Minor chord sad...why? Is it in the numbers?

Greetings group! Does anyone have any ideas on why minor triads, and
minor keys, in functional harmony, have (subjectively speaking)
a 'sad affect', compared to, say, the major triad, and major keys?

Yikes, Kelly

Maybe because it has a lowered tone of a simple ratio triad as in 4-5-6?

traktus5 wrote:

> Greetings group! Does anyone have any ideas on why minor triads, and
> minor keys, in functional harmony, have (subjectively speaking)
> a 'sad affect', compared to, say, the major triad, and major keys?
>
> Yikes, Kelly
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> Greetings group! Does anyone have any ideas on why minor triads,
and
> minor keys, in functional harmony, have (subjectively speaking)
> a 'sad affect', compared to, say, the major triad, and major keys?

Whenever anyone has asked this in the past, I point out that for
those who know the tradition of a trumpet playing "Taps" at a
funeral, which is simply a major chord, you have to think twice about
what is a naturally occuring function and what is a culturally
inherited set of aesthetics.

Most 'common' people would indicate that lone major arpeggiation on
the trumpet is one of the saddest things they are likely to hear...

Cheers,
Jon

>Greetings group! Does anyone have any ideas on why minor triads, and
>minor keys, in functional harmony, have (subjectively speaking)
>a 'sad affect', compared to, say, the major triad, and major keys?
>
>Yikes, Kelly

I consider this somewhat of a mystery.

Two thought-provoking responses from Kraig and Jon.

My guess has always been that this is somewhat cultural, but that
there is also something physiological going on. Namely, an effect
that is characteristic of smooth chords with weak roots. Chords
like 4:5:6 are smooth and strongly rooted. Chords like 10:12:15
have the same intervals and are therefore nearly as smooth, yet are
less strongly rooted. To my ear, major triads clearly sound most
solid when the 4 is voiced on the bottom. Minor triads don't seem
to care. If true, this should hold, more or less, in the 7-limit.

-Carl

From: "Carl Lumma" <ekin@...>

> >Greetings group! Does anyone have any ideas on why minor triads, and
> >minor keys, in functional harmony, have (subjectively speaking)
> >a 'sad affect', compared to, say, the major triad, and major keys?
> >
> >Yikes, Kelly
>
> I consider this somewhat of a mystery.
>
> Two thought-provoking responses from Kraig and Jon.

Both of which I agree with. The 'sadness' of minor triads and 'happiness' of
major triads seem to be reflected by the former having a lower-pitched note
than the latter. That's my 'Occam's razor' explanation. But I really think a
lot of it is culturally-conditioned. You still can have really sad music in
major keys and quite celebratory tunes in minor. A lot of it has to do with
the animacy of the tempo and rhythm, and the overall timbre and whether it's
bright or warm. And there are other moods that can be implied: peace, anger,
fear...

In microtonal music, of course, there are different shades of 'majorness'
and 'minorness'; in 31-tone (or 49 equal divisions of 3/1 which I prefer to
use), the five thirds approximate the just intervals 7/6, 6/5, 11/9, 5/4 and
9/7. The way I hear it, the distance of the third from 11/9 is proportional
to the amount of 'tension' in the chord. 6/5 is depressed in mood, but more
relaxed than the subminor 7/6; the latter also gives me an impression of
anger. 5/4 is happy and relaxed in mood, thus peaceful, and supermajor 9/7
is ecstatic or manic, but I also get a feeling of fear and worry out of it,
which I really get from augmented triads. The neutral third, 11/9, is very
relaxed, but ambivalent and comes across to me as simultaneously major and
minor, with a tension of its own, however, it's related to my relative lack
of listening experience in quartertone music. Thus my recent obsession with
Arab music; I'm trying to cure that defect and get used to neutral
intervals.

Which leads me to ask this: anybody develop a system of 31-tone jazz chords,
or at least quartertone?

> My guess has always been that this is somewhat cultural, but that
> there is also something physiological going on. Namely, an effect
> that is characteristic of smooth chords with weak roots. Chords
> like 4:5:6 are smooth and strongly rooted. Chords like 10:12:15
> have the same intervals and are therefore nearly as smooth, yet are
> less strongly rooted. To my ear, major triads clearly sound most
> solid when the 4 is voiced on the bottom. Minor triads don't seem
> to care. If true, this should hold, more or less, in the 7-limit.

I always thought that 'minorness' implies utonality, while 'majorness' is
otonal. But that's really only true in 5-limit, since 7/6 is minor yet
otonal. 10:12:15 is rooted in a common overtone (60); 4:5:6 in a common
undertone (1), so I think both are definitely well-rooted, though in
opposite directions. Something like 325:397:514 is definitely not
well-rooted.

(Someone on this list said this is how Partch interpreted things.)

>> My guess has always been that this is somewhat cultural, but that
>> there is also something physiological going on. Namely, an effect
>> that is characteristic of smooth chords with weak roots. Chords
>> like 4:5:6 are smooth and strongly rooted. Chords like 10:12:15
>> have the same intervals and are therefore nearly as smooth, yet are
>> less strongly rooted. To my ear, major triads clearly sound most
>> solid when the 4 is voiced on the bottom. Minor triads don't seem
>> to care. If true, this should hold, more or less, in the 7-limit.
>
>I always thought that 'minorness' implies utonality, while 'majorness'
>is otonal. But that's really only true in 5-limit, since 7/6 is minor
>yet otonal.

No dyad, like 7:6, can be either otonal or utonal. Only triads and
larger chords have this distinction.

