Topic: Otonal / Utonal

1 scales

Thread (53 messages)

From: microtonalist (2005-10-10)
Subject: Otonal / Utonal

One way that has helped me understand the utonal and otonal 
difference is as follows

Otonal - a collection of pitches that can be construed as the 
overtones of a common fundamental: 

5/4 3/2 9/8 for example

Utonal - a collection of pitches that can be construed as 
fundamentals having a common overtone:

4/3 8/5 8/7. These having an overtone of 1/1 (1/1 is the 3/2 of 4/3, 
1/1 is the 5/4 of 8/5 and 1/1 is the 7/4 of 8/7).

An otonal group share a common udentity and a utonal group share a 
common odentity. u for undernumber and o for overnumber.

Here 1/1 refers to a reference pitch. Any pitch can be construed 
either as a new fundamental (the overtone series being the 
overarching example), or as the overtone of a new fundamental.

Partch's tonality diamond takes 1 3 5 7 9 and 11 'identities' and 
treats them each way, as overtone (odentity) and fundamental 
(udentity).

Mark

From: traktus5 (2005-10-11)
Subject: stacked, or hinged? (re  Otonal / Utonal)

This looks like a good explanation, but what notes (indicated as 
scale notes, such as c4-e4-g4) do 5/4 3/2 9/8, and  4/3 8/5 8/7 
actually represent? (are they stacked, or hinged at the bottom,  
etc?...)

thanks, Kelly



--- In [email protected], "microtonalist" <mark@e...> wrote:
>
> One way that has helped me understand the utonal and otonal 
> difference is as follows
> 
> Otonal - a collection of pitches that can be construed as the 
> overtones of a common fundamental: 
> 
> 5/4 3/2 9/8 for example
> 
> Utonal - a collection of pitches that can be construed as 
> fundamentals having a common overtone:
> 
> 4/3 8/5 8/7. These having an overtone of 1/1 (1/1 is the 3/2 of 
4/3, 
> 1/1 is the 5/4 of 8/5 and 1/1 is the 7/4 of 8/7).
> 
> An otonal group share a common udentity and a utonal group share a 
> common odentity. u for undernumber and o for overnumber.
> 
> Here 1/1 refers to a reference pitch. Any pitch can be construed 
> either as a new fundamental (the overtone series being the 
> overarching example), or as the overtone of a new fundamental.
> 
> Partch's tonality diamond takes 1 3 5 7 9 and 11 'identities' and 
> treats them each way, as overtone (odentity) and fundamental 
> (udentity).
> 
> Mark
>

From: monz (2005-10-11)
Subject: Re: stacked, or hinged? (re  Otonal / Utonal)

Hi Kelly,

--- In [email protected], "traktus5" <kj4321@h...> wrote:
>
> This looks like a good explanation, but what notes
> (indicated as scale notes, such as c4-e4-g4) do 5/4 3/2 9/8,
> and  4/3 8/5 8/7 actually represent? (are they stacked,
> or hinged at the bottom, etc?...)


I have no idea what you mean by "hinged at the bottom",
but hopefully i can help a little ...

Partch used G-392 Hz as his 1/1. This is the G above
middle-C, so it would usually be called "G4".

Now, the problem with using regular musical letter-name
nominals to describe Partch's theories is that in addition
to the standard letter-names, you also have to employ either
additional accidentals, or cents deviations, or some such.

I like to use a notation i devised called "HEWM", which
in its simplified form uses 72-edo (72-tone equal-temperament)
as the basis for a small set of accidentals, thus:

lower raise   inflection    cents

  b    #       semitone     100
  v    ^       1/4-tone      50
  <    >       1/6-tone      331/3
  -    +       1/12-tone     162/3

There is a more complicated version which gives an exact
representation of JI, but the 72-edo version does a fairly
good job of representing Partch's 11-limit JI, so i prefer
to use it.

Essentially:

* the plain letter-names represent 3-limit pythagorean 
diatonic tuning;

* the sharp (#) and flat (b) represent pythagorean
chromatic deviation from the diatonic (~114 cents);

* the plus (+) and minus (-) represent deviations from
pythagorean by a syntonic-comma (~22 cents);

* the greater-than (>) and less-than (<) represent
deviations from pythagorean by a septimal-comma (~27 cents);

* the up-arrow (^) and down-arrow (v) represent
deviations from pythagorean by an undecimal-diesis (~53 cents).


You can read a lot more about HEWM here:

http://tonalsoft.com/enc/h/hewm.aspx



So, assuming G4 as the 1/1 ... 5/4 3/2 9/8 can be notated
as B-4 D5 A5, and 4/3 8/5 8/7 is C5 Eb+5 A>4.

If you prefer to use C4 (middle-C) as your 1/1, then you get:
5/4 3/2 9/8 = E-4 G4 D4, and 4/3 8/5 8/7 = F4 Ab+4 D>4.


Hope that helps.




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

From: microtonalist (2005-10-11)
Subject: Re: stacked, or hinged? (re  Otonal / Utonal)

All ratios are expressed in relation to the 1/1, i.e. 5/4 is a just 
major third above the 1/1. This is exactly Partch's stated position.
All you have to do is choose which pitch represents the 1/1.

Therefore 1/1 5/4 3/2 represents the JI major chord.
Therefore 1/1 8/5 4/3 represents the JI minor chord.

In this notation 9/8 is always 9/8. Some microtonalists use a:b to 
indicate an interval, rather than a pitch. Whether a ratio represents 
a pitch (relative to a fixed 1/1) or an interval, as in the 6/5 from 
5/4 up to 3/2, can lead to confusion. Partch himself made this 

No stacking or hinging required.

--- In [email protected], "traktus5" <kj4321@h...> wrote:
>
> This looks like a good explanation, but what notes (indicated as 
> scale notes, such as c4-e4-g4) do 5/4 3/2 9/8, and  4/3 8/5 8/7 
> actually represent? (are they stacked, or hinged at the bottom,  
> etc?...)
> 
> thanks, Kelly
> 
> 
> 
> --- In [email protected], "microtonalist" <mark@e...> wrote:
> >
> > One way that has helped me understand the utonal and otonal 
> > difference is as follows
> > 
> > Otonal - a collection of pitches that can be construed as the 
> > overtones of a common fundamental: 
> > 
> > 5/4 3/2 9/8 for example
> > 
> > Utonal - a collection of pitches that can be construed as 
> > fundamentals having a common overtone:
> > 
> > 4/3 8/5 8/7. These having an overtone of 1/1 (1/1 is the 3/2 of 
> 4/3, 
> > 1/1 is the 5/4 of 8/5 and 1/1 is the 7/4 of 8/7).
> > 
> > An otonal group share a common udentity and a utonal group share 
a 
> > common odentity. u for undernumber and o for overnumber.
> > 
> > Here 1/1 refers to a reference pitch. Any pitch can be construed 
> > either as a new fundamental (the overtone series being the 
> > overarching example), or as the overtone of a new fundamental.
> > 
> > Partch's tonality diamond takes 1 3 5 7 9 and 11 'identities' and 
> > treats them each way, as overtone (odentity) and fundamental 
> > (udentity).
> > 
> > Mark
> >
>

From: Mohajeri Shahin (2005-10-11)
Subject: RE: [tuning] Otonal / Utonal

Dear microtonalist

 

As u wrote : .....An otonal group share a common udentity and a utonal
group share a 
common odentity. u for undernumber and o for overnumber.....

This is the same as I told : 

1- "" utonal systems which I think it is better for me to call them ""
constant/decreasing rational system "" the nominator is constant and
denominator is decreasing """" the nominator here is the udentity.

2- utonal systems which I think it is better for me to call them ""
constant/decreasing rational system "" the nominator is constant
(odentity)and denominator is decreasing

3-  you tell that :""Utonal - a collection of pitches that can be
construed as 
fundamentals having a common overtone:
4/3 8/5 8/7. These having an overtone of 1/1 (1/1 is the 3/2 of 4/3, 
1/1 is the 5/4 of 8/5 and 1/1 is the 7/4 of 8/7).""

I found that each degree of utonal and otonal systems are inverse of
each other due to 2/1(3/2 & 4/3 are inverse of each other so , . so may
be the musical sense of major tonality is inverse of minor tonality
because of that !!!!!

1200-each degree of otonal systems=each degree of utonal system and vice
versa.

4-in otonal and utonal systems with same number of degrees ,
udentity=2*odentity.

 

 

Dear monzo

1- although I see my mails in microsoft outlook , but I can also see the
tables inserted in the mail in internet explorer.

2- as u wrote: "A perfect example of the latter is a JI minor-7th chord 
with ratios 1/1 - 6/5 - 3/2 - 9/5"

In my opinion it is a hybrid chord made from two utonal and otonal
sytems which have some degrees in common :

1/1... 6/5...3/2...2/1

1/1..6/5..7/5..8/5..9/5..2/1

U can also construct this chord in this i/c rational system:

10/10......20/10(1/1...2/1). May be we can divide one rational otonal
system to two or more otonal and utonal systems.

 

 

 

________________________________

From: [email protected] [mailto:[email protected]] On Behalf
Of microtonalist
Sent: Monday, October 10, 2005 5:38 PM
To: [email protected]
Subject: [tuning] Otonal / Utonal

 

One way that has helped me understand the utonal and otonal 
difference is as follows

Otonal - a collection of pitches that can be construed as the 
overtones of a common fundamental: 

5/4 3/2 9/8 for example

Utonal - a collection of pitches that can be construed as 
fundamentals having a common overtone:

4/3 8/5 8/7. These having an overtone of 1/1 (1/1 is the 3/2 of 4/3, 
1/1 is the 5/4 of 8/5 and 1/1 is the 7/4 of 8/7).

An otonal group share a common udentity and a utonal group share a 
common odentity. u for undernumber and o for overnumber.

Here 1/1 refers to a reference pitch. Any pitch can be construed 
either as a new fundamental (the overtone series being the 
overarching example), or as the overtone of a new fundamental.

Partch's tonality diamond takes 1 3 5 7 9 and 11 'identities' and 
treats them each way, as overtone (odentity) and fundamental 
(udentity).

