Yahoo Tuning Groups Ultimate Backup tuning 9-note just diatonic framework

The flurry of posts has been a little overwhelming for me and sometimes ignorance weighs heavily on my soul .... but I've been trying to write music using a scale, gamut, framework, something (but not a temperament!). Someone mentioned wolves --- this framework treats a wolf as the horrible beast of european folklore, not as a romanticised american loner -- the bad sounding fifth between supertonic and pure submediant is avoided.

This framework would seem to be basic:

1. tonic
2. dominant
3. subdominant
4. mediant (5/4 from tonic)
5. leading tone (5/4 from dominant)
6. submediant (5/4 from subdominant)
7. supertonic (3/2 from dominant)
8. low supertonic (4/3 from submediant, and 22 cents or so flatter than the other supertonic)
9. lowered 7th (4/3 from subdominant, the musica ficta flat of old music, gets the devil away with the wolf).

This provides a major scale (and all unaltered modes, but I'm not that interested in the old church modes).

If music modulates to relative minor, one new note is needed, the leading tone in the minor key, 5/4 from its dominant. If music modulates in the dominant direction, to a new major, two new notes are needed per fifth: the new leading tone and the supertonic, both pure tuning from the new dominant (5/4 and 3/2).

To get to the parallel minor, passing through the subdominant, subdominant of subdominant, sub of sub of sub, requires 9 additional notes or 18 total in the framework. To write music within a pure tuning and with harmonic excursions as far as the parallel minor in both directions (from c major to c minor/eb major and to f# minor/a major) requires 27 tones. This includes two different tunings of the tonic note itself, and three tunings of the original leading tone (B in the key of C). It does not offer many notes that Schoenberg might have written: no G flat, C flat, F flat; no B sharp, etc.

You experts, am I climbing some exotic tree for fruit that everyone else thinks is nuts? Or is this really the same as "JI", with more notes needed the farther a music moves from a tonic?

My symphony #4 goes through a slow introduction introducing each of the framework tones (and it sounds pretty traditional despite this): beginning of a recording (mp3 format)

http://www.soundclick.com/util/DownloadSong.cfm?ID=2446027

or find it from www.soundclick.com/guglielmo on the mp3 music page, symphony #4 I introduction.

guglielmo

🔗Dave Keenan <d.keenan@bigpond.net.au>

Dear Guglielmo,

That's very beautiful. Thank you.

I find that easier to understand when I draw a triangular lattice like
this. (Press the "Reply" button to see it formatted correctly if
you're reading on the Yahoo website)

10/9---5/3---5/4--15/8
/ \ / \ / \ / \
/ \ / \ / \ / \
16/9---4/3---1/1---3/2---9/8

D\----A\----E\----B\
/ \ / \ / \ / \
/ \ / \ / \ / \
Bb----F-----C-----G-----D

The "\" means "5-comma down" (syntonic or Didymus comma 80:81, ~21.5
cents).

> You experts, am I climbing some exotic tree for fruit that everyone
> else thinks is nuts?

No way!.

> Or is this really the same as "JI", with more notes
> needed the farther a music moves from a tonic?

It's really JI by anyones definition. But JI doesn't necessarily need
more notes the farther you get from the tonic. If you're doing it
electronically, there's little reason not to do that. But if you were
doing it acoustically there would be no reason to use more than 53
notes (for 5-limit JI), as Helmholtz pointed out. This is because you
can eventually wrap around via the 5-schisma (32768:32805, ~2.0 cents)
which is barely perceptible itself and can be distributed in
imperceptible parts, as in 53-equal.