If the chord in question is 6:7:9, this to me sounds less strongly
rooted than 4:5:6, but perhaps no rougher. But it also approximates
a common-practice minor triad, so it is not a good test of my guess.

By "7-limit" there, I was thinking of otonal vs. utonal 7-limit
tetrads.

>10:12:15 is rooted in a common overtone (60); 4:5:6 in a
>common undertone (1), so I think both are definitely well-rooted,
>though in opposite directions.

I wouldn't call those roots, because the strong 3:2 interval
seems to confer a sense of the 10 and 4 being the roots,
respectively. But common harmonics are another thing to
consider in the major/minor mystery.

-Carl

Ciao.

If you consider diatonic modes and you rearrange them through a
circle of fifths you will have this list: lydian, ionian,
mixolidian, dorian, eolian, phrigian and locrian. Each passage to a
new mode produces the lowering of a note so that, at the end, you
will have lowered any note except the tonic. If you do the same on
this last note you will reach again a lydian mode but an half tone
below.

Considering the structure of these modes you will find that there is
a specularity in the structure between lydian and locrian, ionian
and phrigian, mixolidian and eolian; and that dorian mode is
specular respect himself.

If you assume that any intervals has his own root in the note that
appears before in the harmonic series, you will consider that 3/2,
9/8, 5/4, 15/8, 5/3 have the root below instead of 4/3, 6/5, 8/5
which have the root above. Looking at the modes in this way you will
find that each note in the lydian mode is rooted in bass at the
opposite of locrian where any note is rooted above.

The reason why triads are so important is that these are the only
chords which don't include seventh or seconds.

All these elements confirm that:

1) yes, the major chord is rooted in a stronger way than the major
and this can have some psychological effect on a listener beyond any
cultural influence.
2) yes, the difference between major and minor chords is due to a
specularity model (otonal/utonal, lydian/locrian)
3) yes, the difference between major and minor chords is due to the
lowering of a note.

Ciao

Lorenzo

Very informative comments, all. Thinking of the chord (for example
e-g-b), I believe the affect exists not just in the chord itself (to
me, the effect vanishes in the conglomerate c-e-g-b, or e-g-b-d, or
Russian folk tunes* on scalar notes e-f-g-a-b), but by it's identity
as a tonic chord in a minor key in functional harmony. Therefore,
what is it in functional harmony that causes this 'minor chord
affect'? ...I can't put my finger on it yet, but wonder if it has
something to do with the 'manufactured' nature of minor keys, ie, the
altered (raised) 6th and 7th degrees of the scale for dominant
harmony and melodic reasons, suggesting that the chord, just as it's
less grounded (?), than the major triad is, in the audible harmonic
series, is also less connected, than the major triad is, to the
dominant chord in harmonic progressions?

Also, the minor chord shares with the major seventh chord (c-e-g-b)
the interesting quality (interesting to me, anyways), though to a
lesser degree, of containing elements of both tonic and dominant
combined (e, suggesting the tonic chord c-e-g, and the leading tone
b). Sort of an anti-dominant harmony feature (even more present in
the major seventh chord: c-e, g-b).

SOrry I"m not connecting this more to the JI and tuning points
raised...I really don't know...what do you think? -Kelly

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >> My guess has always been that this is somewhat cultural, but that
> >> there is also something physiological going on. Namely, an
effect
> >> that is characteristic of smooth chords with weak roots. Chords
> >> like 4:5:6 are smooth and strongly rooted. Chords like 10:12:15
> >> have the same intervals and are therefore nearly as smooth, yet
are
> >> less strongly rooted. To my ear, major triads clearly sound most
> >> solid when the 4 is voiced on the bottom. Minor triads don't
seem
> >> to care. If true, this should hold, more or less, in the 7-
limit.
> >
> >I always thought that 'minorness' implies utonality,
while 'majorness'
> >is otonal. But that's really only true in 5-limit, since 7/6 is
minor
> >yet otonal.
>
> No dyad, like 7:6, can be either otonal or utonal. Only triads and
> larger chords have this distinction.
>
> If the chord in question is 6:7:9, this to me sounds less strongly
> rooted than 4:5:6, but perhaps no rougher. But it also approximates
> a common-practice minor triad, so it is not a good test of my guess.
>
> By "7-limit" there, I was thinking of otonal vs. utonal 7-limit
> tetrads.
>
> >10:12:15 is rooted in a common overtone (60); 4:5:6 in a
> >common undertone (1), so I think both are definitely well-rooted,
> >though in opposite directions.
>
> I wouldn't call those roots, because the strong 3:2 interval
> seems to confer a sense of the 10 and 4 being the roots,
> respectively. But common harmonics are another thing to
> consider in the major/minor mystery.
>
> -Carl

..this is fascinating. I have to study this...

