Yahoo Tuning Groups Ultimate Backup tuning Chords

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> >>>3:5:7:9 subminor tetrad
> >>
> >>who named it that??
> >
> >I've been calling it that for some time now, and up until now
> >no one has objected. Since it contains a subminor triad, and
> >the supermajor tetrad a supermajor triad, the meaning seems
> >clear.
>
> "Subminor tetrad" has always meant 12:14:15:21 to me. I've
> called the above a just half-dim. chord...

Why? My chord is minor tetrad with lowered thirds and seventh, and falls into a nice class with the other three. Your chord,
1-15/14-3/2-12/7 doesn't even consist of 9-limit consonaces, and in fact is rather dissonant. I don't see why it even needs a name.

> I think Paul meant he doesn't think they should have names.
> Anyway, that's what I think.

You think Manual should stick with lame names like "Nameless 5-7 Chord"? There aren't that many SSS triads, tetrads and pentads up to the 9-limit that naming them is a problem. "Sans 5 major tetrad", would be one way to do it. You could avoid calling a diminished triad
a "sans 1 major (or minor) triad" if you wanted, and I want to keep using supermajor and subminor tetrad.

🔗Gene Ward Smith <genewardsmith@juno.com>

🔗Carl Lumma <clumma@yahoo.com>

>>I've called the above [5:6:7:9] a just half-dim. chord...
>
>Why?

Because that's a name of the chord in 12-equal that best
approximates it.

>There's standard nomenclature for JI chords?

No. Authors vary quite a bit. But I'm willing to endorse
Dave Keenan's proposal without even looking at it closely.

>>if so, then that's what i would think too,
>>though "subminor seventh chord" is of course clearer.
>
>Much better, but I still don't see why it trumps 6:7:9:10

Because you're chord is natively a 6th chord (unless you're
in a context where it must be a 7th chord).

-Carl

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
/tuning/topicId_40607.html#40629

wrote:
> --- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> > --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
> wrote:
> >
> > > > 3:5:7:9 subminor tetrad
> > >
> > > who named it that??
> >
> > I've been calling it that for some time now, and up until now no
> >one has objected. Since it contains a subminor triad, and the
> >supermajor tetrad a supermajor triad, the meaning seems clear.
>
> dave keenan has some conflicting names, which come a little closer
to
> standard nomenclature.
>
> > > > which seem to be nameless. Anyone care to name them also?
> >
> > > incomplete pentads.
> >
> > I know. Which ones?
>
> otonal pentad no 5, utonal pentad no 1/3, etc.

***Actually, I like that. That's the way I was thinking of them back
when I was doing the "extended" Blackjack stuff with Paul's help...

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@y..., "alternativetuning" <alternativetuning@y...>
wrote:
> --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> > >>I've called the above [5:6:7:9] a just half-dim. chord...
> > >
> > >Why?
> >
> > Because that's a name of the chord in 12-equal that best
> > approximates it.
> >
>
>
> I think that half-diminished is a good term for 5:6:7:9. It's a
> familar term and it distinguishes it from the subharmonic
> tetrad /7:/6:/5:/4 which is mapped identically in some
temperaments,
> but has a different quality and function.
>
> Gabor

all this is wonderful stuff musically, but quite confusing
terminologically (as gene and i have been discussing off-list). in
terms of our common-practice tonal system, and hence ultimately its
nomenclature, springing from meantone temperament, neither of these
chords can be referred to as half-diminished -- the 6:7 would really
have to be constructed as an augmented second. meanwhile, i find that
starting from the 12-equal half-diminished, at least in many timbres
and at least in first inversion, the process of eliminating beating
pulls one very strongly to a 10:12:15:17 tuning. this is (and has
been) certainly an area for fruitful debate and experimentation when
it comes to retuning existing music, but in the arena of proposing
standard terminology, it's a pure nightmare.

