Yahoo Tuning Groups Ultimate Backup tuning-math Basins of Attraction.

At 07:17 AM 5/7/2008, you wrote:
>Is it possible that there is a basin of attraction to Western music? If
>so then what is it? Consider the following where figures are rounded
>off to the nearest cent. C=1/1=0, C#=135/128=92, D=9/8=204,
>Eb=149/128=263, E=5/4=386, F=21/16=471, F#=45/32=590, G=3/2=702, and
>Ab=199/128=764, A=27/16=906, Bb=7/4=969, B=15/8=1088 and
>c=2/1=1200cents. All of these ratios have a common denominator of
>1/128. Forget about limiting your ratios for a moment and consider
>ratios that belong to the same family (ie 1/128). Sink your
>mathematical teeth into exploring another idea. I can assure you that
>it is worth the time and trouble. Consider it an exercise.

This scale could be seen as a subset of the 128th mode of
the harmonic series (as you point out), and see this recent
thread for some stuff along those lines

/tuning/topicId_75816.html#75816

But it's fairly compact on the 7-limit lattice and may be
better seen in that light.

I don't think it's going to work as a 12-ET replacement in
Western music, though there are doubtless some pieces of
music which it will suit.

-Carl

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> At 07:17 AM 5/7/2008, you wrote:
> >Is it possible that there is a basin of attraction to Western
music? If
> >so then what is it? Consider the following where figures are
rounded
> >off to the nearest cent. C=1/1=0, C#=135/128=92, D=9/8=204,
> >Eb=149/128=263, E=5/4=386, F=21/16=471, F#=45/32=590, G=3/2=702,
and
> >Ab=199/128=764, A=27/16=906, Bb=7/4=969, B=15/8=1088 and
> >c=2/1=1200cents. All of these ratios have a common denominator of
> >1/128. Forget about limiting your ratios for a moment and consider
> >ratios that belong to the same family (ie 1/128). Sink your
> >mathematical teeth into exploring another idea. I can assure you
that
> >it is worth the time and trouble. Consider it an exercise.
>
> This scale could be seen as a subset of the 128th mode of
> the harmonic series (as you point out), and see this recent
> thread for some stuff along those lines
>
> /tuning/topicId_75816.html#75816
>
> But it's fairly compact on the 7-limit lattice and may be
> better seen in that light.
>
> I don't think it's going to work as a 12-ET replacement in
> Western music, though there are doubtless some pieces of
> music which it will suit.
>
> -Carl
> Sorry old chap but the 7-limit lattice doesn't mean anything to me.
The idea of limiting musical ratios to low numbers is unscientific
and unproven. I am simply opening up an avenue of enquiry for which I
can supply convincing evidence to support my contentions. Music
theorists have been juggling low limit ratios for centuries. The fact
that these same music theorists have been obsessed with low limit
ratios is no proof of anything at all. I believe in description,
explanation and prediction. By their fruits you shall know them. Look
at the two musical algorithms I have supplied so far. They are
universal for all equal temperaments even though I prefer 22tet. Why
is this? It is because it is the best fit. Music is not mathematics.
From my point of view it is closer to language and geometry although
I suspect that it is a thing unto itself.

🔗Carl Lumma <carl@lumma.org>

Hi Robert,

>> This scale could be seen as a subset of the 128th mode of
>> the harmonic series (as you point out), and see this recent
>> thread for some stuff along those lines
>>
>> /tuning/topicId_75816.html#75816
>>
>> But it's fairly compact on the 7-limit lattice and may be
>> better seen in that light.
>>
>> I don't think it's going to work as a 12-ET replacement in
>> Western music, though there are doubtless some pieces of
>> music which it will suit.
>
>Sorry old chap but the 7-limit lattice doesn't mean anything to me.

Well, check out some of the tutorial materials linked to
on this list's home page.

>The idea of limiting musical ratios to low numbers is unscientific
>and unproven.

Hardly.

>I am simply opening up an avenue of enquiry for which I
>can supply convincing evidence to support my contentions.

Have you made any contentions? I missed them.

>Music theorists have been juggling low limit ratios for centuries.
>The fact that these same music theorists have been obsessed with
>low limit ratios is no proof of anything at all.

But psychoacoustics does provide both a model and experimental
evidence supporting simple ratios.

>Look at the two musical algorithms I have supplied so far. They are
>universal for all equal temperaments even though I prefer 22tet. Why
>is this? It is because it is the best fit.

The best fit to... what exactly?

-Carl

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Hi Robert,
>
> >> This scale could be seen as a subset of the 128th mode of
> >> the harmonic series (as you point out), and see this recent
> >> thread for some stuff along those lines
> >>
> >> /tuning/topicId_75816.html#75816
> >>
> >> But it's fairly compact on the 7-limit lattice and may be
> >> better seen in that light.
> >>
> >> I don't think it's going to work as a 12-ET replacement in
> >> Western music, though there are doubtless some pieces of
> >> music which it will suit.
> >
> >Sorry old chap but the 7-limit lattice doesn't mean anything to me.
>
> Well, check out some of the tutorial materials linked to
> on this list's home page.
>
> >The idea of limiting musical ratios to low numbers is unscientific
> >and unproven.
>
> Hardly.
>
> >I am simply opening up an avenue of enquiry for which I
> >can supply convincing evidence to support my contentions.
>
> Have you made any contentions? I missed them.
>
> >Music theorists have been juggling low limit ratios for centuries.
> >The fact that these same music theorists have been obsessed with
> >low limit ratios is no proof of anything at all.
>
> But psychoacoustics does provide both a model and experimental
> evidence supporting simple ratios.
>
> >Look at the two musical algorithms I have supplied so far. They
are
> >universal for all equal temperaments even though I prefer 22tet.
Why
> >is this? It is because it is the best fit.
>
> The best fit to... what exactly?
>
> -Carl
> Psychoacoustics only provides evidence (not proof) that the basin
of attraction for Western music is close to 12tet. The ratios I
supplied fit into the basin of attraction which conform very closely
with the harmonics 0-386-702-969. The implications of these harmonics
best fit into 22tet. All of the evidence supporting low number ratios
is based on fuzzy perception.

🔗Carl Lumma <carl@lumma.org>

Hi Robert,

>> >The idea of limiting musical ratios to low numbers is unscientific
>> >and unproven.
>>
>> Hardly.
>>
>> >I am simply opening up an avenue of enquiry for which I
>> >can supply convincing evidence to support my contentions.
>>
>> Have you made any contentions? I missed them.
>>
>> >Music theorists have been juggling low limit ratios for centuries.
>> >The fact that these same music theorists have been obsessed with
>> >low limit ratios is no proof of anything at all.
>>
>> But psychoacoustics does provide both a model and experimental
>> evidence supporting simple ratios.
>>
>> >Look at the two musical algorithms I have supplied so far. They
>> >are universal for all equal temperaments even though I prefer
>> >22tet. Why is this? It is because it is the best fit.
>>
>> The best fit to... what exactly?
>
>Psychoacoustics only provides evidence (not proof) that the basin
>of attraction for Western music is close to 12tet.