Mark





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From: traktus5 (2005-10-11)
Subject: Re: Otonal / Utonal

hello Microtonalists!  "microtonalist" <mark@e...> wrote:

> One way that has helped me understand the utonal and otonal 
> difference is as follows> Otonal - a collection of pitches that 
>can be construed as the ...

As one ascends the harmonic series, when can one start considering 
the chords utonally?  Is it the first chord of the harmonic series 
(8:10:13) which, in the subharmonic series, is the first type of 
minor triad (ie, 1/5:4:3)?  

(And as the secondary issue, why do you choose 12:15:20 over 
8:10:13?  Is it because of the purportedly discordant quality of the 
natural 13th harmonic?  Or is 12-15-20 favored because it reduces 
down to the constituent intervals 5/4 and 4/3?  And 12-15-20 is "5-
limit", correct?!)

And, how does one reckon utonality theory with theories which see 
chords as having mutliple root associations?  Is there a good and 
fair critique of utonality, along these or other lines, that's been 
published anywhere?


thanks, Kelly

> 
> An otonal group share a common udentity and a utonal group share a 
> common odentity. u for undernumber and o for overnumber.
> 
> Here 1/1 refers to a reference pitch. Any pitch can be construed 
> either as a new fundamental (the overtone series being the 
> overarching example), or as the overtone of a new fundamental.
> 
> Partch's tonality diamond takes 1 3 5 7 9 and 11 'identities' and 
> treats them each way, as overtone (odentity) and fundamental 
> (udentity).
> 
> Mark
>

From: microtonalist (2005-10-12)
Subject: Re: Otonal / Utonal

--- In [email protected], "traktus5" <kj4321@h...> wrote:
>
> hello Microtonalists!  "microtonalist" <mark@e...> wrote:
> 
> > One way that has helped me understand the utonal and otonal 
> > difference is as follows> Otonal - a collection of pitches that 
> >can be construed as the ...
> 
> As one ascends the harmonic series, when can one start considering 
> the chords utonally?  Is it the first chord of the harmonic series 
> (8:10:13) which, in the subharmonic series, is the first type of 
> minor triad (ie, 1/5:4:3)?  
Chords ascending in the harmonic series are never utonal.
> 
> (And as the secondary issue, why do you choose 12:15:20 over 
> 8:10:13?  Is it because of the purportedly discordant quality of 
the 
> natural 13th harmonic?  Or is 12-15-20 favored because it reduces 
> down to the constituent intervals 5/4 and 4/3?  And 12-15-20 is "5-
> limit", correct?!)
None of these. Simply that the components of one chord are the ratio 
complements of the other. The otonal chord does not contain 16/13, so 
the utonal one does not contain 13/8.
> 
> And, how does one reckon utonality theory with theories which see 
> chords as having mutliple root associations?  Is there a good and 
> fair critique of utonality, along these or other lines, that's been 
> published anywhere?
None. 

However, for interest, Erno Lendvai has written about the concept of 
untonality (though he prefers to separate his tonal universes into 
diatonic and pentatonic, which is an interesting insight) Consider

1/1  5/4  3/2  7/4 these are otonal, and are found in diatonic music
1/1  8/5  4/3  8/7 these are utonal, and are found in pentatonic 
music. (From Lendvai - not me)

Lendvai also demonstrates the complementary quality of the chromatic

C D E Fsharp (as 11/8) G Bflat(as 7/4)
C  Eflat F Aflat (8/5) 

D in the above contexts would either be 9/8 or 8/7 respectively 
(these are my interpretations of Lendvai's chromatic scale form)

Note that to Lendvai it is the form 1/1 4/3 8/5 which is the primary 
mode of presentation of the pentatonic tonic.

But post Partch I am not aware of any significant addition to his 
concept of tonality



>

From: Yahya Abdal-Aziz (2005-10-12)
Subject: RE: Otonal / Utonal

On Mon, 10 Oct 2005, "microtonalist" <mark@...> wrote: 
> 
> One way that has helped me understand the utonal and otonal 
> difference is as follows
> 
> Otonal - a collection of pitches that can be construed as the 
> overtones of a common fundamental: 
> 
> 5/4 3/2 9/8 for example
> 
> Utonal - a collection of pitches that can be construed as 
> fundamentals having a common overtone:
> 
> 4/3 8/5 8/7. These having an overtone of 1/1 (1/1 is the 3/2 of 4/3, 
> 1/1 is the 5/4 of 8/5 and 1/1 is the 7/4 of 8/7).
> 
> An otonal group share a common udentity and a utonal group share a 
> common odentity. u for undernumber and o for overnumber.
> 
> Here 1/1 refers to a reference pitch. Any pitch can be construed 
> either as a new fundamental (the overtone series being the 
> overarching example), or as the overtone of a new fundamental.
> 
> Partch's tonality diamond takes 1 3 5 7 9 and 11 'identities' and 
> treats them each way, as overtone (odentity) and fundamental 
> (udentity).
> 
> Mark

Hi Mark,

This very neat way of putting things does point up
the fundamental duality of the two notions.  As such,
it's a valuable reminder that otonality and utonality
fit together in a larger scheme of things, each with
[expressive] possibilities the other necessarily lacks.

Thank you!

Apart from their suggestive power, is there a concise
definition of the terms "odentity" and "udentity"?

Regards,
Yahya

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From: monz (2005-10-12)
Subject: Re: Otonal / Utonal

Hi Yahya,

--- In [email protected], "Yahya Abdal-Aziz" <yahya@m...> wrote:

> This very neat way of putting things does point up
> the fundamental duality of the two notions.  As such,
> it's a valuable reminder that otonality and utonality
> fit together in a larger scheme of things, each with
> [expressive] possibilities the other necessarily lacks.
> 
> Thank you!


Otonality/Utonality are indeed dualistic ... this was a
fundamental (pardon the pun) aspect of Partch's theory.

But note that they are really only two sides of the
same coin. I just wrote here yesterday explaining how
the same chord may be interpreted as either an Otonality
or Utonality:

http://launch.groups.yahoo.com/group/tuning/message/61301

 
> Apart from their suggestive power, is there a concise
> definition of the terms "odentity" and "udentity"?


odentity = an identity of an Otonality,
found among the numerators of the ratios

udentity = an identity of a Utonality,
found among the denominators of the ratios



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

From: monz (2005-10-12)
Subject: Re: Otonal / Utonal

--- In [email protected], "monz" <monz@t...> wrote:
>
> Hi Yahya,
> 
> --- In [email protected], "Yahya Abdal-Aziz" <yahya@m...> wrote:
> 
> > This very neat way of putting things does point up
> > the fundamental duality of the two notions.  As such,
> > it's a valuable reminder that otonality and utonality
> > fit together in a larger scheme of things, each with
> > [expressive] possibilities the other necessarily lacks.
> > 
> > Thank you!
> 
> 
> Otonality/Utonality are indeed dualistic ... this was a
> fundamental (pardon the pun) aspect of Partch's theory.
> 
> But note that they are really only two sides of the
> same coin. I just wrote here yesterday explaining how
> the same chord may be interpreted as either an Otonality
> or Utonality:
> 
> http://launch.groups.yahoo.com/group/tuning/message/61301
> 
>  
> > Apart from their suggestive power, is there a concise
> > definition of the terms "odentity" and "udentity"?
> 
> 
> odentity = an identity of an Otonality,
> found among the numerators of the ratios
> 
> udentity = an identity of a Utonality,
> found among the denominators of the ratios
 

http://tonalsoft.com/enc/i/identity.aspx

http://tonalsoft.com/enc/o/odentity.aspx

http://tonalsoft.com/enc/u/udentity.aspx


Those definitions are perhaps a little too concise.
But at least the first part of each comes from Partch,
who invented the terms.


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

From: wallyesterpaulrus (2005-10-12)
Subject: Re: Otonal / Utonal

--- In [email protected], "Mohajeri Shahin" <shahinm@k...> wrote:

> 4-in otonal and utonal systems with same number of degrees ,
> udentity=2*odentity.

How did you come to that conclusion?

From: wallyesterpaulrus (2005-10-12)
Subject: Re: Otonal / Utonal

--- In [email protected], "microtonalist" <mark@e...> wrote:

> 
> However, for interest, Erno Lendvai has written about the concept of 
> untonality (though he prefers to separate his tonal universes into 
> diatonic and pentatonic, which is an interesting insight)

I do believe many academics have neglected the possibility and reality of pentatonic 
hearing.

> Consider
> 
> 1/1  5/4  3/2  7/4 these are otonal, and are found in diatonic music

Isn't 1/1 8/5 4/3 8/7 then also (equally, as much) found in diatonic music?

> 1/1  8/5  4/3  8/7 these are utonal, and are found in pentatonic 
> music. (From Lendvai - not me)

Since the pentatonic and diatonic scales are symmetrical about the otonal/utonal "axis", I 
don't see how either could be more one than the other. But I'd love to hear the thinking 
behind this idea.

> But post Partch I am not aware of any significant addition to his 
> concept of tonality

Whose concept? Partch's or Lendvai's?

From: Gene Ward Smith (2005-10-13)
Subject: Re: Otonal / Utonal

--- In [email protected], "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> I do believe many academics have neglected the possibility and
reality of pentatonic 
> hearing.

What does "pentatonic hearing" mean?

From: microtonalist (2005-10-13)
Subject: Re: Otonal / Utonal

--- In [email protected], "wallyesterpaulrus" 
<wallyesterpaulrus@y...> wrote:
>
> --- In [email protected], "microtonalist" <mark@e...> wrote:
> 
> > 
> > However, for interest, Erno Lendvai has written about the concept 
of 
> > untonality (though he prefers to separate his tonal universes 
into 
> > diatonic and pentatonic, which is an interesting insight)
> 
> I do believe many academics have neglected the possibility and 
reality of pentatonic 
> hearing.
> 
> > Consider
> > 
> > 1/1  5/4  3/2  7/4 these are otonal, and are found in diatonic 
music
> 
> Isn't 1/1 8/5 4/3 8/7 then also (equally, as much) found in 
diatonic music?
> 
> > 1/1  8/5  4/3  8/7 these are utonal, and are found in pentatonic 
> > music. (From Lendvai - not me)
> 

Lendvai states that all intervals can be found in all systems. What 
is significant is that the dissonant intervals of one are the 
consonant intervals in the other.

