Yahoo Tuning Groups Ultimate Backup tuning Proportional Beating temperaments

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I'm shamelessly out of the loop here, but does anyone have any audio
> examples of these temperaments and what they sound like? Is the "equal
> beating" effect noticeable? Is the idea that for a chord like C-E-G,
> for example, the C-E would beat equally with the E-G (or in some equal
> proportion, like 2:1 or whatever)?

I'll give you a couple of examples.

For brat=4 the C-E and C-G beat in ratio 1:1, and the C-E and E-G beat in ratio 1:4.

For brat=2 the C-E and C-G beat in ratio 1:5, and the C-E and E-G beat in ratio 1:2.

Synchronous beating sounds something like a vibrato, whereby the chords seem to "sing" (provided, of course, that the beating is less than ~10 hz). Even seventh chords, such as C-E-G-B or B-D-F#-A, sound more harmonious with proportional beating.

> It sounds like a neat concept, I'm wondering if it actually works in practice.

It works very well indeed. Your best bet is to try it out with a retuned synthesizer or with the chromatic clavier in Scala. The best tuning I can suggest for this purpose is my "latest & greatest" temperament (extra)ordinaire,
/tuning/topicId_88708.html#88894
because it has 6 major triads (many more than your garden-variety well temperament) with slow-beating 3rds, all with simple brats:
F, C, & G major, brat = 4
D major brat = 2.75 (D-F# and D-A beat in ratio 1:2)
A major brat = 2.333.. (A-C# and A-E beat in ratio 1:3)
Bb major brat = 1.5 (Bb-F is just (Bb-D and D-F beat in ratio 2:3).

--George

🔗Carl Lumma <carl@...>

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

> > It sounds like a neat concept, I'm wondering if it actually
> > works in practice.
>
> It works very well indeed.

Is there any particular reason you believe this?

One thing that should send up a red flag regarding brats -- and
don't get me wrong, it's an intoxicating pursuit for the scale
theorist and I've spent a pretty hour on it myself -- is their
sensitivity to mistuning. Is a brat of 1.4999 any good? Where
do you draw the line? Of course we already encounter this
problem with the tuning of simple ratios in harmony (harmonic
entropy addresses it).

This list has a poor memory, but I've posted more than a few
synthesized examples of chords with simple and not-so-simple
brats. Listeners seemed to prefer chords where the plain old
tuning error was lower. In fact, at least one person commented
that the simple brats made beating worse, because its amplitude
range is greater. Dave Keenan admitted he'd been wrong about
brats in one of those threads.

-Carl

🔗Mike Battaglia <battaglia01@...>

> One thing that should send up a red flag regarding brats -- and
> don't get me wrong, it's an intoxicating pursuit for the scale
> theorist and I've spent a pretty hour on it myself -- is their
> sensitivity to mistuning. Is a brat of 1.4999 any good? Where
> do you draw the line? Of course we already encounter this
> problem with the tuning of simple ratios in harmony (harmonic
> entropy addresses it).

Right, and the even greater question in my mind is that of phase
coherence between the beats. Since we're dealing with rhythm now, not
pitch, phase becomes all-important. Compare the audible difference
between a 4:5:6 polyrhythm where all the rhythmic components start
synchronously at 1, and a 4:5:6 polyrhythm in which there is no phase
coherence between the three components. The second one will sound
nearly chaotic compared to the first one (although a bit of
periodicity will be detected nonetheless).

So a brat of 1.4999 will probably sound nearly identical to a brat of
1.5, but with the components shifting in and out of phase over time.
But even if the brat was 1.5, would it matter? What are the chances
you're going to get a perfectly synchronous rhythm from just hitting
the chord randomly anyway?

By that logic, 1.49999 would actually be better, since the phase
coherence would slowly circulate over time, going from "in phase" to
"out of phase" back to "in phase."

> This list has a poor memory, but I've posted more than a few
> synthesized examples of chords with simple and not-so-simple
> brats. Listeners seemed to prefer chords where the plain old
> tuning error was lower. In fact, at least one person commented
> that the simple brats made beating worse, because its amplitude
> range is greater. Dave Keenan admitted he'd been wrong about
> brats in one of those threads.

Are they posted in your folder? I can't find them. A quick search
didn't turn up anything on the first 6 pages or so.

-Mike

🔗Carl Lumma <carl@...>

🔗martinsj013 <martinsj@...>

🔗cameron <misterbobro@...>

You're not wrong, in my experience- beating seems to be a kind of... cusp? in the continuum between rhythm and pitch. As far as this contiuum between rhythm and pitch goes, cf. Cowell, Stockhausen, and every musician who has smoked too much grass and given the matter a lot of thought. Well of course you don't have to go into "art" to grok this continuum, it is a scientific reality as well. If I recall correctly, Gordon Reid wrote a very nice introduction to the concept in his Synth Secrets articles in the magazine SOS (available now for free on the web).

At any rate the phenomenon of proportional beating does not require locked phase and rigid tones, in fact it can be quite annoying when strictly synthesized in direct digital synthesis with dead straight and phase-locked tones. Just Intonation is also an unpleasant sensation synthesized so. You can verify these claims for yourself using Csound.

As far as examples as to the benefits of controlled beat rate proportions, Gene's recent piece is plenty enough to suggest that at least in the case of very-near-Just approximations, the phenomenon does have a unifying effect. An icing on the cake at least. In my experience it can be more than that, but I don't have the time to explain at this moment.

-Cameron Bobro

--- In tuning@yahoogroups.com, "martinsj013" <martinsj@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > ... phase coherence between the beats. Since we're dealing with rhythm now, not pitch, phase becomes all-important.
>
> This is a genuine question (since I feel a bit out of my depth): is that true?
> It seems to me that, since the beats are actually sinusoidal fluctuations in amplitude (aren't they?), the situation is not analogous to the polyrhythm case (see below), where each rhythm results from amplitude zero most of the time, then non-zero for a short time (i.e. almost an impulse).
>
> > Compare the audible difference between a 4:5:6 polyrhythm where all the rhythmic components start synchronously at 1, and a 4:5:6 polyrhythm in which there is no phase coherence between the three components. The second one will sound nearly chaotic compared to the first one (although a bit of periodicity will be detected nonetheless).
>
> Preparing myself to be told I'm wrong ...
>
> Steve M.
>

🔗Mike Battaglia <battaglia01@...>

> You're not wrong, in my experience- beating seems to be a kind of... cusp? in the continuum between rhythm and pitch. As far as this contiuum between rhythm and pitch goes, cf. Cowell, Stockhausen, and every musician who has smoked too much grass and given the matter a lot of thought. Well of course you don't have to go into "art" to grok this continuum, it is a scientific reality as well. If I recall correctly, Gordon Reid wrote a very nice introduction to the concept in his Synth Secrets articles in the magazine SOS (available now for free on the web).

Beating is just rhythm. There's no more "pitch" component to it than
there is a pitch component to a tom-tom when you hit it. Either the
peaks of the components are going to coincide, or they won't. If the
brats are whole-integer ratios then you're playing the lottery with
that every time you hit a chord.

> At any rate the phenomenon of proportional beating does not require locked phase and rigid tones, in fact it can be quite annoying when strictly synthesized in direct digital synthesis with dead straight and phase-locked tones. Just Intonation is also an unpleasant sensation synthesized so. You can verify these claims for yourself using Csound.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Wed, May 12, 2010 at 8:50 AM, martinsj013 <martinsj@...> wrote:
> I don't think I quite made my point clear. The polyrhythm may well sound chaotic because it is the result of shortlived sounds that are out of phase, but in the case of the sinusoidal "wavering", it may be much less of a problem if two or more of them are slightly out of phase. Obviously, I don't know.

