Yahoo Tuning Groups Ultimate Backup tuning [tuning] note names for tonal-ji in the key of c

Thought this was worth posting.
It seems to explain conventional music theory harmonic function and note
names very well.
Best viewed in fixed width font on the yahoo site.

Note names for the key (tonal center) C, 6-limit harmonic roots:

C c d eb e f g ab a bb b c
1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1

E c c# d d# e f# g g# a b c
5/4> 1/1 25/24 9/8 75/64 5/4 45/32 3/2 25/16 5/3 15/8 2/1

F c db d eb e f g ab a bb c
4/3> 1/1 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1

G c d eb e f f# g a bb b c
3/2> 1/1 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1

A c c# d e f f# g g# a b c
5/3> 1/1 25/24 10/9 5/4 4/3 25/18 3/2 25/16 5/3 15/8 2/1

All of the below keys can be mistaken for the key C in conventional music
theory:

Note names for the key (tonal center) Ab, 6-limit harmonic roots:

Ab c db eb fb f gb g ab bb cb c
8/5> 1/1 16/15 6/5 32/25 4/3 36/25 3/2 8/5 9/5 48/25 2/1

C c d eb e f g ab a bb b c
1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1

Db c db eb fb f gb ab bbb bb cb c
16/15> 1/1 16/15 6/5 32/25 4/3 64/45 8/5 128/75 16/9 48/25 2/1

Eb c db d eb f gb g ab bb cb c
6/5> 1/1 27/25 9/8 6/5 27/20 36/25 3/2 8/5 9/5 48/25 2/1

F c db d eb e f g ab a bb c
4/3> 1/1 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1

Note names for the key G, 6-limit harmonic roots:

G c d eb e f f# g a bb b c
3/2> 1/1 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1

B c# d d# e f# g g# a a# b
15/8> 135/128 9/8 75/64 5/4 45/32 3/2 25/16 27/16 225/128 15/8

C c d eb e f g ab a bb b c
1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1

D c c# d e f f# g a bb b
9/8> 81/80 135/128 9/8 81/64 27/20 45/32 3/2 27/16 9/5 15/8

E c c# d d# e f# g g# a b c
5/4> 1/1 25/24 9/8 75/64 5/4 45/32 3/2 25/16 5/3 15/8 2/1

Note names for the key F, 6-limit harmonic roots:

F c db d eb e f g ab a bb c
4/3> 1/1 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1

A c c# d e f f# g g# a b c
5/3> 1/1 25/24 10/9 5/4 4/3 25/18 3/2 25/16 5/3 15/8 2/1

Bb c db d eb f gb g ab a bb c
16/9> 1/1 16/15 10/9 32/27 4/3 64/45 40/27 8/5 5/3 16/9 2/1

C c d eb e f g ab a bb b c
1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1

D c c# d e f f# g a bb b c
10/9> 1/1 25/24 10/9 5/4 4/3 25/18 40/27 5/3 16/9 50/27 2/1

Note names for the key Eb, 6-limit harmonic roots:

Eb c db d eb f gb g ab bb cb c
6/5> 1/1 27/25 9/8 6/5 27/20 36/25 3/2 8/5 9/5 48/25 2/1

G c d eb e f f# g a bb b c
3/2> 1/1 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1

Ab c db eb fb f gb g ab bb cb c
8/5> 1/1 16/15 6/5 32/25 4/3 36/25 3/2 8/5 9/5 48/25 2/1

Bb c db d eb f gb g ab a bb
9/5> 81/80 27/25 9/8 6/5 27/20 36/25 3/2 81/50 27/16 9/5

C c d eb e f g ab a bb b c
1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1

We thus arrive at the following possible note names in the key C in
conventional music theory:
c c# db d d# eb e f f# gb g g# ab a bbb a# bb b cb c

Now am I right in thinking this is correct and conventional music theory
indeed gives the above possible note names for the key of C?

Marcel

🔗Chris Vaisvil <chrisvaisvil@...>

Marcel...

I thought the key of C had no sharps or flats.... so how can Ab or Eb be
mistaken for it?

Very confused in Indianapolis.

Chris

On Sun, Apr 11, 2010 at 11:02 PM, Marcel de Velde <m.develde@...>wrote:

🔗Mike Battaglia <battaglia01@...>

Marcel,

I think that for C, D sometimes works best as 10/9, rather than as 9/8. Take
the extremely chord progression ||: Cmaj | Dm | Dm | Cmaj :||

As in, Steely Dan's "Bad Sneakers."

-Mike

On Sun, Apr 11, 2010 at 11:02 PM, Marcel de Velde <m.develde@...>wrote:

>
>
> Thought this was worth posting.
> It seems to explain conventional music theory harmonic function and note
> names very well.
> Best viewed in fixed width font on the yahoo site.
>
>
> Note names for the key (tonal center) C, 6-limit harmonic roots:
>
> C c d eb e f g ab a bb b c
> 1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
>
> E c c# d d# e f# g g# a b c
> 5/4> 1/1 25/24 9/8 75/64 5/4 45/32 3/2 25/16 5/3 15/8 2/1
>
> F c db d eb e f g ab a bb c
> 4/3> 1/1 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1
>
> G c d eb e f f# g a bb b c
> 3/2> 1/1 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1
>
> A c c# d e f f# g g# a b c
> 5/3> 1/1 25/24 10/9 5/4 4/3 25/18 3/2 25/16 5/3 15/8 2/1
>
>
>
> All of the below keys can be mistaken for the key C in conventional music
> theory:
>
> Note names for the key (tonal center) Ab, 6-limit harmonic roots:
>
> Ab c db eb fb f gb g ab bb cb c
> 8/5> 1/1 16/15 6/5 32/25 4/3 36/25 3/2 8/5 9/5 48/25 2/1
>
> C c d eb e f g ab a bb b c
> 1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
>
> Db c db eb fb f gb ab bbb bb cb c
> 16/15> 1/1 16/15 6/5 32/25 4/3 64/45 8/5 128/75 16/9 48/25 2/1
>
> Eb c db d eb f gb g ab bb cb c
> 6/5> 1/1 27/25 9/8 6/5 27/20 36/25 3/2 8/5 9/5 48/25 2/1
>
> F c db d eb e f g ab a bb c
> 4/3> 1/1 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1
>
>
>
> Note names for the key G, 6-limit harmonic roots:
>
> G c d eb e f f# g a bb b c
> 3/2> 1/1 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1
>
> B c# d d# e f# g g# a a# b
> 15/8> 135/128 9/8 75/64 5/4 45/32 3/2 25/16 27/16 225/128 15/8
>
> C c d eb e f g ab a bb b c
> 1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
>
> D c c# d e f f# g a bb b
> 9/8> 81/80 135/128 9/8 81/64 27/20 45/32 3/2 27/16 9/5 15/8
>
> E c c# d d# e f# g g# a b c
> 5/4> 1/1 25/24 9/8 75/64 5/4 45/32 3/2 25/16 5/3 15/8 2/1
>
>
>
> Note names for the key F, 6-limit harmonic roots:
>
> F c db d eb e f g ab a bb c
> 4/3> 1/1 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1
>
> A c c# d e f f# g g# a b c
> 5/3> 1/1 25/24 10/9 5/4 4/3 25/18 3/2 25/16 5/3 15/8 2/1
>
> Bb c db d eb f gb g ab a bb c
> 16/9> 1/1 16/15 10/9 32/27 4/3 64/45 40/27 8/5 5/3 16/9 2/1
>
> C c d eb e f g ab a bb b c
> 1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
>
> D c c# d e f f# g a bb b c
> 10/9> 1/1 25/24 10/9 5/4 4/3 25/18 40/27 5/3 16/9 50/27 2/1
>
>
>
> Note names for the key Eb, 6-limit harmonic roots:
>
> Eb c db d eb f gb g ab bb cb c
> 6/5> 1/1 27/25 9/8 6/5 27/20 36/25 3/2 8/5 9/5 48/25 2/1
>
> G c d eb e f f# g a bb b c
> 3/2> 1/1 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1
>
> Ab c db eb fb f gb g ab bb cb c
> 8/5> 1/1 16/15 6/5 32/25 4/3 36/25 3/2 8/5 9/5 48/25 2/1
>
> Bb c db d eb f gb g ab a bb
> 9/5> 81/80 27/25 9/8 6/5 27/20 36/25 3/2 81/50 27/16 9/5
>
> C c d eb e f g ab a bb b c
> 1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
>
>
>
> We thus arrive at the following possible note names in the key C in
> conventional music theory:
> c c# db d d# eb e f f# gb g g# ab a bbb a# bb b cb c
>
>
> Now am I right in thinking this is correct and conventional music theory
> indeed gives the above possible note names for the key of C?
>
> Marcel
>
>

🔗Marcel de Velde <m.develde@...>

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

🔗Daniel Forró <dan.for@...>

Conventional music theory has two basic rules for extended tonality (altered diatonics):

- it's prohibited to alter tonic triad notes - in C major it's C-E-G. So Cb, C#, Eb, E#, Gb, G# are not allowed as well as double or tripple sharped or flatted alterations.

- it's prohibited to alter neighboring notes of tonic triad that way they become enharmonically altered notes of tonic triad. In C major B#, Dbb, Dx, Fb, Fx, Abb are not allowed.

So altered chromatic C major is this scale:

C Db D D# E F F# G Ab A A# Bb B

If any of those rules is not kept, it's of course not catastrophe, and it's allowed, but then it means we can't talk about C major as we modulated to the different key, or used some chromatic chord as an intentional transitional deviation from the basic key. It can be chord of chromatic third relation (mediant, like Eb minor, major, E major, Ab minor, major, A major), or double dominants, subdominants or diminished sevenths, or other function.
Above mentioned scale also explain why chords like Db major (Phrygian, Napoli chord) or B major (Lydian) are possible in C major in the extended tonality and can serve as substitutions for subdominant or dominant function.