Thus 3/2 is consonant in diatony but dissonant in pentatony. 
Conversely 4/3 is consonant in pentatony but dissonant in diatony.

similarly for other otonal and utonal ratios. Characteristically 
Lendvai makes the six-four minor chord the tonic of a pentatonic 
system i.e. C F Aflat (reading up from C).

There are intervals that for a given 1/1 are neither utonal or otonal:

6/5 5/3 7/5 9/7 etc, as neither odentity or udentity contain powers 
of 2 only. What should we call them - otonal or utonal? - or neither?

Finally, it should be of interest to those who don't already know 
that although a string or a pipe vibrates according to the harmonic 
series, if a string is equally divided or a pipe has holes made at 
equal points along it then a subharmonic series results from the 
resulting scales. It may be interesting to conjecture that perhaps 
for early humans, equal division of the physical object (string or 
bone flute) was easier than logarithmic.

Mark



> Since the pentatonic and diatonic scales are symmetrical about the 
otonal/utonal "axis", I 
> don't see how either could be more one than the other. But I'd love 
to hear the thinking 
> behind this idea.
> 
> > But post Partch I am not aware of any significant addition to his 
> > concept of tonality
> 
> Whose concept? Partch's or Lendvai's?
>
Partch's concept of tonality

From: Kraig Grady (2005-10-13)
Subject: Re: Otonal / Utonal

[email protected] wrote:

>
>
>--- In [email protected], "microtonalist" <mark@e...> wrote:
>
>  
>
>
>  
>
>>But post Partch I am not aware of any significant addition to his 
>>concept of tonality
>>    
>>
 I think that the Eikosany and the othe CPS structures which are like 
completments to the diamonds are quite a step in this direction.
 I wrote an article on this back when which is reproduced here
http://anaphoria.com/cps.PDF

also the scales of Mt Meru are constructed along the line of difference 
and combination tones reinforcing a series of self contained series of 
tones allowing
-- 
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

From: traktus5 (2005-10-13)
Subject: equal divisions, subharmonic?

> Finally, it should be of interest to those who don't already know 
> that although a string or a pipe vibrates according to the harmonic 
> series, if a string is equally divided or a pipe has holes made at 
> equal points 

divided how, exactly?  any division of equal spacing?...

along it then a subharmonic series results from the 
> resulting scales. It may be interesting to conjecture that perhaps 
> for early humans, equal division of the physical object (string or 
> bone flute) was easier than logarithmic.

Can someone elaborate?  

thanks.

From: Yahya Abdal-Aziz (2005-10-14)
Subject: Re: Otonal / Utonal

Hi Monz,

On Wed, 12 Oct 2005, you wrote: 
> Hi Yahya,
> --- In [email protected], "Yahya Abdal-Aziz" 
> <yahya@m...> wrote:
> 
> > This very neat way of putting things does point up
> > the fundamental duality of the two notions.  As such,
> > it's a valuable reminder that otonality and utonality
> > fit together in a larger scheme of things, each with
> > [expressive] possibilities the other necessarily lacks.
> > 
> > Thank you!
> 
> 
> Otonality/Utonality are indeed dualistic ... this was a
> fundamental (pardon the pun) aspect of Partch's theory.
> 
> But note that they are really only two sides of the
> same coin. 
Which is pretty much what dual concepts always are.
An explanation of one that fails to note the other often
lacks something in depth.


> ... I just wrote here yesterday explaining how
> the same chord may be interpreted as either an Otonality
> or Utonality:
> 
> http://launch.groups.yahoo.com/group/tuning/message/61301

Yep, read it, thank you. 

  
> > Apart from their suggestive power, is there a concise
> > definition of the terms "odentity" and "udentity"?
> 
> odentity = an identity of an Otonality,
> found among the numerators of the ratios
> 
> udentity = an identity of a Utonality,
> found among the denominators of the ratios
> 
Too concise! :-)  As you realised, for you wrote later -

> http://tonalsoft.com/enc/i/identity.aspx
> 
> http://tonalsoft.com/enc/o/odentity.aspx
> 
> http://tonalsoft.com/enc/u/udentity.aspx
> 
> 
> Those definitions are perhaps a little too concise.
> But at least the first part of each comes from Partch,
> who invented the terms.

These definitions from Tonalsoft were more informative,
thank you.  The quotes from Partch seemed more like some
kind of mystic mumbo-jumbo than either definition or 
explanation.  Contrariwise, your words shed more light.

Still there seems to be some circularity in the discussion.
Given that there is a natural hierarchy of concepts involved 
here, wouldn't it be best if any explanation started with 
the most fundamental and built on that?

The way the term "identity" is used by Partch is confusing,
too.  It's quite unlike the uses I have encountered in 
abstract mathematics, in philosophy and in psychology.
In the "mathematical calculus of frequency ratios" (to 
dignify our simple calculations for chords), the only true
identity is that ratio, which, when multiplied by any other,
leaves it unchanged, namely the ratio 1:1.  And there is only
one identity possible in such a system, as there is in a 
mathematical group.  But this is not what "identity" means 
in your definitions, is it?

In fact, I suspect that there's a better term waiting to
replace it.  Your expression "pole of tonality" is suggestive, 
when you describe it as -

"one of the odd-number ingredients, one or several or all 
of which act as a pole of tonality [for example, 1-3-5-7-9-11
in Partch's theory]."

What "pole" brings to mind is firstly, the diametrically 
opposite North and South Poles of a globe or of magnetism;
and secondly, a fixed structure, point or pivot around which 
satellites spin, like dancers round a Maypole.  

To use your example 1-3-5-7-9-11, and take "one or several 
or all ... as a pole of tonality", we might take -
a) just the 5; or
b) the 5, 7 and 11; or
c) the 1, 3, 5, 7, 9 and 11
as our "poles of tonality".  Only in case a) do we have a single
"pole" like a Maypole; and in none of these cases do we have 
diametrically opposite poles like the North and South poles.

Perhaps the term "pivot" might suitable generalise the notion
of "poles of tonality".  But I suppose the term "pivot" already
has too many other meanings in music?

Regards,
Yahya

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From: Gene Ward Smith (2005-10-14)
Subject: Re: Otonal / Utonal

--- In [email protected], "microtonalist" <mark@e...> wrote:

> Thus 3/2 is consonant in diatony but dissonant in pentatony. 
> Conversely 4/3 is consonant in pentatony but dissonant in diatony.

Is there any evidence this is so?

From: monz (2005-10-14)
Subject: Re: Otonal / Utonal

Hi Yahya,


--- In [email protected], "Yahya Abdal-Aziz" <yahya@m...> wrote:

> The way the term "identity" is used by Partch is confusing,
> too.  It's quite unlike the uses I have encountered in 
> abstract mathematics, in philosophy and in psychology.
> In the "mathematical calculus of frequency ratios" (to 
> dignify our simple calculations for chords), the only true
> identity is that ratio, which, when multiplied by any other,
> leaves it unchanged, namely the ratio 1:1.  And there is only
> one identity possible in such a system, as there is in a 
> mathematical group.  But this is not what "identity" means 
> in your definitions, is it?
> 
> In fact, I suspect that there's a better term waiting to
> replace it.  Your expression "pole of tonality" is suggestive, 
> when you describe it as -
> 
> "one of the odd-number ingredients, one or several or all 
> of which act as a pole of tonality [for example, 1-3-5-7-9-11
> in Partch's theory]."
> 
> What "pole" brings to mind is firstly, the diametrically 
> opposite North and South Poles of a globe or of magnetism;
> and secondly, a fixed structure, point or pivot around which 
> satellites spin, like dancers round a Maypole.  
> 
> To use your example 1-3-5-7-9-11, and take "one or several 
> or all ... as a pole of tonality", we might take -
> a) just the 5; or
> b) the 5, 7 and 11; or
> c) the 1, 3, 5, 7, 9 and 11
> as our "poles of tonality".  Only in case a) do we have a single
> "pole" like a Maypole; and in none of these cases do we have 
> diametrically opposite poles like the North and South poles.
> 
> Perhaps the term "pivot" might suitable generalise the notion
> of "poles of tonality".  But I suppose the term "pivot" already
> has too many other meanings in music?



Partch's theory is based on the idea of a "numerary nexus",
which you should also look up in the Tonalsoft Encyclopedia.

In a nutshell, Partch's "nexus" simply means that all the
notes of a Utonality or Otonality share a common factor in
either the numerator or denominator of the ratios.

If the nexus is in the denominator, then the chord is best
described as an Otonality, and vice versa: if the nexus is
in the numerator, then the chord is best described as a
Utonality.

"Identity" is the generic word, which can refer to either
Odentities or Udentities. If the nexus is in the denominator,
then the numerators of the ratios give the Odentities, and
vice versa: if the nexus is in the numerator, then the
denominators give the Udentities.


That's the best explanation i can give.



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

From: microtonalist (2005-10-14)
Subject: Re: Otonal / Utonal

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In [email protected], "microtonalist" <mark@e...> wrote:
> 
> > Thus 3/2 is consonant in diatony but dissonant in pentatony. 
> > Conversely 4/3 is consonant in pentatony but dissonant in diatony.
> 
> Is there any evidence this is so?
>
Lendvai provides some examples, which sonically are suggestive, but 
otherwise it's just an assertion of his.

What I will say from my own experience is that consonance and 
dissonance are relative concepts, and can often only be defined in 
the context of the music. Absolute consonance and dissonance are 
chimerae, IMHO.

One of the best examples of this is when an accidental 'consonance' 
creeps into a performance of Webern or similar 'squeaky gate' music - 
it sounds jarring and disturbs the flow.

Mark

PS 'squeaky gate' is used here not in the pejorative sense, but as a 
descriptive term.