That might well be true, that the envelope of the sound might hide
some of this and make it less noticeable. All I know is that if you're
playing on a digital keyboard and the sound you're playing on has a
slight tremolo - let's say at 1 Hz - and if you don't hit all the
notes at the same time, you get a somewhat chaotic result (unless the
patch is set up to just apply the tremolo to the mixed signal instead
of each note individually).

It sounds pretty neat sometimes, but the point is that you're playing
roulette whenever you hit a chord with "equal beating" set up. It
might not be that big a deal, but it's something people should be
aware of. You're not going to get a perfect "hot cup of tea" 3/2
pattern just because the brat is 1.5 or whatever.

-Mike

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
>
> > > It sounds like a neat concept, I'm wondering if it actually
> > > works in practice.
> >
> > It works very well indeed.
>
> Is there any particular reason you believe this?

Yes. I've gone to the trouble of putting a few proportional-beating temperaments on my Scalatron and playing various chord progressions, which is a much better indication of how they'll work out in practice than listening to chords in isolation.

I was completely unaware that I was hearing a proportional-beating temperament the first time I played in one, back in the 1970's. I had been trying to develop a 19-tone well-temperament over the previous several years, with two objectives: to get 5-limit triads with less error in the fifths, and to get better-sounding (major, minor, & especially harmonic) seventh chords (which I believe are 19's greatest weakness). At first I was making the largest 5ths around 5.4 cents (~1/4-comma meantone) on the near side of the 5th-circle, which made me very unhappy with the very narrow 5ths on the far side. I later tried something closer to 19-equal, with the 5ths on the near side sized (6.341 cents narrow) making several of the diminished 4ths (C#-F, G#-C, D#-G, A#-D, E#-A) an exact 7:9, which results in more convincing harmonic 7th chords. I was pleasantly surprised that the triads (major, minor, & subminor) sounded much more like those of 31-equal than of 19-equal, besides having a "singing" quality. It wasn't until a few years ago that I learned that the chain of 5ths in the near side of this well-temperament is very close to Erv Wilson's meta-meantone temperament (5ths 6.325 cents narrow), which gives 1:1:1 (5th:M3,m3) synchronous beat rates in root-position major triads, which accounts for the "singing" quality of my well-temperament. (I have since modified my well-temperament so that the best 5ths are exact meta-meantone, which, for all practical purposes, makes no audible difference.) Another thing that really sets this temperament apart from both 19-equal & 31-equal is that both the M3 & m3 are slow-beating. (Another plus: since some of the diminished 4ths are almost exactly 7:9, the 6:7:9 triads that contain these are very close to proportional-beating.)

Another temperament I tried on my Scalatron, more recently, is my 12-tone temperament (extra)ordinaire (12-TX), which now has the F, C, & G root-position major triads with 1:1:4 (5th:M3,m3) synchronous beat rates. These triads also seem to "sing". Although the minor 3rd is not slow-beating (as in 19-WT), the two slower-beating intervals (5th & M3) tend to mask the faster-beating minor 3rd, so it is not as prominent. Another thing that needs to be emphasized (again) is that, since both major & minor triads are proportional-beating, the larger chords that combine them (M7, m7, M9, etc.) tend to avoid the "janging" effect of a conglomeration of unsynchronized beat rates. This is something you can't fully appreciate until you sit down and play it on a keyboard.

Of course, closely approximated brats (which is what I have on the Scalatron) are okay, just like near-JI is good. In fact, you might prefer that to exact brats (just as I prefer the near-JI of a microtemperament to exact JI), because it mitigates a kind of "antiseptic" or synthetic quality in the sound.

As I observed, a greater amplitude resulting from a 1:1 5th:M3 beat ratio has the advantage of masking the quicker beating of the minor 3rd, just as a vibrato masks the rapid beating of 3rds in 12-equal. So you can turn a "flaw" into a feature: if the beating is slow enough, it's a kind of vibrato, and if it's synched, then it'll sing.

As for wrong conclusions: in the past I subscribed to the idea that a 12-tone circulating temperament (a/k/a well-temperament) should have the combined error of the 5-limit consonances equal to the theoretical minimum -- thus no 5ths wider than just. Now I've come to the conclusion that 5ths a few cents wider than just are desirable on the far side of a 12-tone circulating temperament, because they tend to mask the rapidly beating 3rds in triads and thereby make them less objectionable, which gives me the ability to have a greater number of low-error triads on the near side -- extraordinaire, n'est pas?

--George

🔗Ozan Yarman <ozanyarman@...>

These explanations are satisfactory from my point of view, and I
concur with the observations of George.

Oz.

✩ ✩ ✩
www.ozanyarman.com

On May 13, 2010, at 7:00 AM, gdsecor wrote:

>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>>
>> --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
>>
>>>> It sounds like a neat concept, I'm wondering if it actually
>>>> works in practice.
>>>
>>> It works very well indeed.
>>
>> Is there any particular reason you believe this?
>
> Yes. I've gone to the trouble of putting a few proportional-beating
> temperaments on my Scalatron and playing various chord progressions,
> which is a much better indication of how they'll work out in
> practice than listening to chords in isolation.
>
> I was completely unaware that I was hearing a proportional-beating
> temperament the first time I played in one, back in the 1970's. I
> had been trying to develop a 19-tone well-temperament over the
> previous several years, with two objectives: to get 5-limit triads
> with less error in the fifths, and to get better-sounding (major,
> minor, & especially harmonic) seventh chords (which I believe are
> 19's greatest weakness). At first I was making the largest 5ths
> around 5.4 cents (~1/4-comma meantone) on the near side of the 5th-
> circle, which made me very unhappy with the very narrow 5ths on the
> far side. I later tried something closer to 19-equal, with the 5ths
> on the near side sized (6.341 cents narrow) making several of the
> diminished 4ths (C#-F, G#-C, D#-G, A#-D, E#-A) an exact 7:9, which
> results in more convincing harmonic 7th chords. I was pleasantly
> surprised that the triads (major, minor, & subminor) sounded much
> more like those of 31-equal than of 19-equal, besides having a
> "singing" quality. It wasn't until a few years ago that I learned
> that the chain of 5ths in the near side of this well-temperament is
> very close to Erv Wilson's meta-meantone temperament (5ths 6.325
> cents narrow), which gives 1:1:1 (5th:M3,m3) synchronous beat rates
> in root-position major triads, which accounts for the "singing"
> quality of my well-temperament. (I have since modified my well-
> temperament so that the best 5ths are exact meta-meantone, which,
> for all practical purposes, makes no audible difference.) Another
> thing that really sets this temperament apart from both 19-equal &
> 31-equal is that both the M3 & m3 are slow-beating. (Another plus:
> since some of the diminished 4ths are almost exactly 7:9, the 6:7:9
> triads that contain these are very close to proportional-beating.)
>
> Another temperament I tried on my Scalatron, more recently, is my 12-
> tone temperament (extra)ordinaire (12-TX), which now has the F, C, &
> G root-position major triads with 1:1:4 (5th:M3,m3) synchronous beat
> rates. These triads also seem to "sing". Although the minor 3rd is
> not slow-beating (as in 19-WT), the two slower-beating intervals
> (5th & M3) tend to mask the faster-beating minor 3rd, so it is not
> as prominent. Another thing that needs to be emphasized (again) is
> that, since both major & minor triads are proportional-beating, the
> larger chords that combine them (M7, m7, M9, etc.) tend to avoid the
> "janging" effect of a conglomeration of unsynchronized beat rates.
> This is something you can't fully appreciate until you sit down and
> play it on a keyboard.
>
>> One thing that should send up a red flag regarding brats -- and
>> don't get me wrong, it's an intoxicating pursuit for the scale
>> theorist and I've spent a pretty hour on it myself -- is their
>> sensitivity to mistuning. Is a brat of 1.4999 any good? Where
>> do you draw the line? Of course we already encounter this
>> problem with the tuning of simple ratios in harmony (harmonic
>> entropy addresses it).
>
> Of course, closely approximated brats (which is what I have on the
> Scalatron) are okay, just like near-JI is good. In fact, you might
> prefer that to exact brats (just as I prefer the near-JI of a
> microtemperament to exact JI), because it mitigates a kind of> "antiseptic" or synthetic quality in the sound.
>
>> This list has a poor memory, but I've posted more than a few
>> synthesized examples of chords with simple and not-so-simple
>> brats. Listeners seemed to prefer chords where the plain old
>> tuning error was lower. In fact, at least one person commented
>> that the simple brats made beating worse, because its amplitude
>> range is greater. Dave Keenan admitted he'd been wrong about
>> brats in one of those threads.
>
> As I observed, a greater amplitude resulting from a 1:1 5th:M3 beat
> ratio has the advantage of masking the quicker beating of the minor
> 3rd, just as a vibrato masks the rapid beating of 3rds in 12-equal.
> So you can turn a "flaw" into a feature: if the beating is slow
> enough, it's a kind of vibrato, and if it's synched, then it'll sing.
>
> As for wrong conclusions: in the past I subscribed to the idea that
> a 12-tone circulating temperament (a/k/a well-temperament) should
> have the combined error of the 5-limit consonances equal to the > theoretical minimum -- thus no 5ths wider than just. Now I've come
> to the conclusion that 5ths a few cents wider than just are
> desirable on the far side of a 12-tone circulating temperament,
> because they tend to mask the rapidly beating 3rds in triads and
> thereby make them less objectionable, which gives me the ability to
> have a greater number of low-error triads on the near side --
> extraordinaire, n'est pas?
>
> --George
>
>
>
>
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🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