-- Dave Keenan

🔗Guglielmo <gugliel@guglielmomusic.com>

That lattice is suddenly crystal! How wonderful. Thank you for taking the trouble to format it for email text.

guglielmo

Dave Keenan wrote:

> I find that easier to understand when I draw a triangular lattice like
> this. (Press the "Reply" button to see it formatted correctly if
> you're reading on the Yahoo website)
> > 10/9---5/3---5/4--15/8
> / \ / \ / \ / \
> / \ / \ / \ / \
> 16/9---4/3---1/1---3/2---9/8
> > > D\----A\----E\----B\
> / \ / \ / \ / \
> / \ / \ / \ / \
> Bb----F-----C-----G-----D
> > The "\" means "5-comma down" (syntonic or Didymus comma 80:81, ~21.5
> cents).
> > > It's really JI by anyones definition. But JI doesn't necessarily need
> more notes the farther you get from the tonic. If you're doing it
> electronically, there's little reason not to do that. But if you were
> doing it acoustically there would be no reason to use more than 53
> notes (for 5-limit JI), as Helmholtz pointed out. This is because you
> can eventually wrap around via the 5-schisma (32768:32805, ~2.0 cents)
> which is barely perceptible itself and can be distributed in
> imperceptible parts, as in 53-equal.
> > -- Dave Keenan
> > > > > > You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
> > Yahoo! Groups Links
> > > > > > >

🔗klaus schmirler <KSchmir@online.de>

Guglielmo wrote:

> The flurry of posts has been a little overwhelming for me and sometimes
> ignorance weighs heavily on my soul .... but I've been trying to write
> music using a scale, gamut, framework, something

A gamut or framework, I suspect.

(but not a
> temperament!).

... and the gamut is a temperament or not.

Someone mentioned wolves --- this framework treats a
> wolf as the horrible beast of european folklore, not as a romanticised
> american loner -- the bad sounding fifth between supertonic and pure
> submediant is avoided.
>
> This framework would seem to be basic:
>
> 1. tonic
> 2. dominant
> 3. subdominant
> 4. mediant (5/4 from tonic)
> 5. leading tone (5/4 from dominant)
> 6. submediant (5/4 from subdominant)
> 7. supertonic (3/2 from dominant)
> 8. low supertonic (4/3 from submediant, and 22 cents or so flatter than
> the other supertonic)
> 9. lowered 7th (4/3 from subdominant, the musica ficta flat of old
> music, gets the devil away with the wolf).
>
> This provides a major scale (and all unaltered modes, but I'm not that
> interested in the old church modes).

(This is my pet grieve: If you're not interested in modes, don't
mention them and call what I think you mean something neutral rotations.)

>
> If music modulates to relative minor, one new note is needed, the
> leading tone in the minor key, 5/4 from its dominant. If music
> modulates in the dominant direction, to a new major, two new notes are
> needed per fifth: the new leading tone and the supertonic, both pure
> tuning from the new dominant (5/4 and 3/2).
>
> To get to the parallel minor, passing through the subdominant,
> subdominant of subdominant, sub of sub of sub, requires 9 additional
> notes or 18 total in the framework. To write music within a pure tuning
> and with harmonic excursions as far as the parallel minor in both > directions (from c major to c minor/eb major and to f# minor/a major)
> requires 27 tones. This includes two different tunings of the tonic
> note itself, and three tunings of the original leading tone (B in the
> key of C). It does not offer many notes that Schoenberg might have
> written: no G flat, C flat, F flat; no B sharp, etc.

Schönberg would not have been the first ... More to the point,
Schönberg was interested in moving over the tonal palette fast, and as
long as he considered tonal relations, preferred ambiguous chords
where the same pitch could have many functions (b-d-f-g# = b d f ab =
cb d f ab = cb ebb f ab = b d e# g# = a## c## e# g#).

>
> You experts, am I climbing some exotic tree for fruit that everyone else
> thinks is nuts? Or is this really the same as "JI", with more notes
> needed the farther a music moves from a tonic?

What you found there is known as the "comma pump" and occurs as often
as you replace the 40/27 by a 3/2: It's either a wolf or doubled
versions of most every note, a comma apart.

