Yahoo Tuning Groups Ultimate Backup tuning RE: [tuning] Re: Complexity and inaudible primeness (was: 64:75:9 6)

Jacky wrote,

>A little bit of the fog bank still remains for me. If "there is no
>audible effect or affect due to the introduction of ratios with a new
>prime factor", does mentioning "prime" or "odd" limits have any
>meaning for defining scales other that the mathematical proportions
>behind the tuning?

Odd limit is a great measure of _intervallic_ consonance (it was Partch's),
if you're forcing octave-equivalence on the system. Prime limit is, by
contrast, an important characteristic of a JI _tuning system_, since there
won't be any intervals whose _odd limit_ is a prime number higher than the
tuning system's prime limit. In other words,

Tuning system Intervallic
Prime Limit Odd Limit

3 ----------> 3
5 ----------> 5
7 ----------> 9
11 ----------> 11
13 ----------> 15

However, there may be _very close approximations_ to higher odd-limit
intervals, e.g., Pythagorean tuning (= 3-prime-limit JI) with its schismatic
"5-limit thirds", and 5-prime-limit JI with its 225:128s approximating 7:4s.

>If higher primes can't be perceived, what purpose
>do these labels serve for us other than a mathematical one?

As explained above (hopefully), the prime label gives you an idea of the
resources of the tuning system, though only if you insist on absolutely
exact JI.

🔗ligonj@northstate.net

Paul,

This is indeed interesting, as I refer to one of my favorite JI
systems as being 37 Prime JI, yet the subset 12 and 13 pitch scales
are constructed by order of where the intervals occur in the odd
limits, rather than by order of primes (The total scale has 144
distinctly different pitches). But based on what you are saying here,
I am correct in my definition, because I'm wanting it to be clear
that the prime limit terminates at 37 Prime - whether audibly
perceptable or not.

Thanks for the clarification,

Jacky Ligon

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>
> Odd limit is a great measure of _intervallic_ consonance (it was
Partch's),
> if you're forcing octave-equivalence on the system. Prime limit is,
by
> contrast, an important characteristic of a JI _tuning system_,
since there
> won't be any intervals whose _odd limit_ is a prime number higher
than the
> tuning system's prime limit. In other words,
>
> >If higher primes can't be perceived, what purpose
> >do these labels serve for us other than a mathematical one?
>
> As explained above (hopefully), the prime label gives you an idea
of the
> resources of the tuning system, though only if you insist on
absolutely
> exact JI.

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
> >yet the subset 12 and 13 pitch scales
> >are constructed by order of where the intervals occur in the odd
> >limits, rather than by order of primes
>
> Could you elaborate, if so inclined?

Scale 12:

Ratio Cents Value
1/1 0
24/23 73.6806536
26/23 212.2533145
27/23 277.5906553
27/22 354.5470602
27/20 519.5512887
52/37 589.183623
37/26 610.816377
40/27 680.4487113
44/27 845.4529398
46/27 922.4093447
23/13 987.7466855
23/12 1126.319346
2/1 1200

The 37 Prime limit of this scale is determined by the 2 tritones.

>
> >because I'm wanting it to be clear
> >that the prime limit terminates at 37 Prime - whether audibly
> >perceptable or not.
>
> 37 would only be audibly relevant in a big otonal chord that
included the 37
> identity and many others -- got any of those in your tuning?

Yes, because these subset scales have inversional symmetry, there is
an equal amount of harmonic and subharmonic intervals. But surely you
are correct about them being "audibly relevant" under certain
contexts.

Jacky Ligon

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Jacky wrote,

>> >yet the subset 12 and 13 pitch scales
>> >are constructed by order of where the intervals occur in the odd
>> >limits, rather than by order of primes
>
>> Could you elaborate, if so inclined?