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

> > > It works very well indeed.
> >
> > Is there any particular reason you believe this?
>
> Yes. I've gone to the trouble of putting a few proportional-
>beating temperaments on my Scalatron and playing various chord
>progressions, which is a much better indication of how they'll
>work out in practice than listening to chords in isolation.

I've improvised with MIDI relaying and a regular keyboard,
retuned MIDI files with Scala, and tuned real pianos, to both
proportional-beating and normal WTs. I can't say I notice a
difference, other than differences in error. I did discern
a difference with the lab-grade synthesized chords, and the
proportional-beating versions sounded *worse* (because the
beating is louder).

> As I observed, a greater amplitude resulting from a 1:1 5th:M3
> beat ratio has the advantage of masking the quicker beating of
> the minor 3rd, just as a vibrato masks the rapid beating of 3rds
> in 12-equal. So you can turn a "flaw" into a feature: if the
> beating is slow enough, it's a kind of vibrato, and if it's
> synched, then it'll sing.

I'm trying to keep an open mind. I have liked metameantone in
the past, maybe just a pinch more than I should considering its
narrow generator. But I think I was psyching myself out, and
even if not, proportional beating isn't necessarily responsible.

> As for wrong conclusions: in the past I subscribed to the idea
> that a 12-tone circulating temperament (a/k/a well-temperament)
> should have the combined error of the 5-limit consonances equal
> to the theoretical minimum -- thus no 5ths wider than just. Now
> I've come to the conclusion that 5ths a few cents wider than
> just are desirable on the far side of a 12-tone circulating
> temperament, because they tend to mask the rapidly beating 3rds
> in triads and thereby make them less objectionable, which gives
> me the ability to have a greater number of low-error triads on
> the near side -- extraordinaire, n'est pas?

Hm. I will say I'm not a believer in circulating temperaments
in the first place. The sourness of the distant chords isn't
worth it, even when there's no harmonic waste. But there's
still proportional-beating ETs to consider (and I have).

-Carl

🔗cameron <misterbobro@...>

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

> Beating is just rhythm. There's no more "pitch" component to it than
> there is a pitch component to a tom-tom when you hit it. Either the
> peaks of the components are going to coincide, or they won't. If the
> brats are whole-integer ratios then you're playing the lottery with
> that every time you hit a chord.

If we were talking about white noise steeply gated at haptic rates, we'd have something we could call "just" rhythm. But the rhythm-pitch continuum is real, just think about it some.

Although it is actually roughness- beating accelerated beyond the
rates we're discussing in proportional beating- which most clearly lies in that border region between rhythm and pitch, it is obvious that our perception of proportional beating is also based on RATES just as our perception of pitch is. (NB. we're NOT talking about the beating of a single isolated dyad! which can regarded as purely rhythmic.) If this
were not the case, we would percieve NO difference between simply proportioned beat rates and beat rates in complex/irrational proportions in any situation other than that of strong phase alignment.

-Cameron Bobro

🔗Mike Battaglia <battaglia01@...>

🔗cameron <misterbobro@...>

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

> The border region between rhythm and pitch is somewhere around 20 Hz.

No kidding? Obviously I know that, LOL.

> What we have here is a tone (or a series of tones) with their
> amplitudes being modulated rhythmically.

No kidding? Sorry I have to be sarcastic, I just find your assumption
that I don't the basics ludicrous, when it is obvious that I'm
extrapolating from the basics.

>In that sense, a conga drum
> pattern is also on the border region between rhythm and pitch.

Which it is! The drum school of a friend of mine who is an excellent
drummer (prefers fusion) is called "singing drums". This continuum is
real, as I said. The feel for this is a sine qua non for Eastern
drummers of course, an Albanian percussionist I worked with many years
ago showed me this, very illuminating.

Now, explain to me how it is that proportional beating without strong
phase synchronization could be perceptable at all if it were not true
that we are percieving and comparing RATES of beating, just as we
percieve pitch as rates.

-Cameron Bobro

🔗Mike Battaglia <battaglia01@...>

On Thu, May 13, 2010 at 4:19 AM, cameron <misterbobro@...> wrote:
>
> > In that sense, a conga drum
> > pattern is also on the border region between rhythm and pitch.
>
> Which it is! The drum school of a friend of mine who is an excellent drummer (prefers fusion) is called "singing drums". This continuum is real, as I said. The feel for this is a sine qua non for Eastern drummers of course, an Albanian percussionist I worked with many years ago showed me this, very illuminating.

There's no "continuum" in this example. The fact that a conga drum
pattern contains rhythmic and pitched accents has nothing to do with
the 20 Hz threshold of hearing. We're dealing with a (weakly) pitched
instrument being played in a rhythmic fashion.

> Now, explain to me how it is that proportional beating without strong phase synchronization could be perceptable at all if it were not true that we are percieving and comparing RATES of beating, just as we percieve pitch as rates.

Because we don't perceive pitch as rates, that's why.

If your point is that we can perceive periodicity in polyrhythms due
to the same neural mechanism that allows us to recognize periodicity
in intervals -- the virtual fundamental mechanism -- then my only
response is... maybe.

Or if your point was more philosophical, that rhythm and pitch arise
from the same fundamental concept of periodicity and frequency, then
okay.

