Yahoo Tuning Groups Ultimate Backup tuning Circle of fifths

This is the exact scale that I just refretted a guitar into (except E is the
1/1). Why are you calling this "et"? Its a simple 12 tone JI scale (and
quite sevicable too, except for the couple of funky sounding 40/27 fifths).

Dante

> -----Original Message-----
> From: frizzerius [mailto:lorenzo.frizzera@libero.it]
> Sent: Saturday, January 10, 2004 2:05 PM
> To: tuning@yahoogroups.com
> Subject: [tuning] Circle of fifths
>
>
> Hi.
>
> Look at circle of fifths in 12-Et.
> I see this:
>
> B E A D G C F Bb Eb Ab Db F#
> 15/8 5/4 5/3 9/8 3/2 1/1 4/3 16/9 6/5 8/5 16/15 7/5
>
> ï¿½------5------ï¿½----3----ï¿½--2--ï¿½----3----ï¿½------5-------ï¿½-7-ï¿½
>
> Note, ratio, limit.
>
> In other systems (example 19-Et) seems to be the same.
> Doing a complete circle I hear as more consonance the notes near 1/1.
>
> What do you think?
>
> Lorenzo
>
>
> You do not need web access to participate. You may subscribe through
> email. Send an empty email to one of these addresses:
> tuning-subscribe@yahoogroups.com - join the tuning group.
> tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
> tuning-nomail@yahoogroups.com - put your email message delivery
> on hold for the tuning group.
> tuning-digest@yahoogroups.com - change your subscription to
> daily digest mode.
> tuning-normal@yahoogroups.com - change your subscription to
> individual emails.
> tuning-help@yahoogroups.com - receive general help information.
>
>
>
> Yahoo! Groups Links
>
> To visit your group on the web, go to:
> /tuning/
>
> To unsubscribe from this group, send an email to:
> tuning-unsubscribe@yahoogroups.com
>
> Your use of Yahoo! Groups is subject to:
> http://docs.yahoo.com/info/terms/
>
>

🔗frizzerius <lorenzo.frizzera@libero.it>

🔗Dante Rosati <dante@interport.net>

🔗frizzerius <lorenzo.frizzera@libero.it>

> >In other systems (example 19-Et) seems to be the same.
>
> There are some systems where things are different.

Infact I've written "other" not "all".
But I can't verify if this really happens in 19-et (for example)
since my knoledge is not deep enough in this field.

> >Doing a complete circle I hear as more consonance the notes near
1/1.
>
> In 12-et?

Yes. I know that the word "consonance" is very dangerous...
Anyway I feel that Csus2 and Csus4 are chords with less tension than
major or minor triads (to make an example I prefer to use Asus2
rather than A major to tune my guitar).

Another observation could be that maybe there is a relation with
Utonality and Otonality in this circle since these are specularly
represented on it.

Lorenzo

🔗Carl Lumma <ekin@lumma.org>

🔗frizzerius <lorenzo.frizzera@libero.it>

> It is quite possible you are experiencing absolute pitch effects.
> Most people can hear with no trouble that that F# (at A440) sounds
> somehow more aggressive or "twangier" than D#.
>
> -Carl

To me C G D is the 3-note chord most similar to a single pure fifth.
And a fifth is the 2-note chord most similar to an octave.
This kind of musical sensation is the same for C F G triad although a
little less clear.

When I begin to use thirds or sixts i feel more distance to the sound
of a pure octave.

The word "suspended" reflects this more "neutral" sound respect major
or minor triads. The fact that you can substitute Csus2 with Csus4
without changing the feeling of the music too.

But, to be honest, when I use C F Bb I hear something less neutral.
Anyway these are two consecutive utonal intervals and maybe this is
the reason.