Huh?

Psychoacoustics provides both evidence for a 'simple ratios'
theory of consonance and a model (that fits with anatomy)
explaining why it should be so. The term "proof" is loaded
and I don't know what it means.

>The ratios I supplied fit into the basin of attraction which
>conform very closely with the harmonics 0-386-702-969.

Those harmonics happen to be simple ratios.

>The implications of these harmonics best fit into 22tet. All
>of the evidence supporting low number ratios is based on fuzzy
>perception.

Not sure what you mean here. The model of course allows that
the ratios need not be exact.

-Carl

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Hi Robert,
>
> >> >The idea of limiting musical ratios to low numbers is
unscientific
> >> >and unproven.
> >>
> >> Hardly.
> >>
> >> >I am simply opening up an avenue of enquiry for which I
> >> >can supply convincing evidence to support my contentions.
> >>
> >> Have you made any contentions? I missed them.
> >>
> >> >Music theorists have been juggling low limit ratios for
centuries.
> >> >The fact that these same music theorists have been obsessed with
> >> >low limit ratios is no proof of anything at all.
> >>
> >> But psychoacoustics does provide both a model and experimental
> >> evidence supporting simple ratios.
> >>
> >> >Look at the two musical algorithms I have supplied so far. They
> >> >are universal for all equal temperaments even though I prefer
> >> >22tet. Why is this? It is because it is the best fit.
> >>
> >> The best fit to... what exactly?
> >
> >Psychoacoustics only provides evidence (not proof) that the basin
> >of attraction for Western music is close to 12tet.
>
> Huh?
>
> Psychoacoustics provides both evidence for a 'simple ratios'
> theory of consonance and a model (that fits with anatomy)
> explaining why it should be so. The term "proof" is loaded
> and I don't know what it means.
>
> >The ratios I supplied fit into the basin of attraction which
> >conform very closely with the harmonics 0-386-702-969.
>
> Those harmonics happen to be simple ratios.
>
> >The implications of these harmonics best fit into 22tet. All
> >of the evidence supporting low number ratios is based on fuzzy
> >perception.
>
> Not sure what you mean here. The model of course allows that
> the ratios need not be exact.
>
> -Carl
> Ratios that belong to the same denominator family should be
investigateed.
Robert

🔗Carl Lumma <carl@lumma.org>

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

🔗Carl Lumma <carl@lumma.org>

Hi Robert,

>>>Ratios that belong to the same denominator family should be
>>>investigateed.
>>>Robert
>>
>>They have been.
>>
>>-Carl
>
>Methinks I have sparked a lively debate.

I've tried to be nice, but let's be clear: there's no debate yet.

Like many newcomers to these mailings lists, you may be unaware
that they have been in continuous use for almost 20 years, and
have attracted hundreds of people from all walks of life in that
time, including some very talented musicians and instrument
builders, world-renowned music theorists, well-respected
neuroscientists, mathematicians, and physicists. Composers
and music critics. And before and since these lists began much
work in microtonal work was done in other mediums, which you
may be unaware of.

You therefore may be shocked to learn that your "Universal
3-note chord algorithm" is neither new nor fascinating to any
regular poster here. If you like the results you're getting,
that's great. Post some music if you like! Microtonal music
suffers from an 'embarrassment of riches'. Many techniques
give good results. So congratulations on getting published at
apocatastasis. The more people writing and reading and
listening to microtonal music, the better. But please do take
it down a notch.

-Carl

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> Hi Robert,
>
> >>>Ratios that belong to the same denominator family should be
> >>>investigateed.
> >>>Robert
> >>
> >>They have been.
> >>
> >>-Carl
> >
> >Methinks I have sparked a lively debate.
>
> I've tried to be nice, but let's be clear: there's no debate yet.
>
> Like many newcomers to these mailings lists, you may be unaware
> that they have been in continuous use for almost 20 years, and
> have attracted hundreds of people from all walks of life in that
> time, including some very talented musicians and instrument
> builders, world-renowned music theorists, well-respected
> neuroscientists, mathematicians, and physicists. Composers
> and music critics. And before and since these lists began much
> work in microtonal work was done in other mediums, which you
> may be unaware of.
>
> You therefore may be shocked to learn that your "Universal
> 3-note chord algorithm" is neither new nor fascinating to any
> regular poster here. If you like the results you're getting,
> that's great. Post some music if you like! Microtonal music
> suffers from an 'embarrassment of riches'. Many techniques
> give good results. So congratulations on getting published at
> apocatastasis. The more people writing and reading and
> listening to microtonal music, the better. But please do take
> it down a notch.
>
> -Carl
> OK Carl. So tell me where my Universal 3-note chord algorithm
occurs elsewhere. I've been carrying out microtonal experiments since
1987. I have so far designed five musical algorithms two of which I
have posted to your group. My algorithms are based on experimental
findings and can be used by both teenagers and professors. And the
whole microtonal community benefits. Am I down a notch now?

🔗Carl Lumma <carl@lumma.org>

Robert wrote...

> OK Carl. So tell me where the universal 3-note chord algorithm
> occurs elsewhere.

As you described it, it doesn't even rise to the status of
"algorithm". It appears you are:

1. choosing a triad
2. finding its nearest approximation in steps of 12-ET
[except C-E isn't the best approx of a minor third,
but I'll assume you meant C-Eb-G]
3. connecting other instances of the triad to the first
via common tone relations
[there isn't a unique way to do this most of the time,
but...
4. finding the nearest approximation of the new copies of
the chord in 12-ET
[...let's just say that any way which doesn't clobber
existing mapped 12-ET steps is valid]
5. stopping when all 12-ET steps are mapped

The most popular way of looking at chords connected by common
tones is to use a lattice like this (use message options to
view fixed width if you're reading this on the web)

E - B
/ \ / \
C---G---D

You've seen this before, since you've aggregated a vast amount
of information about microtonality and this is pretty much as
basic as it gets.

Usually theorists doing stuff like this impose further
restrictions (to keep the result from sounding like crap).
The first is to make the rungs of the lattice be consonant
intervals. The second is keep very small intervals from
appearing between notes of the scale.

Even when you do these things, common practice Western music
often sounds bad when retuned with a technique like this,
even if you choose the key center for each piece. The fact
that you suggest a vibraphone timbre is a dead giveaway that
you agree.

