22 tet - harmonic resources

Now that I've got some time to explore 22 tet more systematically than
in the past, I'd like to begin by sorting out some of the terminology
relating to intervals. This would help me greatly in planning some of
the composition I plan to do in 22 tet.

I have found Paul's paper to be most edifying and would liken it to a
treatise on the anatomy of the temperament. What would be of great
benefit to me now is a detailed manual of physiology, ie an
understanding of the inner workings of the temperament, what it can and
can't do harmonically, which progressions are convincing and which
aren't and why, in clear terms. I don't expect anyone to write this
manual for me but I have a clear idea as to what needs to be explained.
So I'll ask the questions as I go.

What is needed in the long run is something similar to Schoenberg's
"Theory" (don't laugh - it's a tall order I know), starting with
connecting triads, then progressions, presumably decatonic rather than
diatonic, all the time taking account of spacings, inversions, cadences
and voice leading. Then tetrads, and presumably the 22tet equivalents of
vagrants and extended chords.

But going back to my first point, I'd like to propose something similar
to Vincent Persichetti's suggestion regarding the naming of intervals in
12 tet.
He suggests the following : -

perfect fifths and octaves - open consonances
major and minor thirds and sixths - soft consonances
minor seconds and major sevenths - sharp dissonances
major seconds and minor sevenths - mild dissonances
perfect fourth - consonant or dissonant (depending on context)
tritone - ambiguous, can be either neutral or restless

For argument's sake I'm quite happy to stick with descriptive terms like
these for just now. I have a chart with all the tones from 1/1 (with
in some cases as many as three names for each tone). The first problem
is that I have Paul's suggestions, all decatonic intervals, for example
step 18 (7/4 approx.) is an major 9 or diminished 10, both names with a
small ten subscript after the name to indicate decatonic. I also have
this as a minor 7 with a small seven superscript to indicate septimal
and as the harmonic seventh. Step 19 (20/11 approx.) is a decatonic
augmented 9 or minor 10, a minor 7 with an 11 superscript after it or a
large minor 7, again with an 11 superscript.

All are quite acceptable, but before I elicit suggestions for the level
of consonance/dissonance for each interval I'd like to ask if there is
any good reason NOT to choose to relate the intervals as far as possible
in the first instance to the familiar names, so that a 4/3 approx, ie
step 9, is 4th rather than a decatonic perfect 5th. I anticipate that
only Paul will pitch in to this discussion and that he will want to go
with his suggestions which is quite understandable. I do envisage a
scenario however where I might write for string quartet and it would
make much more sense to have a terminology consistent with convention
when I come to discuss music with players.

Once (if) we can settle this then I'd like to move on to the
consonance/dissonance terminology.

Kind Regards
a.m.

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:

> But going back to my first point, I'd like to propose something
similar
> to Vincent Persichetti's suggestion regarding the naming of
intervals in
> 12 tet.
> He suggests the following : -
>
> perfect fifths and octaves - open consonances
> major and minor thirds and sixths - soft consonances
> minor seconds and major sevenths - sharp dissonances
> major seconds and minor sevenths - mild dissonances
> perfect fourth - consonant or dissonant (depending on context)
> tritone - ambiguous, can be either neutral or restless

i remember this well -- i gobbled up "Twentieth Century Harmony" way
back when, in my high school library.

> For argument's sake I'm quite happy to stick with descriptive terms
like
> these for just now.

inversions can have more effect on consonance in 7-limit harmony than
they do in 5-limit harmony. chordal context can have a huge effect on
whether a particular interval comes out consonant or dissonant. but
if you wish, i'd be happy to provide such a dyadic "ranking" for 22-
equal. write me on the harmonic entropy list and i'll try to work up
a formula that satisfies you when applied to 12-equal; then we'll
quantize to 22-equal instead and see what comes out.