>Scale 12:

>Ratio Cents Value
>1/1 0
>24/23 73.6806536
>26/23 212.2533145
>27/23 277.5906553
>27/22 354.5470602
>27/20 519.5512887
>52/37 589.183623
>37/26 610.816377
>40/27 680.4487113
>44/27 845.4529398
>46/27 922.4093447
>23/13 987.7466855
>23/12 1126.319346
>2/1 1200

Hmm . . . of the 78 intervals in this 13-tone scale, I'm not seeing any that
would involve odd-limit in a perceptually relevant way . . . the simplest
are 10:11, 10:13, and 12:13 and aren't involved in enough otonal synegies to
bring them into the perceptually relevant arena . . . you also have
intervals as complex as 1369:1352 in there . . .

>> 37 would only be audibly relevant in a big otonal chord that
included the 37
>> identity and many others -- got any of those in your tuning?

>Yes, because these subset scales have inversional symmetry, there is
>an equal amount of harmonic and subharmonic intervals.

Right, but any big otonal chords? If not, I'm afraid I may have to judge the
simplicity of the ratios irrelevant to the audible effect of the scale -- in
other words, if you like the audible effect of the scale, JI has nothing to
do with it and I'm sure you'd be musically well-served by exploring many
non-JI avenues if you so desire.

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>
> Hmm . . . of the 78 intervals in this 13-tone scale, I'm not seeing
any that
> would involve odd-limit in a perceptually relevant way . . . the
simplest
> are 10:11, 10:13, and 12:13 and aren't involved in enough otonal
synegies to
> bring them into the perceptually relevant arena . . . you also have
> intervals as complex as 1369:1352 in there . . .
>
>
> Right, but any big otonal chords? If not, I'm afraid I may have to
judge the
> simplicity of the ratios irrelevant to the audible effect of the
scale -- in
> other words, if you like the audible effect of the scale, JI has
nothing to
> do with it and I'm sure you'd be musically well-served by exploring
many
> non-JI avenues if you so desire.

Paul,

Sorry for not answering the question properly - I did slip, and fail
to mention that this is a scale that I would likely not play chords
with, but would more typically use melodically - say for instance on
a sound such as a flute timbre. Very lovely this way! I really do
enjoy the sound of scales like this one for their melodic properties.

Please explain "synergies".

Jacky

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
I really do
> >enjoy the sound of scales like this one for their melodic
properties.
>
> I'm sure it is -- and I believe you could come up with equally
lovely scales
> without a JI conception.
>

Paul,

I thought it would be of great interest to ask for you to demonstrate
the generation of a scale with "good" melodic properties that
is "without a JI conception". Are you speaking of phi based scales or
ETs here? A good set of 12 or 13 tone melodic scales that are
generated completely outside of JI would be hugely interesting to
hear! May I add too that IMHO this can be a highly subjective art.

I would like to share a melodic property which I favor - that of a
number of intervals which neighbor around the 4/3 and 3/2 (yes, I
know they are inversions):

13/10 454.2139479
30/23 459.9943675
17/13 464.4277477
21/16 470.7809073
25/19 475.1144116
27/20 519.5512887
23/17 523.3189378
19/14 528.6871097
34/25 532.3279818
15/11 536.9507724
26/19 543.0146456

and

19/13 656.9853544
22/15 663.0492276
25/17 667.6720182
28/19 671.3128903
34/23 676.6810622
40/27 680.4487113
38/25 724.8855884
32/21 729.2190927
26/17 735.5722523
23/15 740.0056325
20/13 745.7860521

Many exotically beautiful melodic scales can be constructed without
4/3 and 3/2 being present. I enjoy the melodic quality that one can
give a scale by choosing to go either wider or flatter from these
primary intervals.

