Yahoo Tuning Groups Ultimate Backup tuning Chord names in Scala

I have a question for Manuel regarding Scala chord names found in
file chordnam.par. What is the basis for naming new chords in this
file, and on what basis are additional entries accepted? Is this
essentially a list of chord names that has accumulated in the course
of tuning list communications?

I frequently like to try out just chords containing 13 to see how
they are rendered in various tunings. However, there are very few in
this file, so I have had to make my own copy of the file containing
the chords that I use. With the frequent updates to Scala, it has
become bothersome to have to copy my version of this file each time
and to maintain it to keep current with official updates to the file,
so I would like to have some chords added (with my proposed names
given here, subject to review by others):

4:5:6:7:9:11 Harmonic Eleventh
4:5:6:7:9:11:13 Harmonic Thirteenth
4:5:6:7:9:11:13:15 Harmonic Fourteenth
6:7:9:11:13 Tridecimal Subminor Ninth
9:11:13:15 Isoharmonic Diminished Seventh

There is also another version of the diminished seventh that I use:

15:18:21:25 Contracting Diminished Seventh

In arriving at a name for this, I observed that there are already
diminished seventh chords named:

10:12:14:17 Harmonic Diminished Seventh
25:30:35:42 Diminished Seventh

The harmonic diminished seventh chord has the largest interval
between the outer tones, hence most effictively resolves the
diminished 7th interval (by expansion) to an octave. My
proposed "contracting diminished seventh" chord has the smallest
interval between the outside tones, hence more effectively resolves
the diminished 7th interval (by contraction) to a fifth. (And
perhaps someone can think of a better name for this chord that
conveys the same meaning.)

--George

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > The harmonic diminished seventh chord has the largest interval
> > between the outer tones, hence most effictively resolves the
> > diminished 7th interval (by expansion) to an octave.
>
> How is a diminshed 7th interval supposed to resolve by expansion to
> an octave? One note would have to be chromatically altered in the
> process.

Sorry, I got sloppy with the spelling. In this case the diminished
7th chord would be in first inversion, so the outer tones should be a
major 6th resolving to an octave.

> The traditional resolution of the diminished 7th interval,
> requiring no chromatic shifts, is by contraction to a 5th, which
you
> mentioned later in your message.

Considering that we have at least 3 possible JI diminished 7th chords:
10:12:14:17
15:18:21:25
25:30:35:42
each of which has 3 inversions (for 12 total possibilities), it might
be interesting to experiment with these to rank them in order of
effectiveness for resolutions to various major and minor triads. I
expect that the instances in which the (melodic) semitones are
smallest would be the most effective.

--George

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Alison Monteith <alison.monteith3@which.net>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, Alison Monteith
<alison.monteith3@w...> wrote:
> on 14/1/04 17:56, George D. Secor at gdsecor@y... wrote:
>
>
> >
> > Considering that we have at least 3 possible JI diminished 7th
chords:
> > 10:12:14:17
> > 15:18:21:25
> > 25:30:35:42
> > each of which has 3 inversions (for 12 total possibilities), it
might
> > be interesting to experiment with these to rank them in order of
> > effectiveness for resolutions to various major and minor triads.
I
> > expect that the instances in which the (melodic) semitones are
> > smallest would be the most effective.
> >
> > --George
> >
>
> Not necessarily in my experience. I haven't yet tried resolving the
chords
> above but in working with tetrads from the Eikosany I've found that
the
> smallest interval resolution isn't necessarily the most pleasing to
the ear,
> as indeed is the case in coventional four part harmony.

I don't think that's necessarily the case, nor is it what George was
suggesting. If the possibility exists for a chord progression to be
heard in conventional diatonic terms, then I think George would agree
that resolving by an augmented unison would be less effective than
resolving by a semitone, even if the former is the smaller interval.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, Alison Monteith
> <alison.monteith3@w...> wrote:
> > on 14/1/04 17:56, George D. Secor at gdsecor@y... wrote:
> >
> >
> > >
> > > Considering that we have at least 3 possible JI diminished 7th
> chords:
> > > 10:12:14:17
> > > 15:18:21:25
> > > 25:30:35:42
> > > each of which has 3 inversions (for 12 total possibilities), it
> might
> > > be interesting to experiment with these to rank them in order of
> > > effectiveness for resolutions to various major and minor
triads.
> I
> > > expect that the instances in which the (melodic) semitones are
> > > smallest would be the most effective.
> > >
> > > --George
> > >
> >
> > Not necessarily in my experience. I haven't yet tried resolving
the
> chords
> > above but in working with tetrads from the Eikosany I've found
that
> the
> > smallest interval resolution isn't necessarily the most pleasing
to
> the ear,
> > as indeed is the case in coventional four part harmony.
>
> I don't think that's necessarily the case, nor is it what George
was
> suggesting. If the possibility exists for a chord progression to be
> heard in conventional diatonic terms, then I think George would
agree
> that resolving by an augmented unison would be less effective than
> resolving by a semitone, even if the former is the smaller interval.

By "semitone" I meant "diatonic semitone" = "minor second".

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> > Sorry, I got sloppy with the spelling. In this case the
diminished
> > 7th chord would be in first inversion, so the outer tones should
be
> a
> > major 6th resolving to an octave.
>
> Shouldn't you therefore adjust the ratios accordingly, so that
you're
> giving the 'root position' diminisehd seventh chord?

If 10:12:14:17 is taken as the first inversion, then the root
position would be 17:20:24:28. I don't think you we would want to
replace the former with the latter in the list. Now 25:30:35:42
could be expressed with lower numbers (as 21:21:30:35), but I don't
know offhand which inversion I might want that to be.

> Scala will
> recognize various inversions of a chord in its list, won't it?

As far as I know, that won't work for me. I was running Scala's
chromatic clavier, then clicking on the chord button at the bottom to
open a window with the list of chords. After selecting a chord, I
left that window open and went back to the clavier to right-click on
various tones to play the best approximation of the chord in the
current tuning. If I wanted to invert the chord I would have to
enter an additional line in the chordnam.par file.

On the other hand, if I just wanted to listen to inversions of these
chords in JI, I guess I could just select the '3-3-3' (12-et) chord
and load a scale containing a large harmonic series and right-click
on various harmonics to hear all sorts of diminished 7th chords.

--George

🔗Carl Lumma <ekin@lumma.org>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, Alison Monteith
<alison.monteith3@w...> wrote:
> on 14/1/04 17:56, George D. Secor at gdsecor@y... wrote:
>
> > Considering that we have at least 3 possible JI diminished 7th
chords:
> > 10:12:14:17
> > 15:18:21:25
> > 25:30:35:42
> > each of which has 3 inversions (for 12 total possibilities), it
might
> > be interesting to experiment with these to rank them in order of
> > effectiveness for resolutions to various major and minor triads.
I
> > expect that the instances in which the (melodic) semitones are
> > smallest would be the most effective.
> >
> > --George
>
> Not necessarily in my experience. I haven't yet tried resolving the
chords
> above but in working with tetrads from the Eikosany I've found that
the
> smallest interval resolution isn't necessarily the most pleasing to
the ear,
> as indeed is the case in coventional four part harmony. Nonetheless
I'd be
> interested in hearing the options and when I find time I'll have a
go
> myself.

I agree. I didn't intended this statement to apply to anything other
than intervals of resolution on the order of a semitone, and even
then my use of the word "smallest" might not necessarily apply to
progressions outside those encountered in traditional harmony. My
experience has indicated that in resolving a chord the most effective
melodic semitone is something on the order of 65 to 70 cents, and I
was making the assumption that nothing significantly smaller than
that would be encountered in any progression involving resolution of
a diminished 7th chord to a major or minor triad.

BTW, the region of absolute maximum harmonic entropy in the graph
that Paul prepared for me some time ago is in good agreement with
this size range, which suggests to me that there is some sort of
connection between maximum (harmonic) dissonance and maximum melodic
effectiveness in resolving one (dissonant) chord to another
(consonant chord).

--George

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, Alison Monteith
<alison.monteith3@w...> wrote:
> > > on 14/1/04 17:56, George D. Secor at gdsecor@y... wrote:
> > > >
> > > > Considering that we have at least 3 possible JI diminished
7th chords:
> > > > 10:12:14:17
> > > > 15:18:21:25
> > > > 25:30:35:42
> > > > each of which has 3 inversions (for 12 total possibilities),
it might
> > > > be interesting to experiment with these to rank them in order
of
> > > > effectiveness for resolutions to various major and minor
triads. I
> > > > expect that the instances in which the (melodic) semitones are
> > > > smallest would be the most effective.
> > > >
> > > > --George
> > >
> > > Not necessarily in my experience. I haven't yet tried resolving
the chords
> > > above but in working with tetrads from the Eikosany I've found
that the
> > > smallest interval resolution isn't necessarily the most
pleasing to the ear,
> > > as indeed is the case in coventional four part harmony.
> >
> > I don't think that's necessarily the case, nor is it what George
was
> > suggesting. If the possibility exists for a chord progression to
be
> > heard in conventional diatonic terms, then I think George would
agree
> > that resolving by an augmented unison would be less effective
than
> > resolving by a semitone, even if the former is the smaller
interval.
>
> By "semitone" I meant "diatonic semitone" = "minor second".

If I understand you correctly, then I don't think I would completely
agree with this. In resolving a dissonant chord (such as a
diminished seventh) to a consonant one, I believe that the most
effective minor seconds are those that are in the neighborhood of 65-
70 cents, and I reserve the right to respell a "dissonant" (in terms
of traditional harmony) JI chord in such a way that minor seconds (if
we may still call them by the name) will occur closest to this size
range.

If a JI tuning provides the option of substituting a slightly higher
leading tone than 15/8 in a V-I progression to make the dominant
triad dissonant, I believe that this might serve to enhance the
progression. I would want to spell the interval between this raised
leading tone and the tonic note as a second (not an augmented
unison), but I expect that we might prefer to use a label other
than "minor second".

This sort of effect could also be accomplished using a temperament in
the meantone family by substituting an enharmonic flat in place of
the leading tone (e.g., G-Cb-D), but again I would want to respell
the leading tone so that its resolution to the tonic would be by the
interval of a second of some sort. This could be readily
accomplished by raising the leading tone (B) with a symbol indicating
the 7-comma (63:64) -- B|) in sagittal notation. This would be valid
not only in the entire range of meantone temperaments (including 12-
ET) but also in JI and in some other ETs with fifths wider than 700
cents. So I'm pleased to see that there is a way to notate this in a
general manner -- independent of a particular tuning.