From: microtonalist (2005-10-14)
Subject: Re: equal divisions, subharmonic?

(IF you know all this, please ignore it: else read on)

Suppose one started with a string, and divided it into say twelve equal 
sized parts. The full string would then have (for a given thickness and 
tension of string) a frequency, which we will call f.

Stopping the string 1/12th of the way from one end (the first division) 
will result in a string that is 11/12ths of the original length. If we 
make the assumption that tension does not change as a result of 
stopping the string, then the new frequency will be 12/11ths of the old 
frequency. 

similarly stopping one more 12th along, 10/12ths of the string remain, 
giving a frequency that is 12/10ths of the unstopped string frequency.

And so it goes. With each new step the interval size increases:

Open String = 1/1
1st stop/fret = 12/11
2nd = 12/10 = 6/5
3rd = 12/9 = 4/3
4th = 12/8 = 3/2
5th = 12/7
6th = 12/6 = 2/1 (octave)
etc.

The intervals between adjacent ascending notes is 12/11 11/10 10/9 9/8 
8/7 ... are the same intervals between adjacent notes of the harmonic 
series, but in reverse order.

Of course, any equal divisions along a string produce a subharmonic 
series or a partition of it.

All of the above is true for pipes, with the caveat that pipes suffer 
from end effects, the helmholtz effect (mass of the air where the holes 
are) and other perturbations away from the pure solution.

As an example of a partition of a subharmonic series, suppose the first 
stopping point is 2/13ths of the length of the string. The first note 
is then 13/11. Subsequent stopping points are spaced as 1/8th of the 
unstopped string length. The scale is then

2/13th +1/8th  +2/8th  +3/8th +4/8th ...
13/11  104/75   52/31   52/27  26/17 ...

hopefully this makes some sense.

Mark





--- In [email protected], "traktus5" <kj4321@h...> wrote:
>
> > Finally, it should be of interest to those who don't already know 
> > that although a string or a pipe vibrates according to the harmonic 
> > series, if a string is equally divided or a pipe has holes made at 
> > equal points 
> 
> divided how, exactly?  any division of equal spacing?...
> 
> along it then a subharmonic series results from the 
> > resulting scales. It may be interesting to conjecture that perhaps 
> > for early humans, equal division of the physical object (string or 
> > bone flute) was easier than logarithmic.
> 
> Can someone elaborate?  
> 
> thanks.
>

From: monz (2005-10-14)
Subject: sonance vs. accordance (was: Otonal / Utonal)

Hi Mark,


--- In [email protected], "microtonalist" <mark@e...> wrote:

> What I will say from my own experience is that consonance
> and dissonance are relative concepts, and can often only be
> defined in the context of the music. Absolute consonance and
> dissonance are chimerae, IMHO.
> 
> One of the best examples of this is when an accidental
> 'consonance' creeps into a performance of Webern or similar
> 'squeaky gate' music - it sounds jarring and disturbs
> the flow.



This has come up here several times before. 

First of all, it's been a part of my theory from the
beginning -- following Helmholtz, Schoenberg, and Partch
-- that consonance and dissonance are not opposed in kind
but only in degree. That is, they're not two different
things, but rather two opposite ends of a continuum.

Thus i chose to use the term "sonance" to represent
the whole continuum, instead of always having to say
"relative consonance/dissonance" as Partch did. Thinking
about it this way also greatly clarifies Schoenberg's
thoughts about the subject.

Then, several years ago, it was recognized by a bunch
of us here on this list that sonance is context dependant,
exactly as you say in what i quoted above. So several
of us decided:

* to use the term "sonance" (and the related terms
"consonance" and "dissonance") specifically to refer
to cases where musical context determined the relative
consonance or dissonance of a particular sonority, and

* to employ the term "accordance" (and the related
"concord" and "discord") specifically to refer to the
psychoacoustical perception of a sonority, independent
of its musical context.


I wrote about this here to someone else recently (a couple
of months ago) and it caused a big discussion, with most
people saying that the terms should be used the other
way around: "concord/discord" for the context-dependent
cases and "consonance/dissonance" for the psychoacoustical
perception.

The terms have been defined in the first way in my
Encyclopedia for 7 years now, and obviously are a part
of many Encyclopedia entries, so i'm not about to
change them. So i argued a bit in the recent discussion,
but didn't give it much more thought and don't remember
if there was a consensus, and if so, what it was. 

I'll be continuing to use "accordance/concord/discord" for the
psychoacoustical perception, and "sonance/consonance/dissonance"
for the musical-context-dependent perception.



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

From: Ozan Yarman (2005-10-14)
Subject: Re: [tuning] Otonal / Utonal

This is a very enlightening explanation.
  ----- Original Message ----- 
  From: microtonalist 
  To: [email protected] 
  Sent: 10 Ekim 2005 Pazartesi 17:08 
  Subject: [tuning] Otonal / Utonal


  One way that has helped me understand the utonal and otonal 
  difference is as follows

  Otonal - a collection of pitches that can be construed as the 
  overtones of a common fundamental: 

  5/4 3/2 9/8 for example

  Utonal - a collection of pitches that can be construed as 
  fundamentals having a common overtone:

  4/3 8/5 8/7. These having an overtone of 1/1 (1/1 is the 3/2 of 4/3, 
  1/1 is the 5/4 of 8/5 and 1/1 is the 7/4 of 8/7).

  An otonal group share a common udentity and a utonal group share a 
  common odentity. u for undernumber and o for overnumber.

  Here 1/1 refers to a reference pitch. Any pitch can be construed 
  either as a new fundamental (the overtone series being the 
  overarching example), or as the overtone of a new fundamental.

  Partch's tonality diamond takes 1 3 5 7 9 and 11 'identities' and 
  treats them each way, as overtone (odentity) and fundamental 
  (udentity).

  Mark

From: wallyesterpaulrus (2005-10-14)
Subject: Re: Otonal / Utonal

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In [email protected], "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> 
> > I do believe many academics have neglected the possibility and
> reality of pentatonic 
> > hearing.
> 
> What does "pentatonic hearing" mean?

Many academics in a number of different music theory fields take it 
that when we hear music, we hear partly in terms of generic diatonic 
interval classes -- thus, a 300-cent interval will be heard as an 
augmented second or a minor third (depending on context), which 
correspond to 1 or 2 steps, respectively, in the 7-note diatonic 
scale. In other words, everything is heard in terms of a presumed 
underlying (though flexible) 7-note framework. I'd call this an 
assumption of "diatonic hearing", and it may apply to much Western 
music, but even in the blues I'm pretty sure that quite a bit 
of "pentatonic hearing" happens instead, with 5 rather than 7 generic 
interval sizes per octave.

From: wallyesterpaulrus (2005-10-14)
Subject: Re: Otonal / Utonal

--- In [email protected], "microtonalist" <mark@e...> wrote:

> Thus 3/2 is consonant in diatony but dissonant in pentatony. 
> Conversely 4/3 is consonant in pentatony but dissonant in diatony.

Doesn't jibe with my experience at all, but is reminiscent of Yasser's 
theory.

> similarly for other otonal and utonal ratios. Characteristically 
> Lendvai makes the six-four minor chord the tonic of a pentatonic 
> system i.e. C F Aflat (reading up from C).

What kind of pentatonic system uses that as a tonic?

> There are intervals that for a given 1/1 are neither utonal or otonal:

No interval is either utonal or otonal; you need at least three notes 
for that. Do you mean for 1/1 to be the third note?

> 6/5 5/3 7/5 9/7 etc, as neither odentity or udentity contain powers 
> of 2 only.

Even 5/4 or 8/5 are neither otonal nor utonal: they are just as easily 
expressed as 1/(4/5) and 1/(5/8).

> What should we call them - otonal or utonal? - or neither?

It seems you may be misunderstanding the concept. It takes at least 
three notes to be able to say whether the structure is more like a 
harmonic series or more like a subharmonic series (otonal or utonal).

From: wallyesterpaulrus (2005-10-14)
Subject: Re: sonance vs. accordance (was: Otonal / Utonal)

--- In [email protected], "monz" <monz@t...> wrote:
>
> Hi Mark,
> 
> 
> --- In [email protected], "microtonalist" <mark@e...> wrote:
> 
> > What I will say from my own experience is that consonance
> > and dissonance are relative concepts, and can often only be
> > defined in the context of the music. Absolute consonance and
> > dissonance are chimerae, IMHO.
> > 
> > One of the best examples of this is when an accidental
> > 'consonance' creeps into a performance of Webern or similar
> > 'squeaky gate' music - it sounds jarring and disturbs
> > the flow.

With regard to what Monz wrote below, I'd say that the explanation is 
that there are indeed context-independent things we can 
call 'concordance' and 'discordance' (though these are still relative 
terms, opposite ends of a continuum). And this is the very 
distinction that's needed to explain these disturbances in Webern's 
music -- a concordance stands out like a sore thumb in the context of 
lots of discordance, because it is *sonically* different from a 
discordance, whatever the context.

