guts of my scheme

Begin forwarded message:

> From: Ralph Hill <ascend11@...>
> Date: June 12, 2011 11:52:34 PM PDT
> To: Jonathan Glasier <jonathan.sonicarts@...>, Brink Mcgoogy <mahagoogy@...> >, Elizabeth Glasier <glasier2@...>, Joe Monzo > <monzojoe@...>
> Subject: Fwd: ...general post to Tuning: Battaglia ..... > Vaisaval ..... I appreciate your feedback. I take init. > responses as MAYBE guts of my scheme
>
>
> I've rushed to "get down on paper" the heart of a systematic scheme > for ordering and classifying a set of building blocks composers of a > post 12 equal temperament music can use which I believe has the > power to "electrify their workshops" and enable them to break > through a kind of "glass ceiling veil" which has lain draped unseen > over the 20th century era music so familiar to us.
>
> I'd hoped - and do hope - to do a much better explained and complete > job than this,
>
> Hello -
>
> I'll start by posting to Tuning - verbally only for now - the few > core ideas underlying my scheme for classifying the body of > "comoponents" or "molecules" which form the basic palette of > uniquely distinct harmonies available to composers out of which to > construct their musical creations. I'm leaving out music's other > key elements - rhythm and timing, amplitudes over the music's flow, > stereo balance, emotional meanings touched on over the course of the > music, ... and so many other things. Also I'm not looking at > melodic contour on it's own, but concentrating on the harmonies > sounded in succession as the music proceeds.
>
> In my particular scheme, I take what I call CHORD TRANSITIONS as > the basic building blocks the composer uses in constructing his > composition. Generally music's basic harmonic elements tend to be > thought to be the chords sounded as the music proceeds ..... eg " > major triad on C harmonic seventh chord on F major triad on > C minor triad on A harmonic seventh chord on F major > triad on C " could be analyzed into a stream of six chords the > composer had used there.
>
> That's how I used to think, but at some point it started to dawn on > me that it is really pairs of chords, one sounded after the other > with a first chord "leading into" a second destination chord which > are needed to say something which can stand on its own musically. A > single chord sounded by itself with no other harmony, not even any > implied partner harmony, tends to leave one hanging in suspense. > "Is it supposed to be part of music being played? Or is it the > doorbell. or......"
>
> A major triad on G followed by a major triad on C is a pair of > chords having a degree of completeness. Probably an authentic > cadence occurring in a piece of music in the key of C - at least > with no other information that's what that pair of chords suggests.
>
> In short, I take pairs of chords having direction (C major triad > followed by G major triad is not the same as G major triad first, > followed by C major triad) ...... but C major triad followed by G > major triad IS the same as F major triad followed by C major > excepting for the fact that the latter CHORD TRANSITION sounds at a > pitch level a fourth higher than the former ..... or at a pitch > level a fifth lower than the former.
>
> In my proposed scheme, there can be any of 12 chord root shift > intervals - 1 up a fifth (eg C to G) 2 down a fifth 3 up a major > second (C to D) 4 down a major second (C to B-flat) 5 down a > just minor third (C to A) 6 up a just minor third (C to E-flat) > 7 up a major third (second chord's root frequency 5/4 - just - times > the first chord's root frequency) 8 down a just major third (eg C > to A-flat) 9 down a 15/16 diatonic semitone (C to B) 10 up a > 15/16 diatonic semitone (C to C-sharp) 11 up an augmented fourth > (C to F-sharp) *** very close to down an augmented fourth 12 > first and 2nd chords are on the same root i.e. root shift is zero.
>
> Then (first cut) I take it that the first chord can be any one of > five "types" of chord and 2nd chord can be any one of these five > "types" of chord as I'll explain. This makes the number of possible > combinations - 12 possible root shifts, 5 possible types for the > first chord, 5 possible types for the second or destination chord > (12 times 5 times 5 equals 300).
>
> For "chord type" I'm taking it roughly that a chord can be: 1 a > major triad, the highest small whole integer to which one of its > note frequencies is proportional being 5 2 a harmonic seventh > chord, the highest small whole integer to which one of its note > frequencies is proportional being 7, its other notes having > frequencies proportional to 5, 3, and 1 (root note) - or a related > inversion perhaps having only two other notes with frequencies > proportional to 5 and 3 - or 5 and 1 - or 3 and 1 **** note - these > inversions aren't totally identical or equivalent, but they seem to > belong to a "close family" of harmonically similar chords ***** > Then beyond the harmonic 7th chord we have the harmonic 9th chord > with one of its notes having a frequency proportional to 9 (other > notes having note frequencies proportional to odd integers less than > 9). I'm cutting the odd integers off at 11 and a six note chord > with note frequencies proportional to 1, 3, 5, 7, 9, and 11 is > certainly a striking and unique animal. Added to these four "chord > types" are the minor chords with note frequencies proportional to 3, > 5, and 15 as well as the root having frequency proportional to 1.
