Yahoo Tuning Groups Ultimate Backup tuning some new music

--- In tuning@yahoogroups.com, Dante Rosati <danterosati@...> wrote:
>
> I really I like this one Aaron- great time changes, and effective
> microtonal counterpoint sections. It sounds a bit like a video game
> from another planet. Evokes lots of visuals, so its kinda like sonic
> shrooms too.

Hehe, thanks Dante, right on...I was inspired by Jacob Barton mentioning his exploring doing 'chiptune' or 8-bit style explorations in 41-edo. I haven't heard them yet, but I'm sure he'll have some tasty nuggets.

This one had no proper title until yesterday, when I realized that 'Pahlops & Laugua's Big Adventure' after two of my daughter's imaginary friends, who are actually the index fingers of her left and right hands....she's really cute the way she will have them walk around, doing various things, always full of energy and playful....

AKJ

> Dante
>
> On Fri, Aug 7, 2009 at 12:18 AM, Aaron Johnson<aaron@...> wrote:
> >
> >
> > http://www.akjmusic.com/audio/PuhlopsAndLaugua.mp3
> >
> > --
> >
> > Aaron Krister Johnson
> > http://www.akjmusic.com
> > http://www.untwelve.org
> >
> >
>

🔗Michael <djtrancendance@...>

One may think...that a circle of 4ths followed by alternating 5ths (CFCFC) would produce similar results (far as consonance and beating) as 5ths followed by alternating 4th (CGCGC)... ...In the same way major and minor chords "should" produce the same level of consonance (even though that subject is still much up to debate).

However, I have noticed that the chord C5 F5 C6 actually sounds much steady/less-beating and natural than C5 G5 C6 and was wondering what the rest of you think.

If you look at the picture examples attached, you will see CGC has a shorter period that CFC.
However, CFC appears to have much less beating since the amplitude in the middle of CGC changes a good deal (becomes much lower) while CFC does not (the amplitude becomes lower but much less so) as you can see in the bitmap images attached.
--------------------------------------------------
Correct me if I am wrong, but I get the impression a huge majority of scales are designed to preserve the octave foremost and the 5th interval second when another alternative may be to preserve either the 4th or the 5th (the same intervals used in C(4th)F(5th)C, and preferably in the order whenever possible).

-Michael

________________________________
From: Aaron Johnson <aaron@...>
To: makemicromusic@yahoogroups.com; tuning@yahoogroups.com
Sent: Thursday, August 6, 2009 11:18:42 PM
Subject: [tuning] some new music

http://www.akjmusic.com/audio/PuhlopsAndLaugua.mp3

Aaron Krister Johnson
http://www.akjmusic.com
http://www.untwelve.org

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Aaron Krister Johnson <aaron@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Charles Lucy <lucy@...>

🔗Marcel de Velde <m.develde@...>

🔗Michael <djtrancendance@...>

Chris>"What tuning are you using when listening? That is important - are they pure intervals?"
Just plain old 12TET. Which means the F is 1.33484 instead of 1.3333 and the 5th 1.49831 instead of 1.5: in 12TET these intervals are some of the ones close to pure.

>"The perfect 4th was considered a dissonant interval in the context of choral music that used pure intervals."
Hmm...for example though, if you make the chord C G C using perfect intervals, the perfect 4th still appears between the G and C. And I've seen this appear just about everywhere: power chords, arpeggios in trance, drum tuning, vocal harmonization, etc...I fully believe you that the fourth was/is considered dissonant in pure interval choral music, but don't see how that would make, say, the chord CGC used so much in modern music sour.

>"(this is why I brought up Lucy tuning before - the context is everything for these assessments. )"
I understand the context is important and that, in some cases IE the major "third" interval 12TET differs considerably from pure...but, so far at least, I don't see any differences being large enough to matter (if that's what you're getting at). It seems to me like asking someone if 301/201 sounds different than the ratio 3/2: not mathematically different enough for the ear to tell.

-Michael

🔗Chris <chrisvaisvil@...>

🔗Michael <djtrancendance@...>

Chris>"I'd be curious then as to your assessment of C F Bb vs C G D."
Close, but CGD wins. They both seem to beat around the same amount of amplitude...but CFA# takes longer to repeat its periodicity and thus sounds "shakier". Also if you look at the beating over longer periods of time is does not form much of an even/"waving" curve.
In short, I think it must have more to do with the order of intervals than how periodic each interval is. Because, apparently, stacking an interval on top of itself changes the sense of periodicity IE a 4th followed by a 5th IE CAC is more periodic than two stacked 5ths IE CGD which is more periodic than two stacked 4th IE C F A#.

Perhaps more obviously...even if you look at the graphs of a JI perfect major vs. perfect minor chord (CEG for the first half and CD#G for the second in the attached image)....you'll see how the beating in C-E-G rotates periodically forming artistically pleasing gradual waves (ALA the waving curve I described before) in the graph while the beating in C-D#-G does not (even though they contain the exact same intervals)!

>"Hopefully you've not been using a tuner and tuning your axe to 12 tet. "
I think I get what you're saying: that the ear is very sensitive about the accuracy of 4th and 5th intervals...to the point your ear would do a better job finding them than a 12tet-based tuner. Is that what you are saying?

________________________________
From: Chris <chrisvaisvil@...>
To: tuning@yahoogroups.com
Sent: Saturday, August 8, 2009 5:38:40 PM
Subject: Re: [tuning] Periodicity and beating (and example comparing 4ths and 5ths)

Re: periodicity

I'd be curious then as to your assessment of C F Bb vs C G D. This would be perhaps a more fair comparison since as you pointed out C G C and C F C both contain both a 4th and 5th.

