'", I said no longer dominant in a traditional sense.
> >
> > There is a huge difference, anyone listening to barbershop in comparison with orchestras and choirs can hear it.
>
> Yeah, of course it sounds different. It sounds like a different kind of dominant seventh chord.
>
> If you had said "4:5:6:7 is not a traditional intonation of dominant seventh chords" then I'd have accepted that as obviously true and moved on, but it seemed like you were trying to say something different.
>
> Here, I'll quote the entire paragraph you wrote:
>
> > "Dominant" is a function. Intoning dominant chords with 7/4s causes them to
> > longer be "dominant", not in a traditional sense. AFAIK there is a pretty
> > good consensus on this. This distinction is certainly important to me when
> > making music that is a continuation of Western tradition, rather than
> > breaking with it as per usual.
>
> This doesn't seem like you're simply saying "dominant seventh chords are not traditionally intoned as 4:5:6:7". It seems like you're saying there's some more important difference in "function" between the two things - that you perceive, or that you expect your listeners to perceive, the two chords as "different things" rather than differently-tuned versions of "the same thing".
>
> If all you were trying to say was that 4:5:6:7 is not the traditional intonation, then I apologize for the confusion.
>
> Keenan
>

The confusion here lies in our too-free use of "dominant seventh", on the one hand as a reified chord, on the other as a function. Of course the harmonic tuning can be used in a "dominant seventh chord". I am sure that this happens, or happened in the pre-War era, in performances of even Wagner. But, when the dominant seventh chord is in a position of clear dominant function, V7-I or V7/V, we don't, as far as I've ever heard or heard of, hear it intoned harmonically (in what we'd call mainstream Western tonal music).

Conventional wisdom settled, as far as anything I've ever seen, on the harmonic seventh as an intonational possibility for the augmented sixth and rejected it for the minor seventh.

Exceptions to this create very audible and very noticable stylistic and expressive signposts. Wagner has plenty of seventh chords but does not sound like barbershop, and you can spot swing-era "Wagnerian-style" film music a mile off.

I did not state any personal judgement of whether this conventional stuff is "good" or not. I think it good neither in theory or practice that the (unfortunately named) "dominant seventh" should never be harmonically tuned, or the harmonic limited to the augmented sixth. I also think that it is good neither in theory or practice to simply swap out the harmonic seventh for 16:9 or 9:5. Rather, as should be completely clear by my insistence on have a full complement of 7/6s and 6/5s in a 41-tET subset, I think a seventh chord should be tuned to one or the other according to feel, with the harmonic for more restful or flowing places and the 5-limit for driving (functionally dominant) places. And I think that this is actually completely conventional orchestral practice.

🔗lobawad <lobawad@...>

I can't remember if I used to hate 41 and like 46, or if I've always liked 41 and not 46, but either way, I just can't stand the sound when I try to write in 46. Which is too bad, on paper it should provide pretty mellow sounding harmonic 13th chords.

Anyway I'm curious as to the specific tunings, and I will explore the ones you suggest via the xenwiki. It would be great to get a practical set of pitches.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@...m, "genewardsmith" <genewardsmith@> wrote:
> >
> >
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > I think Cameron was talking specifically about full 11-limit otonal
> > > hexads. This suggests a useful thing to do with EDO's, which is to
> > > find the rank-2 regular temperament that it supports with the lowest
> > > complexity.
> >
> > I'll code that up. Of course, nothing prevents a tie.
> >
>
> 41
> 7 limit: {[5, 1, 12, -10, 5, 25]}
> 9 limit: {[5, 1, 12, -10, 5, 25]}
> 11 limit: {[1, -8, -14, -18, -15, -25, -32, -10, -14, -2], [5, 1, 12, -8, -10, 5, -30, 25, -22, -64], [8, 18, 11, 20, 10, -5, 4, -25, -16, 18]}
> 13 limit: {[9, 10, -3, 2, 16, -5, -30, -28, -8, -35, -30, 0, 16, 56, 48]}
>
> As Graham noted, you get Cassandra also, but in addition you get octacot.
>
> Of course, 41 isn't the only player. For 46, for example, we have
>
> 46
> 7 limit: {[9, 5, -3, -13, -30, -21]}
> 9 limit: {[7, 9, 13, -2, 1, 5]}
> 11 limit: {[1, 21, 15, 11, 31, 21, 14, -24, -47, -21], [9, 5, -3, 7, -13, -30, -20, -21, -1, 30]}
> 13 limit: {[1, 21, 15, 11, 8, 31, 21, 14, 9, -24, -47, -59, -21, -33, -13]}
>