>
> This scheme seems arbitrary as laid out in sketch form here, but a > lot of ear testing and experimentation with chord construction on > overtones and undertones etc., etc., etc. lies behind it. I don't > propose it as a final product, but as something which does embrace a > large swath of the most important "molecular elements" in musical > harmony. These elements in the palette of musical harmonies have > their own unique psychological perceptual effects and merit a place > in the post 12 equal temperament/common practice composer's tool > kit. Very sweet harmonious music can be composed out of these > elements or intriging mysterious sounding music can be built from > them. They put a great deal more power and flexibility and > capability for creating striking, rarely heard novel effects into > composers' hands. By contrast, the harmonic materials 12 equal > temperament puts into a composer's hands have a slight bland > "sameness" which seems to hang over music composed and/or performed > in that system. Quarter comma mean tone gives the composer more > power and if extended beyond 12 notes per octave to 14, 15, ..... 24 > notes per octave laid out in a spiral of fifths flattened by 1/4 > comma (approximating 31 equal temperament) provides a powerful > harmonic toolkit intermediate between the 12 equal tool kit and the > one based on chord transitions with 12 possible root shifts and > chords having note frequencies, the highest integer to which its > note frequency is proportional being 5, 7, 9, 11, or 15. Two such > chords separated by one of the 12 possible root shifts form a unique > "molecule" in this most advanced system I'm proposing.
>
> To repeat a key idea characterizing this palette of harmonies, I > take not the single chord, but rather a chord TRANSITION having > directionally ordered origin and destination chords whose roots are > separated by one of 12 possible integer ratio intervals as the > fundamental element or "molecule" out of which a musical composition > (in its harmonic aspect) is constructed.
>
> My initial first cut system offers about 300 unique building block > elements out of which a composition may be said to be constructed. > Of course there's much more to music, but this system is to bear its > harmonic aspects.
>
>
>
> Begin forwarded message:
>
>> From: Ralph Hill <ascend11@...>
>> Date: June 11, 2011 10:25:05 PM PDT
>> To: tuning@yahoogroups.com, Jonathan Glasier <jonathan.sonicarts@...>> >, Brink Mcgoogy <mahagoogy@...>, Elizabeth Glasier <glasier2@...>> >, Joe Monzo <monzojoe@...>
>> Subject: Fwd: ...general post to Tuning:... Corr. in last >> paragraph - "White Christmas" melody begins on E, not C; C is the >> tonic Re: Twinkletits in 23-EDO
>>
>>
>>
>> Begin forwarded message:
>>
>>> From: Ralph Hill <ascend11@...>
>>> Date: June 11, 2011 10:04:35 PM PDT
>>> To: tuning@yahoogroups.com, Jonathan Glasier <jonathan.sonicarts@...>>> >, Brink Mcgoogy <mahagoogy@...>, Elizabeth Glasier <glasier2@...>>> >, Joe Monzo <monzojoe@...>
>>> Subject: This is a general post to Tuning not specifically >>> directed: JI based "body of thought" on musical pitch & >>> harmony. Re: Twinkletits in 23-EDO
>>>
>>> " Sending 10:25 PM PDT Sat. June 11th, 2011
>>>
>>> Hello -
>>>
>>> I used to be active posting to the Tuning List about 10 years ago >>> but have since then gotten to being much less active, and have >>> contributed posts much less frequently.
>>>
>>> However I've been developing a fairly specific system for >>> organizing the pitch/harmonic side of music one is studying or >>> composing which I believe has value and deserves the attention of >>> musicians (composers, teachers, music lovers)....... "
>>>
>> **********************************
>>
>>> I hope some will give me the benefit of their thoughts as to the >>> suitability of my getting a draft of my thoughts on an organized >>> way of thinking about musical pitch/harmony which could form a >>> replacement (or core of a replacement) for the current compound of >>> common practice quarter comma mean tone systematization >>> confusingly subposed beneath the 12 equal pitch step per octave >>> 20th century piano tuning system which makes no distinction (the >>> latter) between the 24/25 frequency ratio chromatic semitone (eg E->>> flat to E) and the 15/16 frequency ratio diatonic semitone found >>> in the step E to F. THINK OF THE MELODY STARTING ON C FOR "I'M >>> DREAMING OF A WHITE CHRISTMAS"
>>
>>
>>> Melody starts on E, not C. C is tonic.
>>
>>
>>
>>> - the upward step between the 1st and 2nd note of the melody >>> (diatonic semitone) and the downward step between the 3rd and 4th >>> notes of the melody (chromatic semitone) (or upward again between >>> the 4th and 5th notes of the melody (again chromatic semitone)).
>>>
>>> Best wishes, Ralph David Hill
>>
>