Also I'd point our that at those intervals, at least to me, the ear is more sensitive to beating. What I mean is that tuning a guitar to perfect 4ths (between the A and D strings for instance) is much easier than tuning the perfect major 3rd (G and B strings). Hopefully you've not been using a tuner and tuning your axe to 12 tet.
Sent via BlackBerry from T-Mobile

🔗Daniel Forro <dan.for@...>

On 9 Aug 2009, at 10:12 AM, Michael wrote:
>
> Chris>"I'd be curious then as to your assessment of C F Bb vs C G D."
> Close, but CGD wins. They both seem to beat around the same > amount of amplitude...but CFA# takes longer to repeat its > periodicity and thus sounds "shakier". Also if you look at the > beating over longer periods of time is does not form much of an > even/"waving" curve.
> In short, I think it must have more to do with the order of > intervals than how periodic each interval is. Because, > apparently, stacking an interval on top of itself changes the sense > of periodicity IE a 4th followed by a 5th IE CAC is more periodic > than two stacked 5ths IE CGD which is more periodic than two > stacked 4th IE C F A#.

Despite my effort somehow I can't see 4th followed by 5th in your example CAC...

And F A# is not 4th, just an augmented 3rd...

> Perhaps more obviously...even if you look at the graphs of a JI > perfect major vs. perfect minor chord (CEG for the first half and > CD#G for the second in the attached image)....

C D# G is not minor chord... If you want to get one, it must be spelled C Eb G.

Or do you have some special reason for your spelling?

Daniel Forro

🔗Michael <djtrancendance@...>

🔗monz <joemonz@...>

Hi Chris, Michael, and Daniel,

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Chris> "I'd be curious then as to your assessment
> of C F Bb vs C G D."
>
> Close, but CGD wins. They both seem to beat around the same amount of amplitude...but CFA# takes longer to repeat its periodicity and thus sounds "shakier". Also if you look at the beating over longer periods of time is does not form much of an even/"waving" curve.
> In short, I think it must have more to do with the order of intervals than how periodic each interval is. Because, apparently, stacking an interval on top of itself changes the sense of periodicity IE a 4th followed by a 5th IE CAC [sic] is more periodic than two stacked 5ths IE CGD which is more periodic than two stacked 4th IE C F A#.
>
> Perhaps more obviously...even if you look at the graphs of a JI perfect major vs. perfect minor chord (CEG for the first half and CD#G for the second in the attached image)....you'll see how the beating in C-E-G rotates periodically forming artistically pleasing gradual waves (ALA the waving curve I described before) in the graph while the beating in C-D#-G does not (even though they contain the exact same intervals)!
>

As Daniel pointed out, your spelling is strange, because
if you're talking about intervals which are just ratios,
F:A# is a very dissonant augmented-3rd and not any kind
of 4th at all.

I think what you mean by "more periodic" is that the
overall period is shorter, correct? The periodicity and
beating of a triad is not going to be calculated simply
by the sum of its constituent dyad intervals, but rather
by the closeness with which the whole composite relates
to a portion of the harmonic series. The lower the numbers
in the _overall_ proportion, the smaller the period.

Thus, in ascending order and using just ratios, the
overall proportions of your examples are:

* a 4th plus 5th C:F:C = 3:4:6

* two stacked 5ths C:G:D = 4:6:9

* two stacked 4ths C:F:Bb = 9:12:16

* the just major triad C:E:G = 4:5:6

* the just minor triad C:Eb:G = 10:12:15

> > "Hopefully you've not been using a tuner and tuning
> > your axe to 12 tet. "
>
> I think I get what you're saying: that the ear is very sensitive about the accuracy of 4th and 5th intervals...to the point your ear would do a better job finding them than a 12tet-based tuner. Is that what you are saying?

Your ear will always be more sensitive to any just ratio
with single-digit terms than a 12tet-based tuner will be.

By ear it is very easy to tune the just perfect-4th 4:3
and perfect-5th 3:2 until there is no beating. The 12edo
versions of these intervals are only ~2 cents wider and
narrower (respectively) than the just versions, and that
is usually a fairly negligible difference.

It's also very easy to tune the just major-3rd 5:4 and
minor-3rd 6:5 by ear until there is no beating ... but
the sizes of these ratios is so different from those of
12edo that trying to tune the 12edo versions by ear is
very difficult and takes a lot of training.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

🔗Chris Vaisvil <chrisvaisvil@...>

🔗monz <joemonz@...>

Hi Michael,

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>

> > "C D# G is not minor chord... If you want to get one,
> > it must be spelled C Eb G."
>
> There is no special reason for my spelling; I'm just
> not good with en-harmonics. So (private message response
> please so we don't clog the boards): what is the reason
> for using the notation Eb instead of D#?

Interval _names_ are determined by counting the letters of
the notes involved. Thus:

* any kind of C and any kind of D can only make
some kind of 2nd, and

* any kind of C with any kind of E can only make
some kind of 3rd.

etc., regardless of whether there is an accidental with
either of the letters. The presence of accidentals determines
the _quality_ of the interval, that is, "perfect", "major",
"minor", "augmented", or "diminished".

Some aspects of music-theory are determined more by
scientific data, but some aspects are heavily dependent
upon the nomenclature used.

When discussing tuning-theory which involves ratios, the
only unambiguous method is to use the actual ratios in
the discussion.

The notation of pitches using letters was developed
1000 years ago and was only a convenience, employed
primarily by music _practitioners_ (choir-masters, etc.)
who were largely ignorant of the numerical facts concerning
ratios, and just wanted to be able to quickly teach their
subjects to sing chants correctly.