> I have a chart with all the tones from 1/1 (with
> in some cases as many as three names for each tone). The first
problem
> is that I have Paul's suggestions, all decatonic intervals, for
example
> step 18 (7/4 approx.) is an major 9 or diminished 10, both names
with a
> small ten subscript after the name to indicate decatonic. I also
have
> this as a minor 7 with a small seven superscript to indicate
septimal
> and as the harmonic seventh. Step 19 (20/11 approx.) is a decatonic
> augmented 9 or minor 10, a minor 7 with an 11 superscript after it
or a
> large minor 7, again with an 11 superscript.
>
> All are quite acceptable, but before I elicit suggestions for the
level
> of consonance/dissonance for each interval I'd like to ask if there
is
> any good reason NOT to choose to relate the intervals as far as
possible
> in the first instance to the familiar names, so that a 4/3 approx,
ie
> step 9, is 4th rather than a decatonic perfect 5th.

one problem with this is that it will quickly lead you into difficult
morasses when composing. diatonic thinking is conducive to all kinds
of progressions that don't work in 22-equal, as you know. the
quickest way to see this is that a major 2nd plus a perfect 5th does
not equal a major 6th, or else some similar problem will arise, if
you try to name the intervals of 22-equal in this way. UNLESS you
call the 9/7 approx. "major third" and 7/6 approx. "minor third" --
then everything will add up right, and i believe that the notation
system you're using already works this way . . . but of course the
ratios of 5 will now all be "microchromatically altered" intervals.

another problem, from the point of view of my paper, is that you'll
be missing out on the new tonal geometry that decatonicism provides.
the convenient diatonic categories will lead to diatonically-
conceived music (which will often come out very awkward due to the
syntonic comma problem), while 22-equal really shines in its non-
diatonic features. the keyboard mapping i provide is well-suited to a
pairing with the decatonic notation i propose, since the black keys
form a one-to-one correspondence with the "naturals".

on the guitar, though, this may simply be too difficult a re-
orientation for you to manage, so if you wish to stick with a
diatonic notation, with "thirds" and "sixths" lining up with the
ratios of 7 instead of ratios of 5 as described above, then i suppose
i can live with that :)

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41001.html#41018

> another problem, from the point of view of my paper, is that you'll
> be missing out on the new tonal geometry that decatonicism
provides.
> the convenient diatonic categories will lead to diatonically-
> conceived music (which will often come out very awkward due to the
> syntonic comma problem), while 22-equal really shines in its non-
> diatonic features. the keyboard mapping i provide is well-suited to
a
> pairing with the decatonic notation i propose, since the black keys
> form a one-to-one correspondence with the "naturals".
>

***Hi Paul,

So, what is the endemic 22-tET harmony like? I'm assuming it's
consonant, but not diatonic, yes? Is it at all like Blackjack
(probably not) and do you construct it using a lattice?

Thanks!

Joseph

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> /tuning/topicId_41001.html#41018
>
> > another problem, from the point of view of my paper, is that
you'll
> > be missing out on the new tonal geometry that decatonicism
> provides.
> > the convenient diatonic categories will lead to diatonically-
> > conceived music (which will often come out very awkward due to
the
> > syntonic comma problem), while 22-equal really shines in its non-
> > diatonic features. the keyboard mapping i provide is well-suited
to
> a
> > pairing with the decatonic notation i propose, since the black
keys
> > form a one-to-one correspondence with the "naturals".
> >
>
> ***Hi Paul,
>
> So, what is the endemic 22-tET harmony like? I'm assuming it's
> consonant, but not diatonic, yes?

have you heard my 22-tET music? "TIBIA" is hyperchromatic (with a bit
of diatonic parody at the end), "Decatonic Swing" is
decatonic, "Glassic" has a 5-limit porcupine section and a 4:6:7:9
hyperpythagorean section . . .