🔗Joseph Pehrson <jpehrson@rcn.com>

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

/tuning/topicId_40607.html#40689

wrote:
> --- In tuning@y..., "alternativetuning" <alternativetuning@y...>
> wrote:
> > --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> > > >>I've called the above [5:6:7:9] a just half-dim. chord...
> > > >
> > > >Why?
> > >
> > > Because that's a name of the chord in 12-equal that best
> > > approximates it.
> > >
> >
> >
> > I think that half-diminished is a good term for 5:6:7:9. It's a
> > familar term and it distinguishes it from the subharmonic
> > tetrad /7:/6:/5:/4 which is mapped identically in some
> temperaments,
> > but has a different quality and function.
> >
> > Gabor
>
> all this is wonderful stuff musically, but quite confusing
> terminologically (as gene and i have been discussing off-list). in
> terms of our common-practice tonal system, and hence ultimately its
> nomenclature, springing from meantone temperament, neither of these
> chords can be referred to as half-diminished -- the 6:7 would
really
> have to be constructed as an augmented second. meanwhile, i find
that
> starting from the 12-equal half-diminished, at least in many
timbres
> and at least in first inversion, the process of eliminating beating
> pulls one very strongly to a 10:12:15:17 tuning. this is (and has
> been) certainly an area for fruitful debate and experimentation
when
> it comes to retuning existing music, but in the arena of proposing
> standard terminology, it's a pure nightmare.

***I hate to say it, but I find all this nomenclature very
confusing. Can't we just use the numbers, and, if not, why not??

🔗Carl Lumma <clumma@yahoo.com>

🔗Gene Ward Smith <genewardsmith@juno.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@y..., "alternativetuning" <alternativetuning@y...>
wrote:
> "Half-diminished" is not a term that meantone-era theorists would
> have recognized, they probably would not have classed it as a chord
> at all but as a dissonance between chords. So I think we are not
> obligated to fit the chord into meantone terms, but better in terms
> of equal temperament. The half-diminished structure is frequent in
> Bach, Mozart, others, but is only used as a real chord the Tristan
> prelude

i disagree with this "real chord" distinction. it's not a real chord
in bach or mozart? i don't see how you could defend that statement.
meantone-era theorists notated it with the same figured bass notation
they used for other diatonic seventh chords, so i certainly see no
grounds for saying they would have classed it as a "dissonance
between chords" but not a chord itself.

what about the augmented sixth chord in bach and mozart? is that a
real chord? it closely approximates 4:5:7 in meantone, by the
way . . .

🔗Carl Lumma <clumma@yahoo.com>

🔗Dave Keenan <d.keenan@uq.net.au>

--- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> >I think the starting place should be JI, the equivalences and
> >additions would be individual to each temperament.
>
> Agreed, so I should point out again that the starting point of
> all the names you've suggested has been the diatonic scale!
>
> -Carl

Yes the names are extensions of the names of intervals in the diatonic
scales, but they are intended as the names _of_ just intervals.

One eventually forgets the association with the diatonic scale and
simply comes to associate the name with a particular sound and a
particular span on the keyboard or fretboard or whatever.

The extended ratio notation 3:5:7:9 gives us one kind of information
at a glance and the extended-diatonic names another, and the names
like O/Utonal N-ad no I, yet another. They are all useful. Some people
can relate better to some and not others, but within each naming
system it would be nice to have some standardisation.

I've written at length on further extending Fokker's extended-diatonic
naming of just intervals. See
http://dkeenan.com/Music/IntervalNaming.htm
and
http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt
From there it's not too far to standard naming of chords, but I've
never written that up.

By generalising from diatonic chord naming, one thing that seems
obvious to me is that if a chord has a single perfect fifth in it,
then the root of that fifth should be considered the root of the
chord's standard inversion, and to name the chord, the remaining notes
should be transposed by octaves as necessary to place them above, but
as close as possible to, that root.

So for extended-diatonic naming purposes 3:5:7:9 becomes 6:7:9:10. Now
6:7 is a subminor third and so 6:7:9 is a subminor triad. and 6:10 =
3:5 is a major sixth so the whole tetrad is a subminor major sixth
(smM6) chord.