Jacky Ligon

🔗Dave Keenan <D.KEENAN@UQ.NET.AU>

--- In tuning@egroups.com, ligonj@n... wrote:
> Ratio Cents Value
> 1/1 0
> 24/23 73.6806536
> 26/23 212.2533145
> 27/23 277.5906553
> 27/22 354.5470602
> 27/20 519.5512887
> 52/37 589.183623
> 37/26 610.816377
> 40/27 680.4487113
> 44/27 845.4529398
> 46/27 922.4093447
> 23/13 987.7466855
> 23/12 1126.319346
> 2/1 1200

Dear Jacky,

I'm afraid that isn't a JI scale at all, unless you're using it with
some pretty wild timbres, e.g. having no odd harmonics below the 8th
and lots between 20 and 37, and even then it's doubtful.

For ordinary timbres, the only JI intervals here, apart from the
octaves, are the 8:9s (or 4:9s) between 24/23 and 27/23 and between
46/27 and 23/12. The simplest large-ish otonalities I can find are
20:22:23:27 and 23:24:26:27. It is barely conceivable that we might be
able to hear a locking in (or beat cancellation or clarification) of
these if a note were mistuned and then brought back into tune. But
that still leaves an enormous amount of freedom to adjust the pitches
of this scale without bending any just intervals. In other words, for
most of the pitches, the fact that they are medium integer ratios is
totally irrelevant to the way the scale sounds. Almost everything
important about the scale would be given by the cent values (and you
don't need the decimal places).

You said you mainly use it melodically and I can see why. Whether or
not a scale is JI is fundamentally a harmonic property, whether or not
the scale is used for harmony.

It may be quite nice melodically, but can I ask you to try an
experiment? For each pitch (except 1/1) flip a coin to see if you will
change it or not, and then flip again to see if you will sharpen it by
5 cents or flatten it by 5 cents. Then get somone to play the same
things in both the original and modified scale. Each time flipping a
coin to see which tuning they play it in first, and keeping a record
of the flips. Then you listen and try to pick which is the original
scale each time and keep a record. After you've done it enough times
or with enough different pieces, stop and see how well you did. We
need a blind test like this to be sure that you're only being
influenced by the sound, not by what you believe about the numbers.

Regards,
-- Dave Keenan

🔗ligonj@northstate.net

--- In tuning@egroups.com, "Dave Keenan" <D.KEENAN@U...> wrote:
>
> Dear Jacky,
>
> I'm afraid that isn't a JI scale at all, unless you're using it
with
> some pretty wild timbres, e.g. having no odd harmonics below the
8th
> and lots between 20 and 37, and even then it's doubtful.

Even though I don't think I was calling it JI here, you are correct
in assuming that I was considering it to be so. Admittedly, it is
an "extreme" scale - being of mostly melodic interest to me.

Going by your definition of JI - that of tuning out the beats from
intervals (also appealing to me, but does not rule my world either),
there are many rational scales I use which could not fairly be called
JI. I'm not at all dogmatic about the definition of JI being the
blanket term for all the ration based scales I like to use (and there
are a plenty!). For my own purposes, the melodic possibilities of
such scales are their really alluring aspect. True, if you analyze
the dyads you'll hear beating, but tune up a nice flute sample and
play the notes sequentially in a developed melodic theme and it can
be pure magic. There's a beautiful tension/energy about this that is
ineffable. I think one can obviously do a great job of chord
analysis, but melodic analysis is much more illusive (and
subjective).

OM, Context, Context, Context, Context, OM : )

Almost everything
> important about the scale would be given by the cent values (and
you
> don't need the decimal places).

The data was just pasted from my spread sheet. If anything the ratios
immediately show the symmetry of the scale (perhaps these kinds of
things are only important here).

>
> You said you mainly use it melodically and I can see why. Whether
or
> not a scale is JI is fundamentally a harmonic property, whether or
not
> the scale is used for harmony.

This is something I will certainly bear in mind. A good point!

>
> It may be quite nice melodically, but can I ask you to try an
> experiment?

Such an experiment would be an interesting listening test. I don't
think I could set up something like this myself without tainting the
results though, since during the process of playing, composing and or
singing parts, I expose myself for long periods of time to the
tuning. Perhaps I could try something such as this when my current
plate of musical responsibilities is cleared - but I think I would
tend to just prefer to outright compose new music - this is just one
slice of the higher prime ratios I use from a much larger total
scale, and it is indeed a rich and exotic landscape.