The letter notation caught on so deeply and universally
that it was picked up very soon by music-theorists, and
is so deeply entrenched now that despite many proposals
to overhaul the notation system, none have stuck.

In 12edo, Eb and D# are exactly the same pitch, but that
is not the case in most other tunings.

There are a lot of pages in my Encyclopedia which can
help with understanding this stuff ... try reading these
in this order:

http://tonalsoft.com/enc/n/notation.aspx
http://tonalsoft.com/enc/p/pseudo-odo_dialogus.aspx
http://tonalsoft.com/enc/i/interval.aspx
http://tonalsoft.com/enc/p/pythagorean.aspx
http://tonalsoft.com/enc/m/meantone.aspx
http://tonalsoft.com/enc/number/12edo.aspx

(The page on pseudo-Odo was never completed, so some
graphics are still missing, but they concern the modes,
the part about measurements and notation is complete.)

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

🔗Michael <djtrancendance@...>

>"I think what you mean by "more periodic" is that the
overall period is shorter, correct?"
Yes. A factor of that mostly, and, secondarily, how much the waveform beats between the lowest and highest humps in a time-domain graph (note: a single sine wave has all the humps the same height, so that's an ideal limit though apparently not possible to hit perfectly with more than one tone played together at once).

Joe>
>"Thus, in ascending order and using just ratios, the
>overall proportions of your examples are:
>* a 4th plus 5th C:F:C = 3:4:6
>* two stacked 5ths C:G:D = 4:6:9
>* two stacked 4ths C:F:Bb = 9:12:16
>* the just major triad C:E:G = 4:5:6
>* the just minor triad C:Eb:G = 10:12:15
>"

Exactly, that's what I was testing.

>"The periodicity and
>beating of a triad is not going to be calculated simply
>by the sum of its constituent dyad intervals, but rather
>by the closeness with which the whole composite relates
>to a portion of the harmonic series."

I'm not quite sure I understand this.
So basically you are saying (as I understand it) is the most periodic triad covering an octave would be simply
frequency*3/2 (1.5) frequency*4/2 (2) frequency*5/2 (2.5) frequency*6/2 (3) (in which case the root notes of the triad would actually be parts of the harmonic series and the notes of the chord would align perfectly with the timbre)?
In that case (if that is true) the notes (in the case of the timbre of the instrument playing the notes matching the harmonic series perfectly) would be 1/1 4/3 (2/1.5 = 1.333333) and 5/3 (2.5/1.5=1.6666666666), which seems to correlate closely with notes C, F, A.

-Michael

🔗monz <joemonz@...>

Hi Michael,

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> > "I think what you mean by "more periodic" is that the
> > overall period is shorter, correct?"
>
> Yes. A factor of that mostly, and, secondarily,
> how much the waveform beats between the lowest and
> highest humps in a time-domain graph (note: a single
> sine wave has all the humps the same height, so that's
> an ideal limit though apparently not possible to hit
> perfectly with more than one tone played together at once).
>
> Joe>
> > "Thus, in ascending order and using just ratios, the
> > overall proportions of your examples are:
> > * a 4th plus 5th C:F:C = 3:4:6
> > * two stacked 5ths C:G:D = 4:6:9
> > * two stacked 4ths C:F:Bb = 9:12:16
> > * the just major triad C:E:G = 4:5:6
> > * the just minor triad C:Eb:G = 10:12:15
> > "
>
> Exactly, that's what I was testing.

OK, good. You can see by the numbers exactly which
triads have the shortest periods. Smaller numbers =
shorter period. Pretty straightforward -- except that
it gets more complicated when you start comparing
numbers which are neighbors but have a totally different
prime-factorization (more on this below).

(PS - "Joe" is my name, but please refer to me as
"monz" around here ... the tuning list has known me
as "monz" for 11 years.)

> > "The periodicity and
> > beating of a triad is not going to be calculated simply
> > by the sum of its constituent dyad intervals, but rather
> > by the closeness with which the whole composite relates
> > to a portion of the harmonic series."
>
>
> I'm not quite sure I understand this.
> So basically you are saying (as I understand it) is [sic]
> the most periodic triad covering an octave would be simply
> frequency*3/2 (1.5) frequency*4/2 (2) frequency*5/2 (2.5)
> frequency*6/2 (3) (in which case the root notes of the triad
> would actually be parts of the harmonic series and the notes
> of the chord would align perfectly with the timbre)?

First of all, your example here is strictly speaking not
a triad (3 notes), but a tetrad (4 notes). Generally in
the context of discussing harmony in music-theory we do
ignore the 2:1 ratio, because it is almost always considered
to be the equivalence-interval or identity-interval. But
when discussing the physics of a vibrating sound, you have
to be more careful.

Secondly, i'm not sure i understand what you mean by "the
root notes of the triad". In any chord which is tuned to
just ratios, the pitches will fit into a subset of the
harmonic series. That's by definition. And from a music-theory
perspective, there is only one note which can be the
"root" of a triad.

Thirdly, you're invoking the timbre of the instrument as
part of the discussion, but this doesn't have anything to
do with periodictiy _per se_. Periodicity is a phenomenon
which comes out of the numbers describing the pitch
vibrations. A listener's _perception_ of consonance will
have a lot to do with how the tuning of the pitches aligns
(or does not align) with the instrument's timbre, and so
an examination of beating will have to take this into
account. But the mathematics of periodicity taken by itself
doesn't concern that.