As far as naming which inversion it is, I'm afraid I haven't thought
about it much.

I'm not here.

🔗Carl Lumma <clumma@yahoo.com>

🔗gdsecor <gdsecor@yahoo.com>

--- In tuning@y..., "Dave Keenan" <d.keenan@u...> wrote:
> --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> > >I think the starting place should be JI, the equivalences and
> > >additions would be individual to each temperament.
> >
> > Agreed, so I should point out again that the starting point of
> > all the names you've suggested has been the diatonic scale!
> >
> > -Carl
>
> Yes the names are extensions of the names of intervals in the
diatonic
> scales, but they are intended as the names _of_ just intervals.
>
> One eventually forgets the association with the diatonic scale and
> simply comes to associate the name with a particular sound and a
> particular span on the keyboard or fretboard or whatever.
>
> The extended ratio notation 3:5:7:9 gives us one kind of information
> at a glance and the extended-diatonic names another, and the names
> like O/Utonal N-ad no I, yet another. They are all useful. Some
people
> can relate better to some and not others, but within each naming
> system it would be nice to have some standardisation.
>
> I've written at length on further extending Fokker's extended-
diatonic
> naming of just intervals. See
> http://dkeenan.com/Music/IntervalNaming.htm
> and
> http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt
> From there it's not too far to standard naming of chords, but I've
> never written that up.
>
> By generalising from diatonic chord naming, one thing that seems
> obvious to me is that if a chord has a single perfect fifth in it,
> then the root of that fifth should be considered the root of the
> chord's standard inversion, and to name the chord, the remaining
notes
> should be transposed by octaves as necessary to place them above,
but
> as close as possible to, that root.

This is something that was "obvious" to me when I started out as
a "pop" musician, so that C-Eb-G-A was clearly a Cm6 chord. But in
my harmony classes I learned that this was really the first inversion
of an A minor 7th chord with a flatted fifth (or simply the seventh
chord on the seventh degree of the major scale), the lesson being
that in diatonic harmony chords are built in thirds. ("Half-
diminished-seventh chord" is also a "pop" term that isn't really a
legitimate description.) You could also consider it a dominant 9th
chord without the root.

> So for extended-diatonic naming purposes 3:5:7:9 becomes 6:7:9:10.
Now
> 6:7 is a subminor third and so 6:7:9 is a subminor triad. and 6:10 =
> 3:5 is a major sixth so the whole tetrad is a subminor major sixth
> (smM6) chord.

So does a dominant 9th chord 4:5:6:7:9 become 8:9:10:12:14? I think
not!

> As far as naming which inversion it is, I'm afraid I haven't thought
> about it much.

I say stick with the thirds and consider 5:6:7:9 as the root position.

> I'm not here.

Translation: Dave's "on holidays" for several months and isn't
reading everything. (I suspect he's just searching the digests for
his name and jumped in here when he saw it.)

--George

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗Dave Keenan <d.keenan@uq.net.au>