🔗lobawad <lobawad@...>

🔗Mike Battaglia <battaglia01@...>

I'll respond to Cameron and Kalle at the same time:

On Mon, Feb 6, 2012 at 5:11 PM, lobawad <lobawad@...> wrote:
>
> That's what I was taught, and I'm sure that happens in many cases. Of course, in this case, and in the similar case of being taught to sharpen major thirds in certain places, we could argue that this sharpening is actually combatting a natural tendency to tune to 7/4, or to 5/4 in the case of thirds. Nevertheless the result, at least in the instances where the seventh chord is functioning as a dominant (V, V/V etc.), I don't think there is any serious doubt that the intonation is well sharp of 7/4. In "common practice" music and its close relatives, that is. To my ears, swing-era orchestras playing "lighter", or film music, in a manner that is considered quaint or schmaltzig these days (a manner which I love) tend toward a lot more of the seventh partial overall.

On Mon, Feb 6, 2012 at 6:32 PM, Kalle Aho <kalleaho@...> wrote:
>
> Sharpen the seventh of the dominant 7th chord? Wouldn't flattening the
> seventh make more sense in regard to the 4-3 resolution?
>
> Kalle

So in both of these cases, I hear the sharpened 7th as being more
melodically effective. I don't know why. It could be because it adds
harmonic tension, or because it's closer to the note from the scale,
or, I dunno. I really don't. I think it's the latter, actually,
because in mavila[9] I note that the 7/4 does a better job of being a
dominant 7 than the thing which is "two fourths," which ends up being
like 1050 cents.

To me it just has to do with the effect that you want. For nice
melodic stuff sharpen the 7th and for nice harmonic stuff flatten it.
But man, that sharpened 7 is nice, though...

-Mike

🔗genewardsmith <genewardsmith@...>

🔗lobawad <lobawad@...>

"Barbershop uses harmonically tuned dominant sevenths. Barbershop is Western music. Therefore all Western music uses harmonically tuned dominant sevenths." is, appropriately, a fallacy of composition.

No, pointing out your fallacy of composition does does not constitute my committing a no true Scotsman fallacy.

This discussion goes back to the early 18th century at least (cf. J. Fasch) and "common practice" ultimately clearly separated the seventh partial from the dominant seventh chord.

Whether doing so is "right" or "good" is beside the point.

You guys clearly simply do not know what you are talking about. Out here in real life, no one would even blink if I said I wanted to be able to tune my minor sevenths in two different ways.