The same rules are valid for minor key. C Aeolian altered diatonics will be:

C Db D Eb Fb F F# G Ab A A# Bb B

But I think I have explained this some time ago here.

Daniel Forro

On 12 Apr 2010, at 12:40 PM, Marcel de Velde wrote:

>
>
> We thus arrive at the following possible note names in the key C in > conventional music theory:
> c c# db d d# eb e f f# gb g g# ab a bbb a# bb b cb c
>
> I accidently left out fb.
> So that should read:
>
> We thus arrive at the following possible note names in the key C in > conventional music theory:
> c c# db d d# eb e fb f f# gb g g# ab a bbb a# bb b cb c
>
> Marcel

🔗genewardsmith <genewardsmith@...>

🔗caleb morgan <calebmrgn@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Daniel Forró <dan.for@...>

Thanks, Chris, you understand perfectly. It's exactly as you have explained.

This is a basic rule of tonality, and tonal center - keeping the tonic function. Tonal center must be protected, and locked against the changes. If you move with its notes intentionally, you change it and depending on the context you just deviate shortly (for the contrast or surprise) or you go to the other key (modulate). Of course such changes happen in classical music very often, it's not necessary to stay in one tonality during whole composition. This oscillation of tonal centres, and relation between harmonic functions in tonality is a base of tonal and extended tonal music. Beauty in it is that one and the same chord can have different functions depending on the context, and that we can use any chord in tonality, if only it's "properly" written. So there can be F# major triad in C major tonality, if only it will be written as F#-A#-Db or F#-Bb-Db. The other question is which harmonic function such chord will have - first one will be probably altered II, second one altered VII, or if they will be used isolated then they can be considered as chromatic mediants. Resolution of such chords usually follows natural direction, sharps usually go up, flats down. But the first chord can go as well to F-A-D or any other chord. The beauty of such chords is mainly in their transition role, they can stay between two common tonal chords and has as much narrow chromatic movements as possible. So for example (for the second chord, with added bass) D----F-A-D ..... D#----F#-Bb-Db .... E----G-A-C. Functionally it will be II - double altered VII - T6 (in inversion)... Or they can be used to confuse the listeners and surprise them.

When composers realized this, they were not far from more orthographically simple writing of such chords (and in fact aiming to extended tonality and atonality). Of course it's easier to read F#-A#-C# than F#-A#-Db. First one is graphically triad, the other one first inversion of triad.
There are many examples even in Baroque music (Bach, and especially Scarlatti), but it took another 100 years to be fully accepted and used (Wagner, Liszt, Debussy, Skriabin, Rachmaninoff...). Skriabin's last works are atonal, even Liszt was very near.

Daniel Forro

On 12 Apr 2010, at 9:53 PM, Chris Vaisvil wrote:

>
> It seems clear to me that people's heads won't explode.
>
> BUT if you play C minor in C in C major you will not be in C major > anymore. So it IS prohibited if you want to *be* in C major.
> Think of the Picardy 3rd - minor, minor - tada!! end on the major > tonic which denies the minor key previous in the piece.
>
> Since obviously there is music that uses the interchange of major - > minor it is a matter of common practice convention.
>
> - it's prohibited to alter tonic triad notes - in C major it's C-E-G.
> So Cb, C#, Eb, E#, Gb, G# are not allowed as well as double or
> tripple sharped or flatted alterations.
>
> - it's prohibited to alter neighboring notes of tonic triad that way
> they become enharmonically altered notes of tonic triad. In C major
> B#, Dbb, Dx, Fb, Fx, Abb are not allowed.
>
> So altered chromatic C major is this scale:
>

🔗Daniel Forró <dan.for@...>

In practice of music composition (even historical) nothing is
prohibited and we can find many examples of trespassing the usual
rules of the period.

But here we talk about theory, about tonal theory, and about key
(tonality) C major.

Yes, C minor triad doesn't exist in C major tonality. If you want to
use this chord and keep C major as a tonal center, then you're right
- it must be written as C-D#-G. Or you can write C-Eb-G, but than you
left C major tonality.

Good example is altered seventh chord on VII in minor key used
especially in Classicism (Haydn, Moyart, Beethoven). For example in C
minor it's Ab-C-Eb-F#. Why do you think the composers wrote F# and
not Gb? And if you change F# for Gb and continue in Db major, why
it's called enharmonic modulation? I'm sure you will find the answers.

What's so difficult in understanding this main and basic principle of all tonal and extended tonal music?

Daniel Forro

On 12 Apr 2010, at 9:21 PM, genewardsmith wrote:

>
>
>
> --- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
> >
> > Conventional music theory has two basic rules for extended tonality
> > (altered diatonics):
> >
> > - it's prohibited to alter tonic triad notes - in C major it's C-
> E-G.
> > So Cb, C#, Eb, E#, Gb, G# are not allowed as well as double or
> > tripple sharped or flatted alterations.
>
> What does "prohibited" mean? If you played a C minor triad while in
> the key of C major, everyone's head would explode? You can play the
> triad, but you must notate it C-D#-G? What?
>

🔗caleb morgan <calebmrgn@...>

I knew you wouldn't fail to explain yourself eloquently.

Some of us might use some words a little differently, because we are half-educated, because the meaning of words is their usage, because of our intuitions, and perhaps because we live in a metaphysical (and tonal) 'flatland'.

The word in question is 'tonal'.

Perhaps some of us use the word 'tonal' more broadly than you do, to distinguish it from 'atonal'--music that has no sense of tonal center.

Stravinsky's early and neo-classical music sounds 'tonal'' -- it has tonal centers.

It freely mixes major and minor without disrupting the sense of tonal center, so we call it' tonal.'

What words do you use to describe it?

For jazz-based musicians, as well, there is 'tonal' music that mixes it up.

I would be surprised if, upon listening to Scriabin's music, that I would call it 'atonal'.

Perhaps this simply comes down to definitions of words, as do so many discussions.

Caleb

On Apr 12, 2010, at 10:00 AM, Daniel Forró wrote:

> In practice of music composition (even historical) nothing is
> prohibited and we can find many examples of trespassing the usual
> rules of the period.
>
> But here we talk about theory, about tonal theory, and about key
> (tonality) C major.
>
> Yes, C minor triad doesn't exist in C major tonality. If you want to
> use this chord and keep C major as a tonal center, then you're right
> - it must be written as C-D#-G. Or you can write C-Eb-G, but than you
> left C major tonality.
>
> Good example is altered seventh chord on VII in minor key used
> especially in Classicism (Haydn, Moyart, Beethoven). For example in C
> minor it's Ab-C-Eb-F#. Why do you think the composers wrote F# and
> not Gb? And if you change F# for Gb and continue in Db major, why
> it's called enharmonic modulation? I'm sure you will find the answers.
>
> What's so difficult in understanding this main and basic principle of
> all tonal and extended tonal music?
>
> Daniel Forro
>
> On 12 Apr 2010, at 9:21 PM, genewardsmith wrote:
>
> >
> >
> >
> > --- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
> > >
> > > Conventional music theory has two basic rules for extended tonality
> > > (altered diatonics):
> > >
> > > - it's prohibited to alter tonic triad notes - in C major it's C-
> > E-G.
> > > So Cb, C#, Eb, E#, Gb, G# are not allowed as well as double or
> > > tripple sharped or flatted alterations.
> >
> > What does "prohibited" mean? If you played a C minor triad while in
> > the key of C major, everyone's head would explode? You can play the
> > triad, but you must notate it C-D#-G? What?
> >
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

I have to observe:

none of the examples below are "common practice".

If Marcel is NOT talking about common practice tonal theory I suggest he
state so.

My understanding is that he IS talking about common practice, which would be
quite appropriate for a Beethoven piece.

The question isn't really the use of the word tonal. The question is what
does Marcel mean when he says tonal / tonality/ tonic.

Chris

On Mon, Apr 12, 2010 at 10:24 AM, caleb morgan <calebmrgn@...> wrote:

>
>
> I knew you wouldn't fail to explain yourself eloquently.
>
> Some of us might use some words a little differently, because we are
> half-educated, because the meaning of words is their usage, because of our
> intuitions, and perhaps because we live in a metaphysical (and tonal)
> 'flatland'.
>
> The word in question is 'tonal'.
>
> Perhaps some of us use the word 'tonal' more broadly than you do, to
> distinguish it from 'atonal'--music that has no sense of tonal center.
>
> Stravinsky's early and neo-classical music sounds 'tonal'' -- it has tonal
> centers.
>
> It freely mixes major and minor without disrupting the sense of tonal
> center, so we call it' tonal.'
>
> What words do you use to describe it?
>
> For jazz-based musicians, as well, there is 'tonal' music that mixes it up.
>
> I would be surprised if, upon listening to Scriabin's music, that I would
> call it 'atonal'.
>
> Perhaps this simply comes down to definitions of words, as do so many
> discussions.
>
> Caleb
>
>
> O
>

🔗Daniel Forró <dan.for@...>

I had also feeling from the terms he used (key C, tonic, tonal center, conventional music theory) that he was talking about tonality and tonal theory. So my answer just followed this...