> Is it at all like Blackjack
> (probably not) and do you construct it using a lattice?

you could, if you wanted to. the lattice would of course extend
infinitely in three dimensions, filling up all of space, since you
can construct any tetrad on any pitch, any tetrad on any pitch of
*that* tetrad, and so on. it's unlike blackjack in that it has
no "kinks" where you find that certain kinds of tetrads can't be
constructed (in blackjack, for example, you can't construct a 7-limit
tetrad using A as the root). however, i tend to think in subset
scales or keys of 22-equal, modulating between them over the course
of a piece . . . each of these could be latticed if one wished . . .

wallyesterpaulrus wrote:

> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
> > But going back to my first point, I'd like to propose something
> similar
> > to Vincent Persichetti's suggestion regarding the naming of
> intervals in
> > 12 tet.
> > He suggests the following : -
> >
> > perfect fifths and octaves - open consonances
> > major and minor thirds and sixths - soft consonances
> > minor seconds and major sevenths - sharp dissonances
> > major seconds and minor sevenths - mild dissonances
> > perfect fourth - consonant or dissonant (depending on context)
> > tritone - ambiguous, can be either neutral or restless
>
> i remember this well -- i gobbled up "Twentieth Century Harmony" way
> back when, in my high school library.
>
> > For argument's sake I'm quite happy to stick with descriptive terms
> like
> > these for just now.
>
> inversions can have more effect on consonance in 7-limit harmony than
> they do in 5-limit harmony. chordal context can have a huge effect on
> whether a particular interval comes out consonant or dissonant. but
> if you wish, i'd be happy to provide such a dyadic "ranking" for 22-
> equal. write me on the harmonic entropy list and i'll try to work up
> a formula that satisfies you when applied to 12-equal; then we'll
> quantize to 22-equal instead and see what comes out.

Good, then the next step is to come up with some workable descriptive terms. I appreciate the
points on inversions and context. But I have to start somewhere nonetheless. For my purposes I'd
like to look at chords and progressions from several points of view. On re-reading Persichetti
with 22 tet in mind I quite like the idea of categorising the consonance/dissonance levels of
each interval, six in a tetrad, but obviously in 22 tet there are more possible interval types. I
find the "nondiatonic" approaches to modern 12 tet harmony applicable in some cases to 22 tet and
it's given me some good starting points for what I want to achieve, which is something along the
lines of pieces in two, three and four parts, as much for my benefit as for the listener, though
hopefully satisfying to both.

A further step would be to look at intervals plus the octave. Your second point, chordal context,
I agree with entirely. This is why I'm looking for a firm base - so that I can get a feel for
progressions in motion and for what arises contrapuntally.

> > I have a chart with all the tones from 1/1 (with
> > in some cases as many as three names for each tone). The first
> problem
> > is that I have Paul's suggestions, all decatonic intervals, for
> example
> > step 18 (7/4 approx.) is an major 9 or diminished 10, both names
> with a
> > small ten subscript after the name to indicate decatonic. I also
> have
> > this as a minor 7 with a small seven superscript to indicate
> septimal
> > and as the harmonic seventh. Step 19 (20/11 approx.) is a decatonic
> > augmented 9 or minor 10, a minor 7 with an 11 superscript after it
> or a
> > large minor 7, again with an 11 superscript.
> >
> > All are quite acceptable, but before I elicit suggestions for the
> level
> > of consonance/dissonance for each interval I'd like to ask if there
> is
> > any good reason NOT to choose to relate the intervals as far as
> possible
> > in the first instance to the familiar names, so that a 4/3 approx,
> ie
> > step 9, is 4th rather than a decatonic perfect 5th.
>
> one problem with this is that it will quickly lead you into difficult
> morasses when composing. diatonic thinking is conducive to all kinds
> of progressions that don't work in 22-equal, as you know. the
> quickest way to see this is that a major 2nd plus a perfect 5th does
> not equal a major 6th, or else some similar problem will arise, if
> you try to name the intervals of 22-equal in this way. UNLESS you
> call the 9/7 approx. "major third" and 7/6 approx. "minor third" --
> then everything will add up right, and i believe that the notation
> system you're using already works this way . . . but of course the
> ratios of 5 will now all be "microchromatically altered" intervals.
>
> another problem, from the point of view of my paper, is that you'll
> be missing out on the new tonal geometry that decatonicism provides.
> the convenient diatonic categories will lead to diatonically-
> conceived music (which will often come out very awkward due to the
> syntonic comma problem), while 22-equal really shines in its non-
> diatonic features. the keyboard mapping i provide is well-suited to a
> pairing with the decatonic notation i propose, since the black keys
> form a one-to-one correspondence with the "naturals".
>
> on the guitar, though, this may simply be too difficult a re-
> orientation for you to manage, so if you wish to stick with a
> diatonic notation, with "thirds" and "sixths" lining up with the
> ratios of 7 instead of ratios of 5 as described above, then i suppose
> i can live with that :)