That's where a more sophisticated approach comes in: adaptive
tuning. There are all kinds of schemes for automatically
inferring a key center based on an incoming MIDI stream; some
of them in production. Hermode tuning is one -- there's a
website about it, and several famous keyboards support it out
of the box. Your Kurzweil (if it's a K2xxx series) supports
manual key-center changes, thanks to Wendy Carlos (several
software synths also support this).

It turns out one of the best such systems was developed already
in the 16th century by an Italian musician/theorist named
Vicentino. You can read about his system on the Tonalsoft
encyclopedia.

We shouldn't leave out Groven's system from the 1930s,
implemented recently with Yamaha disklaviers and Max/MSP by
David Code.
http://www.wmich.edu/mus-theo/groven/

Finally, the most AI-like system was developed by
John de Laubenfels, in cooperation with members from this list
including yours truly.
http://personalpages.bellsouth.net/j/d/jdelaub/jstudio.htm

> I've been carrying out microtonal experiments since
> 1988 and have sorted and evaluated a vast amount of microtonal
> information. I don't accept everything that is bandied about.
> I still have three more musical algorithms which are so far
> unpublished. John Chalmers emailed saying that he wrote a paper
> along similar lines. I have designed a simple little algorithm
> which can be used by teenagers today.

Fire away! Maybe one of them will even be interesting!

>Other people might want to claim precedence. That's fine. I've
>given away for free two of my five algorithms.

For FREE! Wow! How much do the others cost?

-Carl

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Robert wrote...
>
> > OK Carl. So tell me where the universal 3-note chord algorithm
> > occurs elsewhere.
>
> As you described it, it doesn't even rise to the status of
> "algorithm". It appears you are:
>
> 1. choosing a triad
> 2. finding its nearest approximation in steps of 12-ET
> [except C-E isn't the best approx of a minor third,
> but I'll assume you meant C-Eb-G]
> 3. connecting other instances of the triad to the first
> via common tone relations
> [there isn't a unique way to do this most of the time,
> but...
> 4. finding the nearest approximation of the new copies of
> the chord in 12-ET
> [...let's just say that any way which doesn't clobber
> existing mapped 12-ET steps is valid]
> 5. stopping when all 12-ET steps are mapped
>
> The most popular way of looking at chords connected by common
> tones is to use a lattice like this (use message options to
> view fixed width if you're reading this on the web)
>
> E - B
> / \ / \
> C---G---D
>
> You've seen this before, since you've aggregated a vast amount
> of information about microtonality and this is pretty much as
> basic as it gets.
>
> Usually theorists doing stuff like this impose further
> restrictions (to keep the result from sounding like crap).
> The first is to make the rungs of the lattice be consonant
> intervals. The second is keep very small intervals from
> appearing between notes of the scale.
>
> Even when you do these things, common practice Western music
> often sounds bad when retuned with a technique like this,
> even if you choose the key center for each piece. The fact
> that you suggest a vibraphone timbre is a dead giveaway that
> you agree.
>
> That's where a more sophisticated approach comes in: adaptive
> tuning. There are all kinds of schemes for automatically
> inferring a key center based on an incoming MIDI stream; some
> of them in production. Hermode tuning is one -- there's a
> website about it, and several famous keyboards support it out
> of the box. Your Kurzweil (if it's a K2xxx series) supports
> manual key-center changes, thanks to Wendy Carlos (several
> software synths also support this).
>
> It turns out one of the best such systems was developed already
> in the 16th century by an Italian musician/theorist named
> Vicentino. You can read about his system on the Tonalsoft
> encyclopedia.
>
> We shouldn't leave out Groven's system from the 1930s,
> implemented recently with Yamaha disklaviers and Max/MSP by
> David Code.
> http://www.wmich.edu/mus-theo/groven/
>
> Finally, the most AI-like system was developed by
> John de Laubenfels, in cooperation with members from this list
> including yours truly.
> http://personalpages.bellsouth.net/j/d/jdelaub/jstudio.htm
>
> > I've been carrying out microtonal experiments since
> > 1988 and have sorted and evaluated a vast amount of microtonal
> > information. I don't accept everything that is bandied about.
> > I still have three more musical algorithms which are so far
> > unpublished. John Chalmers emailed saying that he wrote a paper
> > along similar lines. I have designed a simple little algorithm
> > which can be used by teenagers today.
>
> Fire away! Maybe one of them will even be interesting!
>
> >Other people might want to claim precedence. That's fine. I've
> >given away for free two of my five algorithms.
>
> For FREE! Wow! How much do the others cost?
>
> -Carl
> An algorithm is any step by step procedure etc. I meant C-E-G and
not C-Eb-G. I suspect that you are analysing the chord algorithm on
paper rather than carrying out experiments to determine its value as
an educational tool. Even seemingly ridiculous chords like 0-5-
10cents can be put into the algorithm to study Just Noticeable
Differences. All sorts of outlandish theories can be examined. I'm
sure that some of the members out in internetland have added the
previously mentioned two algorithms to their box of musical tricks.
My other algorithms are too compicated to explain over the internet.

🔗Carl Lumma <carl@lumma.org>

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Robert Martin wrote...
>
> > I meant C-E-G and not C-Eb-G.
>
> All this means is that the scale you end up with won't
> necessarily be monotonically ascending. However if you're
> retuning existing common practice music and you want to
> hear the generating triad a lot, mapping to 1-3-5 no matter
> what is the right thing to do.
>
> > I suspect that you are analysing the chord algorithm on
> > paper rather than carrying out experiments to determine its
> > value as an educational tool.
>
> I've improvised with, and retuned existing music in, many
> many scales like this.
>
> So far you still seem to be ignoring these two things:
> 1. Why are you recommending a vibraphone timbre?
> 2. What is 22-ET a good fit for if not small number ratios?
>
> -Carl
> Vibraphones, marimbas, metallophones and metallic timbres seem to
do the theory more justice than plucked strings etc. People are free
to use whatever timbre they like. Plucked strings tend to decay very
quickly. When I improvise I usually use a choir type timbre so that I
can sustain the notes longer while playing figures with the other
hand. 0-386-702-969 are indeed small number ratios which can be
extrapolated to produce other small number ratios. It just so happens
that my research has led me to exploring and considering the 128
partials of the 7th octave of the harmonic series. To be sure this is
a long way up into the stratosphere. But a person has to do something
while he is awake. About the 2nd question: 22tet can be interpreted
as a good fit for small number ratios. But when does a small number
ratio become a large number ratio? What is the cutoff point? Who
decides? Is 128 a small or large number and why?