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> No true Scotsman
>
> Graham
>
> ------Original message------
> From: lobawad <lobawad@...>
> To: <tuning@yahoogroups.com>
> Date: Monday, February 6, 2012 7:37:58 PM GMT-0000
> Subject: [tuning] Re: Relevant psychoacoustics literature on the virtual fundamental phenomenon
>
>
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
> >
> > --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> > > >Then yes, I agree. Intoning dominant 7's as 7/4 is magical, just
> > > > like intoning major thirds as 5/4 is magical.
> > >
> > > "Dominant" is a function. Intoning dominant chords with 7/4s causes them to longer be "dominant", not in a traditional sense. AFAIK there is a pretty good consensus on this. This distinction is certainly important to me when making music that is a continuation of Western tradition, rather than breaking with it as per usual.
> >
> > There's consensus about something?? There's never consensus about anything.
> >
> > I strongly disagree with the above. Barbershop quartets intone dominant seventh chords as 4:5:6:7 all the time and they're still dominant sevent chords. Nothing about the intonation "causes them to no longer be 'dominant'".
> >
> > Speak up if you agree with me.
> >
> > Keenan
> >
>
> Come on Keenan, the whole world can see the cheap sophistry you're trying to pull here. I did not say "causes them to no longer be 'dominant'", I said no longer dominant in a traditional sense.
>
> There is a huge difference, anyone listening to barbershop in comparison with orchestras and choirs can hear it.
>
>
>
>
> ------------------------------------
>
> You can configure your subscription by sending an empty email to one
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🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'll respond to Cameron and Kalle at the same time:
>
> On Mon, Feb 6, 2012 at 5:11 PM, lobawad <lobawad@...> wrote:
> >
> > That's what I was taught, and I'm sure that happens in many cases. Of course, in this case, and in the similar case of being taught to sharpen major thirds in certain places, we could argue that this sharpening is actually combatting a natural tendency to tune to 7/4, or to 5/4 in the case of thirds. Nevertheless the result, at least in the instances where the seventh chord is functioning as a dominant (V, V/V etc.), I don't think there is any serious doubt that the intonation is well sharp of 7/4. In "common practice" music and its close relatives, that is. To my ears, swing-era orchestras playing "lighter", or film music, in a manner that is considered quaint or schmaltzig these days (a manner which I love) tend toward a lot more of the seventh partial overall.
>
> On Mon, Feb 6, 2012 at 6:32 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > Sharpen the seventh of the dominant 7th chord? Wouldn't flattening the
> > seventh make more sense in regard to the 4-3 resolution?
> >
> > Kalle
>
> So in both of these cases, I hear the sharpened 7th as being more
> melodically effective. I don't know why. It could be because it adds
> harmonic tension, or because it's closer to the note from the scale,
> or, I dunno. I really don't. I think it's the latter, actually,
> because in mavila[9] I note that the 7/4 does a better job of being a
> dominant 7 than the thing which is "two fourths," which ends up being
> like 1050 cents.
>
> To me it just has to do with the effect that you want. For nice
> melodic stuff sharpen the 7th and for nice harmonic stuff flatten it.
> But man, that sharpened 7 is nice, though...
>
> -Mike
>

Your take on this is in keeping with the general conclusion reached by "common practice" music over the couple/several centuries since the possibility of tuning sevenths harmonically was brought up (and tested).

🔗Mike Battaglia <battaglia01@...>

On Tue, Feb 7, 2012 at 1:05 AM, lobawad <lobawad@...> wrote:
>
> "Barbershop uses harmonically tuned dominant sevenths. Barbershop is Western music. Therefore all Western music uses harmonically tuned dominant sevenths." is, appropriately, a fallacy of composition.
>
> No, pointing out your fallacy of composition does does not constitute my committing a no true Scotsman fallacy.

That's not what was said. You said that "dominant" was a function, and
that intoning dominant chords with 7/4's causes them to no longer have
the "dominant" function in a traditional sense. Barbershop harmony
serves as a counterexample to that.

There's no fallacy of composition, because the leap wasn't made to
state that -all- Western music tunes dominant 7 chords like that. If
that claim was made, it would have been the fallacy of composition.
Instead, the claim was made that -some- Western music tunes dominant 7
chords like that, which is an appropriate counterexample to your
argument.

Now it seems like what you're saying is that, just like one can use
4:5:6:7:9:11 to contrast something like lydian dominant, one can also
use 4:5:6:7 to contrast something like a dominant 7 chord. I don't
think that anyone will disagree with that claim, but I'm not sure why
you didn't just say it instead of saying that the two have different
"tonal functions" as thought everyone can immediately hear that.

> You guys clearly simply do not know what you are talking about. Out here in real life, no one would even blink if I said I wanted to be able to tune my minor sevenths in two different ways.

