Yahoo Tuning Groups Ultimate Backup tuning What is the Most "Out-Of-Tune" or "Dissonant" Interval in Equal Temperament??

Hi all!!

This question may SEEM very basic, but I'd like to see what everyone
ACTUALLY believes is the most "out-of tune" sounding (or "dissonant")
interval in Equal Temperament.

There are obviously both opinions that are going to be involved here
as well as facts.

Obviously, certain people are going to hear different intervals
differently. That is where the "opinions" come in.

But what about the facts, meaning the mathematical "certainties" that
answer the question for us, but where are our aural senses (and thus
our individual "opinions") answer the question quite differently.

I'd just like to know, once and for all, what each one of you think is
the most "out-of-tune" sounding (or "dissonant") interval in the Equal
Temperament system...

Thanks for your answers in advance,

Frank Wilson, Ph.D (Musicology)

🔗caleb morgan <calebmrgn@...>

my answer:

>minor 9th, almost any register.

>then minor 2cnd, ditto.

>then tritone.

This is because I have a jazz background, even went to Berklee, and minor 9ths are rare-ish in anything but "dominant function" chords. Unless you're Bill Frisell, that is, in which case you play a guitar-voicing like:

G#2,C#3,E3,A3 with some slithering pitch-bend, and it sounds as glorious as America itself, with Obama as leader.

But, widely spaced intervals or the same intervals with some extra pitches added, sound different to me.

To me, the 012 (any combination with two adjacent minor seconds) is where my ear starts to say "not tonal" and "really dissonant" and even "Do you really want to write that?" but even there, you can have
something like: C,Db,Eb,F,G,Ab,B, which if set up properly in a musical context, won't sound that tense.

Then, as they never tired of insisting at NEC--because they were unregenerate modernists and structuralists--context makes a big difference. In a context of nothing but minor 9ths, a C-E-G triad would sound surprising. I simply wouldn't use the word "dissonant" to describe that surprise. Rather: consonant, but surprising.

caleb

On Jan 21, 2009, at 11:48 AM, micro_piano wrote:

> Hi all!!
>
> This question may SEEM very basic, but I'd like to see what everyone
> ACTUALLY believes is the most "out-of tune" sounding (or "dissonant")
> interval in Equal Temperament.
>
> There are obviously both opinions that are going to be involved here
> as well as facts.
>
> Obviously, certain people are going to hear different intervals
> differently. That is where the "opinions" come in.
>
> But what about the facts, meaning the mathematical "certainties" that
> answer the question for us, but where are our aural senses (and thus
> our individual "opinions") answer the question quite differently.
>
> I'd just like to know, once and for all, what each one of you think is
> the most "out-of-tune" sounding (or "dissonant") interval in the Equal
> Temperament system...
>
> Thanks for your answers in advance,
>
> Frank Wilson, Ph.D (Musicology)
>
>
>

🔗Mike Battaglia <battaglia01@...>

On Wed, Jan 21, 2009 at 1:00 PM, caleb morgan <calebmrgn@...> wrote:
> my answer:
>>minor 9th, almost any register.
>>then minor 2cnd, ditto.
>>then tritone.
> This is because I have a jazz background, even went to Berklee, and minor
> 9ths are rare-ish in anything but "dominant function" chords. Unless you're
> Bill Frisell, that is, in which case you play a guitar-voicing like:
> G#2,C#3,E3,A3 with some slithering pitch-bend, and it sounds as glorious as
> America itself, with Obama as leader.
>
> But, widely spaced intervals or the same intervals with some extra pitches
> added, sound different to me.
> To me, the 012 (any combination with two adjacent minor seconds) is where my
> ear starts to say "not tonal" and "really dissonant" and even "Do you really
> want to write that?" but even there, you can have
> something like: C,Db,Eb,F,G,Ab,B, which if set up properly in a musical
> context, won't sound that tense.
> Then, as they never tired of insisting at NEC--because they were
> unregenerate modernists and structuralists--context makes a big difference.
> In a context of nothing but minor 9ths, a C-E-G triad would sound
> surprising. I simply wouldn't use the word "dissonant" to describe that
> surprise. Rather: consonant, but surprising.
> caleb

I like the way you put that. I'm at Univ. of Miami now studying jazz
and the "rule" around here is that b9's are only "allowed" over the
root in jazz harmony. So C E G Bb Db is ok, and C E G Bb D F is not,
since that E-F b9 exists over a note that isn't the root. It's the
same as the Berklee concept of the "avoid note", I think.