🔗Carl Lumma <carl@lumma.org>

At 02:02 PM 5/8/2008, you wrote:
>--- In tuning-math@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>>
>> Robert Martin wrote...
>>
>> > I meant C-E-G and not C-Eb-G.
>>
>> All this means is that the scale you end up with won't
>> necessarily be monotonically ascending. However if you're
>> retuning existing common practice music and you want to
>> hear the generating triad a lot, mapping to 1-3-5 no matter
>> what is the right thing to do.
>>
>> > I suspect that you are analysing the chord algorithm on
>> > paper rather than carrying out experiments to determine its
>> > value as an educational tool.
>>
>> I've improvised with, and retuned existing music in, many
>> many scales like this.
>>
>> So far you still seem to be ignoring these two things:
>> 1. Why are you recommending a vibraphone timbre?
>> 2. What is 22-ET a good fit for if not small number ratios?
>>
>> -Carl
>
>Vibraphones, marimbas, metallophones and metallic timbres seem to
>do the theory more justice than plucked strings etc. People are free
>to use whatever timbre they like. Plucked strings tend to decay very
>quickly. When I improvise I usually use a choir type timbre so that
>I can sustain the notes longer while playing figures with the other
>hand. 0-386-702-969 are indeed small number ratios which can be
>extrapolated to produce other small number ratios. It just so happens
>that my research has led me to exploring and considering the 128
>partials of the 7th octave of the harmonic series. To be sure this is
>a long way up into the stratosphere. But a person has to do something
>while he is awake. About the 2nd question: 22tet can be interpreted
>as a good fit for small number ratios. But when does a small number
>ratio become a large number ratio? What is the cutoff point? Who
>decides? Is 128 a small or large number and why?

The cutoff point will depend on the timbre, how many notes are
sounding, what notes have come before (musical context), the
listener (experience/training listening to that timbre, microtonal
intervals, music in general), etc. etc.

Nevertheless, Paul Erlich's harmonic entropy model gives some
clues about the cutoffs for dyads (and potentially for larger
chords too). It suggests that for a dyad n/d in isolation, the
basin of attraction (now you've got me saying it) is proportional
to 1/sqrt(n*d). To turn that into cents you need to know the
width of the basin around 1/1, which you can get by calculating
a harmonic entropy curve. This gradually stops working as the
product n*d gets much bigger than 50. For ratios with n*d above
that, you can just convert to cents and look at the corresponding
point on the entropy curve directly. You can also do things like
look at the derivatives of the curve (for instance, Dave Keenan's
"justness" is the 2nd derivative of harmonic entropy).

128 by itself is a very high pitch, and the maximum dissonance
that can be created falls off at the extremes of the musical
register. If you're talking about all harmonics 128-256 or
something... some of the dyads between them will indeed be very
complex, and others will be very simple. If you start playing
more than 2 notes at a time, the answer gets more complicated.

-Carl

🔗Carl Lumma <carl@lumma.org>

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

🔗Carl Lumma <carl@lumma.org>

Robert Martin wrote...

>>> Vibraphones, marimbas, metallophones and metallic timbres seem to
>>> do the theory more justice than plucked strings etc. People are free
>>> to use whatever timbre they like. Plucked strings tend to decay very
>>> quickly. When I improvise I usually use a choir type timbre
>>
>> First off, there are more choices than just metallophone and
>> plucked strings. These two choices both have quick decays,
>> and tend to minimize dissonance interactions that undoubtedly
>> result when retuning common practice music using your
>> procedure. Typical "choir ahhs" synth sounds, while having
>> a long sustain, also do this. Try a clean organ or piano
>> patch. And maybe do yourself a favor and follow some of the
>> links I provided.
>>
>> -Carl
>
> I've been following all the links that everyone has provided.

Have you listened to the adaptune MIDI files then? Or the
Groven piano? Howabout Monz's Vicentino retunings?

>The most complex
>ratio that I use is 199/128. How does this fit into your scheme of
>things?

It's unlikely to be interpreted by the brain as 199/128. It is
more likely to be interpreted as 14/9 or 8/5, depending on the
context.
That's as a bare dyad. You get it to be heard as 199/128 if you
play a bunch of x/128 harmonics along with it.

-Carl

🔗Dave Keenan <d.keenan@bigpond.net.au>

🔗Carl Lumma <carl@lumma.org>

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

🔗Paul G Hjelmstad <phjelmstad@msn.com>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning-math@yahoogroups.com, Carl Lumma <carl@> wrote:
> >
> > Hi Robert,
> >
> > >> This scale could be seen as a subset of the 128th mode of
> > >> the harmonic series (as you point out), and see this recent
> > >> thread for some stuff along those lines
> > >>
> > >> /tuning/topicId_75816.html#75816
> > >>
> > >> But it's fairly compact on the 7-limit lattice and may be
> > >> better seen in that light.
> > >>
> > >> I don't think it's going to work as a 12-ET replacement in
> > >> Western music, though there are doubtless some pieces of
> > >> music which it will suit.
> > >
> > >Sorry old chap but the 7-limit lattice doesn't mean anything to
me.
> >
> > Well, check out some of the tutorial materials linked to
> > on this list's home page.
> >
> > >The idea of limiting musical ratios to low numbers is
unscientific
> > >and unproven.
> >
> > Hardly.
> >
> > >I am simply opening up an avenue of enquiry for which I
> > >can supply convincing evidence to support my contentions.
> >
> > Have you made any contentions? I missed them.
> >
> > >Music theorists have been juggling low limit ratios for
centuries.
> > >The fact that these same music theorists have been obsessed with
> > >low limit ratios is no proof of anything at all.
> >
> > But psychoacoustics does provide both a model and experimental
> > evidence supporting simple ratios.
> >
> > >Look at the two musical algorithms I have supplied so far. They
> are
> > >universal for all equal temperaments even though I prefer 22tet.
> Why
> > >is this? It is because it is the best fit.
> >
> > The best fit to... what exactly?
> >
> > -Carl
> > Psychoacoustics only provides evidence (not proof) that the basin
> of attraction for Western music is close to 12tet. The ratios I
> supplied fit into the basin of attraction which conform very
closely
> with the harmonics 0-386-702-969. The implications of these
harmonics
> best fit into 22tet. All of the evidence supporting low number
ratios
> is based on fuzzy perception.

22-tET? Could you show it? That would be cool, I am having trouble
getting 22-tET to work very well, without well-tempering it.
Then you have to deal with Superpythagorean, Porcupine, Magic and
Diaschisma.