Thanks for the truly enlightening suggestions!

Best Regards,

Jacky Ligon

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

> http://www.egroups.com/message/tuning/16073
>
> As explained above (hopefully), the prime label gives
> you an idea of the resources of the tuning system, though
> only if you insist on absolutely exact JI.

Paul, as I've said I do think that you and I pretty much
agree now on the significance of 'prime-ness' in tuning.

But with all due respect, I think I'd have to say exactly
the opposite of what you say here. I think primes are
important because they indicate the simplest irreducible
implications of any given tuning.

So that, for example, a performance may actually be
tuned in 12-tET, a meantone, a well-temperament, or
whatever, but will *imply* a tuning with a specific
set of prime-factors. Which prime-factors are implied
will depend, of course, on the amount of deviation between
the actual tuning and the implied prime-limits of the JI
analysis and on the listener's experience.

Again, this is not to say that other types of tunings
do not convey information specific to their particular
mathematical properties. I simply believe, myself, that
any individual's experience will give him a sense of
a musical performance as conveying a certain type of
low-integer JI tuning; which type, again, depends on
the discrepancy between analysis and performance and
on the listener's experience.

In short, I think the primes provide some kind of template
into which the ear/brain system attempts to fit what it hears.

I can't point to any rigorous experiments which prove this
hypothesis; all I can do is refer the reader to the various
JI analyses and compositions I've given on my webpages and
ask him to draw his own conclusions.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:

> http://www.egroups.com/message/tuning/16113
>
> Monz wrote,
>
> > So that, for example, a performance may actually be
> > tuned in 12-tET, a meantone, a well-temperament, or
> > whatever, but will *imply* a tuning with a specific
> > set of prime-factors.
>
> I absolutely disagree, and have spent an inconceivable number
> of words over the last few years emphasizing this point. For
> example, in a C major scale, the note "D" in any of the tunings
> above can imply 9/8, 10/9, or both simultaneously, depending
> on the context; but what JI fails to capture is that in the
> repertoire, this is aurally, structurally, and motivically
> _one note_ and only one note.
>
> > In short, I think the primes provide some kind of template
> > into which the ear/brain system attempts to fit what it hears.
>
> I think not, because no musician ignorant of JI theory has
> ever noticed any kind of ambiguity as regards the note "D"
> in the major scale . . .

But Paul, in tonal music, even listeners ignorant of JI theory
will recognize a 12-tET 'D' (in the key of 'C') as functioning
as a 9/8, 10/9, 8/7, or whatever the harmonic/melodic context
is implying. That was my point.

A listener's reception of *any* tuning is totally dependent
on his previous listening experience, and also to varying degrees
on his music-theoretical knowledge.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

🔗Paul Erlich <PERLICH@ACADIAN-ASSET.COM>

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
>
> --- In tuning@egroups.com, "Paul H. Erlich" <PERLICH@A...> wrote:
>
> > I think not, because no musician ignorant of JI theory has
> > ever noticed any kind of ambiguity as regards the note "D"
> > in the major scale . . .
>
> But Paul, in tonal music, even listeners ignorant of JI theory
> will recognize a 12-tET 'D' (in the key of 'C') as functioning
> as a 9/8, 10/9, 8/7, or whatever the harmonic/melodic context
> is implying. That was my point.