--- In tuning@yahoogroups.com, "frizzerius" <lorenzo.frizzera@l...>
wrote:
> Ciao.
>
> If you consider diatonic modes and you rearrange them through a
> circle of fifths you will have this list: lydian, ionian,
> mixolidian, dorian, eolian, phrigian and locrian. Each passage to a
> new mode produces the lowering of a note so that, at the end, you
> will have lowered any note except the tonic. If you do the same on
> this last note you will reach again a lydian mode but an half tone
> below.
>
> Considering the structure of these modes you will find that there
is
> a specularity in the structure between lydian and locrian, ionian
> and phrigian, mixolidian and eolian; and that dorian mode is
> specular respect himself.
>
> If you assume that any intervals has his own root in the note that
> appears before in the harmonic series, you will consider that 3/2,
> 9/8, 5/4, 15/8, 5/3 have the root below instead of 4/3, 6/5, 8/5
> which have the root above. Looking at the modes in this way you
will
> find that each note in the lydian mode is rooted in bass at the
> opposite of locrian where any note is rooted above.
>
> The reason why triads are so important is that these are the only
> chords which don't include seventh or seconds.
>
> All these elements confirm that:
>
> 1) yes, the major chord is rooted in a stronger way than the major
> and this can have some psychological effect on a listener beyond
any
> cultural influence.
> 2) yes, the difference between major and minor chords is due to a
> specularity model (otonal/utonal, lydian/locrian)
> 3) yes, the difference between major and minor chords is due to the
> lowering of a note.
>
> Ciao
>
> Lorenzo

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> Greetings group! Does anyone have any ideas on why minor triads,
and
> minor keys, in functional harmony, have (subjectively speaking)
> a 'sad affect', compared to, say, the major triad, and major keys?
>
> Yikes, Kelly

Hi Kelly,

In the terms I was using in my previous posts to you, a minor triad
is both "soft" and "smooth". It's "soft" because it doesn't have that
hard or perhaps 'happy' feeling associated with a clear harmonic
series sound, such as a major triad. But it's "smooth" because, like
the major triad, it has a very low level of "roughness", the term for
disturbing interaction between two tones in the cochlea of the ear.

Cheers,
Paul

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:
> From: "Carl Lumma" <ekin@>
>
> > >Greetings group! Does anyone have any ideas on why minor triads,
and
> > >minor keys, in functional harmony, have (subjectively speaking)
> > >a 'sad affect', compared to, say, the major triad, and major
keys?
> > >
> > >Yikes, Kelly
> >
> > I consider this somewhat of a mystery.
> >
> > Two thought-provoking responses from Kraig and Jon.
>
> Both of which I agree with. The 'sadness' of minor triads
and 'happiness' of
> major triads seem to be reflected by the former having a lower-
pitched note
> than the latter.

What do you mean by "lower-pitched note"? What tuning are the minor
and major triads assumed to be in? What if we assume 12-equal?

> Which leads me to ask this: anybody develop a system of 31-tone
jazz chords,
> or at least quartertone?

Hmm . . . good idea ;)

> I always thought that 'minorness' implies utonality,
while 'majorness' is
> otonal. But that's really only true in 5-limit, since 7/6 is minor
yet
> otonal.

The triad 6:7:9 is otonal. Not sure if that's what you meant.

> 10:12:15 is rooted in a common overtone (60); 4:5:6 in a common
> undertone (1), so I think both are definitely well-rooted, though in
> opposite directions. Something like 325:397:514 is definitely not
> well-rooted.
>
> (Someone on this list said this is how Partch interpreted things.)

Yes, but he did so without wanting to reference physical overtones or
undertones.

--- In tuning@yahoogroups.com, "frizzerius" <lorenzo.frizzera@l...>
wrote:
> Ciao.
>
> If you consider diatonic modes and you rearrange them through a
> circle of fifths you will have this list: lydian, ionian,
> mixolidian, dorian, eolian, phrigian and locrian. Each passage to a
> new mode produces the lowering of a note so that, at the end, you
> will have lowered any note except the tonic. If you do the same on
> this last note you will reach again a lydian mode but an half tone
> below.
>
> Considering the structure of these modes you will find that there
is
> a specularity in the structure between lydian and locrian, ionian
> and phrigian, mixolidian and eolian; and that dorian mode is
> specular respect himself.

By "specularity" do you mean "mirrorring"?

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> Very informative comments, all. Thinking of the chord (for
example
> e-g-b), I believe the affect exists not just in the chord itself
(to
> me, the effect vanishes in the conglomerate c-e-g-b, or e-g-b-d, or
> Russian folk tunes* on scalar notes e-f-g-a-b),

Indeed -- the phrygian mode was actually considered quite emotionally
positive, not negative, before the advent of triadic harmony at the
end of the Middle Ages.

...I can't put my finger on it yet, but wonder if it has
> something to do with the 'manufactured' nature of minor keys, ie,
the
> altered (raised) 6th and 7th degrees of the scale for dominant
> harmony and melodic reasons,

Yes, I think that's a factor.

> suggesting that the chord, just as it's
> less grounded (?), than the major triad is, in the audible harmonic
> series, is also less connected, than the major triad is, to the
> dominant chord in harmonic progressions?

Depending on how you define the dominant chord, this could indeed be
considered the case.

> Also, the minor chord shares with the major seventh chord (c-e-g-b)
> the interesting quality (interesting to me, anyways), though to a
> lesser degree, of containing elements of both tonic and dominant
> combined (e, suggesting the tonic chord c-e-g, and the leading tone
> b).

Yes, if you mean the E minor triad contains suggestions of both the C
(major) and G (major) roots, in addition to a root at e. Depending on
the tuning, other roots such as A might be simultaneously implied as
well.

> Sort of an anti-dominant harmony feature (even more present in
> the major seventh chord: c-e, g-b).

I'm not sure if this is intended to tie in in some way to western
functional harmonic practice. Can you fill in the blanks for me?

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> What do you mean by "lower-pitched note"? What tuning are the minor
> and major triads assumed to be in? What if we assume 12-equal?

Taps, when played on a bugle (or more likely on a trumpet using open
valves) is playing natural harmonics, not 12-eq. While some may lip
the pitch up or down after years of 12et indoctrination :), it still
stands to reason that a major triad, arpeggiated, is sad in this case
strictly from cultural conditioning.