> This has come up here several times before. 
> 
> First of all, it's been a part of my theory from the
> beginning -- following Helmholtz, Schoenberg, and Partch
> -- that consonance and dissonance are not opposed in kind
> but only in degree. That is, they're not two different
> things, but rather two opposite ends of a continuum.
> 
> Thus i chose to use the term "sonance" to represent
> the whole continuum, instead of always having to say
> "relative consonance/dissonance" as Partch did. Thinking
> about it this way also greatly clarifies Schoenberg's
> thoughts about the subject.
> 
> Then, several years ago, it was recognized by a bunch
> of us here on this list that sonance is context dependant,
> exactly as you say in what i quoted above. So several
> of us decided:
> 
> * to use the term "sonance" (and the related terms
> "consonance" and "dissonance") specifically to refer
> to cases where musical context determined the relative
> consonance or dissonance of a particular sonority, and
> 
> * to employ the term "accordance" (and the related
> "concord" and "discord") specifically to refer to the
> psychoacoustical perception of a sonority, independent
> of its musical context.
> 
> 
> I wrote about this here to someone else recently (a couple
> of months ago) and it caused a big discussion, with most
> people saying that the terms should be used the other
> way around: "concord/discord" for the context-dependent
> cases and "consonance/dissonance" for the psychoacoustical
> perception.
> 
> The terms have been defined in the first way in my
> Encyclopedia for 7 years now, and obviously are a part
> of many Encyclopedia entries, so i'm not about to
> change them. So i argued a bit in the recent discussion,
> but didn't give it much more thought and don't remember
> if there was a consensus, and if so, what it was. 
> 
> I'll be continuing to use "accordance/concord/discord" for the
> psychoacoustical perception, and "sonance/consonance/dissonance"
> for the musical-context-dependent perception.
> 
> 
> 
> -monz
> http://tonalsoft.com
> Tonescape microtonal music software
>

From: monz (2005-10-15)
Subject: "pentatonic hearing" (was: Otonal / Utonal)

Hi Paul and Gene,


--- In [email protected], "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> --- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
> >
> > --- In [email protected], "wallyesterpaulrus"
> > <wallyesterpaulrus@y...> wrote:
> > 
> > > I do believe many academics have neglected the
> > > possibility and reality of pentatonic hearing.
> > 
> > What does "pentatonic hearing" mean?
> 
> Many academics in a number of different music theory fields
> take it that when we hear music, we hear partly in terms
> of generic diatonic interval classes -- thus, a 300-cent
> interval will be heard as an augmented second or a minor
> third (depending on context), which correspond to 1 or 2
> steps, respectively, in the 7-note diatonic scale. 
> In other words, everything is heard in terms of a presumed
> underlying (though flexible) 7-note framework. I'd call
> this an assumption of "diatonic hearing", and it may apply
> to much Western music, but even in the blues I'm pretty
> sure that quite a bit of "pentatonic hearing" happens
> instead, with 5 rather than 7 generic interval sizes per
> octave.



I agree with Paul 100%, about both the academic neglect
of "pentatonic hearing", and its relevance to the blues.



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

From: Gene Ward Smith (2005-10-15)
Subject: Re: "pentatonic hearing" (was: Otonal / Utonal)

--- In [email protected], "monz" <monz@t...> wrote:

> I agree with Paul 100%, about both the academic neglect
> of "pentatonic hearing", and its relevance to the blues.

Blues sounds decidedly un-pentatonic to me. I'd say a good scale for
producing a vaguely bluesy sound is Orwell[9]; not that it's a blues
scale, but all those 7/6s give it a sort of blue note feel. Isn't that
what you need for blues--a few blue notes?

From: Gene Ward Smith (2005-10-15)
Subject: Re: Otonal / Utonal

--- In [email protected], "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> Many academics in a number of different music theory fields take it 
> that when we hear music, we hear partly in terms of generic diatonic 
> interval classes -- thus, a 300-cent interval will be heard as an 
> augmented second or a minor third (depending on context), which 
> correspond to 1 or 2 steps, respectively, in the 7-note diatonic 
> scale. In other words, everything is heard in terms of a presumed 
> underlying (though flexible) 7-note framework. I'd call this an 
> assumption of "diatonic hearing", and it may apply to much Western 
> music, but even in the blues I'm pretty sure that quite a bit 
> of "pentatonic hearing" happens instead, with 5 rather than 7 generic 
> interval sizes per octave.

From your language it seems the underlying assumption is some kind of
meantone system (since we have augmented seconds vs minor thirds,
etc.) Is this another of those Eytan Agmon deals, where people assume
meantone without, apparently, realizing they are doing so?

From: Carl Lumma (2005-10-15)
Subject: Re: "pentatonic hearing" (was: Otonal / Utonal)

> I agree with Paul 100%, about both the academic neglect
> of "pentatonic hearing", and its relevance to the blues.

I don't know about its neglect (not that I doubt it), but
I certainly agree about its import.

-Carl

From: klaus schmirler (2005-10-15)
Subject: Re: [tuning] Re: "pentatonic hearing" (was: Otonal / Utonal)

Gene Ward Smith wrote:

> --- In [email protected], "monz" <monz@t...> wrote:
> 
> 
>>I agree with Paul 100%, about both the academic neglect
>>of "pentatonic hearing", and its relevance to the blues.
> 
> 
> Blues sounds decidedly un-pentatonic to me. I'd say a good scale for
> producing a vaguely bluesy sound is Orwell[9]; not that it's a blues
> scale, but all those 7/6s give it a sort of blue note feel. Isn't that
> what you need for blues--a few blue notes?

I play 7/6, which raises a few eyebrows but is generally accepted. 
Monz found 19/16 used as a blue note. But the general definition in 
practically all the literature (I don't know any exceptions) speaks 
about neutral thirds and sevenths. Guitarists play it like that.

I've asked before and do it again: Who brought up the notion that blue 
notes are septimal intervals, or are extra low thirds?

klaus

From: monz (2005-10-15)
Subject: Re: "pentatonic hearing" (was: Otonal / Utonal)

Hi Gene and klaus,


--- In [email protected], klaus schmirler <KSchmir@o...> wrote:
>
> Gene Ward Smith wrote:
> 
> > --- In [email protected], "monz" <monz@t...> wrote:
> > 
> > 
> >> I agree with Paul 100%, about both the academic neglect
> >> of "pentatonic hearing", and its relevance to the blues.
> > 
> > 
> > Blues sounds decidedly un-pentatonic to me. I'd say a
> > good scale for producing a vaguely bluesy sound is 
> > Orwell[9]; not that it's a blues scale, but all those
> > 7/6s give it a sort of blue note feel. Isn't that
> > what you need for blues--a few blue notes?


Blues is founded essentially on the minor pentatonic scale
-- to take the simplest example: A C D E G. 

Just try a little improvising with that scale, making sure
that you keep the tonic on A, and not C or another note,
and what you play will probably already sound quite bluesy,
even in 12-edo.

The way blues guitartists play the blues, they basically
fret those 5 notes, and then apply strategic pitch-bending
wherever they feel that it belongs, most usually bending
up the minor-3rd and the 4th ... and remember that on the
guitar, the bending only goes in one direction: up.

And the blues was originally (back in the late 1800s)
a strictly vocal music, so the guitar style evolved
after the manner of the vocals, which we know is free
to roam wherever the singer wants it to.

A blues scale typically played by keyboard players
would be: A C D D#/Eb E G G#/Ab. Those chromatic notes
are simply an analgoue of what the guitarists do,
since you can't bend notes on a regular piano.
 

> I play 7/6, which raises a few eyebrows but is generally
> accepted.  Monz found 19/16 used as a blue note. But the
> general definition in practically all the literature 
> (I don't know any exceptions) speaks about neutral thirds
> and sevenths. Guitarists play it like that.
> 
> I've asked before and do it again: Who brought up the
> notion that blue notes are septimal intervals, or are
> extra low thirds?


I'm certain that the idea that blue notes are septimal
ratios comes from the fact that in the blues, *every*
chord is a dominant-7th chord. 

This is fundamentally different from Euro-style 
"common-practice" usage, where the dominant-7th chord
is a dissonance which must be resolved, and typically
only appears as the "dominant" (V), with the root of
the chord on the 5th degree of the diatonic scale ...
or it functions exactly like that in cases where a
different chord has chromatic substitutions.

In blues this is not the case. *Every* chord is a
dominant-7th chord, and none of them set up the kind
of tension-->resolution expectation as they do in
Euro-style music.

Thus, in blues the dominant-7th chord is the funadamental
consonance. This IMO encourages the listener's ears to
interpret *every* chord as a 4:5:6:7 proportion.

So let's say we have a vocalist or guitarist jamming
away on the A C D E G pentatonic scale with pitch-bends.
The chords which go with that scale in the blues 
typically follow the 12-measure progression: 
A7 / / / D7 / A7 / E7 D7 A7 E7.

If the listener's ear is already hearing the melodic G
as a 7/4 above A, the melodic C as a 7/4 above D, and
the melodic D as a 7/4 above E, and with all the bending
going on, the guitarist and vocalist may indeed be 
*playing* those notes lower in pitch so that they
really *are* septimal intervals.

If the D is approximately a 4/3 above the tonic A, and
the C is approximately a 7/4 above the D, then when the
A7 comes back around, that C will be heard as a 7/6.

So that's my theory on why theorists persist in claiming
that septimal intervals are important to the blues.

Of course the real situation is much more complicated
than that. Old-school (i.e., Delta) blues musicians
didn't know anything about Western music-theory, and
played and sang whatever damn notes they felt. For an
example of the richness of notes available to them, see:

http://sonic-arts.org/monzo/rjohnson/drunken.htm

The tonic of this piece is D. The scale Johnson used
in his vocals in this song is interesting in that,
if you try to describe it in terms of 12-edo or meantone,
you basically get: D F# G G#/Ab A A#/Bb B C C#.
So it's essentially a chromatic scale, but with a
big gap between the D and F#. But it could still,
with less accuracy, be notated and performed simply 
with D F G A C, and it wouldn't really sound "wrong".

And keep in mind that this tune is one of Robert Johnson's
*simplest* performances. Given all the time i spent on
analyzing this, i wish i had done _Hellhound On My Trail_
instead, which is mind-boggling in its pitch complexity,
considering that it's just one guy playing a guitar and
singing.



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

From: Gene Ward Smith (2005-10-15)
Subject: Re: "pentatonic hearing" (was: Otonal / Utonal)

--- In [email protected], "monz" <monz@t...> wrote:

> In blues this is not the case. *Every* chord is a
> dominant-7th chord, and none of them set up the kind
> of tension-->resolution expectation as they do in
> Euro-style music.

It seems to me there is a contradiction here. You can't very well have 
a lot of dominant seventh chords *and* a scale with only five notes in it.

> Thus, in blues the dominant-7th chord is the funadamental
> consonance. This IMO encourages the listener's ears to
> interpret *every* chord as a 4:5:6:7 proportion.

That makes more sense if in fact the chords are not dominant seventh
chords in a strict sense, but chords like CEGA#, with augmented
seconds; but then you might be getting blue notes in the form
GA#, etc.