I was always a bit unsatisfied with this, as b9's exist in the
overtone series and don't sound quite so bad, so I came up with a few
chords that manage to sound good despite this, voiced from bottom to
top:

D F B E A D F#
D A F# B E A#
A G C# E# G#

To my ears, they sound functional. Consonant, but complex, rather than
"that guy messed his voicings up." So the rule I'm at now is that it
seems that if you have a "diatonic" b9 in there, it doesn't sound too
hot. If you have a "chromatic" b9, it does. And it's hard to find the
distinction in 12-equal, but it seems to have to do with implied
harmonic relationships among the notes.

The thing I don't understand: phrygian mode uses the diatonic b9 all
of the time, but it certainly works to create a mood, sounds
functional, 'consonant', etc. Nonetheless, if you play a chord like C
E G Bb D F, that b9 in there is going to be pretty hard to swallow.
Why?

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Claudio Di Veroli <dvc@...>

I am happy to contribute - with some tongue in cheek - to this interesting
question.
My answer will certainly not be a surprise to our "temperati" members:

"The MAJOR THIRD and then the MINOR SIXTH!"

PROOF:
[Please note: the detail below is just a simple exercise addressed to
newcomers to tuning. My sincere apologies to many distinguished members of
this forum which - unlike myself - are deeply knowledgeable in musical
acoustics and do not need to be reminded these elementary matters.]

A. Most answers have interpreted the question literally: "Given Equal
Temperament, which interval is more dissonant?".
I prefer to understand it as "Given consonant intervals, which one is heard
most out of tune in E.T.?".
The second interpretation thus goes beyond absolute perception and relates
rather to how well does E.T. approximate consonant intervals.
B. Quite obviously, if an interval is heard as dissonant even if pure, its
E.T. approximation will be just a bit more dissonant, so the mistuning is
not really relevant: this point is found in ancient treatises.
C. Thus the mistuning of E.T. is only relevant to consonant intervals. For
simplicity let us limit ourselves to intervals not greater than the octave.
D. There has been agreement since Renaissance times -this forum included-
that mathematics and experience coincide in considering consonant those
musical intervals ratios involving integers not larger than 5.
E. The borderline case is the Minor Third 6:5, which however it is not
perceived as really consonant due to the beats caused by its proximity with
the Small Minor Third 7:6. This is why, from Baroque times on, most
theoreticians lost interest forever in how well or badly a temperament tunes
minor thirds.
F. Thus we need to concentrate in intervals involving numbers not greater
than 5. Let us see each one except the trivial unison 1:1.
G. 2:1 is the octave, tuned pure in E.T. (except for strecthing etc.), no
issue here.
H. 3:2 is the fifth, mistuned by 2 Cents in E.T. By comparison with most
historical temperaments this is a small amount and E.T. is historically the
temperament with the best fifths.
I. 4:3 is the fourth, complementary with the fifth within the pure octave,
thus as good as the fifths in E.T.
J. 5:4 is the major third. After Pythagorean (which uses major thirds as
dissonances), E.T. is the worst historical temperament for the "average" or
"most usually played" major thirds, with 13.7 Cents of mistuning for each
one. Terrible!
K. 5:3 is the major sixth. Slightly less consonant than the major third, but
deviated by 15.7 Cents in E.T., thus also badly affected.
There are no further consonant intervals within the octave. q.e.d.

Please be kind with the rebuttals ... :-)

Kind regards,
Claudio

_____

From: tuning@yahoogroups.com [mailto:tuning@yahoogroups.com] On Behalf Of
Carl Lumma
Sent: 21 January 2009 19:12
To: tuning@yahoogroups.com
Subject: [tuning] Re: What is the Most "Out-Of-Tune" or "Dissonant" Interval
in Equal Temperament??