But if what you're saying is that "beating" is some sort of
psychoacoustic phenomenon that is neither rhythm nor pitch, but some
strange nether-state in between, then that's not quite it. It's just a
frequency being modulated in volume rhythmically.

Keep in mind that "beating" and "amplitude modulation" are equivalent.
If you're at home, listening to a 440 Hz tone coming out of your
speaker system, and you turn the volume knob on and off in perfectly
sinusoidal fashion every second or so, you have just turned your
original signal into 439 Hz, 440 Hz, and 441 Hz. Gadzooks! Now that's
beating.

So yes, the end result is the intersection of rhythm and pitch in that
it's a pitch being modulated... rhythmically. Was your point that the
rhythm arises out of two presumably "static" pitches colliding? Maybe
I'm misunderstanding.

-Mike

🔗cameron <misterbobro@...>

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

> > Now, explain to me how it is that proportional beating without
>strong phase synchronization could be perceptable at all if it were
>not true that we are percieving and comparing RATES of beating, just
>as we percieve pitch as rates.
>
> Because we don't perceive pitch as rates, that's why.

Perception of pitch is based primarily on a RATE: usually measured in
cycles per second, it is simply a frequency of vibration. Higher, lower
: faster, slower.

Notice that I did not say that perception of pitch is ONLY based on rate
(that wouldn't be true, there are amplitude and spectral considerations
as well), just as I did not say that we percieve beats as pitched tones.
We don't percieve beats as pitched tones but we do percieve proportions
between beat RATES. Obviously: would you like to claim that there is no
audible difference between fast beating and slow beating? We don't need
phase synchronization to percieve one beating as faster than another,
just as we don't need phase synchronization to percieve one pitch as
higher than another: the rate alone gives us this information.

Notice that when you break it down like this- and actually understand
it- it is strongly implied that proportional beat rates do not need to
be "perfect" in order to be felt/effective, just as a Just interval
doesn't have to be "perfect" in order to sound Just (outside of specific
artistic usages in which "perfection" is more or less achievable, and
deemed important).

-Cameron Bobro

🔗Mike Battaglia <battaglia01@...>

On Thu, May 13, 2010 at 8:40 AM, cameron <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > Now, explain to me how it is that proportional beating without >strong phase synchronization could be perceptable at all if it were >not true that we are percieving and comparing RATES of beating, just >as we percieve pitch as rates.
> >
> > Because we don't perceive pitch as rates, that's why.
>
> Perception of pitch is based primarily on a RATE: usually measured in cycles per second, it is simply a frequency of vibration. Higher, lower : faster, slower.

Pitches aren't usually perceived as "rates" of anything. When we hear
a static pitch, we aren't hearing anything fluctuate over time. The
fact that pitch physiologically stems from periodic sound waves is
quite counterintuitive for most people at first.

However, rhythm is, perceptually, entirely about rate, unlike pitch.
And phase is all important in terms of rhythm, and almost completely
irrelevant in terms of pitch.

> Notice that I did not say that perception of pitch is ONLY based on rate (that wouldn't be true, there are amplitude and spectral considerations as well), just as I did not say that we percieve beats as pitched tones. We don't percieve beats as pitched tones but we do percieve proportions between beat RATES. Obviously: would you like to claim that there is no audible difference between fast beating and slow beating? We don't need phase synchronization to percieve one beating as faster than another, just as we don't need phase synchronization to percieve one pitch as higher than another: the rate alone gives us this information.

I don't know if we perceive proportions between beat rates when the
phase is all out of whack. It's pretty easy to figure out a 4:5:6:7
polyrhythm if they're all phase-locked to coincide at beat 1. If not,
I doubt most people could figure out that it's a 4:5:6:7 polyrhythm,
although they might be able to figure out the recurring pattern if you
give them long enough.

> Notice that when you break it down like this- and actually understand it- it is strongly implied that proportional beat rates do not need to be "perfect" in order to be felt/effective, just as a Just interval doesn't have to be "perfect" in order to sound Just (outside of specific artistic usages in which "perfection" is more or less achievable, and deemed important).

Certainly, but I still don't understand why you think that beating is
somewhere within the nebulous middle ground of pitch and rhythm.

-Mike

🔗Michael <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

🔗Mario Pizarro <piagui@...>

The progression of musical cells has rejected 1.75, 3.5, 7, 11, 13... + prime numbers. How it is possible to prove that these numbers are not non--consonance makers?

Regards

Mario Pizarro
Lima, May 13
----- Original Message -----
From: Michael
To: tuning@yahoogroups.com
Sent: Thursday, May 13, 2010 5:10 PM
Subject: [tuning] Scale NOT based on achieving perfect 5ths or near-perfect 5ths

What are some examples of scales (not tunings, but scales) that don't revolve around the idea of maintaining all ratios between about 7/5 and 8/5 as perfect fifths?

I of course realize fifths are good for basic triads...but also sense there are many other intervals within that range IE 50/33, 13/9, 22/15, and others that sound very interesting for other types of chords and am sure I'm not the only one who has messed around with them but don't know where to look to find works of others who've deal with generating scales both from non-5th interval and/or which don't "cross" near them.

__________ Información de ESET NOD32 Antivirus, versión de la base de firmas de virus 5113 (20100513) __________

ESET NOD32 Antivirus ha comprobado este mensaje.

http://www.eset.com

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http://www.eset.com

🔗Michael <djtrancendance@...>

MikeB>"That's not quite what a flanger does."
I've written Flanger DSP code myself simply by taking a copy of a sound and mixing it with the same sound with a slight moving delay. Heck, I can even make a non-moving flanger sound by playing the same note over itself with slight delay in a MIDI file.

So please explain...how does the nature of a flanger fail to prove how phase effects sense of pitch? I figure it may indeed make certain frequencies either cancel out some via phase cancellations or louden them by the opposite...but that's still a change in apparent pitch, correct?

________________________________
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Thu, May 13, 2010 6:25:55 PM
Subject: Re: [tuning] Re: Proportional Beating temperaments

> I wouldn't go that far. Changes in phase are heard as changes in pitch...and it you take two copies of a sound with any sort of frequency modulation of beating going on and phase-shift one, the sense of pitch can be altered a good deal "even" with a constant/non- moving phase shift (a non-moving flanger effect being one obvious example of this).

That's not quite what a flanger does.

-Mike

🔗gdsecor <gdsecor@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, May 13, 2010 at 12:00 AM, gdsecor <gdsecor@...> wrote:
> >
> > Yes. I've gone to the trouble of putting a few proportional-beating temperaments on my Scalatron and playing various chord progressions, which is a much better indication of how they'll work out in practice than listening to chords in isolation.
>
> Do you have any listening examples of these temperaments or of any of
> the other ones listed? I messed around with your meantone and liked it
> quite a bit, I'm curious to hear how it would sound in practice.

I guess that you mean my 19-tone well-temperament, based on Wilson's meta-meantone. I should point out that it's actually a subset of my 19+3 well temperament, which I developed as a triple-purpose tuning that could be implemented on instruments of fixed pitch. I introduced it on the tuning list 8 years ago as the solution to a challenge I posed:
/tuning/topicId_38076.html#38287

The Scala listing is:

! secor_19p3.scl
!
George Secor's 19+3 well temperament (v.0) with ten ~5/17-comma (equal-beating) fifths and 3 pure 9:11
! Aux=1,10,19
22
!
34.29925
69.41306
131.54971
191.26088
260.67394
317.95963
382.52175
451.93481
504.36956
538.66882
573.78263
638.34474
695.63044
765.04350
824.75467
886.89131
956.30438
1011.16460
1043.03838
1078.15219
1145.13978
2/1

Anyway to answer your question, yes, I do have a sound file of the composition I entered in the Untwelve competition last year. I originally wrote this for a 13-limit near-just tuning, using a constant-structure 9-tone scale, with E minor as the "tonic" triad: 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 1/1, 9/8, 7/6. The scale is clearly presented by all of the tones being played consecutively in the introduction and interlude.