> If the listener's ear is already hearing the melodic G
> as a 7/4 above A, the melodic C as a 7/4 above D, and
> the melodic D as a 7/4 above E, and with all the bending
> going on, the guitarist and vocalist may indeed be 
> *playing* those notes lower in pitch so that they
> really *are* septimal intervals.

It makes sense to me, but do they?

> The tonic of this piece is D. The scale Johnson used
> in his vocals in this song is interesting in that,
> if you try to describe it in terms of 12-edo or meantone,
> you basically get: D F# G G#/Ab A A#/Bb B C C#.

What does G#/Ab signify?

From: monz (2005-10-15)
Subject: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

Hi Gene,


--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In [email protected], "monz" <monz@t...> wrote:
> 
> > In blues this is not the case. *Every* chord is a
> > dominant-7th chord, and none of them set up the kind
> > of tension-->resolution expectation as they do in
> > Euro-style music.
> 
> It seems to me there is a contradiction here. You can't
> very well have a lot of dominant seventh chords *and* a
> scale with only five notes in it.



Yes, absolutely correct -- i should have gone into more
detail in my explanation.

In effect, blues actually uses two different pitch-class sets
simultaneously -- one melodically and another harmonically. 

Melodically, the scale basis is the minor pentatonic, and
harmonically, the chords are all dominant-7th chords.

Thus, for the example i used where the tonic is "A", the
melodic basis is the A C D E G minor pentatonic, with lots
of pitch-bending and sliding around allowed. The harmonic
basis is the 9-note scale A B C C# D E F# G G#, which gives
all the notes necessary for the A7, D7, and E7 chords.

This 9-note scale is interesting in itself, because it
exhibits tetrachordal similarity: A B C C# D and E F# G G# A
both have the same tone(t) and semitone(s) pattern: t s s s,
with a "tone of disjunction" between D and E which mirrors
the tone between A and B so that one might also recognize
pentachordal similarity. But that scale is really only an
artifact of the chords. Notice also that the A C D E G
minor pentatonic is included as a subset within it.

 
> > Thus, in blues the dominant-7th chord is the funadamental
> > consonance. This IMO encourages the listener's ears to
> > interpret *every* chord as a 4:5:6:7 proportion.
> 
> That makes more sense if in fact the chords are not
> dominant seventh chords in a strict sense, but chords
> like CEGA#, with augmented seconds; but then you might
> be getting blue notes in the form GA#, etc.


What you're saying is correct, and in fact the G A#
augmented-2nd is quite close to the 7/6 ratio i mentioned
later. But i doubt very strongly that any blues musician,
at least from the first half of the 20th century, was
using meantone either in theory or practice in any form.
The basic blues instrument has always been the 12-edo guitar.


 
> > If the listener's ear is already hearing the melodic G
> > as a 7/4 above A, the melodic C as a 7/4 above D, and
> > the melodic D as a 7/4 above E, and with all the bending
> > going on, the guitarist and vocalist may indeed be 
> > *playing* those notes lower in pitch so that they
> > really *are* septimal intervals.
> 
> It makes sense to me, but do they?


As i said, blues musicians and vocalists bend and slide
the pitches of the notes all over the place ... unless
they simply can't, as on a piano -- in which case, they
actually often resort to playing two notes a semitone
apart simultaneously, in order to sort of trick the ear 
into accepting that it is hearing a note that lies between
those two.

This is a standard part of blues piano technique, and
something that the visionary jazz pianist/composer 
Thelonius Monk made into a distinctive part of his
harmonic style.


 
> > The tonic of this piece is D. The scale Johnson used
> > in his vocals in this song is interesting in that,
> > if you try to describe it in terms of 12-edo or meantone,
> > you basically get: D F# G G#/Ab A A#/Bb B C C#.
> 
> What does G#/Ab signify?


* That if one insists on labeling the notes in Johnson's
vocal with the standard meantone names, then one would
have to call it G# when ascending and Ab when descending.

* That if one insists on labeling the notes in Johnson's
vocal as 12-edo notes, then it is equally valid to call
that 12-edo note by either name.

Same thing goes for A#/Bb.

But my point really is that Johnson's vocal is so rich in
microtonal subtlety that it's pointless to force it into
these notational straight-jackets.


I've written here many times before about how hard it was
for me, and how long it took, to recognize what was really
going on pitch-wise in the blues, because of the fact that
i had gotten so firmly indoctrinated into standard Western
(Euro) music-theory. 

It wasn't until i finally got a firm grasp on Partch's
theories and on microtonality in general that i finally was
able to really recognize and copy what blues musicians do.
Before that, my attempts to make blues music were truly
laughable.



-monz
http://tonalsoft.com
Tonescape microtonal music theory

From: monz (2005-10-15)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

--- In [email protected], "monz" <monz@t...> wrote:

> > > Thus, in blues the dominant-7th chord is the funadamental
> > > consonance. This IMO encourages the listener's ears to
> > > interpret *every* chord as a 4:5:6:7 proportion.
> > 
> > That makes more sense if in fact the chords are not
> > dominant seventh chords in a strict sense, but chords
> > like CEGA#, with augmented seconds; but then you might
> > be getting blue notes in the form GA#, etc.
> 
> 
> What you're saying is correct, and in fact the G A#
> augmented-2nd is quite close to the 7/6 ratio i mentioned
> later. But i doubt very strongly that any blues musician,
> at least from the first half of the 20th century, was
> using meantone either in theory or practice in any form.
> The basic blues instrument has always been the 12-edo guitar.



Of course, 12-edo is also a meantone, so i should have
been more accurate and said that "i doubt very strongly that
any blues musician ... was using a non-12edo meantone ...".



-monz
http://tonalsoft.com
Tonescape microtonal music theory

From: Gene Ward Smith (2005-10-16)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

--- In [email protected], "monz" <monz@t...> wrote:

> This 9-note scale is interesting in itself, because it
> exhibits tetrachordal similarity: A B C C# D and E F# G G# A
> both have the same tone(t) and semitone(s) pattern: t s s s,
> with a "tone of disjunction" between D and E which mirrors
> the tone between A and B so that one might also recognize
> pentachordal similarity. But that scale is really only an
> artifact of the chords. Notice also that the A C D E G
> minor pentatonic is included as a subset within it.

I note that Orwell[9] is also a 9-note scale with a lot of septimal
harmony, though no tetrads. The pattern there is SLSLSLSLS. 

> It wasn't until i finally got a firm grasp on Partch's
> theories and on microtonality in general that i finally was
> able to really recognize and copy what blues musicians do.
> Before that, my attempts to make blues music were truly
> laughable.

Which scales or tunings would you regard as suitable for making a more
or less bluesy sound? Would you consider Orwell[9], for instance, as
too far from the requirements?

From: monz (2005-10-16)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In [email protected], "monz" <monz@t...> wrote:
> 
> > This 9-note scale is interesting in itself, because it
> > exhibits tetrachordal similarity: A B C C# D and E F# G G# A
> > both have the same tone(t) and semitone(s) pattern: t s s s,
> > with a "tone of disjunction" between D and E which mirrors
> > the tone between A and B so that one might also recognize
> > pentachordal similarity. But that scale is really only an
> > artifact of the chords. Notice also that the A C D E G
> > minor pentatonic is included as a subset within it.
> 
> I note that Orwell[9] is also a 9-note scale with a lot of
> septimal harmony, though no tetrads. The pattern there
> is SLSLSLSLS. 
> 
> > It wasn't until i finally got a firm grasp on Partch's
> > theories and on microtonality in general that i finally was
> > able to really recognize and copy what blues musicians do.
> > Before that, my attempts to make blues music were truly
> > laughable.
> 
> Which scales or tunings would you regard as suitable for
> making a more or less bluesy sound? Would you consider
> Orwell[9], for instance, as too far from the requirements?
>



Honestly, i never tried setting up an actual tuning and
composing a blues in it until just now. I pretty much
just did it "on the fly" before, bending notes on either
the guitar or synthesizer.

Do you mean the 9-note orwell MOS which i show on the
graphs at the bottom of the Encyclopedia page, with a
generator of ~271.304 cents?

http://tonalsoft.com/enc/o/orwell.aspx


I set it up in Tonescape and started composing a blues
in it, but i made A the tonic and it lacks anything
close to a G.

Recommend an orwell[9] for me which would be good with
A as tonic. Cents values are fine ... if you can give
enough info for me to set up a lattice of at least
2 dimensions that would be great.



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

From: Ozan Yarman (2005-10-16)
Subject: Re: [tuning] Re: "pentatonic hearing" (was: Otonal / Utonal)

No wonder Erkan Ogur seems to incorporate Maqam Music so easily with the Blues style.
  ----- Original Message ----- 
  From: klaus schmirler 
  To: [email protected] 
  Sent: 15 Ekim 2005 Cumartesi 12:29 
  Subject: Re: [tuning] Re: "pentatonic hearing" (was: Otonal / Utonal)


  Gene Ward Smith wrote:

  > --- In [email protected], "monz" <monz@t...> wrote:
  > 
  > 
  >>I agree with Paul 100%, about both the academic neglect
  >>of "pentatonic hearing", and its relevance to the blues.
  > 
  > 
  > Blues sounds decidedly un-pentatonic to me. I'd say a good scale for
  > producing a vaguely bluesy sound is Orwell[9]; not that it's a blues
  > scale, but all those 7/6s give it a sort of blue note feel. Isn't that
  > what you need for blues--a few blue notes?

  I play 7/6, which raises a few eyebrows but is generally accepted. 
  Monz found 19/16 used as a blue note. But the general definition in 
  practically all the literature (I don't know any exceptions) speaks 
  about neutral thirds and sevenths. Guitarists play it like that.

  I've asked before and do it again: Who brought up the notion that blue 
  notes are septimal intervals, or are extra low thirds?

  klaus

From: Mohajeri Shahin (2005-10-17)
Subject: RE: [tuning] Re: equal divisions, subharmonic?