My opinion is that your assumptions and the basics of your thinking, only as I glean from this post of course, are the very embodiment of one of major "glass cieling"s holding microtonal music back. Leaving aside ideas like "major triad" is, IMO, pretty much "step number one".

--- In tuning@yahoogroups.com, Ralph Hill <ASCEND11@...> wrote:
>
>
>
> Begin forwarded message:
>
> > From: Ralph Hill <ascend11@...>
> > Date: June 12, 2011 11:52:34 PM PDT
> > To: Jonathan Glasier <jonathan.sonicarts@...>, Brink Mcgoogy <mahagoogy@...
> > >, Elizabeth Glasier <glasier2@...>, Joe Monzo
> > <monzojoe@...>
> > Subject: Fwd: ...general post to Tuning: Battaglia .....
> > Vaisaval ..... I appreciate your feedback. I take init.
> > responses as MAYBE guts of my scheme
> >
> >
> > I've rushed to "get down on paper" the heart of a systematic scheme
> > for ordering and classifying a set of building blocks composers of a
> > post 12 equal temperament music can use which I believe has the
> > power to "electrify their workshops" and enable them to break
> > through a kind of "glass ceiling veil" which has lain draped unseen
> > over the 20th century era music so familiar to us.
> >
> > I'd hoped - and do hope - to do a much better explained and complete
> > job than this,
> >
> > Hello -
> >
> > I'll start by posting to Tuning - verbally only for now - the few
> > core ideas underlying my scheme for classifying the body of
> > "comoponents" or "molecules" which form the basic palette of
> > uniquely distinct harmonies available to composers out of which to
> > construct their musical creations. I'm leaving out music's other
> > key elements - rhythm and timing, amplitudes over the music's flow,
> > stereo balance, emotional meanings touched on over the course of the
> > music, ... and so many other things. Also I'm not looking at
> > melodic contour on it's own, but concentrating on the harmonies
> > sounded in succession as the music proceeds.
> >
> > In my particular scheme, I take what I call CHORD TRANSITIONS as
> > the basic building blocks the composer uses in constructing his
> > composition. Generally music's basic harmonic elements tend to be
> > thought to be the chords sounded as the music proceeds ..... eg "
> > major triad on C harmonic seventh chord on F major triad on
> > C minor triad on A harmonic seventh chord on F major
> > triad on C " could be analyzed into a stream of six chords the
> > composer had used there.
> >
> > That's how I used to think, but at some point it started to dawn on
> > me that it is really pairs of chords, one sounded after the other
> > with a first chord "leading into" a second destination chord which
> > are needed to say something which can stand on its own musically. A
> > single chord sounded by itself with no other harmony, not even any
> > implied partner harmony, tends to leave one hanging in suspense.
> > "Is it supposed to be part of music being played? Or is it the
> > doorbell. or......"
> >
> > A major triad on G followed by a major triad on C is a pair of
> > chords having a degree of completeness. Probably an authentic
> > cadence occurring in a piece of music in the key of C - at least
> > with no other information that's what that pair of chords suggests.
> >
> > In short, I take pairs of chords having direction (C major triad
> > followed by G major triad is not the same as G major triad first,
> > followed by C major triad) ...... but C major triad followed by G
> > major triad IS the same as F major triad followed by C major
> > excepting for the fact that the latter CHORD TRANSITION sounds at a
> > pitch level a fourth higher than the former ..... or at a pitch
> > level a fifth lower than the former.