The following link is a slightly modified version of the piece, in the original tuning, with the first 3 measures changed to 5-limit harmony in order to make the introduction of the 13-limit intervals less abrupt. Listen to this first in the near-just tuning:
http://xenharmony.wikispaces.com/space/showimage/Clouds-29HTT4.ogg

Then listen to the same thing retuned to 19+3:
http://xenharmony.wikispaces.com/space/showimage/Clouds-19p3-4.ogg

The original (near-just) tuning has fifths tempered ~1.6 cents wide and the harmonic 7th (4:7) exact, while the 19+3 temperament has fifths ~6.3 cents narrow and the harmonic 7th ~12.5 cents narrow. Would you say that the difference is more or less noticeable than you expected?

--George

🔗Mike Battaglia <battaglia01@...>

On Thu, May 13, 2010 at 10:17 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"That's not quite what a flanger does."
> I've written Flanger DSP code myself simply by taking a copy of a sound and mixing it with the same sound with a slight moving delay. Heck, I can even make a non-moving flanger sound by playing the same note over itself with slight delay in a MIDI file.

That has nothing to do with what we're talking about here and is only
tangentially related to the general concept of "phase".

> So please explain...how does the nature of a flanger fail to prove how phase effects sense of pitch? I figure it may indeed make certain frequencies either cancel out some via phase cancellations or louden them by the opposite...but that's still a change in apparent pitch, correct?

To take what you're saying to an absurd extreme, when you take the
signal and invert its polarity, and add it back to the original, it
cancels out entirely and you get silence, so therefore changes in
phase bring silence.

In reality, what happens when you add a signal to a delayed version of
itself is you get feedforward comb filtering, and notches appear in
the spectrum. This has nothing to do with the "phase" of each pitch,
and to make that connection is... a stretch.

If you take a signal and take every single component and shift it 90,
or 180, or however many degrees out of phase you want, you will hear
absolutely no difference. The only time you'll hear a difference is if
the graph of the phase response isn't linear across the board.

-Mike

🔗Michael <djtrancendance@...>

Me>"Heck, I can even make a non-moving flanger sound by playing the same note over itself with slight delay in a MIDI file."

MikeB>"That has nothing to do with what we're talking about here and is only
tangentially related to the general concept of "phase"."
Ok then please clarify, what type of phase are you talking about as supposedly not effecting pitch?

>"In reality, what happens when you add a signal to a delayed version of
itself is you get feedforward comb filtering, and notches appear in
the spectrum. This has nothing to do with the "phase" of each pitch,
and to make that connection is... a stretch."
I get it...but when I hear such an effect "even" this canceling out of phase brings focus to different notes as certain harmonics become canceled out and stop masking other ones, thus bringing new "previously hidden" tones into focus...correct? So even if that's not mathematically what's going on it seems your ear would focus on different pitches.

>"If you take a signal and take every single component and shift it 90,
or 180, or however many degrees out of phase you want, you will hear
absolutely no difference."
Right...assuming you only have one sound and you are not, say, shifting the phase of one sound vis-a-vis another. It's relative phase (comparing phases of sounds relative to each other) and not absolute phase that you hear as pitch. But, unless you're talking exclusively about absolute phase...I don't see how phase doesn't effect sense of pitch, as relative phase effects sense of pitch.

>"The only time you'll hear a difference is if the graph of the phase response isn't linear across the board."
Meaning the rotation is different for different frequencies in the same sound, correct?

________________________________
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Fri, May 14, 2010 12:26:47 AM
Subject: Re: [tuning] Re: Proportional Beating temperaments

On Thu, May 13, 2010 at 10:17 PM, Michael <djtrancendance@...m> wrote:
>
> MikeB>"That's not quite what a flanger does."
> I've written Flanger DSP code myself simply by taking a copy of a sound and mixing it with the same sound with a slight moving delay. Heck, I can even make a non-moving flanger sound by playing the same note over itself with slight delay in a MIDI file.

That has nothing to do with what we're talking about here and is only
tangentially related to the general concept of "phase".

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, May 14, 2010 at 2:05 AM, Michael <djtrancendance@...> wrote:
>
> Me>"Heck, I can even make a non-moving flanger sound by playing the same note over itself with slight delay in a MIDI file."
>
> MikeB>"That has nothing to do with what we're talking about here and is only
> tangentially related to the general concept of "phase"."
> Ok then please clarify, what type of phase are you talking about as supposedly not effecting pitch?

The concept of altering the phase of the spectrum while leaving
magnitude unaltered. On the one hand, it can matter quite a bit (this
is basically how reverb works, for example). On the other hand, it
might not (altering the phase of everything 90 degrees, for example).

> >"In reality, what happens when you add a signal to a delayed version of
> itself is you get feedforward comb filtering, and notches appear in
> the spectrum. This has nothing to do with the "phase" of each pitch,
> and to make that connection is... a stretch."
> I get it...but when I hear such an effect "even" this canceling out of phase brings focus to different notes as certain harmonics become canceled out and stop masking other ones, thus bringing new "previously hidden" tones into focus...correct? So even if that's not mathematically what's going on it seems your ear would focus on different pitches.

OK, but the canceling has to do with you adding the
phase-shifted/delayed version back to the original signal, not the
phase shifting itself. I'm not sure why you brought the latter up
since the original discussion was about the importance of phase in the
rhythmic aspects of music, and we aren't going to be adding a
phase-shifted version of some equal beating triad to the original in
any sense (although it could happen).

> >"If you take a signal and take every single component and shift it 90,
> or 180, or however many degrees out of phase you want, you will hear
> absolutely no difference."
> Right...assuming you only have one sound and you are not, say, shifting the phase of one sound vis-a-vis another.

If you change the phase of all of the frequencies differently, you
won't hear a difference unless the group delay (derivative of phase)
isn't a constant value across the board. And if we're talking about a
chord that you're playing and holding, you are definitely not going to
hear a difference at all, ever, no matter what, except for the onset
and release of the chord.

> It's relative phase (comparing phases of sounds relative to each other) and not absolute phase that you hear as pitch. But, unless you're talking exclusively about absolute phase...I don't see how phase doesn't effect sense of pitch, as relative phase effects sense of pitch.

OK, but we're getting into obscure facets of signal processing that
aren't really relevant anymore and somewhat off-topic. Yes, to give
you trivial examples proving your point, the only difference between
an impulse, white noise, and a chirp (sine sweep) is the phase
response. There are similar principles that apply to rhythm as well.
My point was that the human ear can't detect the difference between a
4:5:6 chord where all of the components are in vs out of phase with
one another, except perhaps for some clever stuff happening with
attack and release of the chord.