If that is the case, why couldn't cultures develop music in minor
tonalities that they consider 'happy', and some in major tonalities
that would make them weep?

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > What do you mean by "lower-pitched note"? What tuning are the
minor
> > and major triads assumed to be in? What if we assume 12-equal?
>
> Taps, when played on a bugle (or more likely on a trumpet using
open
> valves) is playing natural harmonics, not 12-eq.

Here the notes are not sounded together in a chord, or even a quick
arpeggio, so the 'single clear root' considerations (which involve
the virtual pitch and combinational tone phenomena) doesn't even have
a chance to apply. If anything, a melody that outlines a pure minor
triad, rather than a pure major triad, might be the psychologically
more 'coherent', since the overtones in common between all the
pitches are audible -- even if usually subconsciously -- and form a
spectral 'pedal tone'.

Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> Here the notes are not sounded together in a chord, or even a quick
> arpeggio, so the 'single clear root' considerations (which involve
> the virtual pitch and combinational tone phenomena) doesn't even
have
> a chance to apply.

If you read the original post, he didn't ask for anywhere near that
specific a set of circumstances.

> If anything, a melody that outlines a pure minor
> triad, rather than a pure major triad, might be the psychologically
> more 'coherent', since the overtones in common between all the
> pitches are audible -- even if usually subconsciously -- and form a
> spectral 'pedal tone'.

Great. Lots of words, but taps is taps. Is it cultural that it is a
sad 'song'? I think so. What do you think?

Cheers,
Jon

--- In tuning@yahoogroups.com, "Jon Szanto" <JSZANTO@A...> wrote:
> Paul,
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...>
wrote:
> > Here the notes are not sounded together in a chord, or even a
quick
> > arpeggio, so the 'single clear root' considerations (which
involve
> > the virtual pitch and combinational tone phenomena) doesn't even
> have
> > a chance to apply.
>
> If you read the original post, he didn't ask for anywhere near that
> specific a set of circumstances.

Well I apologize to him right now if I said anything that took his
question in too narrow a sense. But here, you seem to have just taken
what *I* said and tried to apply it in a sense very different from my
original intent, and I did my best to follow along anyhow.

> > If anything, a melody that outlines a pure minor
> > triad, rather than a pure major triad, might be the
psychologically
> > more 'coherent', since the overtones in common between all the
> > pitches are audible -- even if usually subconsciously -- and form
a
> > spectral 'pedal tone'.
>
> Great. Lots of words, but taps is taps. Is it cultural that it is a
> sad 'song'? I think so. What do you think?

I agree with you. And very dependent on performance, too. One could
play taps as a bright fanfare, but this would be inappropriate for a
funeral.

- Sort of an anti-dominant harmony feature (even more present in
> > the major seventh chord: c-e, g-b).
>
> I'm not sure if this is intended to tie in in some way to western
> functional harmonic practice. Can you fill in the blanks for me?--

Hi Paul. Indeed, that's my main interest in music, is alternative
functional harmonies (hearing them, writing them)...chord
successsions which have the semblence of a standard progression, but
without 'dominant' propulsion, and where chord sonorority (and
texture) is a functional element as important as melody and 'harmony'
were in earlier classical music; the holy grail would be finding a
connection between how some of these non dominant but somehow
propulsive progressions, and the chords they contain, tie into the
harmonic series (and the physics of music), similar to the clear
connections between 'the physics of music' and scale formation and
common practice harmony; (that's what Hindemeth did? I can't listen
to his music...)That's why I'm so interested in chord environments
which are free of the 'pushy' dominant 7th chord (always wanting to
resolve to one, or travel the circle of 5ths), but which have
sonorous intervallic combinations. That's why I find the
disccussions at this group so interesting.

(My pet theory about non-dominant harmony is that, though you loose
the triangular harmonic balance of classical compositions which are
based on functional harmony (that being the balanceing tonal centers
of I, IV, and V, and how they reflectively become each others
dominant, etc), you gain some serenity or something like that in the
shift to hearing intervals and chords just for their sonority and
vibration! --and Number, too, if you're into that!) Kelly

In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> > Very informative comments, all. Thinking of the chord (for
> example
> > e-g-b), I believe the affect exists not just in the chord itself
> (to
> > me, the effect vanishes in the conglomerate c-e-g-b, or e-g-b-d,
or
> > Russian folk tunes* on scalar notes e-f-g-a-b),
>
> Indeed -- the phrygian mode was actually considered quite
emotionally
> positive, not negative, before the advent of triadic harmony at the
> end of the Middle Ages.
>
> ...I can't put my finger on it yet, but wonder if it has
> > something to do with the 'manufactured' nature of minor keys, ie,
> the
> > altered (raised) 6th and 7th degrees of the scale for dominant
> > harmony and melodic reasons,
>
> Yes, I think that's a factor.
>
> > suggesting that the chord, just as it's
> > less grounded (?), than the major triad is, in the audible
harmonic
> > series, is also less connected, than the major triad is, to the
> > dominant chord in harmonic progressions?
>
> Depending on how you define the dominant chord, this could indeed
be
> considered the case.
>
> > Also, the minor chord shares with the major seventh chord (c-e-g-
b)
> > the interesting quality (interesting to me, anyways), though to a
> > lesser degree, of containing elements of both tonic and dominant
> > combined (e, suggesting the tonic chord c-e-g, and the leading
tone
> > b).
>
> Yes, if you mean the E minor triad contains suggestions of both the
C
> (major) and G (major) roots, in addition to a root at e. Depending
on
> the tuning, other roots such as A might be simultaneously implied
as
> well.
>
> >

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:

> That's why I'm so interested in chord environments
> which are free of the 'pushy' dominant 7th chord (always wanting to
> resolve to one, or travel the circle of 5ths), but which have
> sonorous intervallic combinations. That's why I find the
> disccussions at this group so interesting.