PGH
"You can tune a piano, but your can't tuna fish"

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<phjelmstad@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, Carl Lumma <carl@> wrote:
> > >
> > > Hi Robert,
> > >
> > > >> This scale could be seen as a subset of the 128th mode of
> > > >> the harmonic series (as you point out), and see this recent
> > > >> thread for some stuff along those lines
> > > >>
> > > >> /tuning/topicId_75816.html#75816
> > > >>
> > > >> But it's fairly compact on the 7-limit lattice and may be
> > > >> better seen in that light.
> > > >>
> > > >> I don't think it's going to work as a 12-ET replacement in
> > > >> Western music, though there are doubtless some pieces of
> > > >> music which it will suit.
> > > >
> > > >Sorry old chap but the 7-limit lattice doesn't mean anything
to
> me.
> > >
> > > Well, check out some of the tutorial materials linked to
> > > on this list's home page.
> > >
> > > >The idea of limiting musical ratios to low numbers is
> unscientific
> > > >and unproven.
> > >
> > > Hardly.
> > >
> > > >I am simply opening up an avenue of enquiry for which I
> > > >can supply convincing evidence to support my contentions.
> > >
> > > Have you made any contentions? I missed them.
> > >
> > > >Music theorists have been juggling low limit ratios for
> centuries.
> > > >The fact that these same music theorists have been obsessed
with
> > > >low limit ratios is no proof of anything at all.
> > >
> > > But psychoacoustics does provide both a model and experimental
> > > evidence supporting simple ratios.
> > >
> > > >Look at the two musical algorithms I have supplied so far.
They
> > are
> > > >universal for all equal temperaments even though I prefer
22tet.
> > Why
> > > >is this? It is because it is the best fit.
> > >
> > > The best fit to... what exactly?
> > >
> > > -Carl
> > > Psychoacoustics only provides evidence (not proof) that the
basin
> > of attraction for Western music is close to 12tet. The ratios I
> > supplied fit into the basin of attraction which conform very
> closely
> > with the harmonics 0-386-702-969. The implications of these
> harmonics
> > best fit into 22tet. All of the evidence supporting low number
> ratios
> > is based on fuzzy perception.
>
> 22-tET? Could you show it? That would be cool, I am having trouble
> getting 22-tET to work very well, without well-tempering it.
> Then you have to deal with Superpythagorean, Porcupine, Magic and
> Diaschisma.
>
> PGH
> "You can tune a piano, but your can't tuna fish"
>
From Robert. The figures in cents which are given in message 17251
are 0-92-204-263-386-471-590-702-764-906-969-1088-1200. If you graph
these figures and line them up with 0-109-218-273-382-491-600-709-764-
927-982-1091-1200 then there is room to add all of the other figures
from 22tet. It is a bit rough. Or if you prefer working with
harmonics then you might get better results adding 53-155-?-429-551-?-
807-841-1030-1145. These harmonic figures including the question
marks are only tentative because I have not yet figured out a way to
rigorously test them as I have done with the figures in message 17251.

🔗Paul G Hjelmstad <phjelmstad@msn.com>

Ich folge nicht. What do you mean "there is room" and what are
the harmonics? Over powers of 2 in the denominator? Sorry....

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

🔗Paul G Hjelmstad <phjelmstad@msn.com>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> <phjelmstad@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > <robertthomasmartin@> wrote:
> > >
> > > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > > <phjelmstad@> wrote:
> > > >
> > > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > > <robertthomasmartin@> wrote:
> > > > >
> > > > > --- In tuning-math@yahoogroups.com, Carl Lumma <carl@>
wrote:
> > > > > >
> > > > > > Hi Robert,
> > > > > >
> > > > > > >> This scale could be seen as a subset of the 128th mode
of
> > > > > > >> the harmonic series (as you point out), and see this
> recent
> > > > > > >> thread for some stuff along those lines
> > > > > > >>
> > > > > > >>
/tuning/topicId_75816.html#75816
> > > > > > >>
> > > > > > >> But it's fairly compact on the 7-limit lattice and may
be
> > > > > > >> better seen in that light.
> > > > > > >>
> > > > > > >> I don't think it's going to work as a 12-ET
replacement
> in
> > > > > > >> Western music, though there are doubtless some pieces
of
> > > > > > >> music which it will suit.
> > > > > > >
> > > > > > >Sorry old chap but the 7-limit lattice doesn't mean
> anything
> > > to
> > > > me.
> > > > > >
> > > > > > Well, check out some of the tutorial materials linked to
> > > > > > on this list's home page.
> > > > > >
> > > > > > >The idea of limiting musical ratios to low numbers is
> > > > unscientific
> > > > > > >and unproven.
> > > > > >
> > > > > > Hardly.
> > > > > >
> > > > > > >I am simply opening up an avenue of enquiry for which I
> > > > > > >can supply convincing evidence to support my contentions.
> > > > > >
> > > > > > Have you made any contentions? I missed them.
> > > > > >
> > > > > > >Music theorists have been juggling low limit ratios for
> > > > centuries.
> > > > > > >The fact that these same music theorists have been
> obsessed
> > > with
> > > > > > >low limit ratios is no proof of anything at all.
> > > > > >
> > > > > > But psychoacoustics does provide both a model and
> experimental
> > > > > > evidence supporting simple ratios.
> > > > > >
> > > > > > >Look at the two musical algorithms I have supplied so
far.
> > > They
> > > > > are
> > > > > > >universal for all equal temperaments even though I
prefer
> > > 22tet.
> > > > > Why
> > > > > > >is this? It is because it is the best fit.
> > > > > >
> > > > > > The best fit to... what exactly?
> > > > > >
> > > > > > -Carl
> > > > > > Psychoacoustics only provides evidence (not proof) that
the
> > > basin
> > > > > of attraction for Western music is close to 12tet. The
ratios
> I
> > > > > supplied fit into the basin of attraction which conform
very
> > > > closely
> > > > > with the harmonics 0-386-702-969. The implications of these
> > > > harmonics
> > > > > best fit into 22tet. All of the evidence supporting low
> number
> > > > ratios
> > > > > is based on fuzzy perception.
> > > >
> > > > 22-tET? Could you show it? That would be cool, I am having
> trouble
> > > > getting 22-tET to work very well, without well-tempering it.
> > > > Then you have to deal with Superpythagorean, Porcupine, Magic
> and
> > > > Diaschisma.
> > > >
> > > > PGH
> > > > "You can tune a piano, but your can't tuna fish"
> > > >
> > > From Robert. The figures in cents which are given in message
> > 17251
> > > are 0-92-204-263-386-471-590-702-764-906-969-1088-1200. If you
> > graph
> > > these figures and line them up with 0-109-218-273-382-491-600-
709-
> > 764-
> > > 927-982-1091-1200 then there is room to add all of the other
> > figures
> > > from 22tet. It is a bit rough. Or if you prefer working with
> > > harmonics then you might get better results adding 53-155-?-429-
> 551-
> > ?-
> > > 807-841-1030-1145. These harmonic figures including the
question
> > > marks are only tentative because I have not yet figured out a
way
> > to
> > > rigorously test them as I have done with the figures in message
> > 17251.
> >
> > Ich folge nicht. What do you mean "there is room" and what are
> > the harmonics? Over powers of 2 in the denominator? Sorry....
> >
> From Robert. If you think in terms of 1/4 tones then there is
room
> between 764 and 906 to add two notes and no room beteen 702 and 764
> to add any notes. No room between 204 and 263. No room between 906
> and 969. Room between 0 and 92. Room between 263 and 386 etc. The
> ratios for the harmonics I gave are 132/128=53, 140/128=155,
> 164/128=429, 176/128=551, 204/128=807, 208/128=841, 232/128=1030
and
> 248/128=1145.