You said "tune my minor sevenths" in two different ways, thus
acknowledging that you perceive both as "types of" minor sevenths. If
you don't find that objectionable, it baffles me why you'd find it
objectionable that someone states that both chords are "types of"
dominant seventh chords.

-Mike

🔗lobawad <lobawad@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Feb 7, 2012 at 1:05 AM, lobawad <lobawad@...> wrote:
> >
> > "Barbershop uses harmonically tuned dominant sevenths. Barbershop is Western music. Therefore all Western music uses harmonically tuned dominant sevenths." is, appropriately, a fallacy of composition.
> >
> > No, pointing out your fallacy of composition does does not constitute my committing a no true Scotsman fallacy.
>
> That's not what was said. You said that "dominant" was a function, and
> that intoning dominant chords with 7/4's causes them to no longer have
> the "dominant" function in a traditional sense. Barbershop harmony
> serves as a counterexample to that.

No. Barbershop illustrates that if you do use harmonic sevenths in dominant functions, it is a very distinctive and different sound from traditional Western harmony.

>
> Now it seems like what you're saying is that, just like one can use
> 4:5:6:7:9:11 to contrast something like lydian dominant, one can also
> use 4:5:6:7 to contrast something like a dominant 7 chord. I don't
> think that anyone will disagree with that claim, but I'm not sure why
> you didn't just say it instead of saying that the two have different
> "tonal functions" as thought everyone can immediately hear that.

I mistakenly assumed that you guys are aware of the history of what we are talking about. So, have you looked up Fasch yet? Have you hit JSTOR for papers on the history of the seventh partial in Western common practice music?

But I don't think you guys will understand what I am saying until you separate musical verbs from musical nouns, so to speak.

🔗Mike Battaglia <battaglia01@...>

🔗lobawad <lobawad@...>

Think about verbs, not nouns, and you will see what I mean.

🔗clamengh <clamengh@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "clamengh" <clamengh@...> wrote:
> Hi all,
> I was rather intrigued by the recent discussion about counterpoint and 11 limit scales, so, after browsing scala archive, I'd have a question about
> temp31smith.scl -31 Gene Ward Smith, {225/224, 385/384, 1331/1323}, 11-limit TOP
> please.
> My question is rather simple:
> The first harmonics (if fundamental is C) correspond to:
> 3rd ~ G ~ 18
> 5th ~ E ~ 10
> 7th ~ A# or Bb; ~ 25
> 11th ~ F| ~ 14
> is this correct?
> I would like to adapt one of my existing pieces to the 11 limit framework.
> Many thanks,
> Claudi

This is "slender" temperament, which is stupid. I beg of you to use 31edo rather than slender. It makes no sense not to temper out the extra comma.

The harmonics you identified are correct, but only in that specific mode of the slender[31] scale, and three other modes (which are right next to it). In 31edo, they're correct in all modes.

31edo has 31 complete 11-limit hexads in it (or 62 if you count utonal ones). You know how many slender[31] has? *Zero*.

Here's a scala file you should use instead of temp31smith.scl:

! 31edo-top.scl
!
31EDO, 5-, 7-, and 11-limit TOP tuning (all identical)
31
!
38.75702
77.51403
116.27105
155.02807
193.78509
232.54210
271.29912
310.05614
348.81315
387.57017
426.32719
465.08421
503.84122
542.59824
581.35526
620.11227
658.86929
697.62631
736.38333
775.14034
813.89736
852.65438
891.41140
930.16841
968.92543
1007.68245
1046.43946
1085.19648
1123.95350
1162.71052
1201.46753

Keenan

🔗genewardsmith <genewardsmith@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@> wrote:
>
> > This is "slender" temperament, which is stupid.
>
> Slender is capable of much more accuracy than 31edo provides; tuning Slender[31] in 3\94 or 4\125 or 15\469 for that matter is not the same thing as 31 equal. And while you may not care about niceties of tuning, Cameron does. So no, Slender[31] is not "stupid"; it may or may not be what you want or need, but it isn't stupid.