[Michael:]
> In that case (if that is true) the notes (in the case
> of the timbre of the instrument playing the notes matching
> the harmonic series perfectly) would be 1/1 4/3 (2/1.5
> = 1.333333) and 5/3 (2.5/1.5=1.6666666666), which seems
> to correlate closely with notes C, F, A.

The proportion of the triad would be 3:4:5, which is indeed
the shortest period possible for a 5-limit triad.

So i think what you might be asking is this: which is more
consonant, a 3:4:6 (C:F:C) or a 3:4:5 (C:F:A)? (pardon me if
i'm wrong).

The 3:4:6 C:F:C is more consonant because it only involves
prime-factors 2 and 3, whereas 3:4:5 involves 2, 3, and 5;
the inclusion of 5 makes it have a much longer period.

This gets into the realm of my postulate that the perception
of accordance has two separate parameters:

1) the size of the prime-factors which are involved in the ratio;

2) the size of the exponents of those prime-factors;

and that accordance is directly proportional to the size
of both of those numbers.

IOW, if you plot the intervals on a prime-space lattice,
the most consonant intervals will be those which are most
closely-packed near the 1:1 origin-point ... but the size
of the prime-factors which form the dimensional axes of
the lattice also plays a role.

-monz
http://tonalsoft.com/tonescape.aspx
Tonescape microtonal music software

🔗martinsj013 <martinsj@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:

> As Daniel pointed out, your spelling is strange, because
> if you're talking about intervals which are just ratios,
> F:A# is a very dissonant augmented-3rd and not any kind
> of 4th at all.

In my opinion, if we're talking about JI chords we should
be using numbers (e.g. 2:3:4). Using letter names, I think
people have no option but to assume 12-ET, unless some other
context is clearly provided (and this context can easily be
lost in quoting-and-replying).

> I think what you mean by "more periodic" is that the
> overall period is shorter, correct? The periodicity and
> beating of a triad is not going to be calculated simply
> by the sum of its constituent dyad intervals, but rather
> by the closeness with which the whole composite relates
> to a portion of the harmonic series. The lower the numbers
> in the _overall_ proportion, the smaller the period.
>
> Thus, in ascending order and using just ratios, the
> overall proportions of your examples are:
>
> * a 4th plus 5th C:F:C = 3:4:6
> * two stacked 5ths C:G:D = 4:6:9
> * two stacked 4ths C:F:Bb = 9:12:16
> * the just major triad C:E:G = 4:5:6
> * the just minor triad C:Eb:G = 10:12:15

Yeah, like that. :)

-Carl

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "monz" <joemonz@...> wrote:

> Thirdly, you're invoking the timbre of the instrument as
> part of the discussion, but this doesn't have anything to
> do with periodictiy _per se_. Periodicity is a phenomenon
> which comes out of the numbers describing the pitch
> vibrations. A listener's _perception_ of consonance will
> have a lot to do with how the tuning of the pitches aligns
> (or does not align) with the instrument's timbre, and so
> an examination of beating will have to take this into
> account. But the mathematics of periodicity taken by itself
> doesn't concern that.

You can't know the period of the resultant waveform of
three pitches without making some assumptions about the
timbre.

> So i think what you might be asking is this: which is more
> consonant, a 3:4:6 (C:F:C) or a 3:4:5 (C:F:A)? (pardon me if
> i'm wrong).

I haven't followed along as well as I'd like, but I think
the original comparison was C:G:C' vs. C:F:C', which of
course would be 2:3:4 vs. 3:4:6. Anyway, I'd like to point
out that 99.44% of all people find the former chord more
consonant.

> This gets into the realm of my postulate that the perception
> of accordance has two separate parameters:
>
> 1) the size of the prime-factors which are involved in the ratio;
> 2) the size of the exponents of those prime-factors;
> and that accordance is directly proportional to the size
> of both of those numbers.

Monz, with all due respect, hasn't everything that occurred
in the last 12 years shown these postulates to be false?
Can you explain on what basis you're still postulating them?

> IOW, if you plot the intervals on a prime-space lattice,
> the most consonant intervals will be those which are most
> closely-packed near the 1:1 origin-point ... but the size
> of the prime-factors which form the dimensional axes of
> the lattice also plays a role.

Paul Erlich showed that the Tenney lattice is the only lattice
ever proposed by music theorists on which distance corresponds
to psychoacoustic consonance (and even then, still subject
to TOLERANCE). I think by "size of the prime-factors", you're
referring to the scaling of the axes. In that case, it doesn't
just play a role, it's absolutely critical to whether the
lattice reflects perception.

-Carl

🔗Petr Parízek <p.parizek@...>

🔗Michael <djtrancendance@...>

Monz,

Monz>"OK, good. You can see by the numbers exactly which
triads have the shortest periods."
For the most part, this concept makes perfect sense to me. Except, for example (comparing the two chords in my original message to Chris)
1) C:F:C = 3:4:6 vs
2) C:G:C = 2:3:4
...because, at least to my ear, C:F:C sounds smoother and seems to beat less dramatically, even though C:G:C's period is shorter.

>"Generally in the context of discussing harmony in music-theory we do
ignore the 2:1 ratio, because it is almost always considered
to be the equivalence- interval or identity-interval. But
when discussing the physics of a vibrating sound, you have
to be more careful."
Ah, ok...indeed you are right I made the "2:1 is ignored" assumption.

>"Secondly, i'm not sure i understand what you mean by "the
root notes of the triad"."
When I say root note, I mean not including overtones.

>"But the mathematics of periodicity taken by itself doesn't concern that."
Ah, ok...so overtone alignment is not an issue here.