--- In tuning@yahoogroups. <mailto:tuning%40yahoogroups.com> com,
"micro_piano" <frankw802@...> wrote:
>
> Hi all!!
>
> This question may SEEM very basic, but I'd like to see what
> everyone ACTUALLY believes is the most "out-of tune" sounding
> (or "dissonant") interval in Equal Temperament.

Easy! Minor 2nd!

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

A minor 2nd.... maybe.

I don't know if the concept of dissonant, and especially out of tune,
applies anymore, especially in this particular group of composers/listeners.

All intervals are equally useful, just in different ways. Western music
harmony evolved to hide dissonance, especially the 7th. In our age this
interval is accepted without special treatment. Harmony often is just color.

A more proper question would be most "tense" and again minor 2nd...

Chris

On Wed, Jan 21, 2009 at 11:48 AM, micro_piano <frankw802@...> wrote:

🔗djtrancendance@...

This message below from Claudio answers what I believe to be part of the question very well IE which intervals in equal temperament deviate most from their just-interval equivalents.

    One thing I have noticed...is that both closeness and periodicity come into play in dissonance and that even the purest/most-periodic intervals have to pay their dues to being "destroyed" beyond a point. And, yes, that even appears to apply to the "perfect" harmonic series itself.

   Take a scale generated from a root note (keep on multiplying each note by the last note)
     *9/8 *10/9 *11/10 *12/11 *9/8 *10/9 *11/10
And now compare that to the harmonic series equivalent
     *9/8 *10/9 *11/10 *12/11 *13/12 *14/13
*15/14

At least to my ears, the first scale actually sounds more pure than the harmonic series!!!
Why? My guess is that, at a certain point, avoid beating generated by tones which are too close becomes more of a concern than maintaining perfect periodicity.

--- On Wed, 1/21/09, Claudio Di Veroli <dvc@...> wrote:

From: Claudio Di Veroli <dvc@braybaroque.ie>
Subject: RE: [tuning] Re: What is the Most "Out-Of-Tune" or "Dissonant" Interval in Equal Temperament??
To: tuning@yahoogroups.com
Date: Wednesday, January 21, 2009, 1:42 PM

I am happy to
contribute - with some tongue in cheek - to this interesting question.
My
answer will certainly not be a surprise to our "temperati"
members:

"The MAJOR
THIRD and then the MINOR
SIXTH!"

PROOF:
[Please note: the detail below is just a
simple exercise addressed to newcomers to tuning. My sincere apologies to
many distinguished members of this forum which - unlike myself - are deeply
knowledgeable in musical acoustics and do not need to be reminded these
elementary matters.]

A. Most
answers have interpreted the question literally: "Given Equal Temperament,
which interval is more dissonant?".
I prefer to understand it as "Given consonant
intervals, which one is heard most out of tune in E.T.?".

The second interpretation thus goes beyond
absolute perception and relates rather to how well does E.T. approximate
consonant intervals.
B. Quite obviously,
if an interval is heard as dissonant even if pure, its E.T. approximation
will be just a bit more dissonant, so the
mistuning is not really relevant: this
point is found in ancient treatises.
C. Thus the mistuning of E.T. is only relevant
to consonant intervals. For simplicity let us limit ourselves to intervals not
greater than the octave.
D. There has
been agreement since Renaissance times -this forum included- that mathematics
and experience coincide in considering consonant those musical
intervals ratios involving
integers not larger than 5.
E. The borderline case is the Minor Third
6:5, which however it is not perceived as
really consonant due to the beats caused by its proximity with the Small Minor
Third 7:6. This is why, from Baroque times on, most theoreticians lost interest
forever in how well or badly a temperament tunes minor thirds.
F. Thus we need to concentrate in intervals
involving numbers not greater than 5. Let us see each one except the trivial
unison 1:1.
G. 2:1 is the octave, tuned pure in E.T. (except
for strecthing etc.), no issue here.
H.
3:2 is the fifth, mistuned by 2 Cents in E.T. By comparison with most historical
temperaments this is a small amount and E.T. is historically the temperament with the best fifths.
I. 4:3 is the fourth, complementary with the
fifth within the pure octave, thus as good as the fifths in E.T.
J. 5:4 is the major third. After Pythagorean
(which uses major thirds as dissonances) , E.T. is the worst historical
temperament for the "average" or
"most usually played" major thirds, with 13.7 Cents of mistuning for each
one. Terrible!
K. 5:3 is the major sixth. Slightly less consonant than the major third,
but deviated by 15.7 Cents in E.T., thus also
badly affected.
There are no further consonant intervals within the
octave. q.e.d.