As for the nuts, many people think comma shifts are hideous. I don't
mind and have used comma differences in monophony to imply the
harmony, but I've also felt the general resentment.

klaus

>
> My symphony #4 goes through a slow introduction introducing each of the
> framework tones (and it sounds pretty traditional despite this):
> beginning of a recording (mp3 format)
>
> http://www.soundclick.com/util/DownloadSong.cfm?ID=2446027
>
> or find it from www.soundclick.com/guglielmo on the mp3 music page,
> symphony #4 I introduction.
>
> guglielmo

🔗Ozan Yarman <ozanyarman@superonline.com>

Why, that is none other than Zarlino's diatonical gamut, with the distinction made between major and minor whole tones.

The excellent functions ascribed to degrees are akin to those used in Maqam Music. Do you think, Guglielmo, that I may be allowed to use them in this regard?

Thusly, in a major diatonical scale:

1st degree is tonic,
5th degree is dominant, 3/2
4th degree is sub-dominant, 4/3
3rd degree is the mediant, 5/4
7th degree is the leading tone, 15/8
6th degree is the sub-mediant, 5/3
2nd degree is the super-tonic (major whole tone), 9/8
2nd degree again is the low super-tonic (minor whole tone), 10/9
While the lowered 7th degree would be 16/9.

Now, all this information leads to the key of .... major, yes?

Cordially,
Ozan
----- Original Message -----
From: Guglielmo
To: tuning@yahoogroups.com
Sent: 09 Haziran 2005 Perşembe 14:14
Subject: Re: [tuning] Re: 9-note just diatonic framework

That lattice is suddenly crystal! How wonderful. Thank you for taking
the trouble to format it for email text.

guglielmo

Dave Keenan wrote:

> I find that easier to understand when I draw a triangular lattice like
> this. (Press the "Reply" button to see it formatted correctly if
> you're reading on the Yahoo website)
>
> 10/9---5/3---5/4--15/8
> / \ / \ / \ / \
> / \ / \ / \ / \
> 16/9---4/3---1/1---3/2---9/8
>
>
> D\----A\----E\----B\
> / \ / \ / \ / \
> / \ / \ / \ / \
> Bb----F-----C-----G-----D
>
> The "\" means "5-comma down" (syntonic or Didymus comma 80:81, ~21.5
> cents).
>
>
> It's really JI by anyones definition. But JI doesn't necessarily need
> more notes the farther you get from the tonic. If you're doing it
> electronically, there's little reason not to do that. But if you were
> doing it acoustically there would be no reason to use more than 53
> notes (for 5-limit JI), as Helmholtz pointed out. This is because you
> can eventually wrap around via the 5-schisma (32768:32805, ~2.0 cents)
> which is barely perceptible itself and can be distributed in
> imperceptible parts, as in 53-equal.
>
> -- Dave Keenan
>
>
>
>
>
> You can configure your subscription by sending an empty email to one
> of these addresses (from the address at which you receive the list):
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - leave the group.
> tuning-nomail@yahoogroups.com - turn off mail from the group.
> tuning-digest@yahoogroups.com - set group to send daily digests.
> tuning-normal@yahoogroups.com - set group to send individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>
>
>
>

You can configure your subscription by sending an empty email to one
of these addresses (from the address at which you receive the list):
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - leave the group.
tuning-nomail@yahoogroups.com - turn off mail from the group.
tuning-digest@yahoogroups.com - set group to send daily digests.
tuning-normal@yahoogroups.com - set group to send individual emails.
tuning-help@yahoogroups.com - receive general help information.

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🔗klaus schmirler <KSchmir@online.de>

klaus schmirler wrote:

a message with many words missing. I hope this is better.

Guglielmo wrote:

>> The flurry of posts has been a little overwhelming for me and
sometimes
>> ignorance weighs heavily on my soul .... but I've been trying to
write
>> music using a scale, gamut, framework, something

A gamut or framework, I suspect.

(but not a

>> temperament!).

... and the gamut is IN a temperament or not.