--George

🔗Kurt Bigler <kkb@breathsense.com>

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

🔗George D. Secor <gdsecor@yahoo.com>

🔗Alison Monteith <alison.monteith3@which.net>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, Alison Monteith
> <alison.monteith3@w...> wrote:
> > > > on 14/1/04 17:56, George D. Secor at gdsecor@y... wrote:
> > > > >
> > > > > Considering that we have at least 3 possible JI diminished
> 7th chords:
> > > > > 10:12:14:17
> > > > > 15:18:21:25
> > > > > 25:30:35:42
> > > > > each of which has 3 inversions (for 12 total
possibilities),
> it might
> > > > > be interesting to experiment with these to rank them in
order
> of
> > > > > effectiveness for resolutions to various major and minor
> triads. I
> > > > > expect that the instances in which the (melodic) semitones
are
> > > > > smallest would be the most effective.
> > > > >
> > > > > --George
> > > >
> > > > Not necessarily in my experience. I haven't yet tried
resolving
> the chords
> > > > above but in working with tetrads from the Eikosany I've
found
> that the
> > > > smallest interval resolution isn't necessarily the most
> pleasing to the ear,
> > > > as indeed is the case in coventional four part harmony.
> > >
> > > I don't think that's necessarily the case, nor is it what
George
> was
> > > suggesting. If the possibility exists for a chord progression
to
> be
> > > heard in conventional diatonic terms, then I think George would
> agree
> > > that resolving by an augmented unison would be less effective
> than
> > > resolving by a semitone, even if the former is the smaller
> interval.
> >
> > By "semitone" I meant "diatonic semitone" = "minor second".
>
> If I understand you correctly, then I don't think I would
completely
> agree with this. In resolving a dissonant chord (such as a
> diminished seventh) to a consonant one, I believe that the most
> effective minor seconds are those that are in the neighborhood of
65-
> 70 cents, and I reserve the right to respell a "dissonant" (in
terms
> of traditional harmony) JI chord in such a way that minor seconds
(if
> we may still call them by the name) will occur closest to this size
> range.

Right -- meaning the small intervals are capable, in some sense, of
being heard as minor seconds.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > ... In resolving a dissonant chord (such as a
> > diminished seventh) to a consonant one, I believe that the most
> > effective minor seconds are those that are in the neighborhood of
65-
> > 70 cents, and I reserve the right to respell a "dissonant" (in
terms
> > of traditional harmony) JI chord in such a way that minor seconds
(if
> > we may still call them by the name) will occur closest to this
size
> > range.
>
> Right -- meaning the small intervals are capable, in some sense, of
> being heard as minor seconds.

Yes, and I would say that the condition for an interval to be
interpreted as such is that its 3:4-complement is capable of being
heard as a (large) major third. I am assuming that the listener
would be able to interpret the result as consisting of 12 interval-
classes, with (a generous amount of) flexible pitch.

Now if this sort of thing were achieved with a fixed-pitch instrument
having enharmonic or commatic pairs of tones for each pitch, we would
probably want to distinguish these alternate tones (and intervals)
with separate names and to notate them as such.

And come to think of it, it wouldn't be a bad idea if parts for
conventional flexible-pitch instruments were also notated to indicate
adjustments in intonation -- say by single degrees of 72-ET up or
down to achieve an increase or decrease in the restlessness (or
dissonance) of a vertical sonority, as well for melodic
expressiveness. (And this would also be good for helping players to
get very close to the pitches required for adaptive JI, relative to
12-ET.) Should something like this be formally taught to
instrumentalists, I think that it's important that *real* 72-ET
symbols be used for this purpose, not just all-purpose (qualitative
or generic) arrows that could mean anything from a schisma to a large
diesis.

--George

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > ... In resolving a dissonant chord (such as a
> > > diminished seventh) to a consonant one, I believe that the most
> > > effective minor seconds are those that are in the neighborhood
of
> 65-
> > > 70 cents, and I reserve the right to respell a "dissonant" (in
> terms
> > > of traditional harmony) JI chord in such a way that minor
seconds
> (if
> > > we may still call them by the name) will occur closest to this
> size
> > > range.
> >
> > Right -- meaning the small intervals are capable, in some sense,
of
> > being heard as minor seconds.
>
> Yes, and I would say that the condition for an interval to be
> interpreted as such is that its 3:4-complement is capable of being
> heard as a (large) major third. I am assuming that the listener
> would be able to interpret the result as consisting of 12 interval-
> classes, with (a generous amount of) flexible pitch.

I'm a little lost . . . can you list these 12 interval classes?

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> > wrote:
> > > > ... In resolving a dissonant chord (such as a
> > > > diminished seventh) to a consonant one, I believe that the
most
> > > > effective minor seconds are those that are in the
neighborhood of 65-
> > > > 70 cents, and I reserve the right to respell a "dissonant"
(in terms
> > > > of traditional harmony) JI chord in such a way that minor
seconds (if
> > > > we may still call them by the name) will occur closest to
this size
> > > > range.
> > >
> > > Right -- meaning the small intervals are capable, in some
sense, of
> > > being heard as minor seconds.
> >
> > Yes, and I would say that the condition for an interval to be
> > interpreted as such is that its 3:4-complement is capable of
being
> > heard as a (large) major third. I am assuming that the listener
> > would be able to interpret the result as consisting of 12
interval-
> > classes, with (a generous amount of) flexible pitch.
>
> I'm a little lost . . . can you list these 12 interval classes?

Just the 12 "buckets" centered on the 12 interval-classes of 12-ET
into which a non-microtonally oriented listener would mentally sort
the intervals heard in a microtonal performance in which the
intention is to produce conventional harmonies using alternative
pitches to achieve a sort of flexible intonation. Given the proper
musical context, intervals on the order of 9/5, 16/9, and 7/4 will
all be heard as minor sevenths (or alternatively as augmented sixths,
depending on the particular context), while anything ranging from ~63
to ~126 cents (1 and 2degs of 19-ET) will be heard as semitones
(either minor seconds or augmented unisons, depending on context).
Thus the interval *size* will determine the interval-class
(or "bucket"), while the musical *context* will determine the
interval spelling.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > > > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> > > wrote:
> > > > > ... In resolving a dissonant chord (such as a
> > > > > diminished seventh) to a consonant one, I believe that the
> most
> > > > > effective minor seconds are those that are in the
> neighborhood of 65-
> > > > > 70 cents, and I reserve the right to respell a "dissonant"
> (in terms
> > > > > of traditional harmony) JI chord in such a way that minor
> seconds (if
> > > > > we may still call them by the name) will occur closest to
> this size
> > > > > range.
> > > >
> > > > Right -- meaning the small intervals are capable, in some
> sense, of
> > > > being heard as minor seconds.
> > >
> > > Yes, and I would say that the condition for an interval to be
> > > interpreted as such is that its 3:4-complement is capable of
> being
> > > heard as a (large) major third. I am assuming that the listener
> > > would be able to interpret the result as consisting of 12
> interval-
> > > classes, with (a generous amount of) flexible pitch.
> >
> > I'm a little lost . . . can you list these 12 interval classes?
>
> Just the 12 "buckets" centered on the 12 interval-classes of 12-ET
> into which a non-microtonally oriented listener would mentally sort
> the intervals heard in a microtonal performance in which the
> intention is to produce conventional harmonies using alternative
> pitches to achieve a sort of flexible intonation. Given the proper
> musical context, intervals on the order of 9/5, 16/9, and 7/4 will
> all be heard as minor sevenths (or alternatively as augmented sixths,
> depending on the particular context), while anything ranging from ~63
> to ~126 cents (1 and 2degs of 19-ET) will be heard as semitones
> (either minor seconds or augmented unisons, depending on context).
> Thus the interval *size* will determine the interval-class
> (or "bucket"), while the musical *context* will determine the
> interval spelling.

Sounds like you're basically agreeing with Eytan Agmon. A bunch of us
had an offlist conversation with him a while back, and were pretty
hasty to reject his theory. Maybe you should have been in on it . . .
of course, you probably would stop short of agreeing with him that the
number of buckets can be 8, 12, 16, . . . for "cognitive" (or
something) reasons -- including a requirement of one and only one
'ambiguous' interval (the half-octave, which is either a diminished
this or an augmented that in all these systems) -- and that
psychoacoustics narrows the choice down to 12.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > > ...
> > > I'm a little lost . . . can you list these 12 interval classes?
> >
> > Just the 12 "buckets" centered on the 12 interval-classes of 12-
ET
> > into which a non-microtonally oriented listener would mentally
sort
> > the intervals heard in a microtonal performance in which the
> > intention is to produce conventional harmonies using alternative
> > pitches to achieve a sort of flexible intonation. Given the
proper
> > musical context, intervals on the order of 9/5, 16/9, and 7/4
will
> > all be heard as minor sevenths (or alternatively as augmented
sixths,
> > depending on the particular context), while anything ranging from
~63
> > to ~126 cents (1 and 2degs of 19-ET) will be heard as semitones
> > (either minor seconds or augmented unisons, depending on
context).
> > Thus the interval *size* will determine the interval-class
> > (or "bucket"), while the musical *context* will determine the
> > interval spelling.
>
> Sounds like you're basically agreeing with Eytan Agmon. A bunch of
us
> had an offlist conversation with him a while back, and were pretty
> hasty to reject his theory. Maybe you should have been in on
it . . .
> of course, you probably would stop short of agreeing with him that
the
> number of buckets can be 8, 12, 16, . . . for "cognitive" (or
> something) reasons -- including a requirement of one and only one
> 'ambiguous' interval (the half-octave, which is either a diminished
> this or an augmented that in all these systems) -- and that
> psychoacoustics narrows the choice down to 12.

Yes, I would indeed limit the number of "buckets" to 12 for cognitive
reasons. When we listen to a diatonic composition with only two
voice parts (such as a Bach two-part keyboard invention), we are able
to "hear" harmonies that are there only in the sense that they are
implied by tonal relationships already familiar to both the composer
and the listener. A two-voice composition in some non-diatonic scale
subset of a non-12 tuning, on the other hand, would very likely not
have the same effect, but would be heard basically as a progression
of intervals -- unless the composer had first written other
(successful) pieces in that scale using full harmonies and the
listener had also become familiar with them. In other words, the
diatonic system is really a musical language, and our success in
creating music in alternative tunings may depend on our ability to
create (or discover) other musical languages that are capable of
becoming meaningful to the general listener.

--George

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > > ...
> > > > I'm a little lost . . . can you list these 12 interval
classes?
> > >
> > > Just the 12 "buckets" centered on the 12 interval-classes of 12-
> ET
> > > into which a non-microtonally oriented listener would mentally
> sort
> > > the intervals heard in a microtonal performance in which the
> > > intention is to produce conventional harmonies using
alternative
> > > pitches to achieve a sort of flexible intonation. Given the
> proper
> > > musical context, intervals on the order of 9/5, 16/9, and 7/4
> will
> > > all be heard as minor sevenths (or alternatively as augmented
> sixths,
> > > depending on the particular context), while anything ranging
from
> ~63
> > > to ~126 cents (1 and 2degs of 19-ET) will be heard as semitones
> > > (either minor seconds or augmented unisons, depending on
> context).
> > > Thus the interval *size* will determine the interval-class
> > > (or "bucket"), while the musical *context* will determine the
> > > interval spelling.
> >
> > Sounds like you're basically agreeing with Eytan Agmon. A bunch
of
> us
> > had an offlist conversation with him a while back, and were pretty
> > hasty to reject his theory. Maybe you should have been in on
> it . . .
> > of course, you probably would stop short of agreeing with him
that
> the
> > number of buckets can be 8, 12, 16, . . . for "cognitive" (or
> > something) reasons -- including a requirement of one and only one
> > 'ambiguous' interval (the half-octave, which is either a
diminished
> > this or an augmented that in all these systems) -- and that
> > psychoacoustics narrows the choice down to 12.
>
> Yes, I would indeed limit the number of "buckets" to 12 for
cognitive
> reasons.

That seems like a disagreement, not an agreement (read the above
again). It also surprises me that you would say that, especially
given the below.