You can make the dominant 7th chord unpushy by moving it in the
direction of a 1-3-5-7 overtone chord--the major tetrad. You can get
away from circles of fifths by choosing a temperament which is not
based on fifths.

P,

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> I agree with you. And very dependent on performance, too. One could
> play taps as a bright fanfare, but this would be inappropriate for
a
> funeral.

I thought about that. Pump it up with an entire brass choir,
utilizing harmony, and I bet that lone melody would have a hard time
being a 'sad' one. I never posted a link, but I hope you've seen
recent accounts of the digital trumpet/bugle that the armed forces
have been using. Due to a shortage of buglers, someone developed a
thing that looks like a trumpet, but in the bell is a digital
playback system. The guy/gal may hold it up to their lips, but all
that is happening is a recording being played back, the sound coming
out of the speaker mounted in the bell.

Wouldn't it be great to never hear that song again, for other reasons?

Over and out,
Jon

Jon Szanto wrote:

>>If anything, a melody that outlines a pure minor >>triad, rather than a pure major triad, might be the psychologically >>more 'coherent', since the overtones in common between all the >>pitches are audible -- even if usually subconsciously -- and form a >>spectral 'pedal tone'.
>> >>
>
>Great. Lots of words, but taps is taps. Is it cultural that it is a >sad 'song'? I think so. What do you think?
>
>Cheers,
>Jon
>
Keep in mind that the 5/4 is a flatted 3rd. A flat Major third.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

From: "wallyesterpaulrus" <paul@...>

> > Both of which I agree with. The 'sadness' of minor triads
> and 'happiness' of
> > major triads seem to be reflected by the former having a lower-
> pitched note
> > than the latter.
>
> What do you mean by "lower-pitched note"? What tuning are the minor
> and major triads assumed to be in? What if we assume 12-equal?

I should've said lower-pitched in relation to the tonic note, and in
hindsight, I might've been too shortsighted. Occam's razor turned out to be
dull this time. I have a hunch that this is all a matter of cultural
conditioning.

Don't see how it would matter if it was 12-equal, 19-equal or 31-equal
though. A major is a major and a minor is a minor. In really weird equal
temperament tunings it might be different, if the major and minor intervals
are way off of just.

> > Which leads me to ask this: anybody develop a system of 31-tone
> jazz chords,
> > or at least quartertone?
>
> Hmm . . . good idea ;)

Sigh... too many projects going on at once. I outta get to work on this, but
I'm really trying to get started writing a book, composing music AND
learning a language.

I thought about the possible number of combinations of notes in 31-equal,
and even applying some limitations like not allowing two consecutive
'quarter-tones' and no more than seven notes in a chord, I still came up
with about a hundred thousand.

> > I always thought that 'minorness' implies utonality,
> while 'majorness' is
> > otonal. But that's really only true in 5-limit, since 7/6 is minor
> yet
> > otonal.
>
> The triad 6:7:9 is otonal. Not sure if that's what you meant.

I'm not sure what I meant either. ;) It leads me to ask 7/6 is really a
minor. Its 31-tone equivalent is an augmented second.

I also get the opposite feeling for 9/7, the supermajor third, or more
properly, the diminished fourth. The Arabic maqam Saba is considered one of
the most melancholy of the maqamat, and it has a diminished fourth (and a
diminished octave!), which of course would be equal to a major third in
12-tone. Another case where a major third doesn't really imply majorness.

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:
> From: "wallyesterpaulrus" <paul@>
>
> > > Both of which I agree with. The 'sadness' of minor triads
> > and 'happiness' of
> > > major triads seem to be reflected by the former having a lower-
> > pitched note
> > > than the latter.
> >
> > What do you mean by "lower-pitched note"? What tuning are the
minor
> > and major triads assumed to be in? What if we assume 12-equal?
>
> I should've said lower-pitched in relation to the tonic note,

I'm still not clear on what you had in mind.

> Don't see how it would matter if it was 12-equal, 19-equal or 31-
equal
> though.

Think 10:12:15 vs. 16:19:24 vs. 6:7:9, for example.

Danny Wier wrote:

>A major is a major and a minor is a minor. >
Only in 12tet.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:

> Keep in mind that the 5/4 is a flatted 3rd. A flat Major third.

A very 12-centric point of view. In Zarlino's 2/7-comma meantone, it's
a sharp major third.

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:

> I thought about the possible number of combinations of notes in
31-equal,
> and even applying some limitations like not allowing two consecutive
> 'quarter-tones' and no more than seven notes in a chord, I still came up
> with about a hundred thousand.

Here's a list of the number of n-tone octave-equivalent chords, for n
from 1 to 10, with no restrictions:

1 31
2 465
3 4495
4 31465
5 169911
6 736281
7 2629575
8 7888725
9 20160075
10 44352165

Even triads are getting out of hand.

Wow...I'd like to hear that! (major tetrad, with tuning not based on
fifths). Can you direct me? (And ever consider calling it a 'square
chord', since 1+3+5+7 is a square number, and that the diaganol of a
unit-1 square is ~7/5?)