Daniel Forro

On 12 Apr 2010, at 11:34 PM, Chris Vaisvil wrote:

>
> I have to observe:
>
> none of the examples below are "common practice".
>
> If Marcel is NOT talking about common practice tonal theory I > suggest he state so.
>
> My understanding is that he IS talking about common practice, which > would be quite appropriate for a Beethoven piece.
>
> The question isn't really the use of the word tonal. The question > is what does Marcel mean when he says tonal / tonality/ tonic.
>
>
> Chris
>
>
> On Mon, Apr 12, 2010 at 10:24 AM, caleb morgan > <calebmrgn@...> wrote:
>
>
> I knew you wouldn't fail to explain yourself eloquently.
>
> Some of us might use some words a little differently, because we > are half-educated, because the meaning of words is their usage, > because of our intuitions, and perhaps because we live in a > metaphysical (and tonal) 'flatland'.
>
> The word in question is 'tonal'.
>
> Perhaps some of us use the word 'tonal' more broadly than you do, > to distinguish it from 'atonal'--music that has no sense of tonal > center.
>
> Stravinsky's early and neo-classical music sounds 'tonal'' -- it > has tonal centers.
>
> It freely mixes major and minor without disrupting the sense of > tonal center, so we call it' tonal.'
>
> What words do you use to describe it?
>
> For jazz-based musicians, as well, there is 'tonal' music that > mixes it up.
>
> I would be surprised if, upon listening to Scriabin's music, that I > would call it 'atonal'.
>
> Perhaps this simply comes down to definitions of words, as do so > many discussions.
>
> Caleb

🔗martinsj013 <martinsj@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> Thought this was worth posting. It seems to explain conventional music theory harmonic function and note names very well. <snip> We thus arrive at the following possible note names in the key C in
> conventional music theory:
> c c# db d d# eb e fb f f# gb g g# ab a bbb a# bb b cb c
> Now am I right in thinking this is correct and conventional music theory indeed gives the above possible note names for the key of C?

I think the answer is no. FWIW, a few thoughts from me:

1) as Daniel stated, conventional music theory "prohibits" the use of certain accidentals in certain keys - but I think in many ways this is just a "rule of thumb" that helps students to learn the thing - e.g. in UK we have the "Associated Board" Theory of Music handbook and examinations - and if you don't notate your chromatic scale correctly, the answer will be marked "wrong". Of course, in this context, the chromatic scale consists of precisely 12 notes, as opposed to your list of 20.

2) elsewhere I have seen a list of 25 note names in "chain of 5ths" order) from Dbb to Cx (aka C##) which was explained as what Telemann or Mozart would have used - this is bigger than your list, of course, but is not confined to the key of C. As Gene stated, that list would have been thought of in a "meantone" context - i.e. a single size of (tempered) 5th generating a chain of notes, whereas yours appears to derive from JI ratios.

3) Talking of which, 10 of your notes seem to have two different values depending on context, e.g. D = 9/8 or 10/9. Even F and G have two values. Not sure what to think about this.

4) I don't understand how you choose which notes to include - yes, you start with a group of 10 notes "around" C, and then extend this by going to E, F, G, A (why not D and B? and why not Ab Eb and Bb?); and then you iterate the process "around" G and F, and Eb (why?) (and why not E and A? and D and B? etc). And I don't understand "the below keys can be mistaken for C", at all ...? (It does allow inclusion of the notes "around" Ab and Eb, and Db)

5) If you add Ebb and E# to your list, you have a representation of the Indian 22 sruti relative to a tonic of C (but your ratios are different e.g the Indian version wouldn't have G# as 25/16 or Gb as 36/25).

Steve M.

🔗jonszanto <jszanto@...>

🔗cameron <misterbobro@...>

🔗Marcel de Velde <m.develde@...>

Hi all,

Thanks very much for the replies!

So if I were to combine in conventional tonal theory the major and minor
tonality, I'd get:
C D D# Eb E Fb F F# G Ab A A# Bb B

The reason I (wrongly) thought conventional tonal theory may give the note
names I said had several reasons.

First of all, my own theory of tonality is based on a harmonic model of
C(1/1) D(9/8) Eb(6/5) E(5/4) F(4/3) G(3/2) Ab(8/5) A(5/3) Bb(9/5) B(15/8)
C(2/1) (one can play any combination of these notes together, where the root
of the chord is 1/1 C).
All these notes come from direct permutations of the harmonic series
(limited to the 6th harmonic), so the C E G chord.
Tonality is in my theory holding (virtually) the C E G tonic chord, so all
notes and chords within this tonality must harmonize with the C E G (1/1 5/4
3/2) chord (and they must harmonize according to the harmonic model I gave
above).
We then find that a 1/1 5/4 3/2 chord is present at the following places in
the harmonic model: C E G, Eb G Ab, F A C, G B D, Ab C Eb.
So each of these 5 chords can be the tonic C E G chord, and we find 5
harmonic model roots in the (6-limit) tonality of C (both major and minor in
one) (the harmonic model roots are then at 1/1, 5/4, 4/3, 3/2 and 5/3)

Now I was thinking that normal music theory had come to something similar.
(but less similar than I thought I see now)
Yet when I searched google, I got many different answers for what is the
chromatic scale for the tonality of C.

I also had a talk (more of a fight) with my father.
He's graduated from conservatory (music school) in both piano and music
theory and used to be a professor of music theory.
But sadly I can't talk with my father normally about anything involving
music as he's extremely conservative and dominant and we get into a fight
immidiately when the subject comes on (he also thinks 12tet is the only
correct way to tune etc).
But nevertheless in the most recent "fight" with him, we had a few words
about tonality and he said that in C every note gets both a flat and a
sharp.

And he also gave an example of why anything other than 12tet will never
work, because for instance enharmonically different minor seventh notes must
be "undeterminded" as that's how they're used in common practice music.
He gave the example in the key of C:
C-G-C-E, F-A-C-F, G-B-D-F, C-G-C-E, F-A-C-F, G-B-D-E#, F#-B-D-F#
He said, enharmonically different tones F and E# would be tuned differently
when tuned just, and this would not work.
I replied:
C(1/1)-G(3/2)-C(2/1)-E(5/2), F(4/3)-A(5/3)-C(2/1)-F(8/3),
G(3/2)-B(15/8)-D(9/4)-F(8/3), C(1/1)-G(3/2)-C(2/1)-E(5/2),
F(4/3)-A(5/3)-C(2/1)-F(8/3), G(3/2)-B(15/8)-D(20/9)!-F(8/3)!,
F#(25/18)-B(15/8)-D(20/9)-F#(25/9)
And I said one could continue for instance like this:
E(5/4)-B(15/8)-D(20/9)-G#(25/16), A(5/6)-E(5/4)-A(5/3)-C#(25/12)-A(10/3)
And that in just intonation it matters where you're going for the tuning of
things, not just where you're comming from (this part he actually agreed
with beeing sensible).
And that the G(3/2)-B(15/8)-D(20/9)!-F(8/3)! where there is not an E# but an
F which goes to F#, and that this F doesn't change tuning, but instead the D
changes tuning (but still has the same enharmonic note name), and that this
chord can allready be seen as having it's root at A, and that this chord
progression is all still in the tonic of C and that his spelling doesn't
make sense in the tonic of C no matter how I look at it, etc.
And the fight continued lol

So I spelled out all the note names for my tonal system.
And all possible confusions where it's possible to play in 1 tonality (that
isn't C) that do have a root at C (so play the major scale on C).
And even in all those possiblities there isn't a E#. So where he got that E#
from idunno.
He sais F can't go to F#, that E# must go to F# blabla.

Well I've just about had it with normal music theory I thought.
But yet what's beeing said on this list is completely different what my
father said (yet the A# in C in normal music theory doesn't make much sense
to me)

I think the answer is no. FWIW, a few thoughts from me:
>
> 1) as Daniel stated, conventional music theory "prohibits" the use of
> certain accidentals in certain keys - but I think in many ways this is just
> a "rule of thumb" that helps students to learn the thing - e.g. in UK we
> have the "Associated Board" Theory of Music handbook and examinations - and
> if you don't notate your chromatic scale correctly, the answer will be
> marked "wrong". Of course, in this context, the chromatic scale consists of
> precisely 12 notes, as opposed to your list of 20.
>

12 notes in 12tet, but more than 12 enharmonic note spellings for these 12
notes (even in one key) right?

2) elsewhere I have seen a list of 25 note names in "chain of 5ths" order)
> from Dbb to Cx (aka C##) which was explained as what Telemann or Mozart
> would have used - this is bigger than your list, of course, but is not
> confined to the key of C. As Gene stated, that list would have been thought
> of in a "meantone" context - i.e. a single size of (tempered) 5th generating
> a chain of notes, whereas yours appears to derive from JI ratios.
>
> 3) Talking of which, 10 of your notes seem to have two different values
> depending on context, e.g. D = 9/8 or 10/9. Even F and G have two values.
> Not sure what to think about this.
>

Yes, this is simply because of note spelling in conventional music theory.
For instance, with a root of C(1/1) the D is 9/8. But D is also called D
when it's a fourth from the root A(5/3), and the fourth from root A is
D(10/9).
It's not a problem of my system, it's a deficiency of conventional note
spelling.

> 4) I don't understand how you choose which notes to include - yes, you
> start with a group of 10 notes "around" C, and then extend this by going to
> E, F, G, A (why not D and B? and why not Ab Eb and Bb?); and then you
> iterate the process "around" G and F, and Eb (why?) (and why not E and A?
> and D and B? etc). And I don't understand "the below keys can be mistaken
> for C", at all ...? (It does allow inclusion of the notes "around" Ab and
> Eb, and Db)
>

I hope I've explained it earlyer in this message?
If not I can give a more thorough explenation.