I see about the harmonics. But about making room, I don't understand,
I mean there is always room to put anything between anything else,
or not, so what are you trying to do? Thanks.

PGH

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<phjelmstad@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > <phjelmstad@> wrote:
> > >
> > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > <robertthomasmartin@> wrote:
> > > >
> > > > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > > > <phjelmstad@> wrote:
> > > > >
> > > > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > > > <robertthomasmartin@> wrote:
> > > > > >
> > > > > > --- In tuning-math@yahoogroups.com, Carl Lumma <carl@>
> wrote:
> > > > > > >
> > > > > > > Hi Robert,
> > > > > > >
> > > > > > > >> This scale could be seen as a subset of the 128th
mode
> of
> > > > > > > >> the harmonic series (as you point out), and see this
> > recent
> > > > > > > >> thread for some stuff along those lines
> > > > > > > >>
> > > > > > > >>
> /tuning/topicId_75816.html#75816
> > > > > > > >>
> > > > > > > >> But it's fairly compact on the 7-limit lattice and
may
> be
> > > > > > > >> better seen in that light.
> > > > > > > >>
> > > > > > > >> I don't think it's going to work as a 12-ET
> replacement
> > in
> > > > > > > >> Western music, though there are doubtless some
pieces
> of
> > > > > > > >> music which it will suit.
> > > > > > > >
> > > > > > > >Sorry old chap but the 7-limit lattice doesn't mean
> > anything
> > > > to
> > > > > me.
> > > > > > >
> > > > > > > Well, check out some of the tutorial materials linked to
> > > > > > > on this list's home page.
> > > > > > >
> > > > > > > >The idea of limiting musical ratios to low numbers is
> > > > > unscientific
> > > > > > > >and unproven.
> > > > > > >
> > > > > > > Hardly.
> > > > > > >
> > > > > > > >I am simply opening up an avenue of enquiry for which
I
> > > > > > > >can supply convincing evidence to support my
contentions.
> > > > > > >
> > > > > > > Have you made any contentions? I missed them.
> > > > > > >
> > > > > > > >Music theorists have been juggling low limit ratios
for
> > > > > centuries.
> > > > > > > >The fact that these same music theorists have been
> > obsessed
> > > > with
> > > > > > > >low limit ratios is no proof of anything at all.
> > > > > > >
> > > > > > > But psychoacoustics does provide both a model and
> > experimental
> > > > > > > evidence supporting simple ratios.
> > > > > > >
> > > > > > > >Look at the two musical algorithms I have supplied so
> far.
> > > > They
> > > > > > are
> > > > > > > >universal for all equal temperaments even though I
> prefer
> > > > 22tet.
> > > > > > Why
> > > > > > > >is this? It is because it is the best fit.
> > > > > > >
> > > > > > > The best fit to... what exactly?
> > > > > > >
> > > > > > > -Carl
> > > > > > > Psychoacoustics only provides evidence (not proof) that
> the
> > > > basin
> > > > > > of attraction for Western music is close to 12tet. The
> ratios
> > I
> > > > > > supplied fit into the basin of attraction which conform
> very
> > > > > closely
> > > > > > with the harmonics 0-386-702-969. The implications of
these
> > > > > harmonics
> > > > > > best fit into 22tet. All of the evidence supporting low
> > number
> > > > > ratios
> > > > > > is based on fuzzy perception.
> > > > >
> > > > > 22-tET? Could you show it? That would be cool, I am having
> > trouble
> > > > > getting 22-tET to work very well, without well-tempering it.
> > > > > Then you have to deal with Superpythagorean, Porcupine,
Magic
> > and
> > > > > Diaschisma.
> > > > >
> > > > > PGH
> > > > > "You can tune a piano, but your can't tuna fish"
> > > > >
> > > > From Robert. The figures in cents which are given in
message
> > > 17251
> > > > are 0-92-204-263-386-471-590-702-764-906-969-1088-1200. If
you
> > > graph
> > > > these figures and line them up with 0-109-218-273-382-491-600-
> 709-
> > > 764-
> > > > 927-982-1091-1200 then there is room to add all of the other
> > > figures
> > > > from 22tet. It is a bit rough. Or if you prefer working with
> > > > harmonics then you might get better results adding 53-155-?-
429-
> > 551-
> > > ?-
> > > > 807-841-1030-1145. These harmonic figures including the
> question
> > > > marks are only tentative because I have not yet figured out a
> way
> > > to
> > > > rigorously test them as I have done with the figures in
message
> > > 17251.
> > >
> > > Ich folge nicht. What do you mean "there is room" and what are
> > > the harmonics? Over powers of 2 in the denominator? Sorry....
> > >
> > From Robert. If you think in terms of 1/4 tones then there is
> room
> > between 764 and 906 to add two notes and no room beteen 702 and
764
> > to add any notes. No room between 204 and 263. No room between
906
> > and 969. Room between 0 and 92. Room between 263 and 386 etc. The
> > ratios for the harmonics I gave are 132/128=53, 140/128=155,
> > 164/128=429, 176/128=551, 204/128=807, 208/128=841, 232/128=1030
> and
> > 248/128=1145.
>
> I see about the harmonics. But about making room, I don't
understand,
> I mean there is always room to put anything between anything else,
> or not, so what are you trying to do? Thanks.
>
> PGH
>
From Robert. I'm trying to match the music which I hear in my mind
to an existing model.