OK I've had a good think about this and I'm prepared to go along with your interval names for now
because you've put in a lot more thought into the matter than me. Two problems I have:

- calling 7/6 a major third goes against my better judgement.
- if I wrote a polymicrotonal piece and had several different interval names for an approx 4/3 I'd
be up sh*t street to say the least. I have misgivings about trying to explain these things to
conventionally trained musicians. A completely new system of naming intervals at odds with what
they know might turn them away and God knows it's hard enough to recruit willing and able bodies.
So I'll know who to blame : - )

I look forward to continuing the relevant parts of this discussion on this list. Sincere thanks
for your helpful comments.

Kind Regards
a.m.

>

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> wallyesterpaulrus wrote:
>
> > --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> > > But going back to my first point, I'd like to propose something
> > similar
> > > to Vincent Persichetti's suggestion regarding the naming of
> > intervals in
> > > 12 tet.
> > > He suggests the following : -
> > >
> > > perfect fifths and octaves - open consonances
> > > major and minor thirds and sixths - soft consonances
> > > minor seconds and major sevenths - sharp dissonances
> > > major seconds and minor sevenths - mild dissonances
> > > perfect fourth - consonant or dissonant (depending on context)
> > > tritone - ambiguous, can be either neutral or restless
>
> Good, then the next step is to come up with some workable
descriptive terms. I appreciate the
> points on inversions and context. But I have to start somewhere
nonetheless.

then how about this as a start, maintaining strict inversional
equivalence:

in steps of 22-equal:

9, 13, 22 -- open consonances (ratios of 3)
6, 7, 15, 16 -- soft consonances (ratios of 5)
4, 5, 11, 17, 18 -- mild consodissonances (ratios of 7)
3, 8, 14, 19 -- semisharp consodissonances (ratios of 9)
10, 12 -- unstable/restless (ratios of 11)
2, 20 -- sharp dissonances
1, 21 -- supersharp dissonances

many other categorizations are of course possible, but this seems
right to me at the moment.

> > on the guitar, though, this may simply be too difficult a re-
> > orientation for you to manage, so if you wish to stick with a
> > diatonic notation, with "thirds" and "sixths" lining up with the
> > ratios of 7 instead of ratios of 5 as described above, then i
suppose
> > i can live with that :)
>
> OK I've had a good think about this and I'm prepared to go along
>with your interval names for now
> because you've put in a lot more thought into the matter than me.
>Two problems I have:
>
> - calling 7/6 a major third goes against my better judgement.

but that's *your* name for it (according to the notation system you
were using for 22-equal, last time you presented it, all
the "diatonic", unaltered minor thirds were the approx. 7/6). my name
for it is a major decthird.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41001.html#41046

>
> have you heard my 22-tET music? "TIBIA" is hyperchromatic (with a
bit
> of diatonic parody at the end), "Decatonic Swing" is
> decatonic, "Glassic" has a 5-limit porcupine section and a 4:6:7:9
> hyperpythagorean section . . .
>

***Oh, sure. I've heard _Tibia_ several times... just forgot
temporarily that it's in 22-equal.

Gee, I remember it sounding pretty *diatonic* though, although
through an "extended chord" kind of jazz mirror.