Marcel

🔗genewardsmith <genewardsmith@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗genewardsmith <genewardsmith@...>

🔗Cox Franklin <franklincox@...>

Ab-C-Eb-F# is an augmented 6th chord, leading into the dominant chord. Ab-D-Eb-Gb is a secondary dominant 7th chord going to a Np chord. Neither one is "incorrect." These have two different functions: aug. 6ths resolve upward, chordal 7ths resolve downward. Mozart and other composers would use the two chords in close proximity, creating a sort of musical pun. Neither of these notes (F# or Gb) was originally--in the Renaissance until the 18th century in most places--considered to be an integral part of the chord (a chord on the 6th scale degree in minor, the b6th scale degree in major), as only triads (root position or 6th chords, with occasional passing and dominant-function 6/4's) were allowed; they were originally considered chromatically intensified (F# pushing upward to G) or passing (Gb sinking to F) tones. They were not supposed to sound beautiful or pure, especially the augmented 6th chord.
By the way, the Neapolitan was originally not treated as a bII chord, but rather as a iv chord borrowed from the parallel minor, with the m6th replacing the 5th (this sort of substitution was common in the figured-bass era).
Borrowings from parallel minor and minor were appeared throughout the Baroque period, although they were not as common as in the Romantic period, where the major and minor forms increasingly fused into a sort of major-minor mode. But in C major, a minor i chord is spelled C-Eb-G, not C-D#-G. A D# goes upward, leading to an E; you could have a major VII chord (a V/iii, not terribly common in the Baroque period) with a D# functioning as a leading tone, or a diminished-seventh chord on D# (which Bach uses often); in both cases, the function of the D# is completely different than an Eb. C-D#-G rarely appears in the common practice era. Just look through some Bach cantatas (or Zelenka); you'll find plenty of borrowing from parallel major and minor.
Some of these discussions would be more productive if more people studied the basics of common practice harmony.

Franklin

Dr. Franklin Cox

1107 Xenia Ave.

Yellow Springs, OH 45387

(937) 767-1165

franklincox@...

--- On Mon, 4/12/10, genewardsmith <genewardsmith@...> wrote:

From: genewardsmith <genewardsmith@...>
Subject: [tuning] Re: note names for tonal-ji in the key of c
To: tuning@yahoogroups.com
Date: Monday, April 12, 2010, 6:51 PM

--- In tuning@yahoogroups. com, Daniel Forró <dan.for@... > wrote:

> In practice of music composition (even historical) nothing is

> prohibited and we can find many examples of trespassing the usual

> rules of the period.

> Good example is altered seventh chord on VII in minor key used

> especially in Classicism (Haydn, Moyart, Beethoven). For example in C

> minor it's Ab-C-Eb-F#. Why do you think the composers wrote F# and

> not Gb?

You probably won;t like this answer, but perhaps they were still thinking in meantone terms. Mozart at least, one might think. And of course, it derives from earlier practice, which practice was even more informed by meantone. Assuming meantone, Ab-C-Eb-F# is simply a different, and incidentially a more harmonious, chord than Ab-C-Eb-Gb, and you might notate it that way because you want the perforers to play it that way, as one obvious possibility.

And if you change F# for Gb and continue in Db major, why

> it's called enharmonic modulation? I'm sure you will find the answers.

But will you? I'm wondering if you were taught anything about the significance of meantone ideas to common practice. a topic which seems to be too often neglected.

🔗genewardsmith <genewardsmith@...>

🔗Cox Franklin <franklincox@...>

On a keyboard instrument (unless it was a split-key instrument, which had fallen out of use by the last 1600's), of course they would be. Mozart uses precisely this "pun" in some of his solo keyboard works, as well as his piano concertos.

The jury isn't out on how these intervals would have been performed by flexible-pitch instruments. Barbieri's Enharmonic is the most important recent book in the field. A fine Italian violinist might very well have distinguished the two pitches, but an average fiddler probably not. Mozart's father would have.

I tend to believe that the practice of distinguishing between F# and Gb continued in the older syntonic (essentially, JI) tradition into the 19th century, but the "high leading tone" (often considered Pythagorean) and the "undifferentiated" (i.e., bearing some resemblance to modern ET) were competing approaches in the 19th century, and the syntonic approach appears less and less often.

Franklin

Dr. Franklin Cox

1107 Xenia Ave.

Yellow Springs, OH 45387

(937) 767-1165

franklincox@...

--- On Mon, 4/12/10, genewardsmith <genewardsmith@sbcglobal.net> wrote:

From: genewardsmith <genewardsmith@...>
Subject: [tuning] Re: note names for tonal-ji in the key of c
To: tuning@yahoogroups.com
Date: Monday, April 12, 2010, 8:48 PM

--- In tuning@yahoogroups. com, Cox Franklin <franklincox@ ...> wrote:

> Mozart and other composers would use the two chords in close proximity, creating a sort of musical pun.

When Mozart did that, do you think he was always assuming the notes would be played with the same intonation?

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 12, 2010 at 2:31 PM, genewardsmith
<genewardsmith@...> wrote:
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > It seems clear to me that people's heads won't explode.
> >
> > BUT if you play C minor in C in C major you will not be in C major anymore.
> > So it IS prohibited if you want to *be* in C major.
>
> Is this anything other than stipulation, and if so, what empirical content does it have? I also wonder about Eb major and Ab major in C major, chords which to my ear convey less of a sense of C minor than the C minor triad itself does--in fact, they seem rather supportive of C major to me, not I hasten to add the graduate of any music program teaching common practice style. The B major triad, on the other hand, which seems to be proposed as an alternative since it uses D#, doesn't help C major much at all, it seems to me. But again, what do I know?

Sure it does. Resolve B major upward to C major. Done. Classic 40s
pop-era trick. It can be viewed as an extended Cdim->Cmaj resolution.

In general, and in my experience, the psychoacoustic phenomenon that
is responsible for tonality - whatever it is - is much more flexible
than common practice theory would have you believe.

It always blows my mind that after studying jazz for 4 years, and
learning a much less restrictive theory, that everything I've learned
is often pegged into this "jazz" box as if it is somehow invalid or
otherwise not really the same as normal music.

-Mike

🔗martinsj013 <martinsj@...>

--- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
Marcel> So if I were to combine in conventional tonal theory the major and minor tonality, I'd get: C D D# Eb E Fb F F# G Ab A A# Bb B

Sorry, I don't know how you got that list. If using the diatonic scale, there would be no sharps; if using the chromatic, there would be either a C# or a Db; in neither case would there be a Fb.

Marcel> 12 notes in 12tet, but more than 12 enharmonic note spellings for these 12 notes (even in one key) right?

In the context of the exam I was talking about: No, there is only one correct way to notate the chromatic scale in any given key (IIRC). But composers I am sure use a larger range.

Steve> 4) I don't understand how you choose which notes to include - you start with a group of 10 notes "around" C, and then extend this by going to E, F, G, A ...
Marcel> I hope I've explained it earlier in this message? If not I can give a more thorough explanation.

I didn't get it. Is it to do with the five major triads in the original 10 notes? If so, don't you mean Eb and Ab (not E and A)? By the way, I am seeing this in terms of a lattice diagram (as Cameron also saw); the original 10 notes form a nice symmetrical lattice around C-G, but the expanded set does not. Of course symmetry is not necessarily important but worth considering?

Steve M.

🔗Daniel Forró <dan.for@...>

On 14 Apr 2010, at 12:10 AM, martinsj013 wrote:

>
> --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@...> wrote:
> Marcel> So if I were to combine in conventional tonal theory the > major and minor tonality, I'd get: C D D# Eb E Fb F F# G Ab A A# Bb B
>
> Sorry, I don't know how you got that list. If using the diatonic > scale, there would be no sharps; if using the chromatic, there > would be either a C# or a Db; in neither case would there be a Fb.
>

Only in the case of pure, theoretic, atonal chromatic. Such chromatic upwards from C is:

C C# D D# E F F# G G# A A# B

Chromatic downwards from C is:

C B Bb A Ab G Gb F E Eb D Db

But he is talking about tonality, then chromatic scale looks different way, but not as he wrote. It must be written this way for C major:

C Db D D# E F F# G Ab A A# Bb B

Thanks to keeping the tonic chord intact (by those two basic rules of tonality which I have described in my previous posts) some interesting harmonic functions can be used in the frame of the same extended tonality C major - like Lydian chord (H-D#-F#), Phrygian chord (Db-F-Ab), augmented sixth chord on subdominant (F-A-C-D#), altered seventh chords (like D-F#-Ab-C, D-F#-A#-C, F#-Ab-C-E, F#-A#-C-E, G-B-Db-F, G-B-D#-F, Bb-D-F#-Ab, B-Db-F-A), even double direction altered chords like Dd-F-Ab-B-D# or Ab-C-D#-F#-A#, and lot of extra-tonal chords with enharmonically changed tones (like C-D#-G, D#-G-Bb, F#-A#-Db, A-Db-E-G etc.).

Daniel Forro

🔗cameron <misterbobro@...>

I think Marcel simply has too little knowledge of "conventional theory" for this discussion to go anywhere. (No offence, plenty of people have degrees in music and don't actually truly understand one damn thing).

Marcel:
"So if I were to combine in conventional tonal theory the
> > major and minor tonality, I'd get: C D D# Eb E Fb F F# G Ab A A# >Bb B"

Marcel, rather than thinking on "universal" levels, why not take a few pieces of "common practice" and a first year textbook? You're obviously exceptionally bright, you'll figure it out in no time. Looking at your note names, and considering that you're retuning Beethoven, an immediately puzzling thing for even a first-year student would be, where's your N6? The Neapolitan sixth chord, a bog-standard chromatic event in "common practice", requires the le of fa, that is, minor sixth above the fourth. That's Db. (NOT C#. In usual 5-limit JI terms, 16/15, not 25/24.)

So it is instantly obvious that these note names are NOT sufficient even for downright archaic "conventional theory". And, if you choose one interval to represent both C# and Db, that is called...