> >
> > In my proposed scheme, there can be any of 12 chord root shift
> > intervals - 1 up a fifth (eg C to G) 2 down a fifth 3 up a major
> > second (C to D) 4 down a major second (C to B-flat) 5 down a
> > just minor third (C to A) 6 up a just minor third (C to E-flat)
> > 7 up a major third (second chord's root frequency 5/4 - just - times
> > the first chord's root frequency) 8 down a just major third (eg C
> > to A-flat) 9 down a 15/16 diatonic semitone (C to B) 10 up a
> > 15/16 diatonic semitone (C to C-sharp) 11 up an augmented fourth
> > (C to F-sharp) *** very close to down an augmented fourth 12
> > first and 2nd chords are on the same root i.e. root shift is zero.
> >
> > Then (first cut) I take it that the first chord can be any one of
> > five "types" of chord and 2nd chord can be any one of these five
> > "types" of chord as I'll explain. This makes the number of possible
> > combinations - 12 possible root shifts, 5 possible types for the
> > first chord, 5 possible types for the second or destination chord
> > (12 times 5 times 5 equals 300).
> >
> > For "chord type" I'm taking it roughly that a chord can be: 1 a
> > major triad, the highest small whole integer to which one of its
> > note frequencies is proportional being 5 2 a harmonic seventh
> > chord, the highest small whole integer to which one of its note
> > frequencies is proportional being 7, its other notes having
> > frequencies proportional to 5, 3, and 1 (root note) - or a related
> > inversion perhaps having only two other notes with frequencies
> > proportional to 5 and 3 - or 5 and 1 - or 3 and 1 **** note - these
> > inversions aren't totally identical or equivalent, but they seem to
> > belong to a "close family" of harmonically similar chords *****
> > Then beyond the harmonic 7th chord we have the harmonic 9th chord
> > with one of its notes having a frequency proportional to 9 (other
> > notes having note frequencies proportional to odd integers less than
> > 9). I'm cutting the odd integers off at 11 and a six note chord
> > with note frequencies proportional to 1, 3, 5, 7, 9, and 11 is
> > certainly a striking and unique animal. Added to these four "chord
> > types" are the minor chords with note frequencies proportional to 3,
> > 5, and 15 as well as the root having frequency proportional to 1.
> >
> > This scheme seems arbitrary as laid out in sketch form here, but a
> > lot of ear testing and experimentation with chord construction on
> > overtones and undertones etc., etc., etc. lies behind it. I don't
> > propose it as a final product, but as something which does embrace a
> > large swath of the most important "molecular elements" in musical
> > harmony. These elements in the palette of musical harmonies have
> > their own unique psychological perceptual effects and merit a place
> > in the post 12 equal temperament/common practice composer's tool
> > kit. Very sweet harmonious music can be composed out of these
> > elements or intriging mysterious sounding music can be built from
> > them. They put a great deal more power and flexibility and
> > capability for creating striking, rarely heard novel effects into
> > composers' hands. By contrast, the harmonic materials 12 equal
> > temperament puts into a composer's hands have a slight bland
> > "sameness" which seems to hang over music composed and/or performed
> > in that system. Quarter comma mean tone gives the composer more
> > power and if extended beyond 12 notes per octave to 14, 15, ..... 24
> > notes per octave laid out in a spiral of fifths flattened by 1/4
> > comma (approximating 31 equal temperament) provides a powerful
> > harmonic toolkit intermediate between the 12 equal tool kit and the