>"So i think what you might be asking is this: which is more
consonant, a 3:4:6 (C:F:C) or a 3:4:5 (C:F:A)? (pardon me if
i'm wrong)."
Hehehe...now we're confused b/c my question involved C:F:C vs. C:G:C and before I had just added as an interesting note "to my ears even the larger chord C:F:A:C sounds more consonant than C:G:C".
But, to make it clear, my original point was to compare C:G:C (the chord I'd expect to be most consonant) to C:F:C (the chord that actually sounds most consonant to my ears and looks "cleanest/least-shaky concerning amplitude variation" in a time-domain waveform graph).

>"The 3:4:6 C:F:C is more consonant because it only involves
prime-factors 2 and 3, whereas 3:4:5 involves 2, 3, and 5;
the inclusion of 5 makes it have a much longer period."
Right, because 5 becomes the highest prime vs. 3, if I have that right.

The one thing I can't find in your postulate as I understand it...is an explanation for what happens if a chord has a shorter period but significantly more evidence of vibration to the ear (as C:G:C appears to vs. C:F:C). You can see this in the attached image/graph where C:F:C appears mirrored and the amplitude humps seem to lead up to each other while in C:G:C the humps go consistently down and then bump back up suddenly.
Perhaps "periodicity" isn't the perfect word to describe it, since something can mathematically have a shorter period but "sound" less periodic (IE seem to the ear to be beating more) in the case of C:G:C vs. C:F:C, for example. Perhaps the fact the human ear can only hear in the time domain with accuracy of about 1/10th of a second has something to do with this (IE any shortening of period to a period beyond 1/10th of a second may not matter to the human ear while beating may take over as being the leading sense of consonance in a sound). Any thoughts or loopholes you see in this logic?

-Michael

🔗Michael <djtrancendance@...>

Hi Martin,

Yes I'd say C:F:C sounds more periodic and steady than C:G:C despite C:G:C's mathematically having a shorter period mathematically. That's what makes me wonder...

________________________________
From: martinsj013 <martinsj@...>
To: tuning@yahoogroups.com
Sent: Sunday, August 9, 2009 4:10:59 PM
Subject: [tuning] Re: Periodicity and beating (and example comparing 4ths and 5ths)

--- In tuning@yahoogroups. com, "monz" <joemonz@... > wrote:
>
> Hi Michael,
>
>
> > > "Thus, in ascending order and using just ratios, the
> > > overall proportions of your examples are:
> > > * a 4th plus 5th C:F:C = 3:4:6
> > > * two stacked 5ths C:G:D = 4:6:9
> > > * two stacked 4ths C:F:Bb = 9:12:16
> > > * the just major triad C:E:G = 4:5:6
> > > * the just minor triad C:Eb:G = 10:12:15
> > > "
> >
> > Exactly, that's what I was testing.
>
> OK, good. You can see by the numbers exactly which
> triads have the shortest periods. Smaller numbers =
> shorter period. Pretty straightforward -- except that
> it gets more complicated when you start comparing
> numbers which are neighbors but have a totally different
> prime-factorization (more on this below).

So, to return to Michael's original comparison:
C:G:C = 2:3:4
C:F:C = 3:4:6

but he hears the latter as more X (can't remember the exact adjective!.. )

🔗Michael <djtrancendance@...>

Carl>"I haven't followed along as well as I'd like, but I think
the original comparison was C:G:C' vs. C:F:C', which of
course would be 2:3:4 vs. 3:4:6. Anyway, I'd like to point
out that 99.44% of all people find the former chord more
consonant."

Carl, you're right about the comparison in question being C:G:C vs. C:F:C IE
2:3:4 vs. 3:4:6 (and I'll use that ratio notation from here on in).

But...where exactly are you getting that 99.44% figure (scratches head) and using what kind of timbre (even though Monz seemed to have said timbre is irrelevant in the comparison my ears and reading of Sethares' literature both still tell me it is relevant)?

And, again, look at my graph image above...even in a purely visual sense C:G:C has more drastic transition between the large and small bumps in amplitude on the time-domain amplitude graph despite having the shorter mathematical period...which also makes me wonder.

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Carl>"I haven't followed along as well as I'd like, but I think
> the original comparison was C:G:C' vs. C:F:C', which of
> course would be 2:3:4 vs. 3:4:6. Anyway, I'd like to point
> out that 99.44% of all people find the former chord more
> consonant."
>
> Carl, you're right about the comparison in question being
> C:G:C vs. C:F:C IE 2:3:4 vs. 3:4:6 (and I'll use that ratio
> notation from here on in).
>
> But...where exactly are you getting that 99.44% figure
> (scratches head)

From Ivory soap, of course!

> and using what kind of timbre (even though Monz seemed to have
> said timbre is irrelevant in the comparison my ears and reading
> of Sethares' literature both still tell me it is relevant)?

The timbre's important, but in the vast majority of timbres
in, say, a General MIDI synth, what I said is true, in JI or
in 12-ET. Are you saying 3:4:6 is more consonant? What
timbre are *you* using?

> And, again, look at my graph image above...even in a purely
> visual sense C:G:C has more drastic transition between the
> large and small bumps in amplitude on the time-domain amplitude
> graph despite having the shorter mathematical period...which
> also makes me wonder.

No sure exactly what I'm looking at there, but such visual
comparisons are almost never informative of anything.

-Carl

🔗Michael <djtrancendance@...>

>"Are you saying 3:4:6 is more consonant? What timbre are *you* using?"
Yes I am...at least with pure sine waves (the timbre I am using in the test).