> When we listen to a diatonic composition with only two
> voice parts (such as a Bach two-part keyboard invention), we are
able
> to "hear" harmonies that are there only in the sense that they are
> implied by tonal relationships already familiar to both the
composer
> and the listener.

Sure . . .

> A two-voice composition in some non-diatonic scale
> subset of a non-12 tuning, on the other hand, would very likely not
> have the same effect, but would be heard basically as a progression
> of intervals -- unless the composer had first written other
> (successful) pieces in that scale using full harmonies and the
> listener had also become familiar with them.

Quite possible. Though I'd argue that the full-chordal analogues to
Bach's counterpoint came later, not earlier.

> In other words, the
> diatonic system is really a musical language, and our success in
> creating music in alternative tunings may depend on our ability to
> create (or discover) other musical languages that are capable of
> becoming meaningful to the general listener.

Totally agreed.

So I'm not sure where you get 'Yes, I would indeed limit the number
of "buckets" to 12 for cognitive reasons'. Reasons of culture and
familiarity, it seems you are saying, would imply a diatonic set of
buckets. This is some way removed from a 'dodecaphonic' bucketing,
and is very far removed from cognitive considerations, which would
have to apply regardless of culture and familiarity.

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > > ...
> > > Sounds like you're basically agreeing with Eytan Agmon. A bunch
of us
> > > had an offlist conversation with him a while back, and were
pretty
> > > hasty to reject his theory. Maybe you should have been in on
it . . .
> > > of course, you probably would stop short of agreeing with him
that the
> > > number of buckets can be 8, 12, 16, . . . for "cognitive" (or
> > > something) reasons -- including a requirement of one and only
one
> > > 'ambiguous' interval (the half-octave, which is either a
diminished
> > > this or an augmented that in all these systems) -- and that
> > > psychoacoustics narrows the choice down to 12.
> >
> > Yes, I would indeed limit the number of "buckets" to 12 for
cognitive
> > reasons.
>
> That seems like a disagreement, not an agreement (read the above
> again). It also surprises me that you would say that, especially
> given the below.

I must be misunderstanding what you mean by "cognitive" reasons, and
I guess that I should therefore agree with you that I am in
disagreement. :-)

> ...
> So I'm not sure where you get 'Yes, I would indeed limit the number
> of "buckets" to 12 for cognitive reasons'. Reasons of culture and
> familiarity, it seems you are saying, would imply a diatonic set of
> buckets. This is some way removed from a 'dodecaphonic' bucketing,

A diatonic set of 7 buckets is insufficient to take in chromatic
alterations to chords, including secondary dominants to minor
triads. So our diatonic chain of fifths does not close into a circle
of 7 tones, but must consist of a longer chain. What we have, then,
is essentially a meantone chain of fifths, and, as you well know,
that may be closed into a circle only at certain points -- 12, 19,
26, 31, etc., which excludes 8 or 16. These, then, are the only
possible numbers of buckets or bins that we might allow in a diatonic
(or expanded diatonic) system.

But since you used the phrase "in all these systems", evidently I am
misunderstanding under what conditions you are suggesting that 8 or
16 buckets might be open to debate.

> and is very far removed from cognitive considerations, which would
> have to apply regardless of culture and familiarity.

Then you'll need to explain to me exactly what you mean by "cognitive
considerations".

--George

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > > ...
> > > > Sounds like you're basically agreeing with Eytan Agmon. A
bunch
> of us
> > > > had an offlist conversation with him a while back, and were
> pretty
> > > > hasty to reject his theory. Maybe you should have been in on
> it . . .
> > > > of course, you probably would stop short of agreeing with him
> that the
> > > > number of buckets can be 8, 12, 16, . . . for "cognitive" (or
> > > > something) reasons -- including a requirement of one and only
> one
> > > > 'ambiguous' interval (the half-octave, which is either a
> diminished
> > > > this or an augmented that in all these systems) -- and that
> > > > psychoacoustics narrows the choice down to 12.
> > >
> > > Yes, I would indeed limit the number of "buckets" to 12 for
> cognitive
> > > reasons.
> >
> > That seems like a disagreement, not an agreement (read the above
> > again). It also surprises me that you would say that, especially
> > given the below.
>
> I must be misunderstanding what you mean by "cognitive" reasons,
and
> I guess that I should therefore agree with you that I am in
> disagreement. :-)
>
> > ...
> > So I'm not sure where you get 'Yes, I would indeed limit the
number
> > of "buckets" to 12 for cognitive reasons'. Reasons of culture and
> > familiarity, it seems you are saying, would imply a diatonic set
of
> > buckets. This is some way removed from a 'dodecaphonic'
bucketing,
>
> A diatonic set of 7 buckets is insufficient

I agree (and by diatonic, I meant the full set of categories,
including especially both major and minor interval types), there are
other ways besides 12 buckets to extend the diatonic set of
categories. You mentioned 19, 26, and 31, so it doesn't sound like
you're standing behind your statement above, "I would indeed limit
the number of "buckets" to 12 for cognitive reasons." Am I
misunderstanding you?

As opposed to the options you mention, which appear to make equal
temperaments seem cognitively preferable, I would argue for
a 'hierarchical bucketing', where distinctions between generic
interval classes (second, third, fourth, fifth . . .) are different
from the distinctions between specific sizes of each generic interval
(diminished, minor, major, augmented . . .) and not necessarily
commensurable. This view appears plausible to me and removes the bias
toward equal temperaments.

> But since you used the phrase "in all these systems", evidently I
am
> misunderstanding under what conditions you are suggesting that 8 or
> 16 buckets might be open to debate.

If you mean Eytan's theory, he suggests that psychoacoustics
introduces a powerful set of 'preferred' interval ratios, and thus
the 'cognitive-level' period or equivalence interval inevitably gets
mapped to the 'acoustic-level' 2:1, and the 'cognitive-level'
generator to the 'acoustic-level' 3:2. This, then, makes 12 by far
his most favored choice out of 8, 12, 16, . . . Or was it *my*
reaction to this you don't understand?

> > and is very far removed from cognitive considerations, which
would
> > have to apply regardless of culture and familiarity.
>
> Then you'll need to explain to me exactly what you mean
by "cognitive
> considerations".

Considerations that underlie human thought and communication, and
which allow, in Eytan's theory, a simple one-dimensional pitch
structure to convey meaning in terms of a two-dimensional
representation (one which has an almost exact parallel in tuning
theory, thus confusing Gene). I have little desire to defend his
theory, but I'd encourage you to look into it if you're interested,
as he's among the most respected music theorists in academia.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > > ...
> > > So I'm not sure where you get 'Yes, I would indeed limit the
number
> > > of "buckets" to 12 for cognitive reasons'. Reasons of culture
and
> > > familiarity, it seems you are saying, would imply a diatonic
set of
> > > buckets. This is some way removed from a 'dodecaphonic'
bucketing,
> >
> > A diatonic set of 7 buckets is insufficient
>
> I agree (and by diatonic, I meant the full set of categories,
> including especially both major and minor interval types), there
are
> other ways besides 12 buckets to extend the diatonic set of
> categories. You mentioned 19, 26, and 31, so it doesn't sound like
> you're standing behind your statement above, "I would indeed limit
> the number of "buckets" to 12 for cognitive reasons." Am I
> misunderstanding you?

I maintain that 12, 19, 26, 31, etc. are the only possible numbers of
buckets consistent with a meantone chain of fifths (which completely
excludes 8 and 16 from consideration), but since we do not yet have
systems of 19, 26, or 31 tones in common practice in our culture,
most listeners are not going to perceive at least some of the
intervals in those systems as being in separate classes. For example,
7 and 8 degrees of 31 will both probably be heard as minor thirds,
but if 31-ET came into more widespread use, then listeners would
eventually come to perceive them as being in different interval
classes, giving us more buckets.

I was making the assumption that "cognitive considerations" included
culture and familiarity. Sorry, my mistake.

> As opposed to the options you mention, which appear to make equal
> temperaments seem cognitively preferable, I would argue for
> a 'hierarchical bucketing', where distinctions between generic
> interval classes (second, third, fourth, fifth . . .) are different
> from the distinctions between specific sizes of each generic
interval
> (diminished, minor, major, augmented . . .) and not necessarily
> commensurable. This view appears plausible to me and removes the
bias
> toward equal temperaments.

Ah, now I see what you mean. Yes, I would tend to agree with you
about this.

> > But since you used the phrase "in all these systems", evidently I
am
> > misunderstanding under what conditions you are suggesting that 8
or
> > 16 buckets might be open to debate.
>
> If you mean Eytan's theory, he suggests that psychoacoustics
> introduces a powerful set of 'preferred' interval ratios, and thus
> the 'cognitive-level' period or equivalence interval inevitably
gets
> mapped to the 'acoustic-level' 2:1, and the 'cognitive-level'
> generator to the 'acoustic-level' 3:2. This, then, makes 12 by far
> his most favored choice out of 8, 12, 16, . . . Or was it *my*
> reaction to this you don't understand?

And now that I have reread your original statement about Eytan, would
tend to disagree with his theory.

> > > and is very far removed from cognitive considerations, which
would
> > > have to apply regardless of culture and familiarity.
> >
> > Then you'll need to explain to me exactly what you mean
by "cognitive
> > considerations".
>
> Considerations that underlie human thought and communication, and
> which allow, in Eytan's theory, a simple one-dimensional pitch
> structure to convey meaning in terms of a two-dimensional
> representation (one which has an almost exact parallel in tuning
> theory, thus confusing Gene). I have little desire to defend his
> theory, but I'd encourage you to look into it if you're interested,
> as he's among the most respected music theorists in academia.

I'm not really interested in following up on this. Since my
statement about 12 buckets was based largely on culture and
familiarity, it did not really have much bearing on this issue.

--George

🔗wallyesterpaulrus <paul@stretch-music.com>

Of course -- in Eytan's theory, those don't go with the conventional
diatonic system at all, but go with cognitively equally
feasible 'generalized diatonic' scales of 5 and 9 notes,
respectively. He ends up rejecting these anyway on psychoacoustic
grounds, though they closely resemble systems that have been referred
to as "father" and "pelogic" around here lately, and at least the
latter can sound great with specially selected timbres.

> but since we do not yet have
> systems of 19, 26, or 31 tones in common practice in our culture,
> most listeners are not going to perceive at least some of the
> intervals in those systems as being in separate classes. For
example,
> 7 and 8 degrees of 31 will both probably be heard as minor thirds,
> but if 31-ET came into more widespread use, then listeners would
> eventually come to perceive them as being in different interval
> classes, giving us more buckets.

Yes, my experience is that many performances of conventional music
that sound completely clear and in-tune from a "common practice"
standpoint can sound very inconsistent and all-over-the-place if one
has been immersing oneself in a microtonal system.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> ...
> > but since we do not yet have
> > systems of 19, 26, or 31 tones in common practice in our culture,
> > most listeners are not going to perceive at least some of the
> > intervals in those systems as being in separate classes. For
example,
> > 7 and 8 degrees of 31 will both probably be heard as minor
thirds,
> > but if 31-ET came into more widespread use, then listeners would
> > eventually come to perceive them as being in different interval
> > classes, giving us more buckets.
>
> Yes, my experience is that many performances of conventional music
> that sound completely clear and in-tune from a "common practice"
> standpoint can sound very inconsistent and all-over-the-place if
one
> has been immersing oneself in a microtonal system.