> > one based on chord transitions with 12 possible root shifts and
> > chords having note frequencies, the highest integer to which its
> > note frequency is proportional being 5, 7, 9, 11, or 15. Two such
> > chords separated by one of the 12 possible root shifts form a unique
> > "molecule" in this most advanced system I'm proposing.
> >
> > To repeat a key idea characterizing this palette of harmonies, I
> > take not the single chord, but rather a chord TRANSITION having
> > directionally ordered origin and destination chords whose roots are
> > separated by one of 12 possible integer ratio intervals as the
> > fundamental element or "molecule" out of which a musical composition
> > (in its harmonic aspect) is constructed.
> >
> > My initial first cut system offers about 300 unique building block
> > elements out of which a composition may be said to be constructed.
> > Of course there's much more to music, but this system is to bear its
> > harmonic aspects.
> >
> >
> >
> > Begin forwarded message:
> >
> >> From: Ralph Hill <ascend11@...>
> >> Date: June 11, 2011 10:25:05 PM PDT
> >> To: tuning@yahoogroups.com, Jonathan Glasier <jonathan.sonicarts@...
> >> >, Brink Mcgoogy <mahagoogy@...>, Elizabeth Glasier <glasier2@...
> >> >, Joe Monzo <monzojoe@...>
> >> Subject: Fwd: ...general post to Tuning:... Corr. in last
> >> paragraph - "White Christmas" melody begins on E, not C; C is the
> >> tonic Re: Twinkletits in 23-EDO
> >>
> >>
> >>
> >> Begin forwarded message:
> >>
> >>> From: Ralph Hill <ascend11@...>
> >>> Date: June 11, 2011 10:04:35 PM PDT
> >>> To: tuning@yahoogroups.com, Jonathan Glasier <jonathan.sonicarts@...
> >>> >, Brink Mcgoogy <mahagoogy@...>, Elizabeth Glasier <glasier2@...
> >>> >, Joe Monzo <monzojoe@...>
> >>> Subject: This is a general post to Tuning not specifically
> >>> directed: JI based "body of thought" on musical pitch &
> >>> harmony. Re: Twinkletits in 23-EDO
> >>>
> >>> " Sending 10:25 PM PDT Sat. June 11th, 2011
> >>>
> >>> Hello -
> >>>
> >>> I used to be active posting to the Tuning List about 10 years ago
> >>> but have since then gotten to being much less active, and have
> >>> contributed posts much less frequently.
> >>>
> >>> However I've been developing a fairly specific system for
> >>> organizing the pitch/harmonic side of music one is studying or
> >>> composing which I believe has value and deserves the attention of
> >>> musicians (composers, teachers, music lovers)....... "
> >>>
> >> **********************************
> >>
> >>> I hope some will give me the benefit of their thoughts as to the
> >>> suitability of my getting a draft of my thoughts on an organized
> >>> way of thinking about musical pitch/harmony which could form a
> >>> replacement (or core of a replacement) for the current compound of
> >>> common practice quarter comma mean tone systematization
> >>> confusingly subposed beneath the 12 equal pitch step per octave
> >>> 20th century piano tuning system which makes no distinction (the
> >>> latter) between the 24/25 frequency ratio chromatic semitone (eg E-
> >>> flat to E) and the 15/16 frequency ratio diatonic semitone found
> >>> in the step E to F. THINK OF THE MELODY STARTING ON C FOR "I'M
> >>> DREAMING OF A WHITE CHRISTMAS"
> >>
> >>
> >>> Melody starts on E, not C. C is tonic.
> >>
> >>
> >>
> >>> - the upward step between the 1st and 2nd note of the melody
> >>> (diatonic semitone) and the downward step between the 3rd and 4th
> >>> notes of the melody (chromatic semitone) (or upward again between
> >>> the 4th and 5th notes of the melody (again chromatic semitone)).
> >>>
> >>> Best wishes, Ralph David Hill
> >>
> >
>