Lorenzo

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "frizzerius" <lorenzo.frizzera@l...>
wrote:
> Hi.
>
> Look at circle of fifths in 12-Et.
> I see this:
>
> B E A D G C F Bb Eb Ab Db F#
> 15/8 5/4 5/3 9/8 3/2 1/1 4/3 16/9 6/5 8/5 16/15 7/5
>
> ¦------5------¦----3----¦--2--¦----3----¦------5-------¦-7-¦
>
> Note, ratio, limit.

Of course this could have been done in other ways -- 9/5 for Bb, for
instance . . .

> In other systems (example 19-Et) seems to be the same.
> Doing a complete circle I hear as more consonance the notes near
1/1.

Often this will be the general tendency, but not always. Even in the
case above, it looks like D and Bb are more dissonant against C than
E, A, Eb, or Ab, though D and Bb are the closest.

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "frizzerius" <lorenzo.frizzera@l...>
wrote:
>
> > >In other systems (example 19-Et) seems to be the same.
> >
> > There are some systems where things are different.
>
> Infact I've written "other" not "all".
> But I can't verify if this really happens in 19-et (for example)
> since my knoledge is not deep enough in this field.
>
> > >Doing a complete circle I hear as more consonance the notes near
> 1/1.
> >
> > In 12-et?
>
> Yes. I know that the word "consonance" is very dangerous...
> Anyway I feel that Csus2 and Csus4 are chords with less tension
than
> major or minor triads (to make an example I prefer to use Asus2
> rather than A major to tune my guitar).

Maybe part of the reason is that sus chords are much closer to just
in 12-equal than major or minor triads are??

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "frizzerius" <lorenzo.frizzera@l...>
wrote:

> But, to be honest, when I use C F Bb I hear something less neutral.
> Anyway these are two consecutive utonal intervals and maybe this is
> the reason.

Hi Lorenzo.

There is no such thing as a utonal interval or an otonal interval.
Any interval is simultaneously utonal and otonal to an equal extent,
a point emphasized by the coiner of these terms, Harry Partch.

It is chords of three or more notes that can show "utonal"
or "otonal" propensities. In Partch's theory, the chord you mention
is equally otonal and utonal, since it corresponds to identities 1,
3, and 9 either way you look at it. Even if you drop Partch's
assumption of octave-equivalence, the chord's symmetry reveals that
it can neither be "utonally-biased" or "otonally-biased".

-Paul

🔗frizzerius <lorenzo.frizzera@libero.it>

Hi Paul.

> There is no such thing as a utonal interval or an otonal interval.
> Any interval is simultaneously utonal and otonal to an equal
extent, a point emphasized by the coiner of these terms, Harry Partch.

I apologize for my bad use of these words.
I will try to be clearer.

I'm convinced that every interval has a strong verse and a weak verse.
For example a major third (5/4) is the strong verse respect a minor
sixth (8/5) as if the 2-limit note would always be the "tonic"
despite the octave where it is. At the same way 3/2 is the strong
version, 4/3 is the weak version.

The strong version is the one that appears first in harmonic series.

So 5/3 is stronger than 6/5. 7/5 is stronger than 10/7.

It's interesting that Hindemith comes to the same results in the
analysis of "combination tones".

Considering a lydian scale as 1/1, 9/8, 5/4, 7/5, 3/2, 5/3, 15/8 all
these intervals are strong and I have called them wrongly "otonal
intervals". This scale has the top of quiet in music (jazz musician
know well).

Considering a locrian scale which is specular respect lydian we have
all weak intervals (what I've called "utonal intervals"): 1/1, 16/15,
6/5, 4/3, 10/7, 8/5, 16/9. This mode is the most restless of the
seven available in major scale.

Descending from lydian to ionian, mixolidian, dorian, eolian,
phrigian, locrian we go from stronger version of intervals to weaker.
It's interesting that between the stronger and the weaker mode there
is just a note of difference (C locrian, B lydian).