Indeed! This reminds me of something a high-school choir director
said some years back when I told him I was into microtonality: "Oh,
my students already sing microtones -- quartertones, fifth-tones,
sixth-tones, and everything in-between." He was joking that it was
enough of a task to get them to sing conventional music reasonably in
tune, such that he would never consider microtones as ever being
practical for much of anything.

But our experience demonstrates that exactly the reverse is true: If
you immerse yourself in alternative tunings, your musical ear will
improve, along with your ability to sing conventional music in tune.

--George

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> I agree (and by diatonic, I meant the full set of categories,
> including especially both major and minor interval types), there are
> other ways besides 12 buckets to extend the diatonic set of
> categories.

There's meantone. You can for instance use [<12 19 28|, <7 11 16|> and
get a rank two group of notes. <7 11 16| maps major and minor thirds
into a single bucket, and <12 19 28| distinguishes them. Same for
seconds, etc. This has been implicit in our musical language for a
long time.

You mentioned 19, 26, and 31, so it doesn't sound like
> you're standing behind your statement above, "I would indeed limit
> the number of "buckets" to 12 for cognitive reasons." Am I
> misunderstanding you?
>
> As opposed to the options you mention, which appear to make equal
> temperaments seem cognitively preferable, I would argue for
> a 'hierarchical bucketing', where distinctions between generic
> interval classes (second, third, fourth, fifth . . .) are different
> from the distinctions between specific sizes of each generic interval
> (diminished, minor, major, augmented . . .) and not necessarily
> commensurable.

So you like meantone as a way of understanding our system of music,
which is hardly a surprise.

> Considerations that underlie human thought and communication, and
> which allow, in Eytan's theory, a simple one-dimensional pitch
> structure to convey meaning in terms of a two-dimensional
> representation (one which has an almost exact parallel in tuning
> theory, thus confusing Gene).

If you think Eytan's theories, or what you talk about above, are
separable from meantone then you are the one who is confused. If you
are talking about meantone, why not call it that?

If you want a system to compare to the above, I'd suggest

[<53 84 123|, <12 19 28|]

This has 12 conceptual bins, inside of which the 53 makes more refined
distinctions. This is a perfectly acceptable way of understanding
5-limit music, but if you try to apply it to something other than
schismic, it will fall apart on you. In the same way, Agmon's system,
which you pig-headedly insist isn't meantone simply because Agmon is
confused on that score, *makes no sense* unless we are discussing
meantone. It falls apart into contradiction if we assume we are
talking about 5-limit JI, or schismic.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

In the same way, Agmon's system,
> which you pig-headedly insist isn't meantone simply because Agmon is
> confused on that score, *makes no sense* unless we are discussing
> meantone. It falls apart into contradiction if we assume we are
> talking about 5-limit JI, or schismic.

If you want to extend this bin business to 5-limit or any other JI. In
the 5-limit you might try

[<12 19 28|, <7 11 16|, <3 5 7|]

The final bin is one we don't use, because in fact we *are* thinking
of meantone, not JI. However, it puts things in three buckets, which
we might call the tonic bucket, the dominant bucket, and the
subdominant or perhaps mediant bucket. 1, 10/9, 16/15, 25/24 etc are
all intervals in the same tonic bucket; 6/5, 5/4, and 4/3 are all in
the subdominant bucket, and 3/2, 8/5, 5/3 are all in the dominant
bucket. A triad should have something from each bucket; how consonant
the triad is is a question which brings in the other buckets.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
>
> > I agree (and by diatonic, I meant the full set of categories,
> > including especially both major and minor interval types), there
are
> > other ways besides 12 buckets to extend the diatonic set of
> > categories.
>
> There's meantone.

Yes, either meantone or pythagorean.

> > As opposed to the options you mention, which appear to make equal
> > temperaments seem cognitively preferable, I would argue for
> > a 'hierarchical bucketing', where distinctions between generic
> > interval classes (second, third, fourth, fifth . . .) are
different
> > from the distinctions between specific sizes of each generic
interval
> > (diminished, minor, major, augmented . . .) and not necessarily
> > commensurable.
>
> So you like meantone as a way of understanding our system of music,
> which is hardly a surprise.

This could apply to a categorization resembling meantone or
pythagorean tunings in the diatonic case, or other systems in the
generalized-diatonic case.

> > Considerations that underlie human thought and communication, and
> > which allow, in Eytan's theory, a simple one-dimensional pitch
> > structure to convey meaning in terms of a two-dimensional
> > representation (one which has an almost exact parallel in tuning
> > theory, thus confusing Gene).
>
> If you think Eytan's theories, or what you talk about above,

What I talk about above is stated to be utterly opposite from Eytan's
theories. He insists on 12 and only 12 buckets, each with a curved
shape given by his rate(p) function, as you know.

> In the same way, Agmon's system,
> which you pig-headedly insist isn't meantone simply because Agmon is
> confused on that score,

simply . . . insulting.

> *makes no sense* unless we are discussing
> meantone. It falls apart into contradiction if we assume we are
> talking about 5-limit JI, or schismic.

There is no mention made of frequency ratios of 5 or of any higher
numbers anyway. But the last thing I want to do is re-engage in a
defense of a theory I don't agree with anyway. And doing so on this
list? Forget it.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > ...
> > I maintain that 12, 19, 26, 31, etc. are the only possible
numbers of
> > buckets consistent with a meantone chain of fifths (which
completely
> > excludes 8 and 16 from consideration),
>
> Of course -- in Eytan's theory, those don't go with the
conventional
> diatonic system at all, but go with cognitively equally
> feasible 'generalized diatonic' scales of 5 and 9 notes,
> respectively. He ends up rejecting these anyway on psychoacoustic
> grounds, though they closely resemble systems that have been
referred
> to as "father" and "pelogic" around here lately, and at least the
> latter can sound great with specially selected timbres.

I've been wondering when was the right time to mention this. I'm
curious to see how your pelogic system compares with the tuning Erv
Wilson and I came up with many years ago.

In the summer of 1979 my wife and I rented a room at Erv's house
while we were in the process of house-hunting. One evening we were
just sitting around in the living room with nothing in particular to
do, when I suggested to Erv, "Just for the fun of it, let's create a
new tuning tonight." He said okay, and what did I have in mind? I
suggested that it should have isoharmonic consonant chords with
integers in the ratio a:b:c (such that c-b=b-a) contained within a
low-error linear temperament, but what should a, b, and c be?

Just out of the blue, Erv suggested 11:13:15, so I got out a pencil
and paper and my electronic calculator and started looking for a
generating interval. As it turned out, I didn't have to look very
far, since the most obvious thing was to start with the three
intervals in the chord, and I found that a generator of 11:15 taken
to five places (+5G) came to within a few cents of 13/11. Tempering
11:15 wide by ~0.892 cents (for a generator of ~537.842c) gives an
exact 11:13, so the max. error within the 11:13:15 triad equals the
error of the generator. I next discovered that the tone in the +4G
position came within a few cents of 19/11, so a tetrad approximating
11:13:15:19 was available without adding any more tones to the chain.

I then calculated a dozen or so tones in a chain and put the tuning
on my Scalatron. As I played various chords, it was clear that the
11:13:15 and 11:15:19 triads and the 11:13:15:19 tetrad stood out as
consonances among a host of other dissonant chords, but this was true
only so long as I kept the tones above middle C. While some timbres
worked better than others and that percussive enveloping was better
than sustained tones, I found that the pitch range was more important
to the consonance of these chords (so this temperament would be ideal
for tubular bells). I also discovered that the tone at +8G is within
a cent of 3/2 and that a lower octave of this pitch could be used as
a bass note in conjunction with a consonant triad or tetrad, since it
very nearly coincided with the first-order difference tones produced
by these chords.

As I played with this new tuning, I couldn't help noticing its
resemblance to the pelog scale, at which point I brought out an
Indonesian gamelan recording from my non-12 record collection and
played it, while adjusting the master oscillator on the Scalatron in
an to attempt to match the pitches on the recording. Lo and behold,
all but one on the recording were right on, and even that one
exception was not very far off. I later compared the tones in this
tuning with the cents values for a large number of examples of pelog
scales given in Jaap Kunst's book and was able to confirm that my
observations were correct.

MOS scales of this tuning have 5, 7, 9, 11, 20, and 29 tones, and the
29-tone MOS scale is rather close to 29-ET. But I don't recall
anyone ever having mentioned that a subset of 29-ET is similar to
pelog.

So how does this compare with your idea of what characterizes a
pelogic temperament?

--George

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> >
> > > I agree (and by diatonic, I meant the full set of categories,
> > > including especially both major and minor interval types), there
> are
> > > other ways besides 12 buckets to extend the diatonic set of
> > > categories.
> >
> > There's meantone.
>
> Yes, either meantone or pythagorean.

Do you mean pythagorean used in a tuning system where the consonances
are 4/3, 3/2, 2, 3 etc? If you mean pythagorean as a meantone tuning,
where we happily make use of 81/64 thirds as major thirds, I'd simply
put that under the rubric "meantone".

> What I talk about above is stated to be utterly opposite from Eytan's
> theories. He insists on 12 and only 12 buckets, each with a curved
> shape given by his rate(p) function, as you know.

He has both 7 buckets *and* 7 buckets.

> > In the same way, Agmon's system,
> > which you pig-headedly insist isn't meantone simply because Agmon is
> > confused on that score,
>
> simply . . . insulting.

You can insult me and I can't call you pig-headed? Of course, if you
want to claim "confused" was not an insult, which seems reasonable,
then I will point out it is equally reasonable not to take offense at
"pig-headed". Whichever set of rules you use, please apply them to
yourself along with everyone else.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> An interpretation *he* rejected in no uncertain terms. Since his
> theory is his theory (and his living), I'd give that rejection a
lot
> of weight, but I have no desire to rehash this now.

Oh, come on. You are a graduate of Yale. I have a PhD from Berkeley.
His argument is worth whatever it is worth, and nothing more.

> > In meantone (12 is irrelevant) all of these questions
> > of augmented sixths verses minor sevenths arise.
>
> This is an incorrect interpretation of the issue (as I explained
> offlist). Have you taken any college-level music courses?

Yes, and I even survived the experience.

They all
> assume '12' yet the questions of augmented sixths versus minor
> sevenths are given quite a bit of importance.

They arise *in the context of 12 as a meantone system*. They'd arise
just as much in 31.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > ...
> > > I maintain that 12, 19, 26, 31, etc. are the only possible
> numbers of
> > > buckets consistent with a meantone chain of fifths (which
> completely
> > > excludes 8 and 16 from consideration),
> >
> > Of course -- in Eytan's theory, those don't go with the
> conventional
> > diatonic system at all, but go with cognitively equally
> > feasible 'generalized diatonic' scales of 5 and 9 notes,
> > respectively. He ends up rejecting these anyway on psychoacoustic
> > grounds, though they closely resemble systems that have been
> referred
> > to as "father" and "pelogic" around here lately, and at least the
> > latter can sound great with specially selected timbres.
>
> I've been wondering when was the right time to mention this. I'm
> curious to see how your pelogic system compares with the tuning Erv
> Wilson and I came up with many years ago.