Please be kind with the rebuttals ...
:-)

Kind
regards,
Claudio

From: tuning@yahoogroups. com
[mailto:tuning@ yahoogroups. com] On Behalf Of Carl Lumma
Sent:
21 January 2009 19:12
To: tuning@yahoogroups. com
Subject:
[tuning] Re: What is the Most "Out-Of-Tune" or "Dissonant" Interval in Equal
Temperament? ?

--- In tuning@yahoogroups. com,
"micro_piano" <frankw802@. ..> wrote:
>
> Hi
all!!
>
> This question may SEEM very basic, but I'd like to see
what
> everyone ACTUALLY believes is the most "out-of tune"
sounding
> (or "dissonant") interval in Equal Temperament.

Easy!
Minor
2nd!

-Carl

🔗Daniel Forró <dan.for@...>

Answers can be found if there's some exact and universal definition what "out-of-tune/in tune" and "consonance/dissonance" means. Which I doubt as there are many possible attitudes to this, and lot of this depends on musical context. It's possible to create beautifully sounding music from the most "ugly" intervals and mathematically constructed chord structures, and horrifying one from chords created from harmonics series.

Daniel Forro

On 22 Jan 2009, at 1:48 AM, micro_piano wrote:

🔗massimilianolabardi <labardi@...>

--- In tuning@yahoogroups.com, "micro_piano" <frankw802@...> wrote:
>
> Hi all!!
>
> This question may SEEM very basic, but I'd like to see what
everyone
> ACTUALLY believes is the most "out-of tune" sounding
(or "dissonant")
> interval in Equal Temperament.
>
> There are obviously both opinions that are going to be involved
here
> as well as facts.
>
> Obviously, certain people are going to hear different intervals
> differently. That is where the "opinions" come in.
>
> But what about the facts, meaning the mathematical "certainties"
that
> answer the question for us, but where are our aural senses (and
thus
> our individual "opinions") answer the question quite differently.
>
> I'd just like to know, once and for all, what each one of you
think is
> the most "out-of-tune" sounding (or "dissonant") interval in the
Equal
> Temperament system...
>
> Thanks for your answers in advance,
>
> Frank Wilson, Ph.D (Musicology)
>

I would reply to this question based on Sethares' calculation of
dissonance curves. In my opinion, dissonance of equal-tempered
intervals should be compared with dissonance of the corresponding
just intonation intervals. Dissonance of intervals, however, depends
on the harmonic content of the considered sounds/instruments. So
some intervals could be more or less dissonant depending on which
instrument one is playing.

Briefly, as most of you know (and please correct me if I say
something wrong) Sethares' formula for dissonance (as I learn it
from his paper on J. Acoust. Soc. Am. 94, 1218 (1993)) is based on a
dissonance function for a pure tone dyad from Plomp&Levelt's
experiments and exploiting the concept of critical band. Given a
harmonic spectrum, the two "real" sounds of the dyad
are "convoluted" (in the way described in the cited paper) and a
dissonance value is obtained for each interval, to obtain a
dissonance plot. Typically, such plot has local minima at just
intervals: the lower the value, the lower the dissonance.

Given a harmonic spectrum, let the dissonance of the ET interval be
D_et and the one of the just interval D_ji. In my opinion, the
higher/lower dissonance of the ET case (relative to the JI case) is
expressed by the value D_r = D_et/Dji. D_r will be typically > 1.

In this way, dissonance does not depend only on the the amount
of "detuning" of tempered intervals from just ones, but also on how
much the just interval was consonant/dissonant. To give an example:
if I play a 2nd interval, it will be rather dissonant in both ji and
et. This is because the difference between the dissonance curve
values at the just and tempered value is not much, and also, it does
not depend too much on the detuning. Instead, in the case of the 5th
interval, if you detune it a little you get a strong variation of
the dissonance function, because you are detuning close to a high-
slope (derivative) part of the dissonance curve. I have not made any
calculation yet but I bet that 2 cent detuning of the 5th gives more
dissonance change than a 10 cent detuning of a 2nd....