...TEMPERAMENT

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
>
> On 14 Apr 2010, at 12:10 AM, martinsj013 wrote:
>
> >
> > --- In tuning@yahoogroups.com, Marcel de Velde <m.develde@> wrote:
> > Marcel> So if I were to combine in conventional tonal theory the
> > major and minor tonality, I'd get: C D D# Eb E Fb F F# G Ab A A# Bb B
> >
> > Sorry, I don't know how you got that list. If using the diatonic
> > scale, there would be no sharps; if using the chromatic, there
> > would be either a C# or a Db; in neither case would there be a Fb.
> >
>
> Only in the case of pure, theoretic, atonal chromatic. Such chromatic
> upwards from C is:
>
> C C# D D# E F F# G G# A A# B
>
> Chromatic downwards from C is:
>
> C B Bb A Ab G Gb F E Eb D Db
>
> But he is talking about tonality, then chromatic scale looks
> different way, but not as he wrote. It must be written this way for C
> major:
>
> C Db D D# E F F# G Ab A A# Bb B
>
> Thanks to keeping the tonic chord intact (by those two basic rules of
> tonality which I have described in my previous posts) some
> interesting harmonic functions can be used in the frame of the same
> extended tonality C major - like Lydian chord (H-D#-F#), Phrygian
> chord (Db-F-Ab), augmented sixth chord on subdominant (F-A-C-D#),
> altered seventh chords (like D-F#-Ab-C, D-F#-A#-C, F#-Ab-C-E, F#-A#-C-
> E, G-B-Db-F, G-B-D#-F, Bb-D-F#-Ab, B-Db-F-A), even double direction
> altered chords like Dd-F-Ab-B-D# or Ab-C-D#-F#-A#, and lot of extra-
> tonal chords with enharmonically changed tones (like C-D#-G, D#-G-Bb,
> F#-A#-Db, A-Db-E-G etc.).
>
> Daniel Forro
>

🔗cameron <misterbobro@...>

🔗Marcel de Velde <m.develde@...>

Hi Cameron,

I think Marcel simply has too little knowledge of "conventional theory" for
> this discussion to go anywhere. (No offence, plenty of people have degrees
> in music and don't actually truly understand one damn thing).
>

Yes I agree :) And no offence taken at all.
I have been too stubborn and bussy with JI to study conventional theory.
I should really start studying conventional thoery indeed, and I will.

>
> Marcel:
> "So if I were to combine in conventional tonal theory the
> > > major and minor tonality, I'd get: C D D# Eb E Fb F F# G Ab A A# >Bb B"
>
> Marcel, rather than thinking on "universal" levels, why not take a few
> pieces of "common practice" and a first year textbook? You're obviously
> exceptionally bright, you'll figure it out in no time. Looking at your note
> names, and considering that you're retuning Beethoven, an immediately
> puzzling thing for even a first-year student would be, where's your N6? The
> Neapolitan sixth chord, a bog-standard chromatic event in "common practice",
> requires the le of fa, that is, minor sixth above the fourth. That's Db.
> (NOT C#. In usual 5-limit JI terms, 16/15, not 25/24.)
>
> So it is instantly obvious that these note names are NOT sufficient even
> for downright archaic "conventional theory". And, if you choose one interval
> to represent both C# and Db, that is called...
>
> ...TEMPERAMENT

First thanks for you compliment! :)
Second, the scale I was notating above I was (wrongly) making a major/minor
scale according to conventional theory I thought.
I has nothing to do with my own tuning system.

This is my tuning system in one key (best viewed in fixed width font):

Note names for the key (tonal center) C, 6-limit harmonic roots:

Key C, 6-limit harmonic root at C:
C c d eb e f g ab a bb b c
1/1> 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1

Key C, 6-limit harmonic root at E:
E c c# d d# e f# g g# a b c
5/4> 1/1 25/24 9/8 75/64 5/4 45/32 3/2 25/16 5/3 15/8 2/1

Key C, 6-limit harmonic root at F:
F c db d eb e f g ab a bb c
4/3> 1/1 16/15 10/9 6/5 5/4 4/3 3/2 8/5 5/3 16/9 2/1

Key C, 6-limit harmonic root at G:
G c d eb e f f# g a bb b c
3/2> 1/1 9/8 6/5 5/4 27/20 45/32 3/2 27/16 9/5 15/8 2/1

Key C, 6-limit harmonic root at A:
A c c# d e f f# g g# a b c
5/3> 1/1 25/24 10/9 5/4 4/3 25/18 3/2 25/16 5/3 15/8 2/1

All note names in the key of C (both major and minor at the same time) in my
system:
C C# Db D D# Eb E Fb F F# G G# Ab A Bb B C
All ratios in the key of C in my system:
1/1 25/24 16/15 10/9 9/8 75/64 6/5 5/4 4/3 27/20 25/18 45/32 3/2 25/16 8/5
5/3 27/16 16/9 9/5 15/8 2/1
As you can see I do have a Db, and it is indeed 16/15.

But I've now found further indication that much common practice music which
for instance appears to be in for instance the key of C (and is such
accoding to conventional theory), isn't in that key according to my system.
So I will continue retuning music according to my system and not pay too
much attention to conventional theory or note naming / notation for this (I
was trying to find the things equal in both my theory and conventional
theory in my first post in this thread).

Marcel

🔗Marcel de Velde <m.develde@...>

> But he is talking about tonality, then chromatic scale looks
> different way, but not as he wrote. It must be written this way for C
> major:
>
> C Db D D# E F F# G Ab A A# Bb B
>

What it looks like is that conventional music theory starts out with the
same basic thought as I do.

That tonality comes from holding a single (major or minor) tonic chord, and
that all notes withing the resulting tonality must harmonize with / relate
to this tonic chord.
Conventional theory appears to me to try to achieve this by saying you can't
raise or lower enharmonically any of the tonic chord notes.
And conventional theory treats minor differently from major (which it has to
if you obide by the above rule)

My theory starts out allmost the same. That tonality comes from holding a
single (allways major) tonic chord, and that all notes withing the resulting
tonality must harmonize / relate to the tonic chord.
I achieve this by a a harmonic model (1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5
15/8 2/1 in 6-limit) with roots at C, E, F, G, and A to form the full
tonality, which does allow lowering the third to become minor and still
harmonize with the major chord)
And minor is not the true root tonic chord in my tonality, but a permutation
of the real tonic chord which is allways major. (so my theory is both major
and minor tonality in one)

In the end I think I like my theory better.
But I don't know enough about the conventional tonal theory, and I'm not
impartial :)

Marcel

🔗genewardsmith <genewardsmith@...>

🔗Marcel de Velde <m.develde@...>

Hi gene,

> Conventional theory appears to me to try to achieve this by saying you
> can't
> > raise or lower enharmonically any of the tonic chord notes.
>
> A claim for which I have yet to see the evidence. How does that claim
> handle the "puns" when a composer juxtaposes two enharmonically equivlant
> versions of a chord in close proximity?

I'll leave this one to the people who actually studied music theory. I
personally have no idea.
But I may have used the word enaharmonically wrong in my words. What I ment
is that on can't in C major make a Cb, Eb, Gb, C#, E#, G# in C major key in
normal music theory.

> My theory starts out allmost the same. That tonality comes from holding a
> > single (allways major) tonic chord, and that all notes withing the
> resulting
> > tonality must harmonize / relate to the tonic chord.
> > I achieve this by a a harmonic model (1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5
> > 15/8 2/1 in 6-limit) with roots at C, E, F, G, and A to form the full
> > tonality, which does allow lowering the third to become minor and still
> > harmonize with the major chord)
>
> Why is this a "theory" rather than a personal decision as to how you
> propose to compose music?

Well I see it as a model for harmony, and how melody and tonality come from
this harmonic model.
I see it as a consistent framework, and I see it more that I've "discovered"
it by logic and numbers, than that it is a personal choice / decision on how
to compose music.
(although to stay within one key will still be a compositional choice
offcourse, though I do see deeper value in doing so)

Marcel

🔗Daniel Forró <dan.for@...>

🔗Marcel de Velde <m.develde@...>

> > My theory starts out allmost the same. That tonality comes from holding a
>> > single (allways major) tonic chord, and that all notes withing the
>> resulting
>> > tonality must harmonize / relate to the tonic chord.
>> > I achieve this by a a harmonic model (1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3
>> 9/5
>> > 15/8 2/1 in 6-limit) with roots at C, E, F, G, and A to form the full
>> > tonality, which does allow lowering the third to become minor and still
>> > harmonize with the major chord)
>>
>> Why is this a "theory" rather than a personal decision as to how you
>> propose to compose music?
>
>
> Well I see it as a model for harmony, and how melody and tonality come from
> this harmonic model.
> I see it as a consistent framework, and I see it more that I've
> "discovered" it by logic and numbers, than that it is a personal choice /
> decision on how to compose music.
> (although to stay within one key will still be a compositional choice
> offcourse, though I do see deeper value in doing so)
>
> Marcel

Sorry I should've been more elaborate in my answer.
One other part of why I see it as a "theory" that I've "found" is that I see
it functioning / working consistently for common practice music.
The theory is giving me music theoretical tools to analyse music (I did not
give them to the theory whil making it, the theory gives them to me), and to
tune music. And I see that it's giving me answers on how to tune music that
make a lot of sense, that I would not have found otherwise, and that I see
no other sensible way of doing, and that my ears like and that other
alternative ways do not sound as good to me.
So I see it as something bigger than personal choice or preference.
I think my theory contains "universal truths" about music. But this is in
itself a personal belief right now offcourse :) Time will tell if others
agree.

Marcel

🔗Marcel de Velde <m.develde@...>

🔗Daniel Forró <dan.for@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Marcel de Velde <m.develde@...>

🔗genewardsmith <genewardsmith@...>

🔗Marcel de Velde <m.develde@...>

>
> How do you propose to use your theory to give good sounding results when
> translating the chord sequence I-IV-ii-V7-I to JI?
>

Oh that one's easy :)

1/1 5/4 3/2 2/1
4/3 5/3 2/1 8/3
4/3 5/3 9/4 8/3
3/2 15/8 9/4 8/3
1/1 3/2 2/1 5/2

The easyest way to see the above progression is in the harmonic root of I
1/1, i see no reason to change the root of the chords.
So it's all in 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
And 1/1 is the root of all of the above chords.