-Mike

🔗Mike Battaglia <battaglia01@...>

> Anyway to answer your question, yes, I do have a sound file of the composition I entered in the Untwelve competition last year. I originally wrote this for a 13-limit near-just tuning, using a constant-structure 9-tone scale, with E minor as the "tonic" triad: 5/4, 11/8, 3/2, 13/8, 7/4, 15/8, 1/1, 9/8, 7/6. The scale is clearly presented by all of the tones being played consecutively in the introduction and interlude.
>
> The following link is a slightly modified version of the piece, in the original tuning, with the first 3 measures changed to 5-limit harmony in order to make the introduction of the 13-limit intervals less abrupt. Listen to this first in the near-just tuning:
> http://xenharmony.wikispaces.com/space/showimage/Clouds-29HTT4.ogg
>
> Then listen to the same thing retuned to 19+3:
> http://xenharmony.wikispaces.com/space/showimage/Clouds-19p3-4.ogg
>
> The original (near-just) tuning has fifths tempered ~1.6 cents wide and the harmonic 7th (4:7) exact, while the 19+3 temperament has fifths ~6.3 cents narrow and the harmonic 7th ~12.5 cents narrow. Would you say that the difference is more or less noticeable than you expected?

It wasn't that noticeable to me really, but I think there are places
where it would have a use. I think, for example, that it might sound
amazing if an overdriven guitar were tuned to a scale like this. All
of the nonlinearity going on would probably make a whole hierarchy of
beating, so that a brat of 1.5 becomes brats of 1.5, 3, 4.5, and so
on. Which might be a neat sound.

-Mike

🔗cameron <misterbobro@...>

--- In tuning@yahoogroups.com <mailto:tuning@yahoogroups.com> , Mike
Battaglia <battaglia01@...> wrote:
>
> On Thu, May 13, 2010 at 8:40 AM, cameron <misterbobro@...> wrote:
> >
> > --- In tuning@yahoogroups.com <mailto:tuning@yahoogroups.com> , Mike
Battaglia <battaglia01@> wrote:

>
> Pitches aren't usually perceived as "rates" of anything. When we >hear
> a static pitch, we aren't hearing anything fluctuate over time. The
> fact that pitch physiologically stems from periodic sound waves is
> quite counterintuitive for most people at first.

Oh, I see the source of the communication problem now. You're thinking
in terms of the psychoacoustic mechanism, HOW we percieve, while I'm
thinking in terms of WHAT we percieve. Obviously I'm aware of the
location theory and all that, but I try to leave unproven theory out,
and concentrate on things we "know" (as far as we "know" anything). No
I'm not claiming that our psychoacoustic mechanism is based on comparing
rates against an internal clock or something like that. For all I know
such a strange mechanism might very well be in place as part of our
perception, beats me, but the how of it is not important to what I'm
saying.

We do (whatever the mechanism) indeed distinguish and even identify
rates, frequencies of vibrations. 100 Hz sounds different in a concrete
and consistent way than 200 Hz does. Whether there is any direct
perception (comparison against internal clock for example) of rates in
the psychoacoustic mechanism is not relevant to what I'm saying.

>
> However, rhythm is, perceptually, entirely about rate, unlike pitch.
> And phase is all important in terms of rhythm, and almost completely
> irrelevant in terms of pitch.

Now, think over what you just said. If you do, at some point, perceive
proportional beating in an environment WITHOUT strong phase
synchronization, that means that proportional beating is not perceived
as a purely rhythmic phenomenon, even if beating in a single dyad is.

Just as phase is pretty much irrelevant in terms of pitch, it would
clearly have to be pretty much irrelevant in terms of proportional
beating were we to find that proportional beating is perceptible in
cases with random phase occurrances. So, this rhythmic phenomenon- and
beating is clearly rhythmic in the case of a lone dyad- would clearly be
sharing a property of PITCH (insensitivity to phase).

Now, on the empirical level at least (regardless of our perception
mechanism!), rhythm and pitch most certainly ARE part of a continuum, a
fact easily demonstrated by moving the frequency of an oscillator from
haptic through to ultrasonic rates. So, if we have something which seems
to be a clearly rhythmic phenomenon at first, but which demonstrates
phase insensitivity, which is "wrong" for rhythm but "right" for pitch,
is it not reasonable to think of this phenomenon as occuring in a fuzzy
zone on the rhythm-pitch continuum?

Of course, another explanation could be that the phenomenon is actually
a combination of phenomena, and therefore exhibits these
characteristics. I'm completely open to that explanation as well.

> I don't know if we perceive proportions between beat rates when the
> phase is all out of whack. It's pretty easy to figure out a 4:5:6:7
> polyrhythm if they're all phase-locked to coincide at beat 1. If not,
> I doubt most people could figure out that it's a 4:5:6:7 polyrhythm,
> although they might be able to figure out the recurring pattern if you
> give them long enough.

Well there you go. You start out assuming that the phenomenon can only
be percieved as a distinct polyrhythm. And this would be true if
proportional beating were indeed a strictly rhythmic phenomenon. Your
reasoning is fine there. It is identical to my assumption when I first
heard of "proportional beating". I thought, yeah right, that's only
going to work when the beating takes place between very low ordered
partials, and only in a phase-locked synthetic envirnoment.

Upon listening, I found that I was wrong. And so I was forced to realize
that proportional beating is NOT a strictly rhythmic phenomenon, but
exhibits the pitch-like property of phase insensitivity. Therefore it
must either lie in fuzzy region in the rhythm-pitch continuum, or be
some kind of compound phenomenon.

-Cameron Bobro

🔗Mike Battaglia <battaglia01@...>

On Fri, May 14, 2010 at 3:56 AM, cameron <misterbobro@...> wrote:
>
> Oh, I see the source of the communication problem now. You're thinking in terms of the psychoacoustic mechanism, HOW we percieve, while I'm thinking in terms of WHAT we percieve.

Er, you have that backwards. I'm saying that, in terms of "what" we
perceive, pitch has nothing to do with rates or of any periodic or
repeating pattern over time. In terms of the mechanism that causes the
sensation of pitch to arise, or the "how" we perceive pitch, rates and
so on are obviously the name of the game.

My point was that pitches, perceptually, are static objects that float
around ones consciousness. We don't perceive them as having anything
to do with rates, as that information is discarded by the time it
reaches our brain. Just like we don't perceive colors as having
anything to do with rates. The only thing we really, honestly perceive
as having directly to do with rates is rhythm.

> Obviously I'm aware of the location theory and all that, but I try to leave unproven theory out, and concentrate on things we "know" (as far as we "know" anything). No I'm not claiming that our psychoacoustic mechanism is based on comparing rates against an internal clock or something like that. For all I know such a strange mechanism might very well be in place as part of our perception, beats me, but the how of it is not important to what I'm saying.

What location theory?

> > However, rhythm is, perceptually, entirely about rate, unlike pitch.
> > And phase is all important in terms of rhythm, and almost completely
> > irrelevant in terms of pitch.
>
> Now, think over what you just said. If you do, at some point, perceive proportional beating in an environment WITHOUT strong phase synchronization, that means that proportional beating is not perceived as a purely rhythmic phenomenon, even if beating in a single dyad is.

Proportional beating is no different than amplitude modulation. It
really isn't. If you take 440, 441, and 442 Hz, and you mix them all
together, the same "beating" result is going to happen as if you took
a 441 Hz constant sine wave playing through your speakers and turned
the volume knob up and down sinusoidally, at a rate of once per
second.

It's a pitch whose amplitude is being modulated... rhythmically. Think
playing 16th notes on a vibraphone, except instead of the envelope
being a bunch of sharp attacks and releases, it's a nice smooth
sinusoidal pattern. Obviously the 16th notes on the vibraphone have
both a pitched and rhythmic aspect to what's going on, as does all of
music, and as does "beating."