All this of course depends on the spectrum you are using to plot
your dissonance curve. I take this occasion to make a remark: I have
tried to plot dissonance curves "a la Sethares" by using recorded
spectra of some instruments I have sampled myself (giutar, piano,
violin). It seems to me that the assumption made to plot dissonance
curves in Sethares paper is a lot optimistic (he assumes a
progressive amplitude fall rate of 0.88 for each harmonic). In this
way, many local minima of the dissonance curves can be seen, at
about all degrees of the diatonic just intonation scale. Instead, by
using my spectra, I practically don't see any dip in the dissonance
curve except 5th and to a lesser extent 4th (and of course unison
and octave!) being the rest of the curve practically flat. So my
final conclusion is that the most dissonant "detuning" from ji to et
intervals is the one of the fifth!

Comments are very welcome!

Max

🔗caleb morgan <calebmrgn@...>

I've come to the opinion that 12-tet is only capable of suggesting 5-limit chains.

So, you can almost guide the ear to hear 7-ratios, but not quite.

11-ratios and 13-ratios are just non-existent in 12-tet.

they are more subtle, and require some accuracy (+-5 cents, maybe?) to be heard as themselves.

C-G-E-F#-B-D#

a cool chord, B triad over C.

D# is definitely #2 (or #9) and the scale is C Lydian #3, or E harmonic minor.

caleb

On Jan 21, 2009, at 1:36 PM, Mike Battaglia wrote:

> To make another point about it being context sensitive, this chord,
> voiced from top to bottom:
>
> C G E F# B D#
>
> That D# on top is extremely dissonant (or, as I like to think of it,
> "consonant with complexity") - but while C-D# is an equal-tempered
> minor 3rd, I tend to hear that note on top as being far more
> dissonant. I hear it as fulfilling the role of being a major third
> above the B, which is a major 7th above C. To my ears, it seems that
> every equal tempered interval (or JI interval in general) falls into a
> sort of "gray area" where the other notes in a chord can influence how
> that specific interval is heard, so the question might only make sense
> in the context of dyads alone.
>
> The question: How do you guide one's ear to hear 13:8 in 12-tet? :)
>
> -Mike
>
>

🔗caleb morgan <calebmrgn@...>

rule of thumb: the more dissonant, the more complex the chord, the more time you need to give it, the more space you need to give it to sound? The bigger the voicing, the slower the motion? (Big Bottom)

Mike's examples, with caleb's comments.

D F B E A D F# --lovely

maybe: F# is supported as 5th partial of D upper-structure triad. Lower F is part of D minor consonance, and familar jazz F-B-E-A voicing (G7, F lydian, E phrygian, etc.)

D A F# B E A# --high A# here is relatively unsupported, except as 5th par (down 1 oct) of F#

this one sounds a little stranger to me, but possibly hearable as B minor, with the familiar variability of the 7th scale degree: It has A b7 and A# "raised" 7th scale degree.

A G C# E# G# --your coolest, freshest example. sounds great. I should use this one in a piece, sometime!

Obviously you've got a melding of two structures--A7 altered, with a C# upper-structure triad. The C# upper-s-t is "bright" because C# is an overtone of A.
But it also can be heard as an extension of an A altered scale: A,Bb,C,Db,Eb,F,G with a "b15" (?!) in which the upper Ab is supported as a 3rd partial of Db.

In other words, in an A "altered" (Locrian b4) scale, the real outrigger, the note that doesn't "belong" is the A. The root.

Go figure.

Music is a strange and wonderful thing.

On Jan 21, 2009, at 1:23 PM, Mike Battaglia wrote:

> On Wed, Jan 21, 2009 at 1:00 PM, caleb morgan <calebmrgn@...> > wrote:
> > my answer:
> >>minor 9th, almost any register.
> >>then minor 2cnd, ditto.
> >>then tritone.
> > This is because I have a jazz background, even went to Berklee, > and minor
> > 9ths are rare-ish in anything but "dominant function" chords. > Unless you're
> > Bill Frisell, that is, in which case you play a guitar-voicing like:
> > G#2,C#3,E3,A3 with some slithering pitch-bend, and it sounds as > glorious as
> > America itself, with Obama as leader.
> >
> > But, widely spaced intervals or the same intervals with some extra > pitches
> > added, sound different to me.
> > To me, the 012 (any combination with two adjacent minor seconds) > is where my
> > ear starts to say "not tonal" and "really dissonant" and even "Do > you really
> > want to write that?" but even there, you can have
> > something like: C,Db,Eb,F,G,Ab,B, which if set up properly in a > musical
> > context, won't sound that tense.
> > Then, as they never tired of insisting at NEC--because they were
> > unregenerate modernists and structuralists--context makes a big > difference.
> > In a context of nothing but minor 9ths, a C-E-G triad would sound
> > surprising. I simply wouldn't use the word "dissonant" to describe > that
> > surprise. Rather: consonant, but surprising.
> > caleb
>
> I like the way you put that. I'm at Univ. of Miami now studying jazz
> and the "rule" around here is that b9's are only "allowed" over the
> root in jazz harmony. So C E G Bb Db is ok, and C E G Bb D F is not,
> since that E-F b9 exists over a note that isn't the root. It's the
> same as the Berklee concept of the "avoid note", I think.
>
> I was always a bit unsatisfied with this, as b9's exist in the
> overtone series and don't sound quite so bad, so I came up with a few
> chords that manage to sound good despite this, voiced from bottom to
> top:
>
> D F B E A D F#
> D A F# B E A#
> A G C# E# G#
>
> To my ears, they sound functional. Consonant, but complex, rather than
> "that guy messed his voicings up." So the rule I'm at now is that it
> seems that if you have a "diatonic" b9 in there, it doesn't sound too
> hot. If you have a "chromatic" b9, it does. And it's hard to find the
> distinction in 12-equal, but it seems to have to do with implied
> harmonic relationships among the notes.
>
> The thing I don't understand: phrygian mode uses the diatonic b9 all
> of the time, but it certainly works to create a mood, sounds
> functional, 'consonant', etc. Nonetheless, if you play a chord like C
> E G Bb D F, that b9 in there is going to be pretty hard to swallow.
> Why?
>
>

🔗caleb morgan <calebmrgn@...>

> D F B E A D F#
> D A F# B E A#
> A G C# E# G#

> D F B E A D F# --lovely

maybe: F# is supported as 5th partial of D upper-structure triad. Lower F is part of D minor consonance, and familar jazz F-B-E-A voicing (G7, F lydian, E phrygian, etc.)

> D A F# B E A# --high A# here is relatively unsupported, except as > 5th par (down 2 octs) of F#

this one sounds a little stranger to me, but possibly hearable as B minor, with the familiar variability of the 7th scale degree: It has A b7 and A# "raised" 7th scale degree.

> A G C# E# G# --your coolest, freshest example. sounds great. I > should use this one in a piece, sometime!

In other words, in an A "altered" (Locrian b4) scale, the real outrigger, the note that doesn't "belong" is the A. The root.

Go figure.

Music is a strange and wonderful thing.

On Jan 21, 2009, at 1:23 PM, Mike Battaglia wrote:

> caleb: yep. In more advanced courses, they would let you break the > rules.
>

> Mike Gibbs was enlightened that way. Maybe a high F over C is 3rd > partial of 7, but it's too sharp.
>

>
> I was always a bit unsatisfied with this, as b9's exist in the
> overtone series and don't sound quite so bad, so I came up with a few
> chords that manage to sound good despite this, voiced from bottom to
> top:
>
> D F B E A D F#
> D A F# B E A#
> A G C# E# G#
>
> To my ears, they sound functional. Consonant, but complex, rather than
> "that guy messed his voicings up." So the rule I'm at now is that it
> seems that if you have a "diatonic" b9 in there, it doesn't sound too
> hot. If you have a "chromatic" b9, it does. And it's hard to find the
> distinction in 12-equal, but it seems to have to do with implied
> harmonic relationships among the notes.
>
> The thing I don't understand: phrygian mode uses the diatonic b9 all
> of the time, but it certainly works to create a mood, sounds
> functional, 'consonant', etc. Nonetheless, if you play a chord like C
> E G Bb D F, that b9 in there is going to be pretty hard to swallow.
> Why?
>
>

🔗Michael Sheiman <djtrancendance@...>

---It's possible to create beautifully

---sounding music from the most "ugly" intervals and mathematically
---
constructed chord structures, and horrifying one from chords created
---
from harmonics series.
Of course it is...but my theory is accessibility becomes a huge issue (using ugly intervals) to balance consonance and dissonance.