🔗Paul G Hjelmstad <phjelmstad@msn.com>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> <phjelmstad@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > <robertthomasmartin@> wrote:
> > >
> > > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > > <phjelmstad@> wrote:
> > > >
> > > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > > <robertthomasmartin@> wrote:
> > > > >
> > > > > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > > > > <phjelmstad@> wrote:
> > > > > >
> > > > > > --- In tuning-math@yahoogroups.com, "robert thomas
martin"
> > > > > > <robertthomasmartin@> wrote:
> > > > > > >
> > > > > > > --- In tuning-math@yahoogroups.com, Carl Lumma <carl@>
> > wrote:
> > > > > > > >
> > > > > > > > Hi Robert,
> > > > > > > >
> > > > > > > > >> This scale could be seen as a subset of the 128th
> mode
> > of
> > > > > > > > >> the harmonic series (as you point out), and see
this
> > > recent
> > > > > > > > >> thread for some stuff along those lines
> > > > > > > > >>
> > > > > > > > >>
> > /tuning/topicId_75816.html#75816
> > > > > > > > >>
> > > > > > > > >> But it's fairly compact on the 7-limit lattice and
> may
> > be
> > > > > > > > >> better seen in that light.
> > > > > > > > >>
> > > > > > > > >> I don't think it's going to work as a 12-ET
> > replacement
> > > in
> > > > > > > > >> Western music, though there are doubtless some
> pieces
> > of
> > > > > > > > >> music which it will suit.
> > > > > > > > >
> > > > > > > > >Sorry old chap but the 7-limit lattice doesn't mean
> > > anything
> > > > > to
> > > > > > me.
> > > > > > > >
> > > > > > > > Well, check out some of the tutorial materials linked
to
> > > > > > > > on this list's home page.
> > > > > > > >
> > > > > > > > >The idea of limiting musical ratios to low numbers
is
> > > > > > unscientific
> > > > > > > > >and unproven.
> > > > > > > >
> > > > > > > > Hardly.
> > > > > > > >
> > > > > > > > >I am simply opening up an avenue of enquiry for
which
> I
> > > > > > > > >can supply convincing evidence to support my
> contentions.
> > > > > > > >
> > > > > > > > Have you made any contentions? I missed them.
> > > > > > > >
> > > > > > > > >Music theorists have been juggling low limit ratios
> for
> > > > > > centuries.
> > > > > > > > >The fact that these same music theorists have been
> > > obsessed
> > > > > with
> > > > > > > > >low limit ratios is no proof of anything at all.
> > > > > > > >
> > > > > > > > But psychoacoustics does provide both a model and
> > > experimental
> > > > > > > > evidence supporting simple ratios.
> > > > > > > >
> > > > > > > > >Look at the two musical algorithms I have supplied
so
> > far.
> > > > > They
> > > > > > > are
> > > > > > > > >universal for all equal temperaments even though I
> > prefer
> > > > > 22tet.
> > > > > > > Why
> > > > > > > > >is this? It is because it is the best fit.
> > > > > > > >
> > > > > > > > The best fit to... what exactly?
> > > > > > > >
> > > > > > > > -Carl
> > > > > > > > Psychoacoustics only provides evidence (not proof)
that
> > the
> > > > > basin
> > > > > > > of attraction for Western music is close to 12tet. The
> > ratios
> > > I
> > > > > > > supplied fit into the basin of attraction which conform
> > very
> > > > > > closely
> > > > > > > with the harmonics 0-386-702-969. The implications of
> these
> > > > > > harmonics
> > > > > > > best fit into 22tet. All of the evidence supporting low
> > > number
> > > > > > ratios
> > > > > > > is based on fuzzy perception.
> > > > > >
> > > > > > 22-tET? Could you show it? That would be cool, I am
having
> > > trouble
> > > > > > getting 22-tET to work very well, without well-tempering
it.
> > > > > > Then you have to deal with Superpythagorean, Porcupine,
> Magic
> > > and
> > > > > > Diaschisma.
> > > > > >
> > > > > > PGH
> > > > > > "You can tune a piano, but your can't tuna fish"
> > > > > >
> > > > > From Robert. The figures in cents which are given in
> message
> > > > 17251
> > > > > are 0-92-204-263-386-471-590-702-764-906-969-1088-1200. If
> you
> > > > graph
> > > > > these figures and line them up with 0-109-218-273-382-491-
600-
> > 709-
> > > > 764-
> > > > > 927-982-1091-1200 then there is room to add all of the
other
> > > > figures
> > > > > from 22tet. It is a bit rough. Or if you prefer working
with
> > > > > harmonics then you might get better results adding 53-155-?-
> 429-
> > > 551-
> > > > ?-
> > > > > 807-841-1030-1145. These harmonic figures including the
> > question
> > > > > marks are only tentative because I have not yet figured out
a
> > way
> > > > to
> > > > > rigorously test them as I have done with the figures in
> message
> > > > 17251.
> > > >
> > > > Ich folge nicht. What do you mean "there is room" and what are
> > > > the harmonics? Over powers of 2 in the denominator? Sorry....
> > > >
> > > From Robert. If you think in terms of 1/4 tones then there is
> > room
> > > between 764 and 906 to add two notes and no room beteen 702 and
> 764
> > > to add any notes. No room between 204 and 263. No room between
> 906
> > > and 969. Room between 0 and 92. Room between 263 and 386 etc.
The
> > > ratios for the harmonics I gave are 132/128=53, 140/128=155,
> > > 164/128=429, 176/128=551, 204/128=807, 208/128=841,
232/128=1030
> > and
> > > 248/128=1145.
> >
> > I see about the harmonics. But about making room, I don't
> understand,
> > I mean there is always room to put anything between anything else,
> > or not, so what are you trying to do? Thanks.
> >
> > PGH
> >
> From Robert. I'm trying to match the music which I hear in my
mind
> to an existing model.

I see, but why 1/4 tones? What's so special about them?