HI

AS I TOLD BEFORE THIS SYSTEM WAS FIRST STUDIED BY IBN SINA IN TANBOUR
BAGHDAD.

THANKS

 

________________________________

From: [email protected] [mailto:[email protected]] On Behalf
Of microtonalist
Sent: Friday, October 14, 2005 4:35 PM
To: [email protected]
Subject: [tuning] Re: equal divisions, subharmonic?

 

(IF you know all this, please ignore it: else read on)

Suppose one started with a string, and divided it into say twelve equal 
sized parts. The full string would then have (for a given thickness and 
tension of string) a frequency, which we will call f.

Stopping the string 1/12th of the way from one end (the first division) 
will result in a string that is 11/12ths of the original length. If we 
make the assumption that tension does not change as a result of 
stopping the string, then the new frequency will be 12/11ths of the old 
frequency. 

similarly stopping one more 12th along, 10/12ths of the string remain, 
giving a frequency that is 12/10ths of the unstopped string frequency.

And so it goes. With each new step the interval size increases:

Open String = 1/1
1st stop/fret = 12/11
2nd = 12/10 = 6/5
3rd = 12/9 = 4/3
4th = 12/8 = 3/2
5th = 12/7
6th = 12/6 = 2/1 (octave)
etc.

The intervals between adjacent ascending notes is 12/11 11/10 10/9 9/8 
8/7 ... are the same intervals between adjacent notes of the harmonic 
series, but in reverse order.

Of course, any equal divisions along a string produce a subharmonic 
series or a partition of it.

All of the above is true for pipes, with the caveat that pipes suffer 
from end effects, the helmholtz effect (mass of the air where the holes 
are) and other perturbations away from the pure solution.

As an example of a partition of a subharmonic series, suppose the first 
stopping point is 2/13ths of the length of the string. The first note 
is then 13/11. Subsequent stopping points are spaced as 1/8th of the 
unstopped string length. The scale is then

2/13th +1/8th  +2/8th  +3/8th +4/8th ...
13/11  104/75   52/31   52/27  26/17 ...

hopefully this makes some sense.

Mark





--- In [email protected], "traktus5" <kj4321@h...> wrote:
>
> > Finally, it should be of interest to those who don't already know 
> > that although a string or a pipe vibrates according to the harmonic 
> > series, if a string is equally divided or a pipe has holes made at 
> > equal points 
> 
> divided how, exactly?  any division of equal spacing?...
> 
> along it then a subharmonic series results from the 
> > resulting scales. It may be interesting to conjecture that perhaps 
> > for early humans, equal division of the physical object (string or 
> > bone flute) was easier than logarithmic.
> 
> Can someone elaborate?  
> 
> thanks.
>






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From: microtonalist (2005-10-17)
Subject: Re: equal divisions, subharmonic?

> (If you know all this, please ignore it: else read on)

Also, not everyone knows what you know, and sometimes people like to 
know without having to go find some theorist's work somewhere. What 
is obvious to you is not obvious to another person.

and there's no need to shout, either. See nettiquette rules, please.

Mark

--- In [email protected], "Mohajeri Shahin" <shahinm@k...> wrote:
>
> HI
> 
> AS I TOLD BEFORE THIS SYSTEM WAS FIRST STUDIED BY IBN SINA IN 
TANBOUR
> BAGHDAD.
> 
> THANKS
> 
>  
> 
> ________________________________
> 
> From: [email protected] [mailto:[email protected]] On 
Behalf
> Of microtonalist
> Sent: Friday, October 14, 2005 4:35 PM
> To: [email protected]
> Subject: [tuning] Re: equal divisions, subharmonic?
> 
>  
[snipt]

From: Mohajeri Shahin (2005-10-17)
Subject: RE: [tuning] Re: Otonal / Utonal

EXCUSE ME ...... I MADE A MISTAKE ......IN THESE 2 SYSTEMS ,WHICH THE
FIRST IS OTONAL AND THE LAST UTONAL THE NUMBER OF DEGREES ARE THE SAME
(=8) BUT  THE RELATION BETWEEN THEIR NUMERARY NEXUS(N.N) OF IS SO : 

 

N.N OF UTONAL = 2 * N.N OF OTONAL

 

 

0:          1/1               0.000 unison, perfect prime

  1:          9/8             203.910 major whole tone

  2:          5/4             386.314 major third

  3:         11/8             551.318 undecimal semi-augmented fourth

  4:          3/2             701.955 perfect fifth

  5:         13/8             840.528 tridecimal neutral sixth

  6:          7/4             968.826 harmonic seventh

  7:         15/8            1088.269 classic major seventh

  8:          2/1            1200.000 octave

|

  0:          1/1               0.000 unison, perfect prime

  1:         16/15            111.731 minor diatonic semitone

  2:          8/7             231.174 septimal whole tone

  3:         16/13            359.472 tridecimal neutral third

  4:          4/3             498.045 perfect fourth

  5:         16/11            648.682 undecimal semi-diminished fifth

  6:          8/5             813.686 minor sixth

  7:         16/9             996.090 Pythagorean minor seventh

  8:          2/1            1200.000 octave

 

________________________________

From: [email protected] [mailto:[email protected]] On Behalf
Of wallyesterpaulrus
Sent: Thursday, October 13, 2005 12:37 AM
To: [email protected]
Subject: [tuning] Re: Otonal / Utonal

 

--- In [email protected], "Mohajeri Shahin" <shahinm@k...> wrote:

> 4-in otonal and utonal systems with same number of degrees ,
> udentity=2*odentity.

How did you come to that conclusion?





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________________________________

From: wallyesterpaulrus (2005-10-17)
Subject: Re: "pentatonic hearing" (was: Otonal / Utonal)

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In [email protected], "monz" <monz@t...> wrote:
> 
> > I agree with Paul 100%, about both the academic neglect
> > of "pentatonic hearing", and its relevance to the blues.
> 
> Blues sounds decidedly un-pentatonic to me. I'd say a good scale for
> producing a vaguely bluesy sound is Orwell[9]; not that it's a blues
> scale, but all those 7/6s give it a sort of blue note feel. Isn't that
> what you need for blues--a few blue notes?

The "blue third" is far more commonly a neutral third rather than a 
7/6. Meanwhile, alterations in the pitches don't contradict the 
underlying pentatonic fabric/language, any more than chromatically 
expressive common-practice music contradicts the underlying diatonicism 
thereof.

From: wallyesterpaulrus (2005-10-17)
Subject: Re: Otonal / Utonal

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In [email protected], "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
> 
> > Many academics in a number of different music theory fields take 
it 
> > that when we hear music, we hear partly in terms of generic 
diatonic 
> > interval classes -- thus, a 300-cent interval will be heard as an 
> > augmented second or a minor third (depending on context), which 
> > correspond to 1 or 2 steps, respectively, in the 7-note diatonic 
> > scale. In other words, everything is heard in terms of a presumed 
> > underlying (though flexible) 7-note framework. I'd call this an 
> > assumption of "diatonic hearing", and it may apply to much 
Western 
> > music, but even in the blues I'm pretty sure that quite a bit 
> > of "pentatonic hearing" happens instead, with 5 rather than 7 
generic 
> > interval sizes per octave.
> 
> From your language it seems the underlying assumption is some kind 
of
> meantone system (since we have augmented seconds vs minor thirds,
> etc.)

My assumption was 12-equal. As far as augmented seconds actually 
being tuned differently than minor thirds, you have that in plenty of 
non-meantone systems, including plain old Pythagorean -- but that's 
irrelevant here.

> Is this another of those Eytan Agmon deals, where people assume
> meantone without, apparently, realizing they are doing so?

It seemed to me that that claim of yours was an unfortunate result of 
your fairly willful misunderstanding of his work, but I don't care to 
rehash this here or now.

From: wallyesterpaulrus (2005-10-17)
Subject: Re: "pentatonic hearing" (was: Otonal / Utonal)

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:

> > If the listener's ear is already hearing the melodic G
> > as a 7/4 above A, the melodic C as a 7/4 above D, and
> > the melodic D as a 7/4 above E, and with all the bending
> > going on, the guitarist and vocalist may indeed be 
> > *playing* those notes lower in pitch so that they
> > really *are* septimal intervals.
> 
> It makes sense to me, but do they?

As Monz himself pointed out, guitarists virtually always do the 
opposite, and bend these notes *up* by about a quarter-tone (modulo 
lots of vibrato, etc.). I'll leave my professional experience out of 
this for now . . . I've heard vocalists do both the raising and the 
lowering, in different modern "bluesy" contexts, but the 
old "authentic" blues that I've heard has no traces of 7-limit tuning 
tendencies.

From: Gene Ward Smith (2005-10-17)
Subject: Re: Otonal / Utonal

--- In [email protected], "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:

> It seemed to me that that claim of yours was an unfortunate result of 
> your fairly willful misunderstanding of his work, but I don't care to 
> rehash this here or now.

I wasn't the only one to think what he did looked a hell of a lot like
a description of meantone, please recall.

From: wallyesterpaulrus (2005-10-17)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

--- In [email protected], "monz" <monz@t...> wrote:

> > > If the listener's ear is already hearing the melodic G
> > > as a 7/4 above A, the melodic C as a 7/4 above D, and
> > > the melodic D as a 7/4 above E, and with all the bending
> > > going on, the guitarist and vocalist may indeed be 
> > > *playing* those notes lower in pitch so that they
> > > really *are* septimal intervals.
> > 
> > It makes sense to me, but do they?
> 
> 
> As i said, blues musicians and vocalists bend and slide
> the pitches of the notes all over the place

But not haphazardly. The minutiae of the bending and sliding are an 
integral part of the language, and learning them involves as precise 
and intense a period of practice, listening, and more practice as 
anything in classical music.

> ... unless
> they simply can't, as on a piano -- in which case, they
> actually often resort to playing two notes a semitone
> apart simultaneously, in order to sort of trick the ear 
> into accepting that it is hearing a note that lies between
> those two.

I think it's most relevant to point out here that pianists usually 
play two notes a semitone apart, *both* of which are higher than the 
supposed "septimal note", and that the note that lies between the two 
is the "neutral third" or other neutral scale degree that would be 
achieved by *raising*, not lowering, the minor pentatonic notes.