With scales where almost all intervals are consonant you have many more paths to good-sounding music, which seems to include mostly high consonance with a few distinct parts of songs where tension is used strategically toward the mood, rather than the other way around.

"ugly" scales may be great for interesting pieces among us more mathematician-like types....and I admire anyone who can make something beautiful in something like 10-tet (IE Bill Sethares's "10 strings"), but for the point of convincing the average person that composing music is fun I figure it is best not to frustrate them. And, in "ugly scales", there's always the danger of spending too much time working through the math looking for sweet spots and too little time left for creativity.

And also, for the record, I don't think the harmonic series itself is an ideal consonant scale due to both beating and lack of possibility for different emotions. As a compromise between 12TET and the harmonic series, I have found the scale

1 *9/8 *10/9 *11/12 *12/11 *10/9 * 11/10 2(octave)

for example, to sound MUCH more expressive than 12TET and be less likely the generate intervals more than 5-or-so cents from being "pure"...and yet it still allows for some extra tension when needed. Try it and see how you think it balances "beautiful and ugly".

-Michael

--- On Wed, 1/21/09, Daniel Forró <dan.for@...> wrote:

From: Daniel Forró <dan.for@...>
Subject: Re: [tuning] What is the Most "Out-Of-Tune" or "Dissonant" Interval in Equal Temperament??
To: tuning@yahoogroups.com
Date: Wednesday, January 21, 2009, 6:02 PM

Answers can be found if there's some exact and universal definition

what "out-of-tune/ in tune" and "consonance/ dissonance" means. Which I

doubt as there are many possible attitudes to this, and lot of this

depends on musical context. It's possible to create beautifully

sounding music from the most "ugly" intervals and mathematically

constructed chord structures, and horrifying one from chords created

from harmonics series.

Daniel Forro

On 22 Jan 2009, at 1:48 AM, micro_piano wrote:

> Hi all!!

> This question may SEEM very basic, but I'd like to see what everyone

> ACTUALLY believes is the most "out-of tune" sounding (or "dissonant")

> interval in Equal Temperament.

> There are obviously both opinions that are going to be involved here

> as well as facts.

> Obviously, certain people are going to hear different intervals

> differently. That is where the "opinions" come in.

> But what about the facts, meaning the mathematical "certainties" that

> answer the question for us, but where are our aural senses (and thus

> our individual "opinions") answer the question quite differently.

> I'd just like to know, once and for all, what each one of you think is

> the most "out-of-tune" sounding (or "dissonant") interval in the Equal

> Temperament system...

> Thanks for your answers in advance,

> Frank Wilson, Ph.D (Musicology)

🔗Tom Dent <stringph@...>

This is a mixture of two quite different questions... so perhaps the
questioner should consider just what he means by 'out-of-tune'.

The problem is that 'out-of-tuneness' is not well-defined for very
dissonant intervals. The augmented or diminished octave for example,
both very dissonant, and there is no 'correct' tuning such that they
sound 'best' in any sense.

The classic dissonance of a minor 2nd arises in counterpoint for
example if one takes E-G and ties over E to E-F... now how can one
tell whether E-F is 'in tune' or not? It totally depends on musical
context so there can never be any 'once for all' answer.

Claudio rewrote the question reasonably as 'what interval does ET most
cause to be more dissonant (than its pure or just value)'. And
answered it too.