>"No sure exactly what I'm looking at there, but such visual comparisons are almost never informative of anything."

Why do you say that? The reason I'm using visuals is that one >very< easy way to determine how long the period (with even the simplest verbal definition)...is visually by looking for when the waveform repeats.

Also from a producer's point of view (mastering, compression, etc.) you can look at a visual graph and get a good sense how well mixed a file is. IE if there are lots of sudden spikes (very sudden loud spots followed by soft spots with little lead/fade-in) you can safely assume the instruments either need more compression or to be tuned differently so frequencies don't duplicate and make sudden loud areas. As anyone who produces the stuff can tell you, this is incredibly important in things like dance music where production quality standards are very high...and not easy to do well in a song with many instruments.
The point being that you can either use compression and/or good tuning habits to help you make songs that sound both louder and clearer. And since hard compression often sounds un-natural and applies to some genres (IE pop and techno) more than others (classical and rock)...I figured it would be interesting to look into how much optimization for loudness and clarity (along with consonance) could be achieved by tuning alone.

For the record, lately I've been tuning all my drums to the chord C5 F5 A5 C6 (can't think of the ratios for that chord off the top of my head, feel free to help me out)...and I've noticed I no longer need to worry about compression and aliasing and can still get the same type of loudness I'd expect from a highly compressed master. So, in conclusion, this brings up the question in what ways can tuning be used to lessen the need for un-natural sounding effects (IE ridiculous amounts of compression) in music production?

-Michael

________________________________
From: Carl Lumma <carl@...>
To: tuning@yahoogroups.com
Sent: Sunday, August 9, 2009 6:22:23 PM
Subject: [tuning] Re: Periodicity and beating (and example comparing 4ths and 5ths)

--- In tuning@yahoogroups. com, Michael <djtrancendance@ ...> wrote:

From Ivory soap, of course!

> and using what kind of timbre (even though Monz seemed to have
> said timbre is irrelevant in the comparison my ears and reading
> of Sethares' literature both still tell me it is relevant)?

The timbre's important, but in the vast majority of timbres
in, say, a General MIDI synth, what I said is true, in JI or
in 12-ET. Are you saying 3:4:6 is more consonant? What
timbre are *you* using?

No sure exactly what I'm looking at there, but such visual
comparisons are almost never informative of anything.

-Carl

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> >"Are you saying 3:4:6 is more consonant? What timbre are *you*
> > using?"
>
> Yes I am...at least with pure sine waves (the timbre I am
> using in the test).

You should usually do these kinds of tests with multiple
timbres.

> >"No sure exactly what I'm looking at there, but such visual
> >comparisons are almost never informative of anything."
>
> Why do you say that?

Because there are fundamental differences between how the
eyes and ears work, and unless you're very careful you're
unlikely to show anything meaningful. But I shouldn't be
the one explaining this, YOU should be the one explaining
exactly what it is your visualization shows and exactly
why it ought to correspond to something we can hear.

> The point being that you can either use compression and/or
> good tuning habits to help you make songs that sound both
> louder and clearer.

Huh?? What does this have to do with tuning?

-Carl

🔗Michael <djtrancendance@...>

Carl> "You should usually do these kinds of tests with multiple timbres."
I will...you're right though I wouldn't be at all surprised if the test failed with overtones, especially considering the second overtone of 3/1 (1.5 octaves) is louder than the fourth.
The flip side is...I can't see any reason why electronics/programming can't be used to fit/align the overtones to the scale IE use an FFT to align all partials to one of the following: C5 F5 A5 C6 F6 A6 C7 F7 A7 etc. So it couldn't work for directly acoustic instruments (IE ones not run through a "stomp box") that performs the overtone alignments.

>"Because there are fundamental differences between how the eyes and ears work, and unless you're very careful you're unlikely to show anything meaningful."
This sounds like a generalization to me and although I am listening I'm not convinced yet that what you're saying indicated a loophole in my choice of using graphs (BTW, of course, graphs such as spectrograms and even plain old time-domain graph are used extensively on music production to gauge things like how much EQ/compression/etc. should ideally be used: they certainly can be used to help shape sound to fit the ear in some cases).
I started by saying the period can very easily be found visually and that this discussion focuses on periodicity; and so far as I can tell you never actually pinpointed why visual finding of the period can not work. I agree the ears and eyes work differently (IE the eye has no "critical band" or "virtual pitch"...but I still don't see how this effects periodicity (the main topic in question).

-Michael

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

Carl>"YOU should be the one explaining

>exactly what it is your visualization shows and exactly
>why it ought to correspond to something we can hear.
>What's your response?"

At least with pure sine waves...3:4:6 (C:F:C) simply sounds smoother in the same way a drum beat with a slight cymbal tap "ghost note" slightly before a loud drum in a break-beat sounds smoother than a sudden hit without such a lead-in. Again all this periodicity experimentation seems to have implications to audio production in general and not just tuning.

Also, notice how in the graph of the 3:4:6 chord the peaks work their way down over 3 peaks and then up over 2 peaks while the 2:3:4 (C:G:C) chord's peaks work their way down over 3 peaks and then suddenly up all the way on the 4th peak >even< though, of course, C:G:C has the shorter period (4 total peaks vs. 5). How this translates into sound is that C:G:C sounds more "shaky" than C:F:C despite having a shorter period (sudden loud gains in sound after a period of relatively soft amplitude increases the "shakiness"). Also, I strongly suspect the shakiness is interpreted by the brain as beating.