> > Is it at all like Blackjack
> > (probably not) and do you construct it using a lattice?
>
> you could, if you wanted to. the lattice would of course extend
> infinitely in three dimensions, filling up all of space, since you
> can construct any tetrad on any pitch, any tetrad on any pitch of
> *that* tetrad, and so on. it's unlike blackjack in that it has
> no "kinks" where you find that certain kinds of tetrads can't be
> constructed (in blackjack, for example, you can't construct a 7-
limit
> tetrad using A as the root). however, i tend to think in subset
> scales or keys of 22-equal, modulating between them over the course
> of a piece . . . each of these could be latticed if one wished . . .

***Well, that's pretty amazing. Maybe we need some kind of "virtual
reality" device to work with this lattice... (That's really
smoking! :)

JP

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:

> > OK I've had a good think about this and I'm prepared to go along
> >with your interval names for now
> > because you've put in a lot more thought into the matter than me.
> >Two problems I have:
> >
> > - calling 7/6 a major third goes against my better judgement.
>
> but that's *your* name for it (according to the notation system you
> were using for 22-equal, last time you presented it, all
> the "diatonic", unaltered minor thirds were the approx. 7/6). my
name
> for it is a major decthird.

sorry alison, i thought you said "calling 7/6 a *minor third*" . . .
please accept my apologies for the confusion. your notation system
(the one you adopted some time ago) for 22-equal would simply regard
this as a minor third, and this actually is workable. for me, it's
the bigger of two possible intervals formed by two black keys in my
keyboard mapping, when there's one and only one black key between
them. i go by eye/ear, not language.

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> /tuning/topicId_41001.html#41046
>
> >
> > have you heard my 22-tET music? "TIBIA" is hyperchromatic (with a
> bit
> > of diatonic parody at the end), "Decatonic Swing" is
> > decatonic, "Glassic" has a 5-limit porcupine section and a
4:6:7:9
> > hyperpythagorean section . . .
> >
>
> ***Oh, sure. I've heard _Tibia_ several times... just forgot
> temporarily that it's in 22-equal.
>
> Gee, I remember it sounding pretty *diatonic* though, although
> through an "extended chord" kind of jazz mirror.

well, admittedly it's the most diatonic of the three, in that the
chord functions could be described sort-of-conventionally. that piece
came out the way it did with absolutely no involvement on the part of
Theory -- i simply had the tuning set up on the keyboard, got into a
creative state, and plunked around for a little while -- and out came
the piece. too much chopin and bach in my brain for it to come out
real non-diatonic like.

> > > Is it at all like Blackjack
> > > (probably not) and do you construct it using a lattice?
> >
> > you could, if you wanted to. the lattice would of course extend
> > infinitely in three dimensions, filling up all of space, since
you
> > can construct any tetrad on any pitch, any tetrad on any pitch of
> > *that* tetrad, and so on. it's unlike blackjack in that it has
> > no "kinks" where you find that certain kinds of tetrads can't be
> > constructed (in blackjack, for example, you can't construct a 7-
> limit
> > tetrad using A as the root). however, i tend to think in subset
> > scales or keys of 22-equal, modulating between them over the
course
> > of a piece . . . each of these could be latticed if one
wished . . .
>
>
> ***Well, that's pretty amazing. Maybe we need some kind
of "virtual
> reality" device to work with this lattice... (That's really
> smoking! :)

you can view a thick slice of the full 7-limit lattice (easily
applicable to 22-equal) in Figure 10 of _The Forms Of Tonality_. No
need for goggles or smoking! :) :)

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:

> you can view a thick slice of the full 7-limit lattice (easily
> applicable to 22-equal) in Figure 10 of _The Forms Of Tonality_. No
> need for goggles or smoking! :) :)

actually, the note names on that lattice *are* the 22-equal note
names, as laid out in the appednix (key sigs. and keyboard diagram),
and also in my "famous" paper on 22.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
> wrote:
>
> > you can view a thick slice of the full 7-limit lattice (easily
> > applicable to 22-equal) in Figure 10 of _The Forms Of Tonality_.
No
> > need for goggles or smoking! :) :)
>
> actually, the note names on that lattice *are* the 22-equal note
> names, as laid out in the appednix (key sigs. and keyboard
diagram),
> and also in my "famous" paper on 22.

and, of course, essentailly the same lattice with 22-equal note
*numbers* is visible as Figure 4 in the "famous" paper on 22.

which, in case anyone was wondering, isn't really famous, but you can
find it at:

http://www-math.cudenver.edu/~jstarret/22ALL.pdf

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Oh, sure. I've heard _Tibia_ several times... just forgot
> temporarily that it's in 22-equal.
>
> Gee, I remember it sounding pretty *diatonic* though, although
> through an "extended chord" kind of jazz mirror.

can stepping down through the octave 1/22 oct. at a time sound
diatonic? i guess in this case, it actually can! perhaps the first
piece ever to do something like this?

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41001.html#41062

>
> you can view a thick slice of the full 7-limit lattice (easily
> applicable to 22-equal) in Figure 10 of _The Forms Of Tonality_. No
> need for goggles or smoking! :) :)

***Got it! Forgot all about the 22 stuff being in there... I still
like the *font* on that paper... :) What font was that again?? :)

JP

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41001.html#41066

wrote:
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > ***Oh, sure. I've heard _Tibia_ several times... just forgot
> > temporarily that it's in 22-equal.
> >
> > Gee, I remember it sounding pretty *diatonic* though, although
> > through an "extended chord" kind of jazz mirror.
>
> can stepping down through the octave 1/22 oct. at a time sound
> diatonic? i guess in this case, it actually can! perhaps the first
> piece ever to do something like this?

***Yep, it does. And the "generating structure" of this piece is
really the step-wise "chromatic" bass..

JP

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:

> > can stepping down through the octave 1/22 oct. at a time sound
> > diatonic? i guess in this case, it actually can! perhaps the
first
> > piece ever to do something like this?
>
>
> ***Yep, it does. And the "generating structure" of this piece is
> really the step-wise "chromatic" bass..
>
> JP

actually, the bass does no such thing -- the bass actually carries
the melody -- while the tenor and soprano do the step-wise
microchromatic thing . . .

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41001.html#41085

wrote:
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > > can stepping down through the octave 1/22 oct. at a time sound
> > > diatonic? i guess in this case, it actually can! perhaps the
> first
> > > piece ever to do something like this?
> >
> >
> > ***Yep, it does. And the "generating structure" of this piece is
> > really the step-wise "chromatic" bass..
> >
> > JP
>
> actually, the bass does no such thing -- the bass actually carries
> the melody -- while the tenor and soprano do the step-wise
> microchromatic thing . . .

Oh!... I'll have to listen again, obviously...

JP

wallyesterpaulrus wrote:

then how about this as a start, maintaining strict inversionalequivalence:in steps of 22-equal:

> 9, 13, 22 -- open consonances (ratios of 3)
> 6, 7, 15, 16 -- soft consonances (ratios of 5)
> 4, 5, 11, 17, 18 -- mild consodissonances (ratios of 7)
> 3, 8, 14, 19 -- semisharp consodissonances (ratios of 9)
> 10, 12 -- unstable/restless (ratios of 11)
> 2, 20 -- sharp dissonances
> 1, 21 -- supersharp dissonances
>
> many other categorizations are of course possible, but this seems
> right to me at the moment.

I came up with something similar - at least the inversional idea (which my computer ate).

I suppose your first category settles the 4/3 question. Steps 3 and 19 are closer to 11/10 and
20/11 respectively. I don't know if that clouds the issue but as you are categorising by primes up
to 11 perhaps this is relevant. Consodissonances is a bit of a mouthful - how about concordances?
I'm not up to speed on how consonant or dissonant 11/8 and 16/11 should be considered
scientifically but restless sounds good. And the last two are perfect descriptions.