> Just as phase is pretty much irrelevant in terms of pitch, it would clearly have to be pretty much irrelevant in terms of proportional beating were we to find that proportional beating is perceptible in cases with random phase occurrances. So, this rhythmic phenomenon- and beating is clearly rhythmic in the case of a lone dyad- would clearly be sharing a property of PITCH (insensitivity to phase).

Proportional beating will certainly be perceptible even if random
phase occurances happen. Let's say we have three notes and the beat
ratios are 3/2. Whether it comes out to a perfect "hot cup of tea" or
not, you're still going to, if you listen to the damn thing long
enough, hear some kind of pattern that just keeps repeating. AKA,
given a "3" and a "2" of whatever, you'll find the "1."

But what will not happen is that the 3/2 polyrhythm will be
indistinguishable from a phase-shifted version of itself. However, as
far as pitch is concerned -- it will be indistinguishable.

All of the above characteristics are also shared by regular
polyrhythms that can be played on a non-pitched instrument independent
of this proportional beating stuff. It just hints at similar
characteristics between how we perceive rhythm and pitch is all
(finding the "1" from the upper "overtones" of pitch).

-Mike

🔗cameron <misterbobro@...>

In the interest of fairness and multiplicity of viewpoints, I must point out, though the point serves in argument against my stance that proportional beating is indeed a concrete and valid phenomenon, that the Scalatron is very likely devised on a divide-down oscillator scheme as are several of my vintage analog synthesizers, and therefore it is quite likely that proportional beating schemes are more apparent and more effective on this instrument than they would be when implemented within many different instruments and ensembles, just as certain delicacies of phase motion are strong and delightful on such machines but are absent or synthesized with difficulty in instruments of different construction.

I don't have time to instruct Mike in basic concepts (understanding, not just knowledge) in this matter, but for those looking on who do actually understand I write this.

-Cameron Bobro

--- In tuning@yahoogroups.com, "gdsecor" <gdsecor@...> wrote:
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
> >
> > > > It sounds like a neat concept, I'm wondering if it actually
> > > > works in practice.
> > >
> > > It works very well indeed.
> >
> > Is there any particular reason you believe this?
>
> Yes. I've gone to the trouble of putting a few proportional-beating temperaments on my Scalatron and playing various chord progressions, which is a much better indication of how they'll work out in practice than listening to chords in isolation.
>
> I was completely unaware that I was hearing a proportional-beating temperament the first time I played in one, back in the 1970's. I had been trying to develop a 19-tone well-temperament over the previous several years, with two objectives: to get 5-limit triads with less error in the fifths, and to get better-sounding (major, minor, & especially harmonic) seventh chords (which I believe are 19's greatest weakness). At first I was making the largest 5ths around 5.4 cents (~1/4-comma meantone) on the near side of the 5th-circle, which made me very unhappy with the very narrow 5ths on the far side. I later tried something closer to 19-equal, with the 5ths on the near side sized (6.341 cents narrow) making several of the diminished 4ths (C#-F, G#-C, D#-G, A#-D, E#-A) an exact 7:9, which results in more convincing harmonic 7th chords. I was pleasantly surprised that the triads (major, minor, & subminor) sounded much more like those of 31-equal than of 19-equal, besides having a "singing" quality. It wasn't until a few years ago that I learned that the chain of 5ths in the near side of this well-temperament is very close to Erv Wilson's meta-meantone temperament (5ths 6.325 cents narrow), which gives 1:1:1 (5th:M3,m3) synchronous beat rates in root-position major triads, which accounts for the "singing" quality of my well-temperament. (I have since modified my well-temperament so that the best 5ths are exact meta-meantone, which, for all practical purposes, makes no audible difference.) Another thing that really sets this temperament apart from both 19-equal & 31-equal is that both the M3 & m3 are slow-beating. (Another plus: since some of the diminished 4ths are almost exactly 7:9, the 6:7:9 triads that contain these are very close to proportional-beating.)
>
> Another temperament I tried on my Scalatron, more recently, is my 12-tone temperament (extra)ordinaire (12-TX), which now has the F, C, & G root-position major triads with 1:1:4 (5th:M3,m3) synchronous beat rates. These triads also seem to "sing". Although the minor 3rd is not slow-beating (as in 19-WT), the two slower-beating intervals (5th & M3) tend to mask the faster-beating minor 3rd, so it is not as prominent. Another thing that needs to be emphasized (again) is that, since both major & minor triads are proportional-beating, the larger chords that combine them (M7, m7, M9, etc.) tend to avoid the "janging" effect of a conglomeration of unsynchronized beat rates. This is something you can't fully appreciate until you sit down and play it on a keyboard.
>
> > One thing that should send up a red flag regarding brats -- and
> > don't get me wrong, it's an intoxicating pursuit for the scale
> > theorist and I've spent a pretty hour on it myself -- is their
> > sensitivity to mistuning. Is a brat of 1.4999 any good? Where
> > do you draw the line? Of course we already encounter this
> > problem with the tuning of simple ratios in harmony (harmonic
> > entropy addresses it).
>
> Of course, closely approximated brats (which is what I have on the Scalatron) are okay, just like near-JI is good. In fact, you might prefer that to exact brats (just as I prefer the near-JI of a microtemperament to exact JI), because it mitigates a kind of "antiseptic" or synthetic quality in the sound.
>
> > This list has a poor memory, but I've posted more than a few
> > synthesized examples of chords with simple and not-so-simple
> > brats. Listeners seemed to prefer chords where the plain old
> > tuning error was lower. In fact, at least one person commented
> > that the simple brats made beating worse, because its amplitude
> > range is greater. Dave Keenan admitted he'd been wrong about
> > brats in one of those threads.
>
> As I observed, a greater amplitude resulting from a 1:1 5th:M3 beat ratio has the advantage of masking the quicker beating of the minor 3rd, just as a vibrato masks the rapid beating of 3rds in 12-equal. So you can turn a "flaw" into a feature: if the beating is slow enough, it's a kind of vibrato, and if it's synched, then it'll sing.
>
> As for wrong conclusions: in the past I subscribed to the idea that a 12-tone circulating temperament (a/k/a well-temperament) should have the combined error of the 5-limit consonances equal to the theoretical minimum -- thus no 5ths wider than just. Now I've come to the conclusion that 5ths a few cents wider than just are desirable on the far side of a 12-tone circulating temperament, because they tend to mask the rapidly beating 3rds in triads and thereby make them less objectionable, which gives me the ability to have a greater number of low-error triads on the near side -- extraordinaire, n'est pas?
>
> --George
>

🔗john777music <jfos777@...>

What's a proportional beating temperament?

John.