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In tuning@y..., "Dave Keenan" <d.keenan@u...> wrote:
> > --- In tuning@y..., "Carl Lumma" <clumma@y...> wrote:
> > > >I think the starting place should be JI, the equivalences and
> > > >additions would be individual to each temperament.
> > >
> > > Agreed, so I should point out again that the starting point of
> > > all the names you've suggested has been the diatonic scale!
> > >
> > > -Carl
> >
> > Yes the names are extensions of the names of intervals in the
> diatonic
> > scales, but they are intended as the names _of_ just intervals.
> >
> > One eventually forgets the association with the diatonic scale and
> > simply comes to associate the name with a particular sound and a
> > particular span on the keyboard or fretboard or whatever.
> >
> > The extended ratio notation 3:5:7:9 gives us one kind of information
> > at a glance and the extended-diatonic names another, and the names
> > like O/Utonal N-ad no I, yet another. They are all useful. Some
> people
> > can relate better to some and not others, but within each naming
> > system it would be nice to have some standardisation.
> >
> > I've written at length on further extending Fokker's extended-
> diatonic
> > naming of just intervals. See
> > http://dkeenan.com/Music/IntervalNaming.htm
> > and
> > http://dkeenan.com/Music/Miracle/MiracleIntervalNaming.txt
> > From there it's not too far to standard naming of chords, but I've
> > never written that up.
> >
> > By generalising from diatonic chord naming, one thing that seems
> > obvious to me is that if a chord has a single perfect fifth in it,
> > then the root of that fifth should be considered the root of the
> > chord's standard inversion, and to name the chord, the remaining
> notes
> > should be transposed by octaves as necessary to place them above,
> but
> > as close as possible to, that root.
>
> This is something that was "obvious" to me when I started out as
> a "pop" musician, so that C-Eb-G-A was clearly a Cm6 chord. But in
> my harmony classes I learned that this was really the first inversion
> of an A minor 7th chord with a flatted fifth (or simply the seventh
> chord on the seventh degree of the major scale), the lesson being
> that in diatonic harmony chords are built in thirds. ("Half-
> diminished-seventh chord" is also a "pop" term that isn't really a
> legitimate description.) You could also consider it a dominant 9th
> chord without the root.

But we're talking about naming just chords for purposes other than
diatonic ones, so does it matter if it's "pop"? The principle I'm
suggesting here is that the most consonant interval takes precedence
in determining the nominal root.

>
> > So for extended-diatonic naming purposes 3:5:7:9 becomes 6:7:9:10.
> Now
> > 6:7 is a subminor third and so 6:7:9 is a subminor triad. and 6:10 =
> > 3:5 is a major sixth so the whole tetrad is a subminor major sixth
> > (smM6) chord.
>
> So does a dominant 9th chord 4:5:6:7:9 become 8:9:10:12:14? I think
> not!

No absolutely not. Thanks for pointing out that I screwed up by
writing "the remaining notes should be transposed by octaves as
necessary to place them above, but as close as possible to, that root".

Not only have I not written it up, I haven't even consciously worked
out the rules. I probably should shut up until I do. But yes, thirds
have to come into it next.

But although I would use 4:5:6:7:9 as the root position I wouldn't
call it a dominant 9th chord since I don't consider 4:7 to be a minor
seventh, but a subminor seventh, for reasons given in that article on
my website.

> > As far as naming which inversion it is, I'm afraid I haven't thought
> > about it much.
>
> I say stick with the thirds and consider 5:6:7:9 as the root position.
>

Then I'd have to call it a minor subdiminished minor seventh chord.

> > I'm not here.
>
> Translation: Dave's "on holidays" for several months and isn't
> reading everything. (I suspect he's just searching the digests for
> his name and jumped in here when he saw it.)

Correct.

🔗Gene Ward Smith <genewardsmith@juno.com>

🔗jfos777 <jfos777@...>

I hit "send" by accident, ignore my last post.

Graham,

you said: "Your formula's a function of overtone numbers, which makes it "otonal"". I don't know what this means but my formula has nothing to do with overtones, it just relies on the fundamentals.

I imagine we could spend years arguing back and forth about various points but I'll just make one point about chords. When I began I imagined that quantity would have to be sacrificed for quality and that there would be far fewer "good" chords in my system than there are in Equal Temperament. I was wrong. So far I have identified over 800 chords that work on my "NPT" guitar. (This "chord dictionary" can be downloaded from my web site: www.johnsmusic7.com) These chords are either Major or "Blue Minor". There are even more chords that I haven't identified yet (these are weaker but still good). I suspect that the completed list will have as many as 2000 chords if not a lot more. Also I have discovered several very unusual and exotic chords that contain intervals that are more than 30 cents out of tune with ET. I will concede that (in my system) there are relatively few chords in the key of 15/14 but I feel that the overall advantages of my system compensate for this.

Thanks again for the feedback, I still think my system is the best but I'm keeping an open mind and will consider carefully any criticisms that come my way.

John.