If you care about the niceties of tuning, then use miracle. Or myna, or valentine, or wuerschmidt, or orwell. Or this new-fangled invention called Just Intonation. I could give you some great 31-note JI scales that have *more* consonant chords in them than this tempered scale.

At some point you have to ask - what's the point of tempering this? I'm making everything slightly out of tune... for what? You can have a scale with the same number of notes that's *perfectly* in tune, and have at the very least 6 different 11-limit hexads (rather than 0).

> > 31edo has 31 complete 11-limit hexads in it (or 62 if you count utonal ones). You know how many slender[31] has? *Zero*.
>
> Or else 31, depending on what approximations you are willing to accept.

But that's the whole point, isn't it? If you're willing to accept the slightly-off approximations that are not slender temperament, then you're treating it as 31edo anyway, so why not optimize it for that usage?

If you're *not* willing to accept the second-best approximations, then 31 notes is definitely not going to be enough for you. You need slender[63], or even more notes. Slender[63] might be non-stupid, but if anyone tells people to use slender[31] rather than 31edo then I officially hate them.

Keenan

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "Keenan Pepper" <keenanpepper@...> wrote:

> If you care about the niceties of tuning, then use miracle. Or myna, or valentine, or wuerschmidt, or orwell. Or this new-fangled invention called Just Intonation. I could give you some great 31-note JI scales that have *more* consonant chords in them than this tempered scale.

Show us the money.

> At some point you have to ask - what's the point of tempering this? I'm making everything slightly out of tune... for what? You can have a scale with the same number of notes that's *perfectly* in tune, and have at the very least 6 different 11-limit hexads (rather than 0).

Hexads are hardly the only measure. Slender is much better at no-fives 11-limit chords than it is at complete hexads, for instance, , and that may not be what Cameron wants but lots of people seem to cheer when "no fives" gets mentioned for some reason. There is also the question of circulation; you can regard Slender[31] as a circulating temperament. You keep trying to prove slender is stupid, and you have a problem with that since it actually isn't.

> > > 31edo has 31 complete 11-limit hexads in it (or 62 if you count utonal ones). You know how many slender[31] has? *Zero*.
> >
> > Or else 31, depending on what approximations you are willing to accept.
>
> But that's the whole point, isn't it? If you're willing to accept the slightly-off approximations that are not slender temperament, then you're treating it as 31edo anyway, so why not optimize it for that usage?

If you're willing to accept the off-approximations in Werckmeister III, why not just optimize it to 12edo? It depends on what you want.

🔗genewardsmith <genewardsmith@...>

🔗clamengh <clamengh@...>

🔗genewardsmith <genewardsmith@...>

🔗clamengh <clamengh@...>

🔗genewardsmith <genewardsmith@...>

🔗clamengh <clamengh@...>

genewardsmith>...I could probably answer that if I knew what the question was.

Oh, thanks, my question was a bit obscure indeed. Nevertheless, you just gave an answer to it. I meant 'major third' and 'natural seventh' intevals, i.e. I was seeking a tuning in which they are tuned as close as possible to 5* and 7*.
I'll probably start with undecimal meantone, maybe tempering in part the error on the major third.
Bests,
Claudi

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "clamengh" <clamengh@> wrote:
> >
> > genewardsmith> If you want pure 11s, 74 equal meantone is hard to beat.
> >
> > Many thanks. Does there exixt a 'best' compromise with 7s and 3s instead?
> > So far, the best result I got is: 18 fifths = 11*, but this implies (besides a narrow fifth) +2.87 cents for thirds (with three -15 cent wolves) and +4.13 for sevenths (with seven -11 cent wolves).
>
> There are two good mappings: 11-limit meantone, the one you remark on,
> and meanpop, the one where 13 fourths approximate 44. As for what is 'best', that depends on how you define best. One method is minimax tuning; that would mean choosing the tuning where 11/9 was tuned purely for 11-limit meantone, and choosing 1/4-comma meantone for meanpop.
>
> However, you asked about 7s and 3s, and I could probably answer that if I knew what the question was.
>