It's closer to what Erv described in 1975 as a "septimally negative"
system on page 10 of _On Linear Notations and the Bosanquet
Keyboard_, Xenharmonikon 3:

http://www.anaphoria.com/xen3a.PDF

My "P. E. Logic" system is actually the 5-limit temperament where
135:128 vanishes. When octave-repetition is assumed, the generator
typically comes out to about 522-523 cents. The octaves themselves
can be left pure if necessary, or if not, stretched by about 6-7
cents. A marimba-like timbre works well; strong harmonic timbres are
not recommended. Mapped to the fourths of a standard
keyboard, 'conventional music' turns "upside-down", keyboard minor
triads becoming the approximate 5-limit major triads of this system,
and vice-versa. Thus the same 5- and 7-note scales that 'conventional
music' is based on work great with this tuning; taken out any
further, the generator will produce pairs of notes that are "in the
wrong order" of pitch on the keyboard, a "feature" Erv's notation is
clearly intended to help accomodate.

I'm dubious as to the relevance of proportions like 11:13 to
inharmonic or percussive timbres when distortion or lower members of
a common harmonic series aren't used. However, I find that some
simple 5-limit harmonies can be evoked effectively even when the
errors are fairly large, just as a single holistic pitch can be
evoked by an overtone series in which the overtones are displaced by
fairly large amounts. This is suggested by the clarity with which the
following example is heard as being a single voice, where the
*timbre* is composed of 6 sine-wave partials tuned to a
pelogic 'major chord':

/tuning/files/Erlich/dave.wav

The partials do not fall apart into individual tones, the way the
partials of, say, a carillon bell do. Similarly, the triads of
pelogic, when the timbres are 'gentle' enough, manage to 'cohere' as
harmonic entities, made all the more appealing by the unusual melodic
structure of the scales they arise from.

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

> Date: Tue, 20 Jan 2004 18:33:00 -0000
> From: "Gene Ward Smith" <gwsmith@svpal.org>

> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
>
> > Yes, I would indeed limit the number of "buckets" to 12 for
> cognitive
> > reasons. When we listen to a diatonic composition with only two
> > voice parts (such as a Bach two-part keyboard invention), we are
> able
> > to "hear" harmonies that are there only in the sense that they are
> > implied by tonal relationships already familiar to both the
> composer
> > and the listener.
>
> I could put up a Bach two-part invention in extended meantone to test
> this theory, but first I want to know what you are predicting it will
> sound like. Is there supposedly going to be something funny about it,
> and if so, exactly what?
>
> Extended meantone versions sometimes go in a slightly unexpected
> direction but I'd hardly expect that to happen with a Bach two-part
> invention.
>
> A two-voice composition in some non-diatonic scale
> > subset of a non-12 tuning, on the other hand, would very likely not
> > have the same effect, but would be heard basically as a progression
> > of intervals -- unless the composer had first written other
> > (successful) pieces in that scale using full harmonies and the
> > listener had also become familiar with them.
>
> Do are you talking about 12-et, or the diatonic scale? The two are
> hardly the same.
>
> In other words, the
> > diatonic system is really a musical language, and our success in
> > creating music in alternative tunings may depend on our ability to
> > create (or discover) other musical languages that are capable of
> > becoming meaningful to the general listener.
>
> I think our ears are vastly more adaptable than you suggest.
>
>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> > wrote:
> > >
> > > > I agree (and by diatonic, I meant the full set of categories,
> > > > including especially both major and minor interval types),
there
> > are
> > > > other ways besides 12 buckets to extend the diatonic set of
> > > > categories.
> > >
> > > There's meantone.
> >
> > Yes, either meantone or pythagorean.
>
> Do you mean pythagorean used in a tuning system where the
consonances
> are 4/3, 3/2, 2, 3 etc?

Yes.

> If you mean pythagorean as a meantone tuning,
> where we happily make use of 81/64 thirds as major thirds, I'd
simply
> put that under the rubric "meantone".

By "happily" do you mean "as a stable consonance"? If so, then this
is somewhat reasonable; if not, you'd be calling medieval
polyphony "meantone", which would essentially deprive it of all
meaning.

> > What I talk about above is stated to be utterly opposite from
Eytan's
> > theories. He insists on 12 and only 12 buckets, each with a
curved
> > shape given by his rate(p) function, as you know.
>
> He has both 7 buckets *and* 7 buckets.

You can define buckets however you like, but I was sticking to the
precise meaning they had when George brought them up in this
discussion, because I was hoping to make contribute useful
clarifications to it rather than flying off on tangents. I invite you
to re-read George's posts in this thread, beginning with the first
one. In that sense, Agmon insists on 12 and only 12 buckets.

> > > In the same way, Agmon's system,
> > > which you pig-headedly insist isn't meantone simply because
Agmon is
> > > confused on that score,
> >
> > simply . . . insulting.
>
> You can insult me and I can't call you pig-headed? Of course, if you
> want to claim "confused" was not an insult, which seems reasonable,
> then I will point out it is equally reasonable not to take offense
at
> "pig-headed". Whichever set of rules you use, please apply them to
> yourself along with everyone else.

Though "pig-headed" *is* insulting, it was, rather,
your "simply . . ." assertion that I found insulting.

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> > Date: Tue, 20 Jan 2004 18:33:00 -0000
> > From: "Gene Ward Smith" <gwsmith@s...>
>
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> >
> > > Yes, I would indeed limit the number of "buckets" to 12 for
cognitive
> > > reasons. When we listen to a diatonic composition with only
two
> > > voice parts (such as a Bach two-part keyboard invention), we
are able
> > > to "hear" harmonies that are there only in the sense that they
are
> > > implied by tonal relationships already familiar to both the
composer
> > > and the listener.
> >
> > I could put up a Bach two-part invention in extended meantone to
test
> > this theory, but first I want to know what you are predicting it
will
> > sound like. Is there supposedly going to be something funny about
it,
> > and if so, exactly what?

No, I was just talking about a two-part invention in some tuning in
which it has historically been performed -- either ordinary meantone,
or a well temperament, or 12-ET.

> > Extended meantone versions sometimes go in a slightly unexpected
> > direction but I'd hardly expect that to happen with a Bach two-
part
> > invention.
> >
> > A two-voice composition in some non-diatonic scale
> > > subset of a non-12 tuning, on the other hand, would very likely
not
> > > have the same effect, but would be heard basically as a
progression
> > > of intervals -- unless the composer had first written other
> > > (successful) pieces in that scale using full harmonies and the
> > > listener had also become familiar with them.
> >
> > Do are you talking about 12-et, or the diatonic scale? The two
are
> > hardly the same.

No, here I'm talking about non-12 and non-diatonic -- something
totally new and different to the listener. With no prior listening
experience, one would not be able to flesh out mentally any full
harmonies that might be implied by a two-voice musical skeleton.

> > In other words, the
> > > diatonic system is really a musical language, and our success
in
> > > creating music in alternative tunings may depend on our ability
to
> > > create (or discover) other musical languages that are capable
of
> > > becoming meaningful to the general listener.
> >
> > I think our ears are vastly more adaptable than you suggest.

Then where are all of the compositions in alternative tunings that
have successfully made it into the musical mainstream?

--George

🔗Carl Lumma <ekin@lumma.org>

🔗George D. Secor <gdsecor@yahoo.com>

🔗wallyesterpaulrus <paul@stretch-music.com>

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
>
> > > > In other words, the
> > > > > diatonic system is really a musical language, and our
success
> > in
> > > > > creating music in alternative tunings may depend on our
> ability
> > to
> > > > > create (or discover) other musical languages that are
capable
> > of
> > > > > becoming meaningful to the general listener.
> > > >
> > > > I think our ears are vastly more adaptable than you suggest.
> >
> > Then where are all of the compositions in alternative tunings
that
> > have successfully made it into the musical mainstream?
> >
> > --George
>
> They're all in the musical mainstreams of alternative (by which I
> mean non-Western) cultures!

But how many of those cultures have produced compositions with two
independent voice parts that, when and if we listen to them, imply a
fuller harmony? That's the context in which I asked the question.

--George

🔗Carl Lumma <ekin@lumma.org>

Hi George,

>> > Do are you talking about 12-et, or the diatonic scale? The two
>> > are hardly the same.
>
>No, here I'm talking about non-12 and non-diatonic -- something
>totally new and different to the listener. With no prior listening
>experience, one would not be able to flesh out mentally any full
>harmonies that might be implied by a two-voice musical skeleton.

But if it got close to 5-limit JI, in my case I'd probably try
to hear it as being part of the skeleton I know, whether it was
or not.

>>> In other words, the
>>> diatonic system is really a musical language, and our success
>>> creating music in alternative tunings may depend on our ability
>>> to create (or discover) other musical languages that are capable
>>> of becoming meaningful to the general listener.
>>
>> I think our ears are vastly more adaptable than you suggest.
>
>Then where are all of the compositions in alternative tunings that
>have successfully made it into the musical mainstream?

That very much depends on how you define microtonal. How do you
define it?

-Carl

🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

> As it turned out, I didn't have to look very
> far, since the most obvious thing was to start with the three
> intervals in the chord, and I found that a generator of 11:15 taken
> to five places (+5G) came to within a few cents of 13/11.

This gives you your first comma, 4 (13/11)/(15/11)^5 = 761332/759375

Tempering
> 11:15 wide by ~0.892 cents (for a generator of ~537.842c) gives an
> exact 11:13, so the max. error within the 11:13:15 triad equals the
> error of the generator. I next discovered that the tone in the +4G
> position came within a few cents of 19/11, so a tetrad approximating
> 11:13:15:19 was available without adding any more tones to the chain.

This gives you your second comma, (1/2) (15/11)^4/(19/11) =
50625/50578. Now that you have two commas, you can advantageously
switch to using {286/285, 43875/43681} instead.

I also discovered that the tone at +8G is within
> a cent of 3/2

This gives you your third comma 12/(15/11)^8. If I put it with the
other two commas and TM reduce, I now get {286/285, 363/361,
14621/14625} as a comma basis. This defines a planar temperament on
the JI group generated by {2,3,5,11,13,19}, or {2,3,5,11,13,19}-JI, or
whatever it should be called. Since you are using a single generator,
it would be logical to find another comma in this subgroup and use it
to extend to a linear temperament, but this doesn't seem easy to do.
One can solve the linear system defined by the generator choice of
15/11 and the equivalences of generator powers with intervals. This
leads to the conclusion that any comma we add should be sent to zero
by <0 -8k19+8k13 12k19-11k13 0 -4k13+5k19 k13 0 k19| where k3, etc
means the number of generator steps to that prime. It is easy enough
to find commas which satisfy this; the trick is to find one which is
independent of the three we already have. Evidently such a comma must
be pretty complex and hence the corresponding linear temperament not
too interesting, except as a way to capture what you are proposing.

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Kurt Bigler <kkb@breathsense.com>

on 1/21/04 12:32 PM, Gene Ward Smith <gwsmith@svpal.org> wrote:

> You can insult me and I can't call you pig-headed? Of course, if you
> want to claim "confused" was not an insult, which seems reasonable,
> then I will point out it is equally reasonable not to take offense at
> "pig-headed". Whichever set of rules you use, please apply them to
> yourself along with everyone else.

Did you intend to insult when you used "pig-headed"? Were you in fact at
that point already offended by Paul's use of "confused"? If so please
consider that you could have clarified that at the time and it would have
offered an alternative direction for development of the dialog, in which it
might have developed more clearly and with less compounding of injury.