Kind Regards
a.m.

--- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
>
>
> wallyesterpaulrus wrote:
>
> then how about this as a start, maintaining strict
inversionalequivalence:in steps of 22-equal:
>
> > 9, 13, 22 -- open consonances (ratios of 3)

well, actually 22 steps is a ratio of 1, not of 3.

> > 6, 7, 15, 16 -- soft consonances (ratios of 5)
> > 4, 5, 11, 17, 18 -- mild consodissonances (ratios of 7)
> > 3, 8, 14, 19 -- semisharp consodissonances (ratios of 9)
> > 10, 12 -- unstable/restless (ratios of 11)
> > 2, 20 -- sharp dissonances
> > 1, 21 -- supersharp dissonances
> >
> > many other categorizations are of course possible, but this seems
> > right to me at the moment.
>
> I came up with something similar - at least the inversional idea
(which my computer ate).
>
> I suppose your first category settles the 4/3 question. Steps 3 and
19 are closer to 11/10 and
> 20/11 respectively. I don't know if that clouds the issue but as
you are categorising by primes up
> to 11 perhaps this is relevant.

these are not the only ambiguities. 4 and 18 are pretty close to 9/8
and 16/9, respectively. ambiguity implies entropy. i'll attempt
something more "scientific" on the harmonic entropy list now -- i'll
start by sticking with the inversional equivalence assumption, which
we can always drop later.

however, remember that once we move beyond dyads, context can do a
great job of resolving these ambiguities one way or the other. a
1:3:5:7:9:11 chord (in other words, a harmonic-series chord
consisting of the first 12 harmonics) sounds very convincing in 22-
equal.

> Consodissonances is a bit of a mouthful - how about concordances?

the meaning concordance is too far from the meaning of dissonance.
but i agree with you and thought of a better term last night:
mesonances.

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41001.html#41110

wrote:
> --- In tuning@y..., Alison Monteith <alison.monteith3@w...> wrote:
> >
> >
> > wallyesterpaulrus wrote:
> >
> > then how about this as a start, maintaining strict
> inversionalequivalence:in steps of 22-equal:
> >
> > > 9, 13, 22 -- open consonances (ratios of 3)
>
> well, actually 22 steps is a ratio of 1, not of 3.
>
> > > 6, 7, 15, 16 -- soft consonances (ratios of 5)
> > > 4, 5, 11, 17, 18 -- mild consodissonances (ratios of 7)
> > > 3, 8, 14, 19 -- semisharp consodissonances (ratios of 9)
> > > 10, 12 -- unstable/restless (ratios of 11)
> > > 2, 20 -- sharp dissonances
> > > 1, 21 -- supersharp dissonances
> > >
> > > many other categorizations are of course possible, but this
seems
> > > right to me at the moment.
> >
> > I came up with something similar - at least the inversional idea
> (which my computer ate).
> >
> > I suppose your first category settles the 4/3 question. Steps 3
and
> 19 are closer to 11/10 and
> > 20/11 respectively. I don't know if that clouds the issue but as
> you are categorising by primes up
> > to 11 perhaps this is relevant.
>
> these are not the only ambiguities. 4 and 18 are pretty close to
9/8
> and 16/9, respectively. ambiguity implies entropy. i'll attempt
> something more "scientific" on the harmonic entropy list now --
i'll
> start by sticking with the inversional equivalence assumption,
which
> we can always drop later.
>
> however, remember that once we move beyond dyads, context can do a
> great job of resolving these ambiguities one way or the other. a
> 1:3:5:7:9:11 chord (in other words, a harmonic-series chord
> consisting of the first 12 harmonics) sounds very convincing in 22-
> equal.
>
> > Consodissonances is a bit of a mouthful - how about concordances?
>
> the meaning concordance is too far from the meaning of dissonance.
> but i agree with you and thought of a better term last night:
> mesonances.