*********************************************
The flip side (not explained by the graph) is that the C:G:C indeed sounds happier than C:F:C (and more resolved if you consider the emotion of happiness to more-or-less mean resolved) and I figure some people may equate happiness with consonance to a certain extent. That and the fact culture tends to emphasize 5ths of 4ths and we may well be somewhat trained to favor 5ths for that reason.

-Michael

🔗rick_ballan <rick_ballan@...>

Oh, and just for the record, I play guitar to my 3 yr old niece all the time and she loves it. And this was the case from the word go, so I didn't 'condition' her, which would have been your next argument. I've also played certain 'alternate tuning' pieces from this list and...well, what can I say? Has she been 'biased' by 12 Tet or does she 'just know' when something's out of tune? As I said, basing a tuning system where the frequency intervals are PI fails to recognise that it is an irrational number and therefore its resultant wave is aperiodic and highly dissonant. If you want to check this on a wave graph, go right ahead. PI comes in as a conversion of frequency into angular measures of radians like y(t) = Acos2PI*440Hz*t, not Acos2(PI^2)*t.

What's good enough for the goose is good enough for the gander.
>

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> >"Hopefully you've not been using a tuner and tuning your axe to 12 tet. "
> I think I get what you're saying: that the ear is very sensitive about
> the accuracy of 4th and 5th intervals...to the point your ear would do a
> better job finding them than a 12tet-based tuner. Is that what you are
> saying?
>
> Yes, I think tuning to perfect intervals is much better - something my
> classical guitar teacher showed me. Before then I tuned via the 5th and 4th
> fret which is 12 tet of course. Tuning a guitar with the open strings tuned
> to 12 tet sounds noticeably sour compared tuning to perfect intervals. My
> daughter (who apparently has great ears) refuses to play on a guitar with
> the open strings tuned to 12 TET. I need to throw a guitar tuned to Lucy
> guitar open string specs at her one of these days.
>
Like the 'chimpanzee' experiment Charles posted a week back, here again is the Hollywood myth of the child or animal as tabla rasi, as if they are like 'pristine rain forests' which have yet to be tainted by the prejudices of the adult world and are therefore a source of wisdom. But this says more about the adults than the children. The open strings of a guitar are not meant to be played that way. It does in fact take years of study and practice to become a competent guitarist, so your 'test' is hardly musical or even scientific for that matter.

Rick

🔗Chris Vaisvil <chrisvaisvil@...>

To whom are you addressing this Rick?

I know my daughter != your niece - everyone is an individual.

And what are you saying? That you tune to 12 tet?

On Tue, Aug 11, 2009 at 1:18 AM, rick_ballan <rick_ballan@...>wrote:

>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > >"Hopefully you've not been using a tuner and tuning your axe to 12 tet.
> "
> > I think I get what you're saying: that the ear is very sensitive about
> > the accuracy of 4th and 5th intervals...to the point your ear would do a
> > better job finding them than a 12tet-based tuner. Is that what you are
> > saying?
> >
> > Yes, I think tuning to perfect intervals is much better - something my
> > classical guitar teacher showed me. Before then I tuned via the 5th and
> 4th
> > fret which is 12 tet of course. Tuning a guitar with the open strings
> tuned
> > to 12 tet sounds noticeably sour compared tuning to perfect intervals. My
> > daughter (who apparently has great ears) refuses to play on a guitar with
> > the open strings tuned to 12 TET. I need to throw a guitar tuned to Lucy
> > guitar open string specs at her one of these days.
>
> Oh, and just for the record, I play guitar to my 3 yr old niece all the
> time and she loves it. And this was the case from the word go, so I didn't
> 'condition' her, which would have been your next argument. I've also played
> certain 'alternate tuning' pieces from this list and...well, what can I say?
> Has she been 'biased' by 12 Tet or does she 'just know' when something's out
> of tune? As I said, basing a tuning system where the frequency intervals are
> PI fails to recognise that it is an irrational number and therefore its
> resultant wave is aperiodic and highly dissonant. If you want to check this
> on a wave graph, go right ahead. PI comes in as a conversion of frequency
> into angular measures of radians like y(t) = Acos2PI*440Hz*t, not
> Acos2(PI^2)*t.
>
> What's good enough for the goose is good enough for the gander.
> >
>
>
>

🔗Michael <djtrancendance@...>

>"Has she been 'biased' by 12 Tet or does she 'just know' when something's out of tune?"

More and more I'm starting to think the true answer has to do with the questions "does the waveform repeat as periodic within 1/10th of a second" and "how much does it beat"?
Take the fractions below (all x/6 u-tonal) that form a chord
1/1
7/6 (1.166666666)
4/3
5/3
2/1

....and play them as a chord with a sine wave and you get something that sounds very very smooth and also looks very periodic and very "easy to find loop points for" when loaded into a sample editor.
Even weirder, if you play extra notes an octave up based on the scale above IE 7/6 * 2/1 or 4/3 * 2/1 your ear will ignore them (or at least for my ears...I can't hear the extra tones!). As Carl suggested I also plan to re-test this with non-sine-wave instruments.

Also, the octave, 4th and 5th are among the purest intervals in 12TET (so it makes sense many people would think 12TET is periodic, at least when the focus is on those intervals).

The weird thing is I've noticed certain fractions, such as 6/5 or 1.2 (substituting for 1.166666) make waveforms that are so close to periodic (and yet still minimize beating to a huge degree) that my mind can hardly hear the difference. So it seems obvious to me there are ways to "fudge absolute periodicity" that go beyond u-tonal parts of the harmonic series and, perhaps for someone clever enough to make irrational wave forms that cancel each other out at the right places to form near rational ones: beyond the harmonic series altogether.