To change from one root to another, the "connecting" chord between 2 roots
has to be in both harmonic models at the same time.
The above rule is important.
It will guarantee not only all chords will fit the harmonic model, but all
chord progressions will fit the harmonic model aswell (including chord
progressions where the harmonic model root changes)
What we also find is that there will only be 25/24, 16/15 and 27/25
stepsizes for a semitone (never 135/128 or 256/243 etc)
And only 10/9 and 9/8 stepsizes for the whole tone (never 256/225 etc).
In other words, we will only find stepsizes that are possible among the
notes of the harmonic model 1/1 9/8 6/5 5/4 4/3 3/2 8/5 5/3 9/5 15/8 2/1
(including all octave equivalent steps offcourse), and we will get this even
when the progression changes harmonic root.
So we will also never get an 81/64 etc. Not as a harmonic interval, but also
not as a melodic interval.
Now something like 81/64 is not "illegal" in the abosolute sense, but if it
is used you're no longer in 6-limit permutation based JI (but in 8-limit in
this case) and as far as I'm concerned you've left tonal music by doing so).

Here a more difficult chord progression, the beginning of Beethoven's
Mondschein (moonlight) sonata.
(forgive my note spelling, I'm not checking now if it's correct)

Ab - Db - E
Ab - B - Db - E
A - Db - E
A - D - F#
Ab - C - F#
Ab - Db - E
Ab - Db - Eb
Ab - C - Eb
Db - E - Ab - Db

Now to try to put this in as consonant possible way in normal JI it'd be
easy to do it like this:

Ab(3/2) - Db(2/1) - E(12/5)
Ab(3/2) - B(9/5) - Db(2/1) - E(12/5)
A(8/5) - Db(2/1) - E(12/5)
A(8/5) - D(16/15) - F#(8/3)
Ab(3/2) - C(15/8) - F#(8/3)
Ab(3/2) - Db(2/1) - E(12/5)
Ab(3/2) - Db(2/1) - Eb(9/4)
Ab(3/2) - C(15/8) - Eb(9/4)
Db(1/1) - E(6/5) - Ab(3/2) - Db(2/1)

You'd think, no problem at all for normal JI, all perfectly consonant?
But see for instance the 256/225 stepsize from D to C (not allowed in
6-limit tonal-ji), which is really an indication of an incorrect progression
of the harmonic root.
Now here is how my theory makes sense of it, with a logical progression of
the harmonic roots:

Ab(3/2) - Db(2/1) - E(12/5) Harmonic root is 1/1 Db.
Ab(3/2) - B(9/5) - Db(2/1) - E(12/5) Still 1/1 Db harmonic root.
A(8/5) - Db(2/1) - E(12/5) Could still 1/1 Db harmonic root.
But, the next chord can't exist in the harmonic root of 1/1 Db, as there's
no D from 1/1 Db in the 6-limit harmonic model.
So either we were all wrong putting the previous chords in 1/1 Db (not
likely) or (and this one is correct and happens all the time) we get a
change of harmonic root, or better said, the previous chord can belong to 2
harmonic roots and the next chord belongs to the new harmonic root.
So we find the harmonic roots that will include both the previous chord and
the next chord (and is related to the original harmonic root according to
the 6-limit tonality model)
Well the first logical new root we can find, namely A(8/5) as new harmonic
root will work fine and make perfect sense.
So the previous chord is both in 6-limit harmonic root Db(1/1), as in
6-limit harmonic root A(8/5) (and we've learned something about the possible
tonic of this piece or atleast this part of the piece.. it may be that the
tonic is the A(8/5), or perhaps E(6/5) )
A(8/5) - D(16/15) - F#(8/3) This chord belongs to the new harmonic root
A(8/5)
Ab(3/2) - C(48/25) - F#(8/3) This chord still belong to harmonic root
A(8/5) (and is 15/8 6/5 5/3 seen from the harmonic root, far out chord)
Now you'd think that for the above chord there may be a more consonant
solution without a diminished fourth, but there isn't really, not within
6-limit tonal-ji, not where it's comming from and going to. And the above
chord does function very well this way and is actually more consonant this
way as with the 256/225 stepsize as that one harmonizes aswell if it were
held (even by pedal, which is done in this piece)
Ab(3/2) - Db(2/1) - E(12/5) This chord can be in both the harmonic root of
A(8/5) and Db(2/1), and we're changing harmonic root again (back to Db)
Ab(3/2) - Db(2/1) - Eb(9/4) In harmonic root 1/1 Db
Ab(3/2) - C(15/8) - Eb(9/4) Still in Db root
Db(1/1) - E(6/5) - Ab(3/2) - Db(2/1) Db root

So even in this case where it appears there's no problem with normal JI,
Tonal-JI will give a different tuning.
And actually makes more sense to me, I can play along great with the piece
after tonal-ji analysis. But after normal JI analysis I keep playing notes
that don't sound right (i dont'mean tuning, i mean 12tet notes)

Marcel

🔗Marcel de Velde <m.develde@...>

> Ab(3/2) - Db(2/1) - E(12/5) Harmonic root is 1/1 Db.
> Ab(3/2) - B(9/5) - Db(2/1) - E(12/5) Still 1/1 Db harmonic root.
> A(8/5) - Db(2/1) - E(12/5) Could still 1/1 Db harmonic root.
> But, the next chord can't exist in the harmonic root of 1/1 Db, as there's
> no D from 1/1 Db in the 6-limit harmonic model.
> So either we were all wrong putting the previous chords in 1/1 Db (not
> likely) or (and this one is correct and happens all the time) we get a
> change of harmonic root, or better said, the previous chord can belong to 2
> harmonic roots and the next chord belongs to the new harmonic root.
> So we find the harmonic roots that will include both the previous chord and
> the next chord (and is related to the original harmonic root according to
> the 6-limit tonality model)
> Well the first logical new root we can find, namely A(8/5) as new harmonic
> root will work fine and make perfect sense.
> So the previous chord is both in 6-limit harmonic root Db(1/1), as in
> 6-limit harmonic root A(8/5) (and we've learned something about the possible
> tonic of this piece or atleast this part of the piece.. it may be that the
> tonic is the A(8/5), or perhaps E(6/5) )
> A(8/5) - D(16/15) - F#(8/3) This chord belongs to the new harmonic root
> A(8/5)
> Ab(3/2) - C(48/25) - F#(8/3) This chord still belong to harmonic root
> A(8/5) (and is 15/8 6/5 5/3 seen from the harmonic root, far out chord)
> Now you'd think that for the above chord there may be a more consonant
> solution without a diminished fourth, but there isn't really, not within
> 6-limit tonal-ji, not where it's comming from and going to. And the above
> chord does function very well this way and is actually more consonant this
> way as with the 256/225 stepsize as that one harmonizes aswell if it were
> held (even by pedal, which is done in this piece)
> Ab(3/2) - Db(2/1) - E(12/5) This chord can be in both the harmonic root of
> A(8/5) and Db(2/1), and we're changing harmonic root again (back to Db)
> Ab(3/2) - Db(2/1) - Eb(9/4) In harmonic root 1/1 Db
> Ab(3/2) - C(15/8) - Eb(9/4) Still in Db root
> Db(1/1) - E(6/5) - Ab(3/2) - Db(2/1) Db root
>

Btw I'd like to add that there's a different possiblity aswell.
And right now I have no real means to decide which it should be other than
the following:
Tuning the whole piece and see if there are parts in it that seem to be
repetitions but make clear on of the options so that other parts which were
not clear yet are more logically interpreted the same way.
And also when tuning the whole piece, see which way the piece as a whole
makes the most sense in the 6-limit tonality model (how the harmonic model
roots relate).
If the above things don't give a clear outcome on the possiblities, then
perhaps one can say that certain parts of the piece are open to several
interpretations.

Anyhow, here's the alternative tonal-ji interpretation that makes some
sense:

Ab(3/2) - Db(2/1) - E(12/5) Harmonic model Root Db 1/1
Ab(3/2) - B(9/5) - Db(2/1) - E(12/5) HR Db 1/1
A(8/5) - Db(2/1) - E(12/5) HR Db 1/1 and E 6/5
A(8/5) - D(52/25) - F#(27/10) HR E 6/5 (making 4/3 9/5 9/4 wolf major
triad)
Ab(3/2) - C(48/25) - F#(27/10) HR E 6/5 (making 5/4 8/5 9/4 chord)
Ab(3/2) - Db(2/1) - E(12/5) HR E 6/5 and Db 1/1
Ab(3/2) - Db(2/1) - Eb(9/4) HR Db 1/1
Ab(3/2) - C(15/8) - Eb(9/4) HR Db 1/1
Db(1/1) - E(6/5) - Ab(3/2) - Db(2/1) HR Db 1/1

The above interpretation would indicate the key / tonic for the piece of
either E or G.
Note that even figuring out the tonic for the piece (if the piece were in
one tonic), if it would turn out to be E, than that still wouldn't give
clarity as to which one of the 2 interpretations is better, as both are
still possible in the key/tonic E.

Marcel

🔗Daniel Forró <dan.for@...>

On 16 Apr 2010, at 9:04 AM, Marcel de Velde wrote:
>
> But, the next chord can't exist in the harmonic root of 1/1 Db, as > there's no D from 1/1 Db in the 6-limit harmonic model.
> So either we were all wrong putting the previous chords in 1/1 Db > (not likely) or (and this one is correct and happens all the time) > we get a change of harmonic root, or better said, the previous > chord can belong to 2 harmonic roots and the next chord belongs to > the new harmonic root.
> So we find the harmonic roots that will include both the previous > chord and the next chord (and is related to the original harmonic > root according to the 6-limit tonality model)
> Well the first logical new root we can find, namely A(8/5) as new > harmonic root will work fine and make perfect sense.
> So the previous chord is both in 6-limit harmonic root Db(1/1), as > in 6-limit harmonic root A(8/5) (and we've learned something about > the possible tonic of this piece or atleast this part of the > piece.. it may be that the tonic is the A(8/5), or perhaps E(6/5) )
> A(8/5) - D(16/15) - F#(8/3) This chord belongs to the new > harmonic root A(8/5)

Total nonsense. If you study more about music theory, you will know that this sonata movement is in C# minor key. This tonality can use these chromatic notes (properly written according to two basic rules of tonality):

C# D D# E F F# Fx G# A A# B B#

Chord D-F#-A is Phrygian triad, included in this set. It's harmonic function here is N6 (Neapolitan chord substituting subdominant before dominant).