I disagree that they will recognize these functions, nor will they recognize as
distinct those cases where the D is functioning simultaneously in more than
one of these roles. The only element of JI theory that I might agree has a
correlate in the perception of music in _any_ tuning is the brain's analysis of
simultaneities as parts of a virtual harmonic series (which is what harmonic
entropy models) or the identification of a ratio which is perceived to be low
in roughness, and therefore near a simple integer ratio if harmonic-partial
timbres are used. Neither 9/8 nor 10/9 is describing the perceived
proportions of simultaneous notes in a low-roughness chord or virtual
harmonic series -- they are obtained by _multiplying_ such a proportion (3/4
or 5/6) by a horizonatal interval (3/2 or 4/3, respectively). Such a
multiplication is of course valid if one is working in a JI system and wants to
calculate the frequency of the pitch in question. However, in common-
practice tonal music one simply has the note D which, like all the other notes
in the scale, participates in various consonant triads, and forcing a piece of
such music onto a JI lattice will involve mapping the note now to one point,
then to another point, other times to both points simultaneously if allowed by
the premises of the particular analysis -- and yet these distinctions have no
perceptual correlate and hence no explanatory power. Common-practice
tonal music is best understood in terms of a lattice that wraps around and
meets itself so that there is only one D, which can participate simultaneously
and equally in all the consonances that it traditionally can.
>
> A listener's reception of *any* tuning is totally dependent
> on his previous listening experience, and also to varying degrees
> on his music-theoretical knowledge.

This is ironic -- I would have thought that you would agree with me that the
aspects of the "reception" we are trying to model are largely _innate_, that is,
I'm basing my argument on universal psychoacoustical phenomena, while I
thought you were claiming that the brain performs prime-factorization
regardless of listening experience and music-theoretical knowledge.
>
>
>
> -monz
> http://www.ixpres.com/interval/monzo/homepage.html
> 'All roads lead to n^0'

🔗David J. Finnamore <daeron@bellsouth.net>

Paul Erlich wrote:

> The only element of JI theory that I might agree has a
> correlate in the perception of music in _any_ tuning is the brain's analysis of
> simultaneities as parts of a virtual harmonic series (which is what harmonic
> entropy models) or the identification of a ratio which is perceived to be low
> in roughness, and therefore near a simple integer ratio if harmonic-partial
> timbres are used. Neither 9/8 nor 10/9 is describing the perceived
> proportions of simultaneous notes in a low-roughness chord or virtual
> harmonic series -- they are obtained by _multiplying_ such a proportion (3/4
> or 5/6) by a horizonatal interval (3/2 or 4/3, respectively). Such a
> multiplication is of course valid if one is working in a JI system and wants to
> calculate the frequency of the pitch in question. However, in common-
> practice tonal music one simply has the note D which, like all the other notes
> in the scale, participates in various consonant triads, and forcing a piece of
> such music onto a JI lattice will involve mapping the note now to one point,
> then to another point, other times to both points simultaneously if allowed by
> the premises of the particular analysis -- and yet these distinctions have no
> perceptual correlate and hence no explanatory power.

This is really a good explanation. It rings true to me.

Could it be relevant that the critical band is about 9:8 to 7:6 wide at most musical fundamental pitch frequencies? If so, then I propose as a rule of thumb that intervals
with significantly overlapping critical bands tend not to be heard as parts of a virtual harmonic series. The sticky part here might be pinning down the exact point at which
overlap becomes "significant." I would have to leave that to the "math guys" - it's over my head. The equation in my acoustics book for Equivalent Rectangular Band is

ERB = 6.23*f^2 + 93.3*f + 28.52 Hz
f = freq. in kHz

The critical band gets gradually wider below about 1 kHz until, below about 200 Hz, it's wider than 5:4. That could explain why, for example, 6:5 sounds like a nice, clear
consonance up around mid range but starts to get muddy down in the bass range.

> > A listener's reception of *any* tuning is totally dependent
> > on his previous listening experience, and also to varying degrees
> > on his music-theoretical knowledge.
>
> This is ironic -- I would have thought that you would agree with me that the
> aspects of the "reception" we are trying to model are largely _innate_,

I also thought he contradicted himself there. Monz?

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

David Finnamore wrote,

>This is really a good explanation. It rings true to me.

Thanks. These are very difficult ideas for me to express in words, as I
think very non-verbally, but hopefully we can convince Monz that he's
barking up the wrong tree here.