I wasn't following the thread closely when Paul used "confused" so I'm not
clear what feedback to give him. So I'm not picking on you, I'm just
pointing out what you might have done at that point to offer a way out of
the mess.

To be clear, there is a difference between implying one's hurt state by
offering an insult and simply offering the truth of one's hurt state.
Bottom line: when hurt, don't talk about something else as if it were still
the topic. The topic actually changed for you and it is much less confusing
if that is clarified rather than hidden behind an insult embedded in the
original topic. At least that's one way of describing it. Of course you
might pig-headedly chose to continue with the same topic. ;)

-Kurt

🔗Wernerlinden@aol.com

gdsecor@yahoo.com

in dialogue with Gene Ward Smith, wrote (Subject: Re: Just diminished
7th chords
:
A two-voice composition in some non-diatonic scale
> > > subset of a non-12 tuning, on the other hand, would very likely
not
> > > have the same effect, but would be heard basically as a
progression
> > > of intervals -- unless the composer had first written other
> > > (successful) pieces in that scale using full harmonies and the
> > > listener had also become familiar with them.
> >
> > Do are you talking about 12-et, or the diatonic scale? The two
are
> > hardly the same.

YUP !!! This is just one fine idea I shall explore in my „Septatonic Suite“,
as it is my subject to explore the relations between the Septatonic Intervals
and, what our ears are doing with them.
Thankx an' praises !
Werner Linden

🔗Afmmjr@aol.com

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
> > ...
> > I've been wondering when was the right time to mention this. I'm
> > curious to see how your pelogic system compares with the tuning
Erv
> > Wilson and I came up with many years ago.
>
> It's closer to what Erv described in 1975 as a "septimally
negative"
> system on page 10 of _On Linear Notations and the Bosanquet
> Keyboard_, Xenharmonikon 3:
>
> http://www.anaphoria.com/xen3a.PDF

Yes, that's closer, but Erv didn't indicate a 29-tone octave, which
would be closest to the pelogic temperament that I ended up with (4
years later).

> My "P. E. Logic" system is actually the 5-limit temperament where
> 135:128 vanishes. When octave-repetition is assumed, the generator
> typically comes out to about 522-523 cents. The octaves themselves
> can be left pure if necessary, or if not, stretched by about 6-7
> cents. A marimba-like timbre works well; strong harmonic timbres
are
> not recommended. Mapped to the fourths of a standard
> keyboard, 'conventional music' turns "upside-down", keyboard minor
> triads becoming the approximate 5-limit major triads of this
system,
> and vice-versa. Thus the same 5- and 7-note scales
that 'conventional
> music' is based on work great with this tuning; taken out any
> further, the generator will produce pairs of notes that are "in the
> wrong order" of pitch on the keyboard, a "feature" Erv's notation
is
> clearly intended to help accomodate.
>
> I'm dubious as to the relevance of proportions like 11:13 to
> inharmonic or percussive timbres when distortion or lower members
of
> a common harmonic series aren't used.

I've found that harmonics are largely irrelevant to the success of my
isoharmonic pelogic temperament (what I'll have to call it, until
someone thinks of a better name), hence selection of timbre is not of
great importance. If the tones are kept in a range above 260 hz,
then the beating between the lower harmonics starts to become too
rapid to be perceived, so that these intervals could be interpreted
as having their own identities. But even so, whether anyone might
hear 11:13 as having a separate identity or as some sort of minor
third probably has little or no bearing on the success of this scale.

One thing that I did observe is that 11:15 resembles 3:4 somewhat in
that it tends to establish the upper tone of the ratio as a root of a
chord containing this interval, so melodies in a scale subset of this
temperament are very definitely not atonal. While the 11:13:15 triad
gives the general impression of 6:7:8 (or to a lesser extent of
15:18:20), it quickly becomes evident that the relative consonance of
chords is not the same as in a 5-limit or 7-limit tuning. Since
chordal consonance is established by the near-coincidence of first-
order difference tones, the only timbral requirement is that there be
a strong fundamental (so strong harmonic timbres, though not optimal,
are not excluded), making this an ideal tuning for timbres with
inharmonic partials that do not overpower the fundamental. Examples
of instruments that I think would work well in an ensemble using this
tuning are tubulongs, recorders, and a bass marimba (the latter
consisting of several bars tuned to match first-order difference
tones of a few consonant chords).

I wouldn't notate my isoharmonic pelogic tuning as a chain of
unaltered fifths, inasmuch as its 9-tone MOS scale results in an
almost exact 2:3 between the tones at each end of the chain.

Clearly, you and I have taken very different approaches in arriving
at a pelogic tuning.

Getting back to your pelogic scale:

> However, I find that some
> simple 5-limit harmonies can be evoked effectively even when the
> errors are fairly large, just as a single holistic pitch can be
> evoked by an overtone series in which the overtones are displaced
by
> fairly large amounts. This is suggested by the clarity with which
the
> following example is heard as being a single voice, where the
> *timbre* is composed of 6 sine-wave partials tuned to a
> pelogic 'major chord':
>
> /tuning/files/Erlich/dave.wav
>
> The partials do not fall apart into individual tones, the way the
> partials of, say, a carillon bell do. Similarly, the triads of
> pelogic, when the timbres are 'gentle' enough, manage to 'cohere'
as
> harmonic entities, made all the more appealing by the unusual
melodic
> structure of the scales they arise from.

Yes, the example in the file sounds very much like tones with
harmonic partials, so much so that I was tempted to ask you if you're
sure that's the right file! I find that the duration of each tone is
not long enough for me to home in on any difference I might hear
between these and tones with true harmonics.

But I, in turn, am dubious as to the usefulness of a tuning that
requires artificial timbres containing a distorted harmonic series in
order to be successful. I think that you would have to go to a lot
of trouble to create any music of this sort, and it would seem to
exclude virtually all acoustic instruments.

--George

🔗Gene Ward Smith <gwsmith@svpal.org>

Sorry, we were unable to deliver your message to the following address.

<tuning@yahoogroups.com>:
Remote host said: 451 connection to mail server timed out (#4.4.1)

--- Below this line is a copy of the message.
--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

> The final bin is one we don't use, because in fact we *are* thinking
> of meantone, not JI. However, it puts things in three buckets, which
> we might call the tonic bucket, the dominant bucket, and the
> subdominant or perhaps mediant bucket. 1, 10/9, 16/15, 25/24 etc are
> all intervals in the same tonic bucket; 6/5, 5/4, and 4/3 are all in
> the subdominant bucket, and 3/2, 8/5, 5/3 are all in the dominant
> bucket. A triad should have something from each bucket; how consonant
> the triad is is a question which brings in the other buckets.

Incidentally, if we take only the 12 bucket and the 3 bucket, we get a
conceptual system which Agmon's supposedly non-meantone system cannot
deal with, despite the fact that it is a 12-tone system just as much
as meantone is--augmented, to be exact. Agmon's ideas simply can't
deal with something like the octatonic scale, **because it is
describing meantone**. Why you can't understand that baffles me.

If we put a 12 bucket together with a 4 bucket, we get a dimininised
system of buckets. This comes into its own in the 7-limit, where
7-limit JI can be dealt with by adding a 4 bucket, rather than a 3
bucket, to the 12 and 7 buckets. Then the 12 and 7 buckets together
give dominant seventh, the 12 and 4 buckets together give diminished,
and the 7 and 4 buckets together give the {15/14, 25/24} temperament.
This is a system of buckets appropriate to 36/35-planar; we can extend
it to a JI classification by adding a bucket for 19. Then 12 and 19
together gives meantone, 7 and 19 together gives flattone, and 4 and
19 together gives kleismic. There are other possibilites for the
fourth bucket, however--3, 10, 15, 17, 22, 27 or 31 bins, among others.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> Hi George,
>
> >> > Do are you talking about 12-et, or the diatonic scale? The two
> >> > are hardly the same.
> >
> >No, here I'm talking about non-12 and non-diatonic -- something
> >totally new and different to the listener. With no prior
listening
> >experience, one would not be able to flesh out mentally any full
> >harmonies that might be implied by a two-voice musical skeleton.
>
> But if it got close to 5-limit JI, in my case I'd probably try
> to hear it as being part of the skeleton I know, whether it was
> or not.

I agree. I have encountered the problem in trying to compose in a
scale having other than 5 or 7 nominals.

> >>> In other words, the
> >>> diatonic system is really a musical language, and our success
> >>> creating music in alternative tunings may depend on our ability
> >>> to create (or discover) other musical languages that are
capable
> >>> of becoming meaningful to the general listener.
> >>
> >> I think our ears are vastly more adaptable than you suggest.
> >
> >Then where are all of the compositions in alternative tunings that
> >have successfully made it into the musical mainstream?
>
> That very much depends on how you define microtonal. How do you
> define it?

For the purposes of interpreting my foregoing statement and question,
define it however you like, just so long as the tuning that you're
calling microtonal provides new harmonic resources (preferably, some
of which may be capable of being perceived as consonant).

--George

🔗George D. Secor <gdsecor@yahoo.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > ...
> > > I've been wondering when was the right time to mention this.
I'm
> > > curious to see how your pelogic system compares with the tuning
> Erv
> > > Wilson and I came up with many years ago.
> >
> > It's closer to what Erv described in 1975 as a "septimally
> negative"
> > system on page 10 of _On Linear Notations and the Bosanquet
> > Keyboard_, Xenharmonikon 3:
> >
> > http://www.anaphoria.com/xen3a.PDF
>
> Yes, that's closer, but Erv didn't indicate a 29-tone octave,

Right -- that's why it's closer.

> which
> would be closest to the pelogic temperament that I ended up with (4
> years later).

Exactly.

> > My "P. E. Logic" system is actually the 5-limit temperament where
> > 135:128 vanishes. When octave-repetition is assumed, the
generator
> > typically comes out to about 522-523 cents. The octaves
themselves
> > can be left pure if necessary, or if not, stretched by about 6-7
> > cents. A marimba-like timbre works well; strong harmonic timbres
> are
> > not recommended. Mapped to the fourths of a standard [...]

> One thing that I did observe is that 11:15 resembles 3:4 somewhat
in
> that it tends to establish the upper tone of the ratio as a root of
a
> chord containing this interval, so melodies in a scale subset of
this
> temperament are very definitely not atonal.

Yes, this is exactly what happens in my 'pelogic'.

> While the 11:13:15 triad
> gives the general impression of 6:7:8 (or to a lesser extent of
> 15:18:20), it quickly becomes evident that the relative consonance
of
> chords is not the same as in a 5-limit or 7-limit tuning. Since
> chordal consonance is established by the near-coincidence of first-
> order difference tones,

Bill Sethares's book _Tuning, Timbre, Spectrum, Scale_ examines many
theories of consonance and delivers its strongest rejection to
theories based on difference tones. I think the truth lies somewhere
between you and Bill.

> the only timbral requirement is that there be
> a strong fundamental (so strong harmonic timbres, though not
optimal,
> are not excluded), making this an ideal tuning for timbres with
> inharmonic partials that do not overpower the fundamental.

These are exactly the kind of timbres I was referring to above, and
in the other posts I've made on this tuning to these lists.

> Clearly, you and I have taken very different approaches in arriving
> at a pelogic tuning.