> Ab(3/2) - C(48/25) - F#(8/3) This chord still belong to harmonic > root A(8/5) (and is 15/8 6/5 5/3 seen from the harmonic root, far > out chord)

This is dominant seventh chord with omitted fifth - G#-B#-(D#)-F#.

> Now you'd think that for the above chord there may be a more > consonant solution without a diminished fourth, but there isn't > really, not within 6-limit tonal-ji, not where it's comming from > and going to. And the above chord does function very well this way > and is actually more consonant this way as with the 256/225 > stepsize as that one harmonizes aswell if it were held (even by > pedal, which is done in this piece)
> Ab(3/2) - Db(2/1) - E(12/5) This chord can be in both the harmonic > root of A(8/5) and Db(2/1), and we're changing harmonic root again > (back to Db)
> Ab(3/2) - Db(2/1) - Eb(9/4) In harmonic root 1/1 Db
> Ab(3/2) - C(15/8) - Eb(9/4) Still in Db root
> Db(1/1) - E(6/5) - Ab(3/2) - Db(2/1) Db root
>
> Btw I'd like to add that there's a different possiblity aswell.

For sure, and theoretically right.

> And right now I have no real means to decide which it should be > other than the following:
> Tuning the whole piece and see if there are parts in it that seem > to be repetitions but make clear on of the options so that other > parts which were not clear yet are more logically interpreted the > same way.
> And also when tuning the whole piece, see which way the piece as a > whole makes the most sense in the 6-limit tonality model (how the > harmonic model roots relate).
> If the above things don't give a clear outcome on the possiblities, > then perhaps one can say that certain parts of the piece are open > to several interpretations.
>
> Anyhow, here's the alternative tonal-ji interpretation that makes > some sense:
>
> Ab(3/2) - Db(2/1) - E(12/5) Harmonic model Root Db 1/1
> Ab(3/2) - B(9/5) - Db(2/1) - E(12/5) HR Db 1/1
> A(8/5) - Db(2/1) - E(12/5) HR Db 1/1 and E 6/5
> A(8/5) - D(52/25) - F#(27/10) HR E 6/5 (making 4/3 9/5 9/4 wolf > major triad)
> Ab(3/2) - C(48/25) - F#(27/10) HR E 6/5 (making 5/4 8/5 9/4 chord)
> Ab(3/2) - Db(2/1) - E(12/5) HR E 6/5 and Db 1/1
> Ab(3/2) - Db(2/1) - Eb(9/4) HR Db 1/1
> Ab(3/2) - C(15/8) - Eb(9/4) HR Db 1/1
> Db(1/1) - E(6/5) - Ab(3/2) - Db(2/1) HR Db 1/1
>
> The above interpretation would indicate the key / tonic for the > piece of either E or G.

LOL.

> Note that even figuring out the tonic for the piece (if the piece > were in one tonic), if it would turn out to be E, than that still > wouldn't give clarity as to which one of the 2 interpretations is > better, as both are still possible in the key/tonic E.
>
> Marcel

Daniel Forro

🔗Marcel de Velde <m.develde@...>

Hi Daniel,

No, I will not forgive.

Hehe ok, I won't do it again ;)
I just did it quickly out of my head, but I'll give the effort to spell
correctly in the future.

If you spell notes like this, you only show
> your deep ignorance of basic music theory and all your other
> arguments based on such ignorance can't be taken seriously.

Nono, my arguments are not at all based on spelling.
They're based on the music, no matter how it is spelled.

> For example the first chord in your spelling has nothing to do with the
> inversion of triadic chord C# minor which is in the score.
>

Ok sorry about that.
But if you forget the spelling for a minute you'll see the JI ratios are not
spelled wrong and they tell the story I wanted to tell.

Total nonsense. If you study more about music theory, you will know
> that this sonata movement is in C# minor key. This tonality can use
> these chromatic notes (properly written according to two basic rules
> of tonality):
>
> C# D D# E F F# Fx G# A A# B B#
>
> Chord D-F#-A is Phrygian triad, included in this set. It's harmonic
> function here is N6 (Neapolitan chord substituting subdominant before
> dominant).
>
>
> > Ab(3/2) - C(48/25) - F#(8/3) This chord still belong to harmonic
> > root A(8/5) (and is 15/8 6/5 5/3 seen from the harmonic root, far
> > out chord)
>
> This is dominant seventh chord with omitted fifth - G#-B#-(D#)-F#.
>

Well this is where I disagree.
I do not think this is a normal dominant 7th chord with the fifth omitted.
(which is if it's really a dominant 7th, tuned as 3/2 15/8 (9/4) 8/3, though
I've encountered many more chord which conventional theory calls dominant
7th only to find they're not, and not tuned like this)
This is either a 15/8 6/5 5/3 chord (in which case you can't play the fifth
on the 15/8 to make it a full 7th chord), or a 5/4 8/5 9/4 chord (in which
case you can play a fifth on the 5/4 to make it a full 7th chord 5/4 8/5
(15/8) 9/4, it's the alternative 2nd version I gave).
But in any case, the tonic in my theory is not C# (or Db as I spelled it
wrong before).
But I won't argue with you if you say that the piece is in the tonic of C#
according to conventional music theory.

Marcel

🔗Mike Battaglia <battaglia01@...>

🔗Marcel de Velde <m.develde@...>

🔗Daniel Forró <dan.for@...>

🔗Mike Battaglia <battaglia01@...>

🔗Marcel de Velde <m.develde@...>

Hi Mike,

I only have two things to say
>
> 1) Well, in conventional music theory, that isn't how you spell the
> german sixth chord
>

Yes I said that allready :)
But still, I think spelling G# C D# F# is better than Ab C Eb F#.

> 2) That's not how you would tune the german sixth chord
>

I knew someone was going to say this ;)
But yes I very much stand behind my tuning of the german sixth chord as
25/16 2/1 75/32 45/16
To tune 8/5 2/1 12/5 45/16 is rediculous.
To put these two tunings of the german sixth in a different light:
Tonal-JI: 5/4 8/5 15/8 9/4 (1/1 32/25 3/2 9/5 seen from
5/4)
Old-JI: 5/4 25/16 15/8 1125/1024 (1/1 5/4 3/2 225/128 seen from 5/4)

Tonal-JI one will work when raising the 5/4 to 4/3 making 4/3 8/5 15/8 9/4
chord, will work when lowering 8/5 to 3/2 to become 5/4 3/2 15/8 9/4 chord,
etc etc etc. This chord works beautifully.
It can go to 6/5 8/5 2/1 6/5 (standard german sixth resolution) after which
it's very suitable for harmonic root change. It can go to 6/5 3/2 2/1 6/5,
etc etc. All works out perfectly.

The old-ji tuning of 5/4 25/16 15/8 1125/1024.. pff it's uuuugly!
It sounds allmost like a 5/4 25/16 15/8 35/32 chord, which is a 7-limit
tonal-ji chord, yet it isn't! It's simply out of tune.
5/4 25/16 15/8 1125/1024 (1/1 5/4 3/2 225/128) is silly old non working ji.

And again I really stand behind what I'm saying here about tuning the german
sixth.
I've spent a lot of time investigating it (some of which can be read back on
this list).

> Sincerely,
> Mike
>

Kind regards,
Marcel

🔗Marcel de Velde <m.develde@...>

🔗Daniel Forró <dan.for@...>

🔗cameron <misterbobro@...>

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> Yes, this chord can be VI6# from C minor, or bII6# from G major or
> minor. In works of Haydn, Mozart, Beethoven (and generally
> Classicism) it stays often before dominant (to name well known
> examples - Mozart: A la Turca, Beethoven Fifth Symphony...).

Personally I consider it definitely "of G", the movement of the Ab and F# is far too strong for it to be anything other than part of G, IMO. This is in keeping with note spelling, reflected in tuning interpretations of course, and I think considering it "of G" and not borrowed from parallel minor is important conceptually for tuning, too.

BUT I disagree with the root implication of analizing it as a bII. I feel that the root is actually C, as fa of sol (meaning the Ab is a minor sixth, as in the N6).

Of G, but rooted on C: an ideal state, in C, of strengthening the dominant while maintaining the red thread of the tonic.

Obviously I disagree with the common but not universal analysis of N6 as bII, and simply say N6. And of course I know that what I am saying can be disputed, like this: "well that makes sense for older works where the N6 was specifically a voice-leading thing always voiced with the sixth, but by Beethoven it appears in different inversions so insisting on the historical origin of what is now called ra as really being le-of-fa doesn't hold up anymore".

However, for several reasons I'm sticking to this interpretation, which I'm sure you'll agree is thoughtful and informed even if you disagree with it.

First, I think it helps keep the historical evolution of the sonority in mind.

Second, it insists on keeping counterpoint and voice-leading in mind(because if I hear any more contemporary orchestral film music which is obviously some "composer" laying out block chords in Cubase and then having some poor orchestrator trying to make some semblance of decent voice leading out of it, I'm going to screech like a wild pig).

Third, it's important for JI or expressive or whatever tuning interpretations. And fourth, I think that maintaining these three points is beneficial to creating new music in new tunings.