🔗jfos777 <jfos777@...>

Michael said in message #87180: "Again, I'd say chords here are the frontier...more or more unique intervals may be interesting to some people...but I'd be hard pressed to find a musician who wouldn't love having more chords accessible."

When I began working on my tuning system (NPT) I assumed that quantity would have to be sacrificed for quality (i.e. there would be far fewer "good" chords than are found in 12 tone equal temperament). I was wrong. So far I have identified over 800 chords that have three or more notes that can be played on my "NPT guitar". I classify these chords as "Major" (value 1.0 or higher) or "Blue Minor" (value between 0.75 and 1.0). Each note in these chords have a positive value.

For me a chord is "good" if every interval that occurs in the chord has a value of 0.75 or higher according to my now famous formula:
(2 + 1/x + 1/y - diss)/2 (e.g. a six note chord contains 15 intervals).

I have since discovered three other classifications of "good" chords: (i) "Ultra Minor" (overall value between 0.0 and 0.75 and all notes have a positive value), (ii) "Common Plus" (overall value greater than zero but at least one note has a negative value and (iii) "Common Minus" (overall value less than zero). Again, all intervals that occur have a value of 0.75 or higher.

It is interesting that the often used open E-minor chord on a guitar is a "Common Minus" chord which has a negative overall value.

I suspect that when the list of chords for my NPT guitar is completed (this will require a bit of computer programming to sift through the millions of combinations) the list could have as many as 2000 chords if not a lot more.

Check out chapter 10 of my book where all this is explained.

I think that my "Major", "Blue Minor" and "Ultra Minor" chords are "pure" whereas the "Common Plus" and "Common Minus" chords are somewhat flawed but are perhaps tolerable.

John.

🔗Michael <djtrancendance@...>

>"I think that my "Major", "Blue Minor" and "Ultra Minor" chords are "pure""
Perhaps a more obvious proof of this would be to list a handful (maybe 20 or so) chords that are impossible to play in 12TET (or at least, sound grossly impure in 12TET but at least decent in your scale).

Pardon my skepticism, but I'm guessing your scale have more "possible to play in 12TET, but grossly impure" scales and the former goal is more suitable for scales with odd intervals such as deca-tonic scales in 22TET and things like Ozan's Maqam-like tunings. Admittedly I have a personal bias toward scales that sound both very weird (especially interval-wise) and yet mysteriously consonant, but I can more than appreciate higher-quality-periodicity.scale alternatives that are build to encapsulate standard practice music theory.

BTW (John) the name escapes me but I downloaded an mp3 off your site called something like "John's Song" and it sounds better (a combination of purity and playfulness/variety of tone) than just about any other diatonic-JI style guitar demo I've heard. Also, IMVHO, every one of Marcel's theories sounds better than the last and a few of the latest suggestions for 12TET-replacement tunings have really got my attention as being very consonant and not just, say, close variants of mean-tone but highly original ideas.

It has come to the point where I can hear a fairly clear audible improvement in much of what comes out of this list over 12TET...whereas in diatonic-JI my impression often varies from better to worse vis-a-vis 12TET diatonic depending on the chord (and, I believe, tests on the general public have also shown "mixed results" between if JI or 12TET is "purer" to the untrained listener).

---------------------------

At the very least, I think something on this list is going to eventually make it into, say, Yamaha/Roland/etc. synths and eventually mass-produced acoustic instruments...and once it becomes so easy to buy and learn I think there's no question 7-tone diatonic scales under 12TET won't be the only world-wide commonly-accepted music theory.

Now if we could only get a major synth or keyboard-producing company to pre-package some of these scales with their synths...or (even better) set them as the synth default and market it as an exclusive feature to that synth... :-)

🔗jfos777 <jfos777@...>

Michael,

thanks for the compliment on my tune. If you downloaded the MP3 before Saturday, 3rd April then the lead and chords are a bit out of sync after the first minute or so. I have since remixed the tune and fixed this. With the old version the lead comes in immediately but with the new version the lead comes in on the second "verse". If you are interested you can download the new version from my web site: www.johnsmusic7.com . Alternatively you can play a shorter version by clicking the "Files" link to the left of your screen and scroll down to near the bottom of the list.