There are some very strong similarities as well.

> Getting back to your pelogic scale:
>
> > However, I find that some
> > simple 5-limit harmonies can be evoked effectively even when the
> > errors are fairly large, just as a single holistic pitch can be
> > evoked by an overtone series in which the overtones are displaced
> by
> > fairly large amounts. This is suggested by the clarity with which
> the
> > following example is heard as being a single voice, where the
> > *timbre* is composed of 6 sine-wave partials tuned to a
> > pelogic 'major chord':
> >
> > /tuning/files/Erlich/dave.wav
> >
> > The partials do not fall apart into individual tones, the way the
> > partials of, say, a carillon bell do. Similarly, the triads of
> > pelogic, when the timbres are 'gentle' enough, manage to 'cohere'
> as
> > harmonic entities, made all the more appealing by the unusual
> melodic
> > structure of the scales they arise from.
>
> Yes, the example in the file sounds very much like tones with
> harmonic partials, so much so that I was tempted to ask you if
you're
> sure that's the right file! I find that the duration of each tone
is
> not long enough for me to home in on any difference I might hear
> between these and tones with true harmonics.

Yup -- if you try dave1.wav instead, you'll hear a single tone held
long enough to hear those differences.

> But I, in turn, am dubious as to the usefulness of a tuning that
> requires artificial timbres containing a distorted harmonic series
in
> order to be successful.

You must have completely misunderstood what I wrote. Please re-read
what I say above about timbre, and refer to the original message if
necessary. I had an easy time finding appropriate timbres, both among
the presets on my Ensoniq keyboard, and on Ara's computer's MIDI
soundcard.

> I think that you would have to go to a lot
> of trouble to create any music of this sort, and it would seem to
> exclude virtually all acoustic instruments.

I agree. However, the approach of matching custom-designed tunings
and timbres, though not at all what I was suggesting here, *is* a
very attractive one, as Bill Sethares's musical examples (now a
significant corpus) charmingly demonstrate. For some of
the "exotemperaments" I described recently, such as "grandpa"
and "nana", such an approach would indeed be recommended.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>

> > I think that you would have to go to a lot
> > of trouble to create any music of this sort, and it would seem to
> > exclude virtually all acoustic instruments.
>
> I agree.

Just to clarify -- in case it wasn't clear already -- "music of this
sort" is not at all what I was suggesting with "P. E. Logic", which
tuning system should be very satisfying with all sorts of acoustic
instruments, for which, in your own words, "the only timbral
requirement is that there be a strong fundamental, making this an
ideal tuning for timbres with inharmonic partials that do not
overpower the fundamental".

The point of the "distorted timbre" example was to show that the
harmonic proportions in this tuning are close enough for the virtual
pitch phenomenon to function quite well. I feel that this phenomenon
has more importance to chordal consonance than the coinciding
difference tones phenomenon, since the latter would suggest that 3 :
4 : 5 and 4 : 5 : 6 should be similar in consonance to 3+phi :
4+phi : 5+phi, etc.

Nevertheless, should you be interested in pelog-like tunings
featuring coinciding difference tones, I would encourage you to look
into Kraig Grady's work -- he has shown that among the simplest
scales produced purely from the coinciding difference tone point of
view, one finds a curiously authentic pelog (as well as a curiously
authentic mavila). These are *not* JI scales, at least not in
the 'meta-' or fully converged forms. You might want to search these
archives (for the terms above as well as 'Mt. Meru'), as well as
those of the SpecMus list, for more information -- or ask him
personally.

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> ...
> The point of the "distorted timbre" example was to show that the
> harmonic proportions in this tuning are close enough for the
virtual
> pitch phenomenon to function quite well. I feel that this
phenomenon
> has more importance to chordal consonance than the coinciding
> difference tones phenomenon, since the latter would suggest that
3 :
> 4 : 5 and 4 : 5 : 6 should be similar in consonance to 3+phi :
> 4+phi : 5+phi, etc.

Evidently I have not made my views on the role of difference tones in
establishing consonance clear.

I believe that, for harmonic timbres, small-number ratios (which
result in coinciding harmonics) are much more important than
combinational tones in determining the relative consonance (as we
perceive it) for both intervals and chords -- and I think you will
agree with me that both play a part.

Where inharmonic timbres are concerned, coinciding partials and
combinational tones both play a part, and their relative importance
will depend on the timbre in question, i.e., the pitches and
amplitudes of the partials relative to the fundamental. If the
fundamental is strong in amplitude (relative to the other partials),
then first-order difference tones will play a very significant role.

In a tuning that has no 9-limit consonances (such the 9-tone MOS
subset of my isoharmonic pelog, assuming that we disregard the
leftover 3:4 for the purposes of this discussion), all of the
intervals are so dissonant that any chords constructed from them are
also expected to be dissonant, and usually *more* so, since the
dissonance of the individual component intervals is compounded. But
if chords constructed from dissonant intervals have coinciding first-
order difference tones, they are actually perceived as being
significantly *less* dissonant than any of the intervals which they
contain. Hence it is meaningful to treat these isoharmonic chords as
consonances to which dissonant non-isoharmonic chords may resolve.
So I view consonance and dissonance in such a tuning in relative
terms, for if we were to compare these "consonances" with chords made
up of 9-limit consonances using harmonic timbres, we would
undoubtedly judge the 9-limit chords to be much more consonant.

My purpose in bringing up the isoharmonic pelog tuning is to make the
point that a complete harmonic system (allowing resolution of
dissonance to consonance) may be created, in analogy to our present
diatonic system, that is suitable for non-harmonic timbres using a
scale (pelog) that the musical world has generally viewed as being
unsuitable for harmony. Just as the tones in the diatonic scale are
contained collectively in its three principal triads, all of the
tones of the 9-tone MOS scale are contained collectively in the four
11:13:15 triads built on consecutive roots in a chain of the ~11:15
generator.

> Nevertheless, should you be interested in pelog-like tunings
> featuring coinciding difference tones, I would encourage you to
look
> into Kraig Grady's work -- he has shown that among the simplest
> scales produced purely from the coinciding difference tone point of
> view, one finds a curiously authentic pelog (as well as a curiously
> authentic mavila). These are *not* JI scales, at least not in
> the 'meta-' or fully converged forms. You might want to search
these
> archives (for the terms above as well as 'Mt. Meru'), as well as
> those of the SpecMus list, for more information -- or ask him
> personally.

Thanks for the information, Paul. As I will explain in my next
posting, I regret that I won't be able to follow this up any time
soon.

--George

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:

/tuning/topicId_51743.html#52002

> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
> wrote:
> > > --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
> wrote:
> > > > ...
> > > > I'm a little lost . . . can you list these 12 interval
classes?
> > >
> > > Just the 12 "buckets" centered on the 12 interval-classes of 12-
> ET
> > > into which a non-microtonally oriented listener would mentally
> sort
> > > the intervals heard in a microtonal performance in which the
> > > intention is to produce conventional harmonies using
alternative
> > > pitches to achieve a sort of flexible intonation. Given the
> proper
> > > musical context, intervals on the order of 9/5, 16/9, and 7/4
> will
> > > all be heard as minor sevenths (or alternatively as augmented
> sixths,
> > > depending on the particular context), while anything ranging
from
> ~63
> > > to ~126 cents (1 and 2degs of 19-ET) will be heard as semitones
> > > (either minor seconds or augmented unisons, depending on
> context).
> > > Thus the interval *size* will determine the interval-class
> > > (or "bucket"), while the musical *context* will determine the
> > > interval spelling.
> >
> > Sounds like you're basically agreeing with Eytan Agmon. A bunch
of
> us
> > had an offlist conversation with him a while back, and were pretty
> > hasty to reject his theory. Maybe you should have been in on
> it . . .
> > of course, you probably would stop short of agreeing with him
that
> the
> > number of buckets can be 8, 12, 16, . . . for "cognitive" (or
> > something) reasons -- including a requirement of one and only one
> > 'ambiguous' interval (the half-octave, which is either a
diminished
> > this or an augmented that in all these systems) -- and that
> > psychoacoustics narrows the choice down to 12.
>
> Yes, I would indeed limit the number of "buckets" to 12 for
cognitive
> reasons. When we listen to a diatonic composition with only two
> voice parts (such as a Bach two-part keyboard invention), we are
able
> to "hear" harmonies that are there only in the sense that they are
> implied by tonal relationships already familiar to both the
composer
> and the listener. A two-voice composition in some non-diatonic
scale
> subset of a non-12 tuning, on the other hand, would very likely not
> have the same effect, but would be heard basically as a progression
> of intervals -- unless the composer had first written other
> (successful) pieces in that scale using full harmonies and the
> listener had also become familiar with them. In other words, the
> diatonic system is really a musical language, and our success in
> creating music in alternative tunings may depend on our ability to
> create (or discover) other musical languages that are capable of
> becoming meaningful to the general listener.
>
> --George

***Well, this is an interesting thought. My *own* personal
experience is that people (even the composer!)tend to "shoehorn"
exotic harmonies into our traditional 12-tET harmonic common
practice, so it takes quite a bit of skill and careful scale
selection to go beyond that.

I guess it's a kind of constructional "harmonic entropy" only, in
this case, we're concerned with the approximation to a remembered
common practice, rather than to individual consonant intervals...

This is "sociological harmonic entropy..." :)

J. Pehrson

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

/tuning/topicId_51743.html#52038

> >> >> >> but would be heard basically as a progression
> >> >> >> of intervals -- unless the composer had first written
other
> >> >> >> (successful) pieces in that scale using full harmonies and
> >> >> >> the listener had also become familiar with them.
> >> >> >
> >> >> >Quite possible. Though I'd argue that the full-chordal
> >> >> >analogues to Bach's counterpoint came later, not earlier.
> >> >>
> >> >> Example?
> >> >
> >> >Beethoven.
> >>
> >> Beethoven's what? Beethoven wrote counterpoint not infrequently,
> >> but I couldn't tell you how it's more "full-chordal" than Bach's.
> >
> >The Bach counterpoint in question had only two voices.
>
> Yes, but Bach himself, and many before him, wrote counterpoint
> with three and more voices. And I would argue the tonal context
> George was talking about was in place by Bach's time. I've been
> thinking lately about the coexistence of contrapuntal and tonal
> machinations and it strikes me that Bach does very well at this,
> but he was neither the first nor the last.
>
> -Carl

***But, I think there is a difference in "harmonic motion," Carl. In
Bach, although there are "key regions" there is so much linearity
going on that it's a bit more related to the linear counterpoint of
the Renaissance and earlier ages. By Beethoven, definite chord areas
are established and maintained, so counterpoint in that style has an
even firmer "tonal grounding..." I think.

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Carl Lumma <ekin@lumma.org>

>>>> Beethoven's what? Beethoven wrote counterpoint not infrequently,
>>>> but I couldn't tell you how it's more "full-chordal" than Bach's.
>>>
>>>The Bach counterpoint in question had only two voices.
>>
>> Yes, but Bach himself, and many before him, wrote counterpoint
>> with three and more voices. And I would argue the tonal context
>> George was talking about was in place by Bach's time. I've been
>> thinking lately about the coexistence of contrapuntal and tonal
>> machinations and it strikes me that Bach does very well at this,
>> but he was neither the first nor the last.
>
>***But, I think there is a difference in "harmonic motion," Carl.
>In Bach, although there are "key regions" there is so much linearity
>going on that it's a bit more related to the linear counterpoint of
>the Renaissance and earlier ages. By Beethoven, definite chord
>areas are established and maintained,

I'm not sure this is true of Beethoven's strictly contrapuntal
material. You can hear him reaching for it, but you can hear him
breaking into interludes when he needs tonal variation. I'm not
sure he ever achieves it. I'm not sure it's possible.