-Cameron

🔗Daniel Forró <dan.for@...>

On 16 Apr 2010, at 3:54 PM, cameron wrote:

> Personally I consider it definitely "of G", the movement of the Ab > and F# is far too strong for it to be anything other than part of > G, IMO. This is in keeping with note spelling, reflected in tuning > interpretations of course, and I think considering it "of G" and > not borrowed from parallel minor is important conceptually for > tuning, too.
>

It depends on the context. If few bars before this composer used C minor, then I would explain it as VI grade from C minor. If there's C major, then it's bII from G, and in fact it serves as kind of double dominant chord (exactly said tritone substitution of double dominant D7 before G, which is dominant). Bass note should be Ab.
>
> BUT I disagree with the root implication of analizing it as a bII. > I feel that the root is actually C, as fa of sol (meaning the Ab is > a minor sixth, as in the N6).
>
> Of G, but rooted on C: an ideal state, in C, of strengthening the > dominant while maintaining the red thread of the tonic.
>

It seems to me you mix here two different terms which should be distinguished. Bass note of the chord, and root note of the chord.
In the basic shape of the chord (which means in triadic harmony that chord is made from thirds, of course some of them can be omitted, but basic skeleton of the chord must have triadic structure) root note = bass note. In inversions they differs, but root note of the chord is always the same.

So here in this case the root note is always Ab, and bass note can be Ab, C (yes, the harmonic function here is called N6, but only if the following chord is dominant G, G7, or double dominant D7 before G/G7, or double VII7b F#-A-C-Eb before G/G7, or altered II D#-F#-A-C in the case of C major), Eb or F#.

>
> Obviously I disagree with the common but not universal analysis of > N6 as bII, and simply say N6.
>

To me N6 is only specifically used bII. Yes, it has fixed historical connotations, that's the reason why it's called so when analyzing Baroque and Classicism music. It doesn't change the fact that basic shape of this chord is not sixth chord. Sixth chord is always considered as less stable, weaker chord, only inversion of basic triad, which is strong, and considered satisfying (probably because it has a structure based on the first six harmonics). There are not much works in classical music which will use sixth or sixth-four inversion of triad as final chord of the work.
When we analyze a chord, we usually try to find it's prevailing structure (be it secondal, thirdal or quartal, or combination of them), and the proper root note. Of course this must be done in the context of the period music and style, and follow composer's intention... Nobody with some knowledge will analyze Mozart's chords or harmony progressions from the view of quartal structure, or jazz harmony, or modality, or atonality...

> And of course I know that what I am saying can be disputed, like > this: "well that makes sense for older works where the N6 was > specifically a voice-leading thing always voiced with the sixth, > but by Beethoven it appears in different inversions so insisting on > the historical origin of what is now called ra as really being le-> of-fa doesn't hold up anymore".
>
> However, for several reasons I'm sticking to this interpretation, > which I'm sure you'll agree is thoughtful and informed even if you > disagree with it.
>
> First, I think it helps keep the historical evolution of the > sonority in mind.
>
> Second, it insists on keeping counterpoint and voice-leading in mind> (because if I hear any more contemporary orchestral film music > which is obviously some "composer" laying out block chords in > Cubase and then having some poor orchestrator trying to make some > semblance of decent voice leading out of it, I'm going to screech > like a wild pig).
>
> Third, it's important for JI or expressive or whatever tuning > interpretations. And fourth, I think that maintaining these three > points is beneficial to creating new music in new tunings.
>
> -Cameron
>
I don't see here any connection between this traditional extended tonal chordal structures and functional harmony progressions - and new music in new tunings. But for sure it's very good for composer of New music to be fluent in all historical styles and theories, even when it's not much usable for contemporary composition.

Daniel Forro

🔗cameron <misterbobro@...>

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
>
> On 16 Apr 2010, at 3:54 PM, cameron wrote:
>
> > Personally I consider it definitely "of G", the movement of the >Ab
> > and F# is far too strong for it to be anything other than part >of
> > G, IMO. This is in keeping with note spelling, reflected in >tuning
> > interpretations of course, and I think considering it "of G" and
> > not borrowed from parallel minor is important conceptually for
> > tuning, too.
> >
>
> It depends on the context. If few bars before this composer used C
> minor, then I would explain it as VI grade from C minor.

I hadn't thought of that- in that case, I agree that that would be the best description. Still it is "of G but maintaining C", and we're discussing only interpretations which maintain note names (and therefore tuning) correctly.

>If there's C
> major, then it's bII from G, and in fact it serves as kind of >double
> dominant chord (exactly said tritone substitution of double >dominant
> D7 before G, which is dominant).

"Tritone substitution"?! You young punk! :-) Of course you're accurate here but the terminology is anachronistic in the original sense, ie. out of time. Then again, the term "common practice" is
modern too, WWII-era (Piston IIRC). I'm all for taking this as
(of-the-V)/V but I think "tritone substitution" has connotations way too far from the historical voice leading.

> >
> > BUT I disagree with the root implication of analizing it as a >bII.
> > I feel that the root is actually C, as fa of sol (meaning the Ab is
> > a minor sixth, as in the N6).
> >
> > Of G, but rooted on C: an ideal state, in C, of strengthening the
> > dominant while maintaining the red thread of the tonic.
> >
>
> It seems to me you mix here two different terms which should be
> distinguished. Bass note of the chord, and root note of the chord.
> In the basic shape of the chord (which means in triadic harmony >that
> chord is made from thirds, of course some of them can be omitted, >but
> basic skeleton of the chord must have triadic structure) root note =
> bass note. In inversions they differs, but root note of the chord >is
> always the same.

As you say, Ab should be in the bass- but C IMO is the root. So, I would consider analizing as bII of G to be an example of mixing the terms bass note, root note here. Don't worry, I'm not confusing root and bass, LOL. I don't buy into the exact equation of closest voicing and root, and neither does common practice, otherwise I 6-4 would show up everywhere.

And, where's a German sixth usually going? I 6-4. IMO it's a suspension of rootedness, both chords have this quality, and traditionally so (not just my opinion).

So, I think my analysis of "of V, but maintaining I" is good.

But, I agree that I can't generalize as I have because, preceded by movement in i, VI/i would be a better analysis, which means in that case Ab would be the root, and bII of V would be the most sensible. When not preceded by movement in i, I'm sticking to my analysis.

>
> So here in this case the root note is always Ab, and bass note can >be
> Ab, C (yes, the harmonic function here is called N6, but only if >the
> following chord is dominant G, G7, or double dominant D7 before >G/G7,
> or double VII7b F#-A-C-Eb before G/G7, or altered II D#-F#-A-C in >the
> case of C major), Eb or F#.

I was just comparing it to the N6 to point out what I think is the root (whatever the bass!), by way of historical contrapuntal origin of N6, not calling it an N6. Ger6 is usually going to I 6-4. I think that going anywhere else is asking for parallel fifths but I'd have to work it out.

Can you give me an example of that "altered II D#-F#-A-C" in context? I can see where it's going as far as voice-leading into a dominant-tonic situation obviously but you've thrown me a loop as far as how this is linked to the German sixth or N6. If you remember a standard text where this is demonstrated that would be fine, I'll just get it from the library (my old texts are either in storage, or lost)

>
> >
> > Obviously I disagree with the common but not universal analysis >of
> > N6 as bII, and simply say N6.
> >
>
> To me N6 is only specifically used bII. Yes, it has fixed >historical
> connotations, that's the reason why it's called so when analyzing
> Baroque and Classicism music. It doesn't change the fact that basic
> shape of this chord is not sixth chord. Sixth chord is always
> considered as less stable, weaker chord, only inversion of basic
> triad, which is strong, and considered satisfying (probably >because
> it has a structure based on the first six harmonics). There are >not
> much works in classical music which will use sixth or sixth-four
> inversion of triad as final chord of the work.

It would be a real learning experience for me if you could show me examples of this. Pre-Romantic, and in SATB kind of writing, no orchestral stuff with piles of octave doubling to balance things out. And no fair holding sol over through a cadential 6-4 while the upper voices resolve to root position or some such stunt. I believe you, it's just that I can't recall in the mind's ear such a sound prior to steam trains and laudanum.

> When we analyze a chord, we usually try to find it's prevailing
> structure (be it secondal, thirdal or quartal, or combination of
> them), and the proper root note. Of course this must be done in >the
> context of the period music and style, and follow composer's
> intention... Nobody with some knowledge will analyze Mozart's >chords
> or harmony progressions from the view of quartal structure, or >jazz
> harmony, or modality, or atonality...

Doesn't stop people from analizing everything in terms of 12-tET and Lacan though. Unfortunately.

>
> > And of course I know that what I am saying can be disputed, like
> > this: "well that makes sense for older works where the N6 was
> > specifically a voice-leading thing always voiced with the sixth,
> > but by Beethoven it appears in different inversions so insisting >on
> > the historical origin of what is now called ra as really being le-
> > of-fa doesn't hold up anymore".
> >
> > However, for several reasons I'm sticking to this interpretation,
> > which I'm sure you'll agree is thoughtful and informed even if you
> > disagree with it.
> >
> > First, I think it helps keep the historical evolution of the
> > sonority in mind.
> >
> > Second, it insists on keeping counterpoint and voice-leading in mind
> > (because if I hear any more contemporary orchestral film music
> > which is obviously some "composer" laying out block chords in
> > Cubase and then having some poor orchestrator trying to make some
> > semblance of decent voice leading out of it, I'm going to screech
> > like a wild pig).
> >
> > Third, it's important for JI or expressive or whatever tuning
> > interpretations. And fourth, I think that maintaining these three
> > points is beneficial to creating new music in new tunings.
> >
> > -Cameron
> >
> I don't see here any connection between this traditional extended
> tonal chordal structures and functional harmony progressions - and
> new music in new tunings. But for sure it's very good for composer >of
> New music to be fluent in all historical styles and theories, even
> when it's not much usable for contemporary composition.
>
> Daniel Forro
>

The connection is in the voice-leading and the counterpoint. You can write music in any damn tuning if you can write counterpoint.

-Cameron Bobro