>Could it be relevant that the critical band is about 9:8 to 7:6 wide at
most musical fundamental >pitch frequencies? If so, then I propose as a
rule of thumb that intervals
>with significantly overlapping critical bands tend not to be heard as parts
of a virtual >harmonic series.

I think you're confusing two consonance mechanisms here -- virtual pitch and
critical band roughness. A bunch of tones (even sine waves) with very high
critical band roughness, such as 12:13:14 or a mistuning thereof, can evoke
a very clear virtual pitch and hence be perceived as part of a virtual
harmonic series. However, you're probably right as regards the other
component of consonance -- if the fundamentals are within a critical band of
one another, that often represents a regime of considerably greater
dissonance than when pairs of mere partials are within a critical band of
one another.

>The critical band gets gradually wider below about 1 kHz until, below about
200 Hz, it's wider >than 5:4. That could explain why, for example, 6:5
sounds like a nice, clear
>consonance up around mid range but starts to get muddy down in the bass
range.

You bet!

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "Paul Erlich" wrote:

> http://www.egroups.com/message/tuning/16148
>
> --- In tuning@egroups.com, " Monz" wrote:
> >
> > --- In tuning@egroups.com, "Paul H. Erlich" wrote:
> >
> > > I think not, because no musician ignorant of JI theory has
> > > ever noticed any kind of ambiguity as regards the note "D"
> > > in the major scale . . .
> >
> > But Paul, in tonal music, even listeners ignorant of JI theory
> > will recognize a 12-tET 'D' (in the key of 'C') as functioning
> > as a 9/8, 10/9, 8/7, or whatever the harmonic/melodic context
> > is implying. That was my point.
>
> I disagree that they will recognize these functions, nor
> will they recognize as distinct those cases where the D
> is functioning simultaneously in more than one of these
> roles. The only element of JI theory that I might agree has
> a correlate in the perception of music in _any_ tuning is
> the brain's analysis of simultaneities as parts of a
> virtual harmonic series (which is what harmonic entropy
> models) or the identification of a ratio which is perceived
> to be low in roughness, and therefore near a simple integer
> ratio if harmonic-partial timbres are used. Neither 9/8 nor
> 10/9 is describing the perceived proportions of simultaneous
> notes in a low-roughness chord or virtual harmonic series
> -- they are obtained by _multiplying_ such a proportion
> (3/4 or 5/6) by a horizonatal interval (3/2 or 4/3,
> respectively). Such a multiplication is of course valid
> if one is working in a JI system and wants to calculate
> the frequency of the pitch in question. However, in
> common-practice tonal music one simply has the note
> D which, like all the other notes in the scale, participates
> in various consonant triads, and forcing a piece of such
> music onto a JI lattice will involve mapping the note
> now to one point, then to another point, other times to
> both points simultaneously if allowed by the premises
> of the particular analysis -- and yet these distinctions
> have no perceptual correlate and hence no explanatory
> power. Common-practice tonal music is best understood
> in terms of a lattice that wraps around and meets itself
> so that there is only one D, which can participate
> simultaneously and equally in all the consonances that
> it traditionally can.
>
> >
> > A listener's reception of *any* tuning is totally dependent
> > on his previous listening experience, and also to varying degrees
> > on his music-theoretical knowledge.
>
> This is ironic -- I would have thought that you would agree with me
that the
> aspects of the "reception" we are trying to model are largely
_innate_, that is,
> I'm basing my argument on universal psychoacoustical phenomena,
while I
> thought you were claiming that the brain performs prime-
factorization
> regardless of listening experience and music-theoretical knowledge.
> >

David J. Finnamore:

> http://www.egroups.com/message/tuning/16225
>
> I also thought he contradicted himself there. Monz?

Sorry to take so long to respond to this. I'd appreciate
it if both of you (Paul and David F.) would expand on what
you're saying here; for some reason I'm not seeing how you
disagree with me or how I'm contradicting myself. Probably,
I'm having trouble expressing my true thoughts clearly.