PGH

🔗robert thomas martin <robertthomasmartin@bigpond.com.au>

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<phjelmstad@...> wrote:
>
> --- In tuning-math@yahoogroups.com, "robert thomas martin"
> <robertthomasmartin@> wrote:
> >
> > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > <phjelmstad@> wrote:
> > >
> > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > <robertthomasmartin@> wrote:
> > > >
> > > > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > > > <phjelmstad@> wrote:
> > > > >
> > > > > --- In tuning-math@yahoogroups.com, "robert thomas martin"
> > > > > <robertthomasmartin@> wrote:
> > > > > >
> > > > > > --- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
> > > > > > <phjelmstad@> wrote:
> > > > > > >
> > > > > > > --- In tuning-math@yahoogroups.com, "robert thomas
> martin"
> > > > > > > <robertthomasmartin@> wrote:
> > > > > > > >
> > > > > > > > --- In tuning-math@yahoogroups.com, Carl Lumma
<carl@>
> > > wrote:
> > > > > > > > >
> > > > > > > > > Hi Robert,
> > > > > > > > >
> > > > > > > > > >> This scale could be seen as a subset of the
128th
> > mode
> > > of
> > > > > > > > > >> the harmonic series (as you point out), and see
> this
> > > > recent
> > > > > > > > > >> thread for some stuff along those lines
> > > > > > > > > >>
> > > > > > > > > >>
> > > /tuning/topicId_75816.html#75816
> > > > > > > > > >>
> > > > > > > > > >> But it's fairly compact on the 7-limit lattice
and
> > may
> > > be
> > > > > > > > > >> better seen in that light.
> > > > > > > > > >>
> > > > > > > > > >> I don't think it's going to work as a 12-ET
> > > replacement
> > > > in
> > > > > > > > > >> Western music, though there are doubtless some
> > pieces
> > > of
> > > > > > > > > >> music which it will suit.
> > > > > > > > > >
> > > > > > > > > >Sorry old chap but the 7-limit lattice doesn't
mean
> > > > anything
> > > > > > to
> > > > > > > me.
> > > > > > > > >
> > > > > > > > > Well, check out some of the tutorial materials
linked
> to
> > > > > > > > > on this list's home page.
> > > > > > > > >
> > > > > > > > > >The idea of limiting musical ratios to low numbers
> is
> > > > > > > unscientific
> > > > > > > > > >and unproven.
> > > > > > > > >
> > > > > > > > > Hardly.
> > > > > > > > >
> > > > > > > > > >I am simply opening up an avenue of enquiry for
> which
> > I
> > > > > > > > > >can supply convincing evidence to support my
> > contentions.
> > > > > > > > >
> > > > > > > > > Have you made any contentions? I missed them.
> > > > > > > > >
> > > > > > > > > >Music theorists have been juggling low limit
ratios
> > for
> > > > > > > centuries.
> > > > > > > > > >The fact that these same music theorists have been
> > > > obsessed
> > > > > > with
> > > > > > > > > >low limit ratios is no proof of anything at all.
> > > > > > > > >
> > > > > > > > > But psychoacoustics does provide both a model and
> > > > experimental
> > > > > > > > > evidence supporting simple ratios.
> > > > > > > > >
> > > > > > > > > >Look at the two musical algorithms I have supplied
> so
> > > far.
> > > > > > They
> > > > > > > > are
> > > > > > > > > >universal for all equal temperaments even though I
> > > prefer
> > > > > > 22tet.
> > > > > > > > Why
> > > > > > > > > >is this? It is because it is the best fit.
> > > > > > > > >
> > > > > > > > > The best fit to... what exactly?
> > > > > > > > >
> > > > > > > > > -Carl
> > > > > > > > > Psychoacoustics only provides evidence (not proof)
> that
> > > the
> > > > > > basin
> > > > > > > > of attraction for Western music is close to 12tet.
The
> > > ratios
> > > > I
> > > > > > > > supplied fit into the basin of attraction which
conform
> > > very
> > > > > > > closely
> > > > > > > > with the harmonics 0-386-702-969. The implications of
> > these
> > > > > > > harmonics
> > > > > > > > best fit into 22tet. All of the evidence supporting
low
> > > > number
> > > > > > > ratios
> > > > > > > > is based on fuzzy perception.
> > > > > > >
> > > > > > > 22-tET? Could you show it? That would be cool, I am
> having
> > > > trouble
> > > > > > > getting 22-tET to work very well, without well-
tempering
> it.
> > > > > > > Then you have to deal with Superpythagorean, Porcupine,
> > Magic
> > > > and
> > > > > > > Diaschisma.
> > > > > > >
> > > > > > > PGH
> > > > > > > "You can tune a piano, but your can't tuna fish"
> > > > > > >
> > > > > > From Robert. The figures in cents which are given in
> > message
> > > > > 17251
> > > > > > are 0-92-204-263-386-471-590-702-764-906-969-1088-1200.
If
> > you
> > > > > graph
> > > > > > these figures and line them up with 0-109-218-273-382-491-
> 600-
> > > 709-
> > > > > 764-
> > > > > > 927-982-1091-1200 then there is room to add all of the
> other
> > > > > figures
> > > > > > from 22tet. It is a bit rough. Or if you prefer working
> with
> > > > > > harmonics then you might get better results adding 53-155-
?-
> > 429-
> > > > 551-
> > > > > ?-
> > > > > > 807-841-1030-1145. These harmonic figures including the
> > > question
> > > > > > marks are only tentative because I have not yet figured
out
> a
> > > way
> > > > > to
> > > > > > rigorously test them as I have done with the figures in
> > message
> > > > > 17251.
> > > > >
> > > > > Ich folge nicht. What do you mean "there is room" and what
are
> > > > > the harmonics? Over powers of 2 in the denominator?
Sorry....
> > > > >
> > > > From Robert. If you think in terms of 1/4 tones then there
is
> > > room
> > > > between 764 and 906 to add two notes and no room beteen 702
and
> > 764
> > > > to add any notes. No room between 204 and 263. No room
between
> > 906
> > > > and 969. Room between 0 and 92. Room between 263 and 386 etc.
> The
> > > > ratios for the harmonics I gave are 132/128=53, 140/128=155,
> > > > 164/128=429, 176/128=551, 204/128=807, 208/128=841,
> 232/128=1030
> > > and
> > > > 248/128=1145.
> > >
> > > I see about the harmonics. But about making room, I don't
> > understand,
> > > I mean there is always room to put anything between anything
else,
> > > or not, so what are you trying to do? Thanks.
> > >
> > > PGH
> > >
> > From Robert. I'm trying to match the music which I hear in my
> mind
> > to an existing model.
>
> I see, but why 1/4 tones? What's so special about them?
>
> PGH
>
From Robert. That's what I hear in my mind.ie, Approximate 1/4
tones. I've heard other musicians say similar things. If I only heard
1/2 tones then I probably would never have become interested in
microtonality. I can certainly appreciate all sorts of smaller
intervals but I can't honestly say that I can play them in my mind to
any reasonably accurate degree.

🔗Andreas Sparschuh <a_sparschuh@yahoo.com>

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> Consider the following where figures are rounded
> off to the nearest cent. C=1/1=0, C#=135/128=92, D=9/8=204,
> Eb=149/128=263, E=5/4=386, F=21/16=471, F#=45/32=590, G=3/2=702, and
> Ab=199/128=764, A=27/16=906, Bb=7/4=969, B=15/8=1088 and
> c=2/1=1200cents. All of these ratios have a common denominator of
> 1/128. Forget about limiting your ratios for a moment and consider
> ratios that belong to the same family (ie 1/128). Sink your
> mathematical teeth into exploring another idea. I can assure you that
> it is worth the time and trouble. Consider it an exercise.
>
Hi Robert & all others,
that's corresponds to:

!RTMs17251.scl
12
Robert Thomas Martin's from: yahoo-tuning-math meassage #17251
!
135/128 ! C#
9/8 ! D
149/128 ! Eb
5/4 ! E
21/16 ! F
45/32 ! F#
3/2 ! G
199/128 ! Ab
27/16 ! A
7/4 ! Bb
15/8 ! B
2/1
!
obtainded from the following cycle of 5ths:
C 1
G 3
D 9
A 27
E 5 10 20 40 80 (<81)
B 15
F# 45
C# 135
Ab 199 399 (<405)
Eb 149 298 596 (<597)
Bb 7...448 (>449) attend the wide broade dog-5th-
F 21
C 1...64(< 63) even worser, an 'septimal' comma wide
http://en.wikipedia.org/wiki/Septimal_comma

For another refined angle,
without any wide 5th-dogs look at:
/tuning/topicId_76237.html#76334

Yours Sincerely
A.S.