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> > That's why I'm so interested in chord environments
> > which are free of the 'pushy' dominant 7th chord (always wanting
to
> > resolve to one, or travel the circle of 5ths), but which have
> > sonorous intervallic combinations. That's why I find the
> > disccussions at this group so interesting.
>
> You can make the dominant 7th chord unpushy by moving it in the
> direction of a 1-3-5-7 overtone chord--the major tetrad. You can get
> away from circles of fifths by choosing a temperament which is not
> based on fifths.

Gene Ward Smith wrote:

>--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
>
> >
>>Keep in mind that the 5/4 is a flatted 3rd. A flat Major third.
>> >>
>
>A very 12-centric point of view. In Zarlino's 2/7-comma meantone, it's
>a sharp major third.
>
A 5/4 isn't "12-centric", it's just.
Zarlino's 2/7-comma meantone is just another temperament, like 12-tet.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

From: "wallyesterpaulrus" <paul@...>

> > > What do you mean by "lower-pitched note"? What tuning are the
> minor
> > > and major triads assumed to be in? What if we assume 12-equal?
> >
> > I should've said lower-pitched in relation to the tonic note,
>
> I'm still not clear on what you had in mind.
>
> > Don't see how it would matter if it was 12-equal, 19-equal or 31-
> equal
> > though.
>
> Think 10:12:15 vs. 16:19:24 vs. 6:7:9, for example.

Ohh... I see what you meant. I got lost there. I was saying that a major
third was anything above approx. 350 cents and a minor was below, and the
mood would be influenced by the size of that interval. But that's not taking
into account things like harmonic entropy.

From: "Gene Ward Smith" <gwsmith@...>

> --- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:
>
> > I thought about the possible number of combinations of notes in
> 31-equal,
> > and even applying some limitations like not allowing two consecutive
> > 'quarter-tones' and no more than seven notes in a chord, I still came up
> > with about a hundred thousand.
>
> Here's a list of the number of n-tone octave-equivalent chords, for n
> from 1 to 10, with no restrictions:
>
> 1 31
> 2 465
> 3 4495
> 4 31465
> 5 169911
> 6 736281
> 7 2629575
> 8 7888725
> 9 20160075
> 10 44352165
>
> Even triads are getting out of hand.

I came up with 6^7 = 279,936 - so I misunderestimated. And some redundant
chords would have to be taken out, as the supermajor third and diminished
fourth maps to the same 31-tone note, likewise the supermajor seventh and
diminished octave.

The rules I used: five legal seconds (subminor, minor, neutral, major,
supermajor), five thirds, four fourths/elevenths (diminished,
semidiminished, perfect, semiaugmented, augmented), five fifths, five
sixths, five sevenths and five octaves (I like to use scales and chords with
a non-perfect octave). And not all these intervals have to be present, thus
the six in the base.

You can compare three different tunings of the 'dominant seventh'
chord (including the 4:5:6:7 tuning), as well as five different
tunings of the 'half-diminished seventh' chord, near the top here:

http://www.soundclick.com/bands/5/tuninglabmusic.htm

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> Wow...I'd like to hear that! (major tetrad, with tuning not based
on
> fifths). Can you direct me? (And ever consider calling it
a 'square
> chord', since 1+3+5+7 is a square number, and that the diaganol of
a
> unit-1 square is ~7/5?)
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> >
> > > That's why I'm so interested in chord environments
> > > which are free of the 'pushy' dominant 7th chord (always
wanting
> to
> > > resolve to one, or travel the circle of 5ths), but which have
> > > sonorous intervallic combinations. That's why I find the
> > > disccussions at this group so interesting.
> >
> > You can make the dominant 7th chord unpushy by moving it in the
> > direction of a 1-3-5-7 overtone chord--the major tetrad. You can
get
> > away from circles of fifths by choosing a temperament which is not
> > based on fifths.

--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> Gene Ward Smith wrote:
>
> >--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> >
> >
> >
> >>Keep in mind that the 5/4 is a flatted 3rd. A flat Major third.
> >>
> >>
> >
> >A very 12-centric point of view. In Zarlino's 2/7-comma meantone,
it's
> >a sharp major third.
> >
> A 5/4 isn't "12-centric", it's just.
> Zarlino's 2/7-comma meantone is just another temperament, like 12-
>tet.

You missed Gene's point. Obviously a just 5/4 ratio isn't "12-
centric" or anything like that. Gene's point was that calling 5/4
a "flat" or "narrow" major third assumes that a "normal" major third
is wider. That's true in 12-equal, but it's not true in 2/7-comma
meantone.

wallyesterpaulrus wrote:

>--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
> >
>>Gene Ward Smith wrote:
>>
>> >>
>>>--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:
>>>
>>> >>>
>>> >>>
>>>>Keep in mind that the 5/4 is a flatted 3rd. A flat Major third.
>>>> >>>>
>>>> >>>>
>>>A very 12-centric point of view. In Zarlino's 2/7-comma meantone, >>> >>>
>it's
> >
>>>a sharp major third.
>>>
>>> >>>
>>A 5/4 isn't "12-centric", it's just.
>>Zarlino's 2/7-comma meantone is just another temperament, like 12-
>>tet.
>> >>
>
>You missed Gene's point. Obviously a just 5/4 ratio isn't "12-
>centric" or anything like that. Gene's point was that calling 5/4 >a "flat" or "narrow" major third assumes that a "normal" major third >is wider. That's true in 12-equal, but it's not true in 2/7-comma >meantone.
>
And both of you guys are taking my comment out of context.