Part of the problem may be that I'm so knowledgeable now
about music and tuning theory that I can't really view the
perspective of someone who lacks that training, altho I'm
trying.

(I've often complained to 'musically illiterate' friends
that I can no longer enjoy music they way they do, because
when I hear any music, I'm always analyzing it and 'seeing'
the score in my mind. In other words, my reception of
music is never as a purely visceral experience; it's
always intellectual now. I suppose that has its good
points too, but in any case, my reception is quite
different from that of the 'average listener'.)

I'm trying to express my belief that regardless of
their training, someone who listens to a piece of music
with any real attentiveness, can follow the harmonic
and melodic logic, which I believe can be modelled at
least to some extent mathematically, whether it's by
means of JI theory or ET theory, or whatever type
of analysis is used.

For example, I never placed much stock in Schenker's theories,
but many other theorists have and do, and if it works for
them, then there must be *some* amount of validity to it,
however small in my opinion.

So all I'm trying to point out is that even in
common-practice music (i.e., regardless of the specific
tuning used), harmonic progressions that are based
on JI theory can be perceived by most listeners - at
least that's what I think.

What you say in your big first paragraph, Paul, makes
a lot of sense to me, but I think I'm still a little
unclear on some parts of your argument. I'd appreciate
a little more detail, and from you, David F., a little
more on why you agree with Paul and disagree with me.

I hope what I wrote here helps to get my thoughts across
better.

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

Monz wrote,

>I'd appreciate
>it if both of you (Paul and David F.) would expand on what
>you're saying here; for some reason I'm not seeing how you
>disagree with me or how I'm contradicting myself.

At this point I can only suggest that you clear your mind and look at the
exchange again, including your own posts. I found it difficult enough to
articulate the arguments as it was; I don't think I could do a better job
right now, though if you have specific questions, I could try to answer
them.

>I'm trying to express my belief that regardless of
>their training, someone who listens to a piece of music
>with any real attentiveness, can follow the harmonic
>and melodic logic, which I believe can be modelled at
>least to some extent mathematically, whether it's by
>means of JI theory or ET theory, or whatever type
>of analysis is used.

Right, but _some_ types of analysis might not be applicable to _some_ types
of music. For example, the paper that just came up,
http://web.presby.edu/~danderso/diss/, makes the argument that theorists who
tried to apply Schenkerian analysis to music from the twelfth through
sixteenth centuries were misusing the theory (which is intended to describe
"tonal" music), and their analyses ended up with little or no explanatory
value, since all they were doing was "cramming" the pieces in to a framework
where they didn't belong. I feel the same way about JI analyses of sixteenth
through nineteenth century Western music.

🔗Joseph Pehrson <pehrson@pubmedia.com>

🔗Paul H. Erlich <PERLICH@ACADIAN-ASSET.COM>

🔗Joseph Pehrson <pehrson@pubmedia.com>

🔗David Finnamore <daeron@bellsouth.net>

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:
> and from you, David F., a little
> more on why you agree with Paul and disagree with me.

Gladly. Here's what seems contradictory to me:

[from 16107]
> > In short, I think the primes provide some kind of template
> > into which the ear/brain system attempts to fit what it hears.

[from 16137, where the above was also quoted]
> A listener's reception of *any* tuning is totally dependent
> on his previous listening experience, and also to varying degrees
> on his music-theoretical knowledge.

I don't understand how humans could both have a prime template in our
psycho-acoustical apparatus _and_ be totally dependant on previous
listening experience plus music theory knowledge for reception of any
tuning.

So, since I'm pretty sure I don't understand your point of view, I
can't say that I disagree with you. :-) The reason I found Paul's
explanation so compelling is only that, as I said, it rings true for
me. Intuitively, it fits what I have experienced over 4 years of
fiddling with hundreds of tunings. I haven't worked out an
explanation of my own, I'm afraid.