His music as a whole is definitely more tonal and less linear than
Bach's as a whole. He'll take a contrapuntal idea and treat it as
an atom in a larger structure (coming to mind is piano sonata 13,
3rd mvmt.). But within a contrapuntal atom, I can't think of an
example that's more tonal than your average Bach.

An interesting try on the tonal + counterpoint thing is
Shostakovich's 24 Preludes & Fugues. He'll do things like
transpose down a wholetone in the middle of a theme.

I forget exactly how this relates to George's point. Do we hear
tonal motion in the 2-part Inventions that people of Bach's day
did not? Maybe, but I tend to doubt it.

-Carl

🔗Carl Lumma <ekin@lumma.org>

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> /tuning/topicId_51743.html#52042
>
> > Hi George,
> >
> > >> > Do are you talking about 12-et, or the diatonic scale? The
two
> > >> > are hardly the same.
> > >
> > >No, here I'm talking about non-12 and non-diatonic -- something
> > >totally new and different to the listener. With no prior
> listening
> > >experience, one would not be able to flesh out mentally any full
> > >harmonies that might be implied by a two-voice musical skeleton.
> >
> > But if it got close to 5-limit JI, in my case I'd probably try
> > to hear it as being part of the skeleton I know, whether it was
> > or not.
>
>
> ***I agree with this, Carl. When I'm composing in Blackjack, for
> instance, sometimes I "hear" chords that are not in the system.
> Where are they from? Why, from 12-tET, of course... Initially,
I'm
> disappointed I can't use them, but then I try harder to adjust to
> my "new terrain..."
>
> JP

Maybe they're actually coming from *Canasta*, Joseph. If you're
grounded deep enough in Blackjack, it would make sense that your mind
might want to *transpose* or *modulate* the Blackjack structures it's
already familiar with (whether or not they resemble traditional
materials) . . . wishful thinking?

🔗czhang23@aol.com

> Date: Tue, 27 Jan 2004 05:04:11 -0000
> From: "Joseph Pehrson" <jpehrson@rcn.com>

>--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
>/tuning/topicId_51743.html#52049
>
>> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
>wrote:
>>
>> > Then where are all of the compositions in alternative tunings that
>> > have successfully made it into the musical mainstream?
>>
>> The musical mainstream has dried up.
>
>***The Rap music that I hear sure seems to be in an "alternate
>tuning..." :)

Quite a bit of Techno is also into "tweakin'" ATs and some "New Age" -
like Robert Rich and Dr. Fiorella Terenzi. And don't forget WorldBeat...

---|-----|--------|-------------|---------------------|
Hanuman Zhang, musical mad scientist: "Nah, I don't wanna take over the
world, just the sound spectrum to make it my home."

"Music is a herald, for change is inscribed in noise faster than it
transforms society. ... Listening to music is listening to all noise, realizing
that its appropriation and control is a reflection of power, that is essentially
political." - Jacques Attali, _Noise: The Political Economy of Music_

🔗Kurt Bigler <kkb@breathsense.com>

on 1/27/04 6:16 PM, czhang23@aol.com <czhang23@aol.com> wrote:

>
>> Date: Tue, 27 Jan 2004 05:04:11 -0000
>> From: "Joseph Pehrson" <jpehrson@rcn.com>
>
>> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>>
>> /tuning/topicId_51743.html#52049
>>
>>> --- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
>> wrote:
>>>
>>>> Then where are all of the compositions in alternative tunings that
>>>> have successfully made it into the musical mainstream?
>>>
>>> The musical mainstream has dried up.
>>
>> ***The Rap music that I hear sure seems to be in an "alternate
>> tuning..." :)
>
> Quite a bit of Techno is also into "tweakin'" ATs and some "New Age" -
> like Robert Rich and Dr. Fiorella Terenzi. And don't forget WorldBeat...

Does anybody have any good recommendations for tuned percussion polyrhythmic
stuff where the drums are tuned just, perhaps even to a harmonic series?

Actually I think Carl played me something synthesized along this line
(algorithmic, I think) but I was looking for something of acoustic origin.
Dying to here it.

-Kurt

🔗Joseph Pehrson <jpehrson@rcn.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

/tuning/topicId_51743.html#52212

> > /tuning/topicId_51743.html#52166
> >
> >> But within a contrapuntal atom, I can't think of an
> >> example that's more tonal than your average Bach.
> >
> >***Mozart??
> >
> >JP
>
> Any particular piece? There are Praeludium and Fugue in C, K394
> and Fugue 'Eruditissima' in Gmin, K401 -- both outstanding but
> neither any more tonal than Bach to my ear. The fugue from the
> last movement of the Jupiter might fare better...
>

***That's a good call, Carl, with the Jupiter symphony, and, in
fact, it was exactly what I was thinking of... I don't know the
other pieces, unfortunately...

> I'm thinking... what if 'tonal composition' is in some sense
> mutually exclusive with counterpoint? It almost seems that
> by definition if we have tonality we are loosing some independence
> of parts... or does it?
>
> -Carl

***Well, I don't know if I'd use the term "mutually exclusive..."
How about "inversely proportional..."? :)

🔗monz <monz@attglobal.net>

🔗Carl Lumma <ekin@lumma.org>

>>> I'm thinking... what if 'tonal composition' is in some
>>> sense mutually exclusive with counterpoint? It almost
>>> seems that by definition if we have tonality we are
>>> loosing some independence of parts... or does it?
>>
>> ***Well, I don't know if I'd use the term "mutually
>> exclusive..." How about "inversely proportional..."? :)
>
> hmmm ... this idea is *really* fascinating to me, with
> my heavy interest in Schoenberg's work!
>
> one of the reasons Schoenberg cited for the abandonment
> of traditional tonal centricity, was the need for greater
> independence of the separate voices in his contrapuntal
> fabric.

Hi monz. I've thought a bit more about this...

Maybe counterpointability is in direct proportion to
average chord-change period, in terms of number of note
attacks.

A chord change is basically a resynchronizing of the
voices, a resetting of the scale degree numbers at a
fixed point in time, relative to a single pitch (since
notes will have to be re-interpreted as distances
from the new tonic).

So like Bach has "tonal regions" which are fairly
long (have lots of notes in them), to allow lots of
counterpoint.

I was thinking some Phish jams might be good examples
of tonality with counterpoint, but the sample I listened
to last night was all tonal-region (actually, most of
it was completely static). I clearly need to look
beyond Walls of the Cave and Hood....

It would be a neat exercise to take hymns, add some
passing tones and dots and see if the methodical tonal
motion is preserved...

Maybe this should move to SpecMus...

-Carl

🔗Carl Lumma <ekin@lumma.org>

🔗monz <monz@attglobal.net>

hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

> Hi monz. I've thought a bit more about this...
>
> Maybe counterpointability is in direct proportion to
> average chord-change period, in terms of number of note
> attacks.
>
> A chord change is basically a resynchronizing of the
> voices, a resetting of the scale degree numbers at a
> fixed point in time, relative to a single pitch (since
> notes will have to be re-interpreted as distances
> from the new tonic).
>
> So like Bach has "tonal regions" which are fairly
> long (have lots of notes in them), to allow lots of
> counterpoint.
>
> I was thinking some Phish jams might be good examples
> of tonality with counterpoint, but the sample I listened
> to last night was all tonal-region (actually, most of
> it was completely static). I clearly need to look
> beyond Walls of the Cave and Hood....

how interesting that you should say this to me right now...

i just posted something on metatuning about a show i
saw Saturday night, of Cubensis, a great Grateful Dead
tribute band ... and the main person i was thinking of
was *you*. ... well, OK, paul too, but he's in Boston
and won't get to see Cubensis. they play all over
California and you should check them out.

a bit off-topic here ... but anyway, you'll like them!

-monz

🔗Carl Lumma <ekin@lumma.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:

/tuning/topicId_51743.html#52263

>>
> Hi monz. I've thought a bit more about this...
>
> Maybe counterpointability is in direct proportion to
> average chord-change period, in terms of number of note
> attacks.
>

***Hey Carl!

I don't know if your statement is right, since, generally speaking,
it is considered unwise to view counterpoint in terms of *chord
change...* Usually counterpoint is best defined as what is going on
*despite* or *instead of* chord change... :)

> A chord change is basically a resynchronizing of the
> voices, a resetting of the scale degree numbers at a
> fixed point in time, relative to a single pitch (since
> notes will have to be re-interpreted as distances
> from the new tonic).
>

***Ummm. While this is "techically" correct, it is a *much* more
complex process and topic than this, Carl. There is a big difference
between a "local tonicization" and a true "modulation" and it has a
lot to do with the particular sequence of chords being used, and the
length of the modulatory process. I would urge you to read a theory
text on this, such as the wonderful Elie Siegmeister, _Harmony and
Melody_ if you can find it in the library. Of course, we were
friends of Siegmeister, so I admit a certain bias... :)

> So like Bach has "tonal regions" which are fairly
> long (have lots of notes in them), to allow lots of
> counterpoint.
>

***Well, yes, some passages have a slow "harmonic rhythm," (the term
generally used for this) but some have fast ones, so it "depends..."

> I was thinking some Phish jams might be good examples
> of tonality with counterpoint, but the sample I listened
> to last night was all tonal-region (actually, most of
> it was completely static). I clearly need to look
> beyond Walls of the Cave and Hood....
>
> It would be a neat exercise to take hymns, add some
> passing tones and dots and see if the methodical tonal
> motion is preserved...
>

***It would, since true counterpoint has an underlying structure that
is, in essence, horizontal rather than vertical....

> Maybe this should move to SpecMus...
>

***Well, you have a point, but then *I* wouldn't be reading it, and I
see no harm in discussing some points of *music* and composition on
this list, since some here use microtonality in compositions...

🔗Carl Lumma <ekin@lumma.org>

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

/tuning/topicId_51743.html#52381

> >/tuning/topicId_51743.html#52263
> >
> >> Maybe counterpointability is in direct proportion to
> >> average chord-change period, in terms of number of note
> >> attacks.
> >
> >***Hey Carl!
> >
> >I don't know if your statement is right, since, generally
speaking,
> >it is considered unwise to view counterpoint in terms of *chord
> >change...* Usually counterpoint is best defined as what is going
on
> >*despite* or *instead of* chord change... :)
>
> Exactly. The longer the chord changes take, the more potential
> there is for counterpoint. That's what I'm trying to say, there.
>
> >> So like Bach has "tonal regions" which are fairly
> >> long (have lots of notes in them), to allow lots of
> >> counterpoint.
> >
> >***Well, yes, some passages have a slow "harmonic rhythm," (the
term
> >generally used for this) but some have fast ones, so
it "depends..."
>
> Slow or fast in terms of beats per minute? Howabout in terms of
> number of note attacks?
>
> -Carl

***Hmmm. Well, I suppose that could be used... generally speaking,
harmonic motion is referenced against, specifically, the *BASS*
line.... (from figured bass studies and such like...)