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

--- In tuning@yahoogroups.com, David Beardsley <db@b...> wrote:

> And both of you guys are taking my comment out of context.

Sorry about that. Could you set us right, then?

--- In tuning@yahoogroups.com, "Danny Wier" <dawiertx@s...> wrote:

> I came up with 6^7 = 279,936 - so I misunderestimated.

I could have done it differently by dividing through by 31, so
transpositions didn't get counted. It still gets complicated no matter
what you do; 2^12 we can manage by simple enumeration, but 2^31 is a
lot bigger.

And some redundant
> chords would have to be taken out, as the supermajor third and
diminished
> fourth maps to the same 31-tone note, likewise the supermajor
seventh and
> diminished octave.

I simply gave 31 choose n, so this has no bearing on my table.

>I simply gave 31 choose n, so this has no bearing on my table.

Why stop at 31, if you're not going to remove inversions?

-Carl

--- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:

> Wow...I'd like to hear that! (major tetrad, with tuning not based on
> fifths). Can you direct me?

Much of my music qualifies, for starters. You could try in particular
Bodacious Breed or The 45000 fingers of Dr S, and from the Christmas
2002 album, Stained Glass, Rachmaninov Plays Blackjack, and the
Clinton Variations. All of these emphasize tetrads, and the tetrads
are either justly tuned, or tuned to a temperament which comes close
to JI. None emphasize circles of fifths, or V/I.

http://66.98.148.43/~xenharmo/gene.html

(And ever consider calling it a 'square
> chord', since 1+3+5+7 is a square number, and that the diaganol of a
> unit-1 square is ~7/5?)
>
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
> wrote:
> > --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> >
> > > That's why I'm so interested in chord environments
> > > which are free of the 'pushy' dominant 7th chord (always wanting
> to
> > > resolve to one, or travel the circle of 5ths), but which have
> > > sonorous intervallic combinations. That's why I find the
> > > disccussions at this group so interesting.
> >
> > You can make the dominant 7th chord unpushy by moving it in the
> > direction of a 1-3-5-7 overtone chord--the major tetrad. You can get
> > away from circles of fifths by choosing a temperament which is not
> > based on fifths.

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
>
> > Wow...I'd like to hear that! (major tetrad, with tuning not based
on
> > fifths). Can you direct me?
>
> Much of my music qualifies, for starters. You could try in
particular
> Bodacious Breed or The 45000 fingers of Dr S, and from the Christmas
> 2002 album, Stained Glass, Rachmaninov Plays Blackjack, and the
> Clinton Variations. All of these emphasize tetrads, and the tetrads
> are either justly tuned, or tuned to a temperament which comes close
> to JI. None emphasize circles of fifths, or V/I.
>
> http://66.98.148.43/~xenharmo/gene.html

Hi Gene.

I don't know about you, but the pitch slides in many of these pieces,
which I've pointed out repeatedly on MakeMicroMusic, make me hesitate
to recommend them all, especially in this light (and even more so,
given your website descriptions). I appreciate all the hard work
you've been putting into creating this music, but am I completely off-
base in suggesting that a little bit of attention to the end product
would greatly enhance the value of all the intellectual and creative
effort?

You'll probably think of this as slander, but it's not -- I honestly
*want* your music to be widely appreciated -- you deserve it.

-Paul

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > --- In tuning@yahoogroups.com, "traktus5" <kj4321@h...> wrote:
> >
> > > Wow...I'd like to hear that! (major tetrad, with tuning not based
> on
> > > fifths). Can you direct me?
> >
> > Much of my music qualifies, for starters. You could try in
> particular
> > Bodacious Breed or The 45000 fingers of Dr S, and from the Christmas
> > 2002 album, Stained Glass, Rachmaninov Plays Blackjack, and the
> > Clinton Variations. All of these emphasize tetrads, and the tetrads
> > are either justly tuned, or tuned to a temperament which comes close
> > to JI. None emphasize circles of fifths, or V/I.
> >
> > http://66.98.148.43/~xenharmo/gene.html
>
> Hi Gene.
>
> I don't know about you, but the pitch slides in many of these pieces,
> which I've pointed out repeatedly on MakeMicroMusic, make me hesitate
> to recommend them all, especially in this light (and even more so,
> given your website descriptions).

Heh. I thought you were saying recently that pitch slides were the
wave of the future. :)

I appreciate all the hard work
> you've been putting into creating this music, but am I completely off-
> base in suggesting that a little bit of attention to the end product
> would greatly enhance the value of all the intellectual and creative
> effort?

When I get my new computer, which should be soon, I'll see if Timidity
can do it better. Or I may try it before, hoping things don't crash on
me...

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:

> I don't know about you, but the pitch slides in many of these
pieces,
> which I've pointed out repeatedly on MakeMicroMusic, make me
hesitate
> to recommend them all, especially in this light (and even more so,
> given your website descriptions).

In honor of the first aniversary of xenharmony.org, which I know it
to be since I just got the bill for Year Two, I've put up a new
version, rendered via Timidity++ 2.13, of 45000 Fingers. Timidity
worked far better than I thought it would; I think it's been improved
on. It also seems stable enough to work even with my psychotic
computer, which Audio Compositor can no longer easily do.

Anyway, while there are still things to complain about Timidity seems
better so far as intonation goes; I think it is now the preferable
system.

I appreciate all the hard work
> you've been putting into creating this music, but am I completely
off-
> base in suggesting that a little bit of attention to the end
product
> would greatly enhance the value of all the intellectual and
creative
> effort?