John.

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"I think that my "Major", "Blue Minor" and "Ultra Minor" chords are "pure""
> Perhaps a more obvious proof of this would be to list a handful (maybe 20 or so) chords that are impossible to play in 12TET (or at least, sound grossly impure in 12TET but at least decent in your scale).
>
> Pardon my skepticism, but I'm guessing your scale have more "possible to play in 12TET, but grossly impure" scales and the former goal is more suitable for scales with odd intervals such as deca-tonic scales in 22TET and things like Ozan's Maqam-like tunings. Admittedly I have a personal bias toward scales that sound both very weird (especially interval-wise) and yet mysteriously consonant, but I can more than appreciate higher-quality-periodicity.scale alternatives that are build to encapsulate standard practice music theory.
>
>
> BTW (John) the name escapes me but I downloaded an mp3 off your site called something like "John's Song" and it sounds better (a combination of purity and playfulness/variety of tone) than just about any other diatonic-JI style guitar demo I've heard. Also, IMVHO, every one of Marcel's theories sounds better than the last and a few of the latest suggestions for 12TET-replacement tunings have really got my attention as being very consonant and not just, say, close variants of mean-tone but highly original ideas.
>
> It has come to the point where I can hear a fairly clear audible improvement in much of what comes out of this list over 12TET...whereas in diatonic-JI my impression often varies from better to worse vis-a-vis 12TET diatonic depending on the chord (and, I believe, tests on the general public have also shown "mixed results" between if JI or 12TET is "purer" to the untrained listener).
>
> ---------------------------
>
> At the very least, I think something on this list is going to eventually make it into, say, Yamaha/Roland/etc. synths and eventually mass-produced acoustic instruments...and once it becomes so easy to buy and learn I think there's no question 7-tone diatonic scales under 12TET won't be the only world-wide commonly-accepted music theory.
>
> Now if we could only get a major synth or keyboard-producing company to pre-package some of these scales with their synths...or (even better) set them as the synth default and market it as an exclusive feature to that synth... :-)
>

🔗jfos777 <jfos777@...>

Michael,

you asked for a list of chords that differ greatly fropm 12 tone ET. First of all if E is the tonic then (with my system, NPT) E is 1/1, F is 15/14, G is 6/5, G# is 5/4, A# is 7/5, B is 3/2, D is 9/5 and D# is 15/8.

Here are four, three-note chords that contain intervals that are more than 30 cents out of tune with 12 tone ET. BTW, I'm not sure, does 12TET mean "12 tone equal temperament"?

(i) F, D#, G#......12:21:28
(ii) F, D#, B.......20:35:56
(iii) A#, G, D........7:12:18
(iv) A#, G, E........7:12:20

To test these chords and compare them with 12 tone ET you need a midi keyboard connected to a computer running some tuning software. I suggest that you use a sine wave or similar "voice" on your keyboard for greatest clarity. I tested these chords just a few minutes ago and they sound a bit "raspy" with 12 tone ET but the raspiness disappears with my NPT tuning.

John.

🔗Michael <djtrancendance@...>

Haven't got to try these yet, but I will when I get home from work (yes, I have all the software needed to handle micro-tonal scales...I use OPENMPT, which is free and has microtonal support, as my main DAW).

________________________________
From: jfos777 <jfos777@...>
To: tuning@yahoogroups.com
Sent: Fri, April 9, 2010 11:16:14 AM
Subject: [tuning] Chords

Michael,

Here are four, three-note chords that contain intervals that are more than 30 cents out of tune with 12 tone ET. BTW, I'm not sure, does 12TET mean "12 tone equal temperament" ?

(i) F, D#, G#......12:21: 28
(ii) F, D#, B.......20:35: 56
(iii) A#, G, D........7:12: 18
(iv) A#, G, E........7:12: 20

John.