***Didn't "concordance" also have a very specific meaning, with
Terhardt and such like?? I thought it was "contextually independent"
or some such thing...??

J. Pehrson

Joseph Pehrson wrote:

> ***Didn't "concordance" also have a very specific meaning, with
> Terhardt and such like?? I thought it was "contextually independent"
> or some such thing...??
>
> J. Pehrson
>

I remember some debate on this topic last year. I looked at Monz's dictionary but couldn't find
the term listed there.

Regards
a.m.

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Didn't "concordance" also have a very specific meaning, with
> Terhardt and such like??

blackwood -- see your upcoming book.

> I thought it was "contextually independent"
> or some such thing...??

right -- it's just the smoothness of the sound, not taking into
account tonal function or anything like that. blackwood's favorite
example is the dominant seventh when tuned close to 4:5:6:7 (as in 22-
equal) -- he says it's concordant, but not consonant: it's dissonant
because tonal function demands that dominant seventh chords act as
dissonances (tonal function of course being built off the diatonic
scale) . . .

unfortunately, it seems to me that in retreating from pandissonant
atonalism, blackwood landed in a rather conservative swamp, rather
than trying to build new functionalities out of the basic ingredients
of "concordance" . . . he's a pretty good composer, though . . .

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_41001.html#41132

> right -- it's just the smoothness of the sound, not taking into
> account tonal function or anything like that. blackwood's favorite
> example is the dominant seventh when tuned close to 4:5:6:7 (as in
22-equal) -- he says it's concordant, but not consonant: it's
dissonant because tonal function demands that dominant seventh chords
act as dissonances (tonal function of course being built off the
diatonic scale) . . .

***I believe then, Paul, that this identical situation applies to the
Blackjack tetrads, correct?? They are seventh chords that are
essentially *static*, concordances, and don't really need
to "resolve" to anything, right?? They didn't seem to, as I recall.

>
> unfortunately, it seems to me that in retreating from pandissonant
> atonalism, blackwood landed in a rather conservative swamp, rather
> than trying to build new functionalities out of the basic
ingredients of "concordance" . . . he's a pretty good composer,
though . . .

***Yes, I agree and although, from a theoretical point of view, many
of the "quasi Bach" emulations on the more "diatonic" scales in his
_Microtonal Etudes_ are masterful, they are, in my opinion, of the
lesser of his overall work. The ones he has to "struggle with" and
are most different from the diatonic are, for me, the most
interesting and exploratory. But I'll have to listen to the CD more
carefully. I also have the score now. Every line of the synth part
is fully written out as if they were chamber pieces! This whole
project was funded by the National Endowment for the Humanities, when
they were still doing such things (I think in the 60's as I recall...)

J.P.

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
>
> /tuning/topicId_41001.html#41132
>
> > right -- it's just the smoothness of the sound, not taking into
> > account tonal function or anything like that. blackwood's
favorite
> > example is the dominant seventh when tuned close to 4:5:6:7 (as
in
> 22-equal) -- he says it's concordant, but not consonant: it's
> dissonant because tonal function demands that dominant seventh
chords
> act as dissonances (tonal function of course being built off the
> diatonic scale) . . .
>
>
> ***I believe then, Paul, that this identical situation applies to
the
> Blackjack tetrads, correct?? They are seventh chords that are
> essentially *static*, concordances, and don't really need
> to "resolve" to anything, right?? They didn't seem to, as I recall.

well, blackwood would dispute that. he insists on treating dominant
seventh chords as dissonances, and tends to resolve them
traditionally, no matter how concordantly they're tuned!

> I also have the score now. Every line of the synth part
> is fully written out as if they were chamber pieces! This whole
> project was funded by the National Endowment for the Humanities,
when
> they were still doing such things (I think in the 60's as I
recall...)

it was 1980 . . .