Someone mentioned wolves --- this framework treats a

>> wolf as the horrible beast of european folklore, not as a
romanticised
>> american loner -- the bad sounding fifth between supertonic and pure
>> submediant is avoided.
>>
>> This framework would seem to be basic:
>>
>> 1. tonic
>> 2. dominant
>> 3. subdominant
>> 4. mediant (5/4 from tonic)
>> 5. leading tone (5/4 from dominant)
>> 6. submediant (5/4 from subdominant)
>> 7. supertonic (3/2 from dominant)
>> 8. low supertonic (4/3 from submediant, and 22 cents or so flatter
than
>> the other supertonic)
>> 9. lowered 7th (4/3 from subdominant, the musica ficta flat of old
>> music, gets the devil away with the wolf).
>>
>> This provides a major scale (and all unaltered modes, but I'm not
that
>> interested in the old church modes).

(This is my pet grieve: If you're not interested in modes, don't
mention them and call what I think you mean something neutral LIKE
rotations.)

>>
>> If music modulates to relative minor, one new note is needed, the
>> leading tone in the minor key, 5/4 from its dominant. If music
>> modulates in the dominant direction, to a new major, two new notes
are
>> needed per fifth: the new leading tone and the supertonic, both pure
>> tuning from the new dominant (5/4 and 3/2).
>>
>> To get to the parallel minor, passing through the subdominant,
>> subdominant of subdominant, sub of sub of sub, requires 9 additional
>> notes or 18 total in the framework. To write music within a pure
tuning
>> and with harmonic excursions as far as the parallel minor in both
>> directions (from c major to c minor/eb major and to f# minor/a major)
>> requires 27 tones. This includes two different tunings of the tonic
>> note itself, and three tunings of the original leading tone (B in the
>> key of C). It does not offer many notes that Schoenberg might have
>> written: no G flat, C flat, F flat; no B sharp, etc.

Just intonation is just the opposite, a b that leads into c is
different from a cb moving on to db.

>>
>> You experts, am I climbing some exotic tree for fruit that
everyone else
>> thinks is nuts? Or is this really the same as "JI", with more notes
>> needed the farther a music moves from a tonic?

What you found there is known as the "comma pump" and occurs as often
as you replace the 40/27 by a 3/2: It's either a wolf or doubled
versions of most every note, a comma apart.

As for the nuts, many people think comma shifts are hideous. I don't
mind and have used comma differences in monophony to imply the
harmony, but I've also felt the general resentment.

klaus

🔗Guglielmo <gugliel@guglielmomusic.com>

Guglielmo wrote:
> That lattice is suddenly crystal! Well, not quite crystal, the lower end puzzles me when extended ...???

> >>
>> 10/9---5/3---5/4--15/8
>> / \ / \ / \ / \
>> / \ / \ / \ / \
>>16/9---4/3---1/1---3/2---9/8

?20/18? 10/9---5/3---5/4--15/8--45/32
/ \ / \ / \ / \ / \ / \
/ \ / \ / \ / \ / \ / \
64/27--16/9---4/3---1/1---3/2---9/8--27/16
?64/54?

>>
>>
>> D\----A\----E\----B\
>> / \ / \ / \ / \
>> / \ / \ / \ / \
>>Bb----F-----C-----G-----D

G\ D\ A\ E\ B\ F#\
/ \ / \ / \ / \ / \ / \
/ \ / \ / \ / \ / \ / \
Eb----Bb----F-----C-----G-----D-----A

The lowered G again would be a wolf with the original, central C;
and the Eb is not a nicely tuned minor third (6/5) from the central C, right?

>>
>>The "\" means "5-comma down" (syntonic or Didymus comma 80:81, ~21.5
>>cents).
>
guglielmo

🔗Guglielmo <gugliel@guglielmomusic.com>

klaus schmirler wrote:
> klaus schmirler wrote:
>
> > (This is my pet grieve: If you're not interested in modes, don't
> mention them and call what I think you mean something neutral LIKE > rotations.)
> >
Sorry to bother your pet! And you're right, forget the mention of modes and they would be rotations anyway.

Ozan Yarman wrote:
> Why, that is none other than Zarlino's diatonical gamut, with the
> distinction made between major and minor whole tones.
>
Aha!

> The excellent functions ascribed to degrees are akin to those used in
> Maqam Music. Do you think, Guglielmo, that I may be allowed to use them
> in this regard?