--- In tuning@yahoogroups.com, Ralph Hill <ASCEND11@...> wrote:

> > In my proposed scheme, there can be any of 12 chord root shift
> > intervals - 1 up a fifth (eg C to G) 2 down a fifth 3 up a major
> > second (C to D) 4 down a major second (C to B-flat) 5 down a
> > just minor third (C to A) 6 up a just minor third (C to E-flat)
> > 7 up a major third (second chord's root frequency 5/4 - just - times
> > the first chord's root frequency) 8 down a just major third (eg C
> > to A-flat) 9 down a 15/16 diatonic semitone (C to B) 10 up a
> > 15/16 diatonic semitone (C to C-sharp) 11 up an augmented fourth
> > (C to F-sharp) *** very close to down an augmented fourth 12
> > first and 2nd chords are on the same root i.e. root shift is zero.

You are proposing to take a set of JI chords, and another set of ordered pairs of these chords. In mathematics, a set V together with a set A of ordered pairs of elements of V is called a digraph, or directed graph. If instead you take a set V together with a set E (called "edges") of two-element subsets of V, you get an ordinary or undirected graph. I don't see any payoff from using digraphs, and would suggest that if you allow movement down by 9/8, you also allow movement up by 9/8. Another simplifying assumption would be octave equivalence, so that down by 6/5 and up by 5/3 are counted as the same.

You are proposing to allow complete otonal and utonal chords up to 11. To make things simple, let's confine ourselves to tetrads, 7-limit complete otonalities. It seems to me that your restriction to only 5-limit root movements no longer makes sense. Starting from the otonal tetrad 1-5/4-3/2-7/4, it would make sense to allow root movement up by 7/6 to 1-7/6-7/5-7/4, root movement up by 7/4 to 21/20-21/16-3/2-7/4, and root movement up by 35/24, to 35/32-5/4-35/24-7/4. These all seem to be clearly justified by the fact that they share a dyad with the otonal tetrad. Similarly, from 1-6/5-3/2-12/7, one should at minimum allow root movements by 12/7, 8/7 or 48/35 to an otonal tetrad, on the same grounds.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Ralph Hill <ASCEND11@> wrote:
>
> > > In my proposed scheme, there can be any of 12 chord root shift
> > > intervals - 1 up a fifth (eg C to G) 2 down a fifth 3 up a major
> > > second (C to D) 4 down a major second (C to B-flat) 5 down a
> > > just minor third (C to A) 6 up a just minor third (C to E-flat)
> > > 7 up a major third (second chord's root frequency 5/4 - just - times
> > > the first chord's root frequency) 8 down a just major third (eg C
> > > to A-flat) 9 down a 15/16 diatonic semitone (C to B) 10 up a
> > > 15/16 diatonic semitone (C to C-sharp) 11 up an augmented fourth
> > > (C to F-sharp) *** very close to down an augmented fourth 12
> > > first and 2nd chords are on the same root i.e. root shift is zero.
>
> You are proposing to take a set of JI chords, and another set of ordered pairs of these chords. In mathematics, a set V together with a set A of ordered pairs of elements of V is called a digraph, or directed graph. If instead you take a set V together with a set E (called "edges") of two-element subsets of V, you get an ordinary or undirected graph. I don't see any payoff from using digraphs, and would suggest that if you allow movement down by 9/8, you also allow movement up by 9/8. Another simplifying assumption would be octave equivalence, so that down by 6/5 and up by 5/3 are counted as the same.
>
> You are proposing to allow complete otonal and utonal chords up to 11. To make things simple, let's confine ourselves to tetrads, 7-limit complete otonalities. It seems to me that your restriction to only 5-limit root movements no longer makes sense. Starting from the otonal tetrad 1-5/4-3/2-7/4, it would make sense to allow root movement up by 7/6 to 1-7/6-7/5-7/4, root movement up by 7/4 to 21/20-21/16-3/2-7/4, and root movement up by 35/24, to 35/32-5/4-35/24-7/4. These all seem to be clearly justified by the fact that they share a dyad with the otonal tetrad. Similarly, from 1-6/5-3/2-12/7, one should at minimum allow root movements by 12/7, 8/7 or 48/35 to an otonal tetrad, on the same grounds.
>

Interestingly, the roots of the dyad-sharing tetrads seem to form a
1-3-5-7 hexany. I suppose this is related to the structure of the A3
lattice, right?