Analysing the circle of fifths I've seen that on the right I have
weak intervals of C major (I write F, Bb,... on the right since
reading clockwise is more logic to me) and strong intervals are on
the left.
Furthermore I've seen that over I have notes that approximate low
limit intervals and under I have high limit intervals (maybe it was
better that I apply "otonal" and "utonal" to this... :-)))

For all these reasons C G D is a stronger chord than C F G or C F Bb.
To me this is a stronger chord than C G E or any other three note
chord and it would be a perfect evolution of rock's "power chords" :-
))

I think that all these considerations could be valid in the same way
in 5-et, 7-et and 19-et but I'm not able to calculate limits and
ratios in 19-et. Maybe someone could help me in confirm or contradict
this.

Ciao

Lorenzo

🔗wallyesterpaulrus <paul@stretch-music.com>

--- In tuning@yahoogroups.com, "frizzerius" <lorenzo.frizzera@l...>
wrote:
> Hi Paul.
>
> > There is no such thing as a utonal interval or an otonal
interval.
> > Any interval is simultaneously utonal and otonal to an equal
> extent, a point emphasized by the coiner of these terms, Harry
Partch.
>
> I apologize for my bad use of these words.
> I will try to be clearer.
>
> I'm convinced that every interval has a strong verse and a weak
verse.
> For example a major third (5/4) is the strong verse respect a minor
> sixth (8/5) as if the 2-limit note would always be the "tonic"
> despite the octave where it is. At the same way 3/2 is the strong
> version, 4/3 is the weak version.

So far, it sounds like "strong" means having the otonal root on the
bottom, while "weak" means having the otonal root on the top. But not
below:

> The strong version is the one that appears first in harmonic series.
>
> So 5/3 is stronger than 6/5. 7/5 is stronger than 10/7.

Sure. But in the 'major third' class, aren't 5:2 and 5:1 even
stronger? And for the 'perfect fourth' class, 3:1?

> It's interesting that Hindemith comes to the same results in the
> analysis of "combination tones".

Well, you can use just about anything to get the same result -- for
instance, the member of each class where n*d is smallest -- right?

> Considering a lydian scale as 1/1, 9/8, 5/4, 7/5, 3/2, 5/3, 15/8
all
> these intervals are strong and I have called them wrongly "otonal
> intervals". This scale has the top of quiet in music (jazz musician
> know well).

What do you mean, 'has the top of quiet in music'? Certainly it's a
nice scale for quiet music, and doesn't get used much in louder
music . . . is that what you had in mind? Hopefully it wasn't George
Russell's theory you were thinking of . . . ;)

Also, I would argue that jazz musicians know little of JI, and JI has
little relevance to them. Tempered intervals need to be considered in
their own light/right.

> Considering a locrian scale which is specular respect lydian we
have
> all weak intervals (what I've called "utonal intervals"): 1/1,
16/15,
> 6/5, 4/3, 10/7, 8/5, 16/9. This mode is the most restless of the
> seven available in major scale.

How do you justify assigning 7/5 for lydian and 10/7 for locrian?

> Analysing the circle of fifths I've seen that on the right I have
> weak intervals of C major (I write F, Bb,... on the right since
> reading clockwise is more logic to me) and strong intervals are on
> the left.

Don't you mean "pitches" and not "intervals"? C major has lots of
different intervals in it, for example the tritone F-B.

> Furthermore I've seen that over I have notes that approximate low
> limit intervals and under I have high limit intervals

Hmm . . . not following.

> For all these reasons C G D is a stronger chord than C F G or C F
Bb.

It's more "rooted", I agree.

> To me this is a stronger chord than C G E or any other three note
> chord and it would be a perfect evolution of rock's "power
chords" :-

In 12-equal, I agree. But if you had C G E in JI, wouldn't that be
stronger?

> I think that all these considerations could be valid in the same
way
> in 5-et, 7-et and 19-et but I'm not able to calculate limits and
> ratios in 19-et. Maybe someone could help me in confirm or
contradict
> this.

I'm not sure if you're following any sort of "rule" when you do this
for 12-equal, but I'd be happy to help if I can.