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
> In the interest of fairness and multiplicity of viewpoints, I must point out, though the point serves in argument against my stance that proportional beating is indeed a concrete and valid phenomenon, that the Scalatron is very likely devised on a divide-down oscillator scheme as are several of my vintage analog synthesizers, and therefore it is quite likely that proportional beating schemes are more apparent and more effective on this instrument than they would be when implemented within many different instruments and ensembles, just as certain delicacies of phase motion are strong and delightful on such machines but are absent or synthesized with difficulty in instruments of different construction.
>
> I don't have time to instruct Mike in basic concepts (understanding, not just knowledge) in this matter, but for those looking on who do actually understand I write this.
>
> -Cameron Bobro
>
> --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
> >
> >
> > --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, "gdsecor" <gdsecor@> wrote:
> > >
> > > > > It sounds like a neat concept, I'm wondering if it actually
> > > > > works in practice.
> > > >
> > > > It works very well indeed.
> > >
> > > Is there any particular reason you believe this?
> >
> > Yes. I've gone to the trouble of putting a few proportional-beating temperaments on my Scalatron and playing various chord progressions, which is a much better indication of how they'll work out in practice than listening to chords in isolation.
> >
> > I was completely unaware that I was hearing a proportional-beating temperament the first time I played in one, back in the 1970's. I had been trying to develop a 19-tone well-temperament over the previous several years, with two objectives: to get 5-limit triads with less error in the fifths, and to get better-sounding (major, minor, & especially harmonic) seventh chords (which I believe are 19's greatest weakness). At first I was making the largest 5ths around 5.4 cents (~1/4-comma meantone) on the near side of the 5th-circle, which made me very unhappy with the very narrow 5ths on the far side. I later tried something closer to 19-equal, with the 5ths on the near side sized (6.341 cents narrow) making several of the diminished 4ths (C#-F, G#-C, D#-G, A#-D, E#-A) an exact 7:9, which results in more convincing harmonic 7th chords. I was pleasantly surprised that the triads (major, minor, & subminor) sounded much more like those of 31-equal than of 19-equal, besides having a "singing" quality. It wasn't until a few years ago that I learned that the chain of 5ths in the near side of this well-temperament is very close to Erv Wilson's meta-meantone temperament (5ths 6.325 cents narrow), which gives 1:1:1 (5th:M3,m3) synchronous beat rates in root-position major triads, which accounts for the "singing" quality of my well-temperament. (I have since modified my well-temperament so that the best 5ths are exact meta-meantone, which, for all practical purposes, makes no audible difference.) Another thing that really sets this temperament apart from both 19-equal & 31-equal is that both the M3 & m3 are slow-beating. (Another plus: since some of the diminished 4ths are almost exactly 7:9, the 6:7:9 triads that contain these are very close to proportional-beating.)
> >
> > Another temperament I tried on my Scalatron, more recently, is my 12-tone temperament (extra)ordinaire (12-TX), which now has the F, C, & G root-position major triads with 1:1:4 (5th:M3,m3) synchronous beat rates. These triads also seem to "sing". Although the minor 3rd is not slow-beating (as in 19-WT), the two slower-beating intervals (5th & M3) tend to mask the faster-beating minor 3rd, so it is not as prominent. Another thing that needs to be emphasized (again) is that, since both major & minor triads are proportional-beating, the larger chords that combine them (M7, m7, M9, etc.) tend to avoid the "janging" effect of a conglomeration of unsynchronized beat rates. This is something you can't fully appreciate until you sit down and play it on a keyboard.
> >
> > > One thing that should send up a red flag regarding brats -- and
> > > don't get me wrong, it's an intoxicating pursuit for the scale
> > > theorist and I've spent a pretty hour on it myself -- is their
> > > sensitivity to mistuning. Is a brat of 1.4999 any good? Where
> > > do you draw the line? Of course we already encounter this
> > > problem with the tuning of simple ratios in harmony (harmonic
> > > entropy addresses it).
> >
> > Of course, closely approximated brats (which is what I have on the Scalatron) are okay, just like near-JI is good. In fact, you might prefer that to exact brats (just as I prefer the near-JI of a microtemperament to exact JI), because it mitigates a kind of "antiseptic" or synthetic quality in the sound.
> >
> > > This list has a poor memory, but I've posted more than a few
> > > synthesized examples of chords with simple and not-so-simple
> > > brats. Listeners seemed to prefer chords where the plain old
> > > tuning error was lower. In fact, at least one person commented
> > > that the simple brats made beating worse, because its amplitude
> > > range is greater. Dave Keenan admitted he'd been wrong about
> > > brats in one of those threads.
> >
> > As I observed, a greater amplitude resulting from a 1:1 5th:M3 beat ratio has the advantage of masking the quicker beating of the minor 3rd, just as a vibrato masks the rapid beating of 3rds in 12-equal. So you can turn a "flaw" into a feature: if the beating is slow enough, it's a kind of vibrato, and if it's synched, then it'll sing.
> >
> > As for wrong conclusions: in the past I subscribed to the idea that a 12-tone circulating temperament (a/k/a well-temperament) should have the combined error of the 5-limit consonances equal to the theoretical minimum -- thus no 5ths wider than just. Now I've come to the conclusion that 5ths a few cents wider than just are desirable on the far side of a 12-tone circulating temperament, because they tend to mask the rapidly beating 3rds in triads and thereby make them less objectionable, which gives me the ability to have a greater number of low-error triads on the near side -- extraordinaire, n'est pas?
> >
> > --George
> >
>

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🔗jacques.dudon <fotosonix@...>

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Thanks Jacques,
>
> does "harmonic beatings" mean that the frequencies of the beats correspond to a simple ratio (e.g. 3/2)?
>
> John.

"Harmonic beatings" (or harmonic beats ?), also called "second order beats", are beats occuring between different harmonics (overtones) of the two sounds that form a dyad. For example in a meantone fifth C:G, the main beat will occur between the 3rd h. of C and the 2nd h. of G and its frequency is 3C - 2G.
For a dyad around a major third C:E, the harmonic beating will be 4E - 5C (or 5C - 4E if C:E is lower than 5/4).
And if a tuning, or a temperament has several dyads like those whose harmonic beatings frequencies have simple "harmonic" ratios (what I meant by JI, except that beats are in a lower range than tones...), this tuning or temperament is said to have "proportional beating" qualities.

> --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@> wrote:
> >
> > John wrote :
> >
> > What's a proportional beating temperament?
> >
> >
> > Just to be sure the question has at least one attempt of an answer :),
> >
> > A proportional beating temperament is a temperament in which you can
> > hear,
> > at least for some of its dyads (and other than dyads octaves apart...),
> > harmonic beatings in just intonation.
> >
> > It could probably work also more generally for "tunings", instead of
> > "temperaments", but these are generally also temperaments.
> > - - - - - - -
> > Jacques
> >
>

🔗john777music <jfos777@...>

Thanks again Jacques,
I got it,
John.

--- In tuning@yahoogroups.com, "jacques.dudon" <fotosonix@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "john777music" <jfos777@> wrote:
> >
> > Thanks Jacques,
> >
> > does "harmonic beatings" mean that the frequencies of the beats correspond to a simple ratio (e.g. 3/2)?
> >
> > John.
>
> "Harmonic beatings" (or harmonic beats ?), also called "second order beats", are beats occuring between different harmonics (overtones) of the two sounds that form a dyad. For example in a meantone fifth C:G, the main beat will occur between the 3rd h. of C and the 2nd h. of G and its frequency is 3C - 2G.
> For a dyad around a major third C:E, the harmonic beating will be 4E - 5C (or 5C - 4E if C:E is lower than 5/4).
> And if a tuning, or a temperament has several dyads like those whose harmonic beatings frequencies have simple "harmonic" ratios (what I meant by JI, except that beats are in a lower range than tones...), this tuning or temperament is said to have "proportional beating" qualities.
>
> > --- In tuning@yahoogroups.com, Jacques Dudon <fotosonix@> wrote:
> > >
> > > John wrote :
> > >
> > > What's a proportional beating temperament?
> > >
> > >
> > > Just to be sure the question has at least one attempt of an answer :),
> > >
> > > A proportional beating temperament is a temperament in which you can
> > > hear,
> > > at least for some of its dyads (and other than dyads octaves apart...),
> > > harmonic beatings in just intonation.
> > >
> > > It could probably work also more generally for "tunings", instead of
> > > "temperaments", but these are generally also temperaments.
> > > - - - - - - -
> > > Jacques
> > >
> >
>

Proportional Beating temperaments

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