Historically, people were always complaining about how bad the thirds
sounded in ET.
~~~T~~~

🔗caleb morgan <calebmrgn@...>

oops. make that C Lydian #2.

On Jan 22, 2009, at 9:59 AM, caleb morgan wrote:

>
> I've come to the opinion that 12-tet is only capable of suggesting 5-> limit chains.
>
> So, you can almost guide the ear to hear 7-ratios, but not quite.
>
> 11-ratios and 13-ratios are just non-existent in 12-tet.
>
> they are more subtle, and require some accuracy (+-5 cents, maybe?) > to be heard as themselves.
>
> C-G-E-F#-B-D#
>
> a cool chord, B triad over C.
>
> D# is definitely #2 (or #9) and the scale is C Lydian #3, or E > harmonic minor.
>
> caleb
>
>
>
> On Jan 21, 2009, at 1:36 PM, Mike Battaglia wrote:
>
>> To make another point about it being context sensitive, this chord,
>> voiced from top to bottom:
>>
>> C G E F# B D#
>>
>> That D# on top is extremely dissonant (or, as I like to think of it,
>> "consonant with complexity") - but while C-D# is an equal-tempered
>> minor 3rd, I tend to hear that note on top as being far more
>> dissonant. I hear it as fulfilling the role of being a major third
>> above the B, which is a major 7th above C. To my ears, it seems that
>> every equal tempered interval (or JI interval in general) falls >> into a
>> sort of "gray area" where the other notes in a chord can influence >> how
>> that specific interval is heard, so the question might only make >> sense
>> in the context of dyads alone.
>>
>> The question: How do you guide one's ear to hear 13:8 in 12-tet? :)
>>
>> -Mike
>>
>
>
>

🔗Mike Battaglia <battaglia01@...>

> D A F# B E A# --high A# here is relatively unsupported, except as 5th par
> (down 1 oct) of F#
> this one sounds a little stranger to me, but possibly hearable as B minor,
> with the familiar variability of the 7th scale degree: It has A b7 and A#
> "raised" 7th scale degree.

Try playing it so that the A# on top is a suspension that resolves to
G#. It works that way too. Oddly enough, this works best if played in
a low-mid register - so that the low D is in a bass register or
something.

> A G C# E# G# --your coolest, freshest example. sounds great. I should use
//
> But it also can be heard as an extension of an A altered scale:
> A,Bb,C,Db,Eb,F,G with a "b15" (?!) in which the upper Ab is supported as a
> 3rd partial of Db.
> In other words, in an A "altered" (Locrian b4) scale, the real outrigger,
> the note that doesn't "belong" is the A. The root.
> Go figure.
> Music is a strange and wonderful thing.

Indeed. I generally do think of it as an altered scale sort of thing.
It's altered b1. You can also think of it as a tritone sub:

A G C# E# G# -> A G C# E# G

So that you have a D#sus13 that resolves to a D#7 but being played
over an A in the bass. The A altered scale is the same thing as D#/Eb
Lydian dominant, so the chord posted above is sort of like an
alteration in which you play D# mixolydian over A7 instead of D#
lydian dominant over A7.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Andreas Sparschuh <a_sparschuh@...>

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:

> My answer...:
>
> "The MAJOR THIRD:

1200Cents * ln(5/4)/ln(2) = ~386.313714....Cents

>and then the
>MINOR SIXTH!":

1200Cents * ln(8/5)/ln(2) = ~813.686286...Cents

Agreed, due to ~14Cents off, out of tune.

Dear Claudio,

Quest:
How about to add here also some other 5-limit intervals
that are even worser out of tune:
Minor-3rd:

1200Cents * ln(6/5)/ln(2) = ~315.641287...Cents

and the MAJOR-6th:

1200Cents * ln(5/3)/ln(2) = ~884.358713...Cents

both with @ even ~16Cents out of tune versus 12-ET, so too?

bye
A.S.

What is the Most "Out-Of-Tune" or "Dissonant" Interval in Equal Temperament??

🔗micro_piano <frankw802@...>

🔗caleb morgan <calebmrgn@...>

🔗Mike Battaglia <battaglia01@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Claudio Di Veroli <dvc@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗djtrancendance@...

🔗Daniel Forró <dan.for@...>

🔗massimilianolabardi <labardi@...>

🔗caleb morgan <calebmrgn@...>

🔗caleb morgan <calebmrgn@...>

🔗caleb morgan <calebmrgn@...>

🔗Michael Sheiman <djtrancendance@...>

🔗Tom Dent <stringph@...>

🔗caleb morgan <calebmrgn@...>

🔗Mike Battaglia <battaglia01@...>

🔗Mike Battaglia <battaglia01@...>

🔗Andreas Sparschuh <a_sparschuh@...>