ME think?? Naturally.

guglielmo

🔗Ozan Yarman <ozanyarman@superonline.com>

🔗Gene Ward Smith <gwsmith@svpal.org>

🔗Guglielmo <gugliel@guglielmomusic.com>

Gene Ward Smith wrote:

> > You mentioned 27 notes at one point. What would those notes be?
> This is how I got to 27:

By extending the sphere of modulation in both dominant and subdominant directions -- three keys on each side of the tonic-- in my symphony planning, had calculated moving from D major (the overall tonic) to d minor through F major and also to B major through g# minor, and counted 9 new tuned notes needed in each direction, plus the 9-note original diatonic framework.

I think this matches the lattice structure: each 'lattice step' adds two notes to get to the next major key, and a third note is needed to include its relative minor (e.g., G# added to allow key of a minor from C major). This could very well be mistaken, however!

guglielmo

🔗Carl Lumma <clumma@yahoo.com>

Hi Guglielmo,

> This framework would seem to be basic:
>
> 1. tonic
> 2. dominant
> 3. subdominant
> 4. mediant (5/4 from tonic)
> 5. leading tone (5/4 from dominant)
> 6. submediant (5/4 from subdominant)
> 7. supertonic (3/2 from dominant)
> 8. low supertonic (4/3 from submediant, and 22 cents or so
> flatter than
> the other supertonic)
> 9. lowered 7th (4/3 from subdominant, the musica ficta flat
> of old music, gets the devil away with the wolf).
//
> If music modulates to relative minor, one new note is needed,
> the leading tone in the minor key, 5/4 from its dominant. If
> music modulates in the dominant direction,
//
> You experts, am I climbing some exotic tree for fruit that
> everyone else thinks is nuts? Or is this really the same
> as "JI", with more notes needed the farther a music moves
> from a tonic?

As I think Dave Keenan already stated, around here we would
simply call this "JI" or "5-limit JI". But note Dave, in some
parts "JI" apparently implies 12 fixed note classes.

> My symphony #4 goes through a slow introduction introducing
> each of the framework tones (and it sounds pretty traditional
> despite this)
//
> http://www.soundclick.com/util/DownloadSong.cfm?ID=2446027

This is a nice piece of music. My first impression is that
it sounds closer to how a real orchestra would play it than a
MIDI file in 12-tone equal temperament. In both cases the
tuning is unnaturally rigid, and this is perhaps harder to
hear in 12-equal since it is already out of tune. Especially
in the fast section the accuracy of intonation here sticks
out a bit. But despite this the overall effect seems closer
to real performance than standard MIDI.

Guglielmo, have you considered investigating the higher
harmonics (above 3 and 5)? Then you would get really
surprising sounds. But perhaps that is not what you are
after!

-Carl

🔗Dave Keenan <d.keenan@bigpond.net.au>

--- In tuning@yahoogroups.com, Guglielmo <gugliel@g...> wrote:
> ?20/18? 10/9---5/3---5/4--15/8--45/32
> / \ / \ / \ / \ / \ / \
> / \ / \ / \ / \ / \ / \
> 64/27--16/9---4/3---1/1---3/2---9/8--27/16
> ?64/54?

That would be
40/27--10/9---5/3---5/4--15/8--45/32
/ \ / \ / \ / \ / \ / \
/ \ / \ / \ / \ / \ / \
32/27--16/9---4/3---1/1---3/2---9/8--27/16

going to the right you multiply by three, to the left divide by three.
Then multiply or divide by as many 2's as you need to bring it back
into the range 1/1 to 2/1.

> G\ D\ A\ E\ B\ F#\
> / \ / \ / \ / \ / \ / \
> / \ / \ / \ / \ / \ / \
> Eb----Bb----F-----C-----G-----D-----A
>
> The lowered G again would be a wolf with the original, central C;
> and the Eb is not a nicely tuned minor third (6/5) from the central C,
> right?

Right. A just minor third from C would be Eb/ (note that's a 5-comma
_up_) and would be situated below and to the right of C on the lattice.

-- Dave Keenan