Kalle

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> Interestingly, the roots of the dyad-sharing tetrads seem to form a
> 1-3-5-7 hexany. I suppose this is related to the structure of the A3
> lattice, right?

Right. Starting from a utonal tetrad, all the dyad sharing tetrads are otonal, and all the roots of the otonal tetrads are in an A3 lattice. The hexany is a deep hole of the A3 lattice, with the property that all the otonal tetrads based on it as roots share a dyad with a particular utonal tetrad, so the centers of the holes are in an A3 lattice arrangement. Same starting from an otonal tetrad.

--- In tuning@yahoogroups.com, Ralph Hill <ASCEND11@...> wrote:

> > I've rushed to "get down on paper" the heart of a systematic scheme
> > for ordering and classifying a set of building blocks composers of a
> > post 12 equal temperament music can use which I believe has the
> > power to "electrify their workshops" and enable them to break
> > through a kind of "glass ceiling veil" which has lain draped unseen
> > over the 20th century era music so familiar to us.
> >
> > I'd hoped - and do hope - to do a much better explained and complete
> > job than this,
> >
> > Hello -
> >
> > I'll start by posting to Tuning - verbally only for now - the few
> > core ideas underlying my scheme for classifying the body of
> > "comoponents" or "molecules" which form the basic palette of
> > uniquely distinct harmonies available to composers out of which to
> > construct their musical creations. I'm leaving out music's other
> > key elements - rhythm and timing, amplitudes over the music's flow,
> > stereo balance, emotional meanings touched on over the course of the
> > music, ... and so many other things. Also I'm not looking at
> > melodic contour on it's own, but concentrating on the harmonies
> > sounded in succession as the music proceeds.

What about melody? While I'm sure good music can be "constructed" out
of chord progressions it's the melody that most listeners hear as the
musical foreground. So it seems to me that it would serve the composer
well to think more in terms of melody. Counterpoint and harmony are
complementary ways to look at the same thing but I think there is an
unfortunate overemphasis on harmony in contemporary (tonal) music
theory.

> > In my particular scheme, I take what I call CHORD TRANSITIONS as
> > the basic building blocks the composer uses in constructing his
> > composition. Generally music's basic harmonic elements tend to be
> > thought to be the chords sounded as the music proceeds ..... eg "
> > major triad on C harmonic seventh chord on F major triad on
> > C minor triad on A harmonic seventh chord on F major
> > triad on C " could be analyzed into a stream of six chords the
> > composer had used there.
>
> > That's how I used to think, but at some point it started to dawn on
> > me that it is really pairs of chords, one sounded after the other
> > with a first chord "leading into" a second destination chord which
> > are needed to say something which can stand on its own musically. A
> > single chord sounded by itself with no other harmony, not even any
> > implied partner harmony, tends to leave one hanging in suspense.
> > "Is it supposed to be part of music being played? Or is it the
> > doorbell. or......"
> >
> > A major triad on G followed by a major triad on C is a pair of
> > chords having a degree of completeness. Probably an authentic
> > cadence occurring in a piece of music in the key of C - at least
> > with no other information that's what that pair of chords suggests.
> >
> > In short, I take pairs of chords having direction (C major triad
> > followed by G major triad is not the same as G major triad first,
> > followed by C major triad) ...... but C major triad followed by G
> > major triad IS the same as F major triad followed by C major
> > excepting for the fact that the latter CHORD TRANSITION sounds at a
> > pitch level a fourth higher than the former ..... or at a pitch
> > level a fifth lower than the former.

They definitely are NOT the same if you take the context of key into
account. Those progressions can sound very different depending on what
you hear as the tonic chord.

Kalle Aho