Everyone seems to think so. I get more criticism about my efforts
than everyone else put together, which in a way is a compliment,
since I don't think people would bother if they just didn't care. Of
course useful suggestions are best.

> You'll probably think of this as slander, but it's not -- I
honestly
> *want* your music to be widely appreciated -- you deserve it.

Thanks. I can produce the score, anyway. Once upon a time that was
all that we expected of someone claiming to compose. Ah, for the good
old days.

>In honor of the first aniversary of xenharmony.org, which I know it
>to be since I just got the bill for Year Two, I've put up a new
>version, rendered via Timidity++ 2.13, of 45000 Fingers. Timidity
>worked far better than I thought it would; I think it's been improved
>on. It also seems stable enough to work even with my psychotic
>computer, which Audio Compositor can no longer easily do.

Is there a url for this version?

>Everyone seems to think so. I get more criticism about my efforts
>than everyone else put together,

I have noticed that...

>Thanks. I can produce the score, anyway. Once upon a time that was
>all that we expected of someone claiming to compose. Ah, for the good
>old days.

Not true. Performances were always the responsibility of the
composer, unless you were hoping to be discovered posthumously.
And I don't know of a single composer who didn't have
performances in their lifetime.

I'd consider yourself lucky -- you've got a band in a box, and
despite its psychosis I suspect it's cheaper and easier than
dealing with musicians!

-Carl

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >In honor of the first aniversary of xenharmony.org, which I know it
> >to be since I just got the bill for Year Two, I've put up a new
> >version, rendered via Timidity++ 2.13, of 45000 Fingers. Timidity
> >worked far better than I thought it would; I think it's been improved
> >on. It also seems stable enough to work even with my psychotic
> >computer, which Audio Compositor can no longer easily do.
>
> Is there a url for this version?

I renamed the old version, and am using the same url for the new
version. I could put up a link to that if people are interested in
comparing the two.

> I'd consider yourself lucky -- you've got a band in a box, and
> despite its psychosis I suspect it's cheaper and easier than
> dealing with musicians!

I know. I went through a first round of microtonal composing using a
device Robin (my chess whiz brother) made which gave me four precisely
tuned voices, for which I had a choice of square wave, square wave,
square wav or square wav for the timbre.

>>>In honor of the first aniversary of xenharmony.org, which I know
>>>it to be since I just got the bill for Year Two, I've put up a new
>>>version, rendered via Timidity++ 2.13, of 45000 Fingers. Timidity
>>>worked far better than I thought it would; I think it's been
>>>improved on. It also seems stable enough to work even with my
>>>psychotic computer, which Audio Compositor can no longer easily do.
>>
>>Is there a url for this version?
>
>I renamed the old version, and am using the same url for the new
>version. I could put up a link to that if people are interested in
>comparing the two.

I meant Timidity, but I'll be sure to download your pieces
straightaway. I, of course, have the old versions. What
exactly was updated? Just 45K Fingers?

>> I'd consider yourself lucky -- you've got a band in a box, and
>> despite its psychosis I suspect it's cheaper and easier than
>> dealing with musicians!
>
>I know. I went through a first round of microtonal composing using a
>device Robin (my chess whiz brother) made which gave me four
>precisely tuned voices, for which I had a choice of square wave,
>square wave, square wav or square wav for the timbre.

I think you told me about that when we met. I wouldn't knock
the potential of even those few waveforms, either!

-Carl

--- In tuning@yahoogroups.com, "wallyesterpaulrus" <paul@s...> wrote:
> --- In tuning@yahoogroups.com, "frizzerius"
<lorenzo.frizzera@l...>
> wrote:
> > Ciao.
> >
> > If you consider diatonic modes and you rearrange them through a
> > circle of fifths you will have this list: lydian, ionian,
> > mixolidian, dorian, eolian, phrigian and locrian. Each passage
to a
> > new mode produces the lowering of a note so that, at the end,
you
> > will have lowered any note except the tonic. If you do the same
on
> > this last note you will reach again a lydian mode but an half
tone
> > below.
> >
> > Considering the structure of these modes you will find that
there
> is
> > a specularity in the structure between lydian and locrian,
ionian
> > and phrigian, mixolidian and eolian; and that dorian mode is
> > specular respect himself.
>
> By "specularity" do you mean "mirrorring"?

Yes.

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >>Is there a url for this version?

http://timidity.s11.xrea.com/index.en.html

I used the most recent stable version listed there, a build from March
29. You can always get up-to-the minute versions, and Linux source for
Linux, etc.

> I meant Timidity, but I'll be sure to download your pieces
> straightaway. I, of course, have the old versions. What
> exactly was updated? Just 45K Fingers?

So far, I was hoping for feedback from Paul.

>>Is there a url for this version?
>
>http://timidity.s11.xrea.com/index.en.html
>
>I used the most recent stable version listed there, a build from March
>29. You can always get up-to-the minute versions, and Linux source for
>Linux, etc.

Thanks.

-C.

>I've put up a new
>version, rendered via Timidity++ 2.13, of 45000 Fingers.
>Timidity worked far better than I thought it would; I
>think it's been improved on.
//
> I renamed the old version, and am using the same url for
> the new version. I could put up a link to that if people
> are interested in comparing the two.

I does indeed seem improved, with fewer though still
extant 'warbling willies'.

Also, the stereo mix seems a bit odd. For one thing,
you've got much more power in the left channel than the
right (-19.97dB vs. -23.07dB RMS resp.).

-Carl