At the risk of putting words in his mouth, I think that part of what
Paul might be objecting to is the idea that we hear primeness itself
in intervals. To accept that we hear primeness requires adding some
mysticism to the equation - and to repudiate certain Enlightenment
assumptions in the process. Not necessarilly a bad idea in itself,
but perhaps inappropriate to an academic-like forum such as this
where irrefutable lines of logic and verifiable results are the order
of the day. We can scientifically know that we hear and perceive
things like beating and roughness, consonance and dissonance, and
span in intervals. We may never be able to verify whether or not we
can perceive the mathematical properties themselves in intervals.
There was a time when I was certain we could. But that certainty is
not (yet) warranted.

David Finnamore

🔗Monz <MONZ@JUNO.COM>

--- In tuning@egroups.com, "David Finnamore" <daeron@b...> wrote:

> http://www.egroups.com/message/tuning/16278
>
> --- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

> > and from you, David F., a little
> > more on why you agree with Paul and disagree with me.
>
> Gladly. Here's what seems contradictory to me:
>
>
> [monz, http://www.egroups.com/message/tuning/16107]
>
> > > In short, I think the primes provide some kind of template
> > > into which the ear/brain system attempts to fit what it hears.
>
>
> [monz, http://www.egroups.com/message/tuning/16137,
> where the above was also quoted]
>
> > A listener's reception of *any* tuning is totally dependent
> > on his previous listening experience, and also to varying
> > degrees on his music-theoretical knowledge.
>
>
> I don't understand how humans could both have a prime template
> in our psycho-acoustical apparatus _and_ be totally dependant
> on previous listening experience plus music theory knowledge
> for reception of any tuning.
>
> So, since I'm pretty sure I don't understand your point of view,
> I can't say that I disagree with you. :-)

OK - fair enough.

>
> <snip>
>
> At the risk of putting words in his mouth, I think that part
> of what Paul might be objecting to is the idea that we hear
> primeness itself in intervals.

I totally agree with Paul and you on this! We can't hear
primeness in *intervals* (= dyads), but I think we *do* hear
primeness in an overall systemic sense.

Perhaps characterizing this process by invoking a 'prime template
in our psycho-acoustical apparatus' is not the right way to
go about explaining it. If I did that, sorry.

But the idea that we *reduce* what we hear into terms that can be
modelled as prime-factor proportions simply makes so much sense
to me that I can't let go of it. And the prime proportions that
we *believe* we are hearing will be the result of our prior
experience and knowledge.

I dunno... probably this has more to do with mathematics than
auditory perception, and I'm *far* from being qualified enough
in math to explain it. But I really do think that there's a
connection between the two, and I'm interested enough to keep
pursuing it. If I'm barking up the wrong tree... oh well,
guess I'll eventually lose my voice, then no one will have
to be concerned about listening to me anymore. :)

-monz
http://www.ixpres.com/interval/monzo/homepage.html
'All roads lead to n^0'

🔗Joseph Pehrson <josephpehrson@compuserve.com>

--- In tuning@egroups.com, " Monz" <MONZ@J...> wrote:

http://www.egroups.com/message/tuning/16290

> I dunno... probably this has more to do with mathematics than
> auditory perception, and I'm *far* from being qualified enough
> in math to explain it. But I really do think that there's a
> connection between the two, and I'm interested enough to keep
> pursuing it. If I'm barking up the wrong tree... oh well,
> guess I'll eventually lose my voice, then no one will have
> to be concerned about listening to me anymore. :)
>

Remember when Arnold Schoenberg told John Cage that Cage had no
"feeling" for harmony and probably shouldn't be a composer since he
would be beating his head up against a brick wall?? Cage's famous
response was to tell Arnie that he would spend the rest of his life
hitting his head against that wall...

No overt comparisons, Monz... just the story came back to mind...

________ ___ __ _
Joseph Pehrson