-Michael

🔗rick_ballan <rick_ballan@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
>
> The weird thing is I've noticed certain fractions, such as 6/5 or 1.2 (substituting for 1.166666) make waveforms that are so close to periodic (and yet still minimize beating to a huge degree) that my mind can hardly hear the difference. So it seems obvious to me there are ways to "fudge absolute periodicity" that go beyond u-tonal parts of the harmonic series and, perhaps for someone clever enough to make irrational wave forms that cancel each other out at the right places to form near rational ones: beyond the harmonic series altogether.
>
> -Michael
>
Hi Mike,

just for the record, the set of all fractions like 6/5 and 81/64 is called the rational numbers, and all other numbers, for all intents and purposes here, are called irrational, meaning 'non' rational. Technically speaking, all rationals are periodic. It's just that for higher harmonics the repeat time is very large compared to the period of the component frequencies. (For example, if we take 440Hz and 445Hz then these are the 88th and 89th harmonics of 5Hz, and (1/5)sec is very large in comparison). You said something to this effect when you noticed they must be smaller than (1/10)th sec. Since rationals = periodic, it follows that irrationals are aperiodic by definition.

Rick

🔗Kraig Grady <kraiggrady@...>

🔗Mike Battaglia <battaglia01@...>

Hi Kraig,

This is mathematically impossible unless the 440 was in the signal to
begin with. Any low pass filtering you'd be using is linear in nature,
meaning no frequencies can be added in the process. Can you please
link me to the specific recording of Rick's that you're talking about,
so I can perform my own independent analysis of the signal?

-Mike

On Thu, Aug 13, 2009 at 8:04 AM, Kraig Grady<kraiggrady@...> wrote:
>
>
> i chime in because Rick and I have been talking about this offlist.
> I only want to add to the discussion the result of this experiment that
> shows that the 440 _could not be virtual_ in this case.
> I took Ricks recording, filtered out all the generating pitches with a
> low pass and what remained was 440.
> http://anaphoria.com/440withfilter.mp3
> --
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria.com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>
>
> ',',',',',',',',',',',',',',',',',',',',',',',',',',',',',
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
>

🔗Michael <djtrancendance@...>

Bizarre...
The only time I believe a low-pass can appear to create frequencies in where either

A) The resonance area makes a previously masked frequency peak/partial (which had been masked nearby much louder frequency) loud enough to hear relative to partials around it
OR
B) A masking frequency itself gets cut down in amplitude by a filter to the extent other frequency peaks previously masked by it can begin to be heard.

This would give the auditory illusion a frequency is being created when all it is in reality...is a frequency pushing over an envelope of silence/masking created by nearby frequencies.
When I say masking...I mean the same phenomena used to avoid storing information for frequencies the ear masks because it is too near other frequencies.

-Michael

________________________________
From: Mike Battaglia <battaglia01@...>
To: tuning@yahoogroups.com
Sent: Thursday, August 13, 2009 3:37:15 PM
Subject: Re: [tuning] Re: Periodicity and beating (and example comparing 4ths and 5ths)

Hi Kraig,

-Mike

On Thu, Aug 13, 2009 at 8:04 AM, Kraig Grady<kraiggrady@anaphori a.com> wrote:
>
>
> i chime in because Rick and I have been talking about this offlist.
> I only want to add to the discussion the result of this experiment that
> shows that the 440 _could not be virtual_ in this case.
> I took Ricks recording, filtered out all the generating pitches with a
> low pass and what remained was 440.
> http://anaphoria. com/440withfilte r.mp3
> --
>
> /^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
> Mesotonal Music from:
> _'''''''_ ^North/Western Hemisphere:
> North American Embassy of Anaphoria Island <http://anaphoria. com/>
>
> _'''''''_ ^South/Eastern Hemisphere:
> Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>
>
> ',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,
>
> a momentary antenna as i turn to water
> this evaporates - an island once again
>
>

🔗Mike Battaglia <battaglia01@...>

Allow me to also point out the obvious: what meaning does a 440 Hz low
pass filter even HAVE if we're going to allow the phrase "440 Hz"
there refer to complex tones?

-Mike

some new music

🔗Aaron Johnson <aaron@...>

🔗Dante Rosati <danterosati@...>

🔗Ozan Yarman <ozanyarman@...>

🔗Aaron Krister Johnson <aaron@...>

🔗Michael <djtrancendance@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Aaron Krister Johnson <aaron@...>

🔗Aaron Krister Johnson <aaron@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Charles Lucy <lucy@...>

🔗Marcel de Velde <m.develde@...>

🔗Marcel de Velde <m.develde@...>

🔗Michael <djtrancendance@...>

🔗Chris <chrisvaisvil@...>

🔗Michael <djtrancendance@...>

🔗Daniel Forro <dan.for@...>

🔗Michael <djtrancendance@...>

🔗monz <joemonz@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗monz <joemonz@...>

🔗Michael <djtrancendance@...>

🔗monz <joemonz@...>

🔗martinsj013 <martinsj@...>

🔗Carl Lumma <carl@...>

🔗Carl Lumma <carl@...>

🔗Petr Parízek <p.parizek@...>

🔗Michael <djtrancendance@...>

🔗Michael <djtrancendance@...>

🔗Michael <djtrancendance@...>

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

🔗rick_ballan <rick_ballan@...>

🔗rick_ballan <rick_ballan@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Michael <djtrancendance@...>

🔗rick_ballan <rick_ballan@...>

🔗Kraig Grady <kraiggrady@...>

🔗Mike Battaglia <battaglia01@...>

🔗Michael <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>