From: wallyesterpaulrus (2005-10-17)
Subject: Re: Otonal / Utonal

I believe the numerary nexus is 1 for both systems if each is related 
to a fixed 1/1 common to both, in some kind of Partchian diamondic 
system (and if not, "numerary nexus" doesn't have much meaning here). 
Why do you think otherwise?


--- In [email protected], "Mohajeri Shahin" <shahinm@k...> wrote:
>
> EXCUSE ME ...... I MADE A MISTAKE ......IN THESE 2 SYSTEMS ,WHICH 
THE
> FIRST IS OTONAL AND THE LAST UTONAL THE NUMBER OF DEGREES ARE THE 
SAME
> (=8) BUT  THE RELATION BETWEEN THEIR NUMERARY NEXUS(N.N) OF IS SO : 
> 
>  
> 
> N.N OF UTONAL = 2 * N.N OF OTONAL
> 
>  
> 
>  
> 
> 0:          1/1               0.000 unison, perfect prime
> 
>   1:          9/8             203.910 major whole tone
> 
>   2:          5/4             386.314 major third
> 
>   3:         11/8             551.318 undecimal semi-augmented 
fourth
> 
>   4:          3/2             701.955 perfect fifth
> 
>   5:         13/8             840.528 tridecimal neutral sixth
> 
>   6:          7/4             968.826 harmonic seventh
> 
>   7:         15/8            1088.269 classic major seventh
> 
>   8:          2/1            1200.000 octave
> 
> |
> 
>   0:          1/1               0.000 unison, perfect prime
> 
>   1:         16/15            111.731 minor diatonic semitone
> 
>   2:          8/7             231.174 septimal whole tone
> 
>   3:         16/13            359.472 tridecimal neutral third
> 
>   4:          4/3             498.045 perfect fourth
> 
>   5:         16/11            648.682 undecimal semi-diminished 
fifth
> 
>   6:          8/5             813.686 minor sixth
> 
>   7:         16/9             996.090 Pythagorean minor seventh
> 
>   8:          2/1            1200.000 octave
> 
>  
> 
> ________________________________
> 
> From: [email protected] [mailto:[email protected]] On 
Behalf
> Of wallyesterpaulrus
> Sent: Thursday, October 13, 2005 12:37 AM
> To: [email protected]
> Subject: [tuning] Re: Otonal / Utonal
> 
>  
> 
> --- In [email protected], "Mohajeri Shahin" <shahinm@k...> 
wrote:
> 
> > 4-in otonal and utonal systems with same number of degrees ,
> > udentity=2*odentity.
> 
> How did you come to that conclusion?
> 
> 
> 
> 
> 
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From: monz (2005-10-17)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

Hi Paul,


--- In [email protected], "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:
>
> --- In [email protected], "monz" <monz@t...> wrote:
> 
> > > > If the listener's ear is already hearing the melodic G
> > > > as a 7/4 above A, the melodic C as a 7/4 above D, and
> > > > the melodic D as a 7/4 above E, and with all the bending
> > > > going on, the guitarist and vocalist may indeed be 
> > > > *playing* those notes lower in pitch so that they
> > > > really *are* septimal intervals.
> > > 
> > > It makes sense to me, but do they?
> > 
> > 
> > As i said, blues musicians and vocalists bend and slide
> > the pitches of the notes all over the place
> 
> But not haphazardly. The minutiae of the bending and sliding are an 
> integral part of the language, and learning them involves as precise 
> and intense a period of practice, listening, and more practice as 
> anything in classical music.


Agree 100%, again.

 
> > ... unless
> > they simply can't, as on a piano -- in which case, they
> > actually often resort to playing two notes a semitone
> > apart simultaneously, in order to sort of trick the ear 
> > into accepting that it is hearing a note that lies between
> > those two.
> 
> I think it's most relevant to point out here that pianists
> usually play two notes a semitone apart, *both* of which
> are higher than the supposed "septimal note", and that the
> note that lies between the two is the "neutral third" or
> other neutral scale degree that would be achieved by
> *raising*, not lowering, the minor pentatonic notes.


Yes! Thanks for pointing that out, it's absolutely correct.

As i said, i really think the main reason so many
microtonalists think of blues as "septimal" is because
of the fact that *all* of the chords are dominant-7ths,
and the 7ths are not felt as dissonances in need of
resolution, which leads the ear into perceiving the
harmony *in a general sense* as a bunch of 4:5:6:7 ratios.



-monz
http://tonalsoft.com
Tonescape microtonal music theory

From: monz (2005-10-17)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

Hi Gene,


I guess you missed this. I asked you directly to
furnish me with a scale, because i was inspired to
start composing some Orwell Blues! Please do!

See my original reply for the quote from you:
http://launch.groups.yahoo.com/group/tuning/message/61486


--- In [email protected], "monz" <monz@t...> wrote:
>
> Honestly, i never tried setting up an actual tuning and
> composing a blues in it until just now. I pretty much
> just did it "on the fly" before, bending notes on either
> the guitar or synthesizer.
> 
> Do you mean the 9-note orwell MOS which i show on the
> graphs at the bottom of the Encyclopedia page, with a
> generator of ~271.304 cents?
> 
> http://tonalsoft.com/enc/o/orwell.aspx
> 
> 
> I set it up in Tonescape and started composing a blues
> in it, but i made A the tonic and it lacks anything
> close to a G.
> 
> Recommend an orwell[9] for me which would be good with
> A as tonic. Cents values are fine ... if you can give
> enough info for me to set up a lattice of at least
> 2 dimensions that would be great.
 
 
 
-monz
http://tonalsoft.com
Tonescape microtonal music software

From: Kraig Grady (2005-10-17)
Subject: Re: "pentatonic hearing" (was: Otonal / Utonal)

I think one of the reason the 7/6 has been incorporated into so many 
peoples blues interpretation, is just what the interval 'says'.

>
>Message: 21        
>   Date: Mon, 17 Oct 2005 20:22:25 -0000
>   From: "wallyesterpaulrus" <[email protected]>
>Subject: Re: "pentatonic hearing" (was: Otonal / Utonal)
>
>--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
>  
>
>>>If the listener's ear is already hearing the melodic G
>>>as a 7/4 above A, the melodic C as a 7/4 above D, and
>>>the melodic D as a 7/4 above E, and with all the bending
>>>going on, the guitarist and vocalist may indeed be 
>>>*playing* those notes lower in pitch so that they
>>>really *are* septimal intervals.
>>>      
>>>
>>It makes sense to me, but do they?
>>    
>>
>
>As Monz himself pointed out, guitarists virtually always do the 
>opposite, and bend these notes *up* by about a quarter-tone (modulo 
>lots of vibrato, etc.). I'll leave my professional experience out of 
>this for now . . . I've heard vocalists do both the raising and the 
>lowering, in different modern "bluesy" contexts, but the 
>old "authentic" blues that I've heard has no traces of 7-limit tuning 
>tendencies.
>
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 22        
>   Date: Mon, 17 Oct 2005 20:27:17 -0000
>   From: "Gene Ward Smith" <[email protected]>
>Subject: Re: Otonal / Utonal
>
>--- In [email protected], "wallyesterpaulrus"
><wallyesterpaulrus@y...> wrote:
>
>  
>
>>It seemed to me that that claim of yours was an unfortunate result of 
>>your fairly willful misunderstanding of his work, but I don't care to 
>>rehash this here or now.
>>    
>>
>
>I wasn't the only one to think what he did looked a hell of a lot like
>a description of meantone, please recall.
>
>
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 23        
>   Date: Mon, 17 Oct 2005 20:29:20 -0000
>   From: "wallyesterpaulrus" <[email protected]>
>Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))
>
>--- In [email protected], "monz" <monz@t...> wrote:
>
>  
>
>>>>If the listener's ear is already hearing the melodic G
>>>>as a 7/4 above A, the melodic C as a 7/4 above D, and
>>>>the melodic D as a 7/4 above E, and with all the bending
>>>>going on, the guitarist and vocalist may indeed be 
>>>>*playing* those notes lower in pitch so that they
>>>>really *are* septimal intervals.
>>>>        
>>>>
>>>It makes sense to me, but do they?
>>>      
>>>
>>As i said, blues musicians and vocalists bend and slide
>>the pitches of the notes all over the place
>>    
>>
>
>But not haphazardly. The minutiae of the bending and sliding are an 
>integral part of the language, and learning them involves as precise 
>and intense a period of practice, listening, and more practice as 
>anything in classical music.
>
>  
>
>>... unless
>>they simply can't, as on a piano -- in which case, they
>>actually often resort to playing two notes a semitone
>>apart simultaneously, in order to sort of trick the ear 
>>into accepting that it is hearing a note that lies between
>>those two.
>>    
>>
>
>I think it's most relevant to point out here that pianists usually 
>play two notes a semitone apart, *both* of which are higher than the 
>supposed "septimal note", and that the note that lies between the two 
>is the "neutral third" or other neutral scale degree that would be 
>achieved by *raising*, not lowering, the minor pentatonic notes.
>
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 24        
>   Date: Mon, 17 Oct 2005 20:37:07 -0000
>   From: "wallyesterpaulrus" <[email protected]>
>Subject: Re: No doubt about Lehman's Bach scale
>
>--- In [email protected], "Carl Lumma" <clumma@y...> wrote:
>  
>
>>>>Wow. Are all these beat rates referring to the beating of upper 
>>>>partials in a not-quite-JI chord?
>>>>        
>>>>
>>>For example, if I play an A major triad on my piano with the
>>>A tuned to 220 Hz, the C# to 275 Hz and the E tuned to 331 Hz,
>>>then I'll get beats between the 3rd partial of the A at 660 Hz
>>>and the 2nd partial of the E at 662 Hz.  These beats will be at
>>>662 - 660 = 2 Hz.
>>>      
>>>
>>Hi Yahya,
>>
>>I'll make a few comments.  If you want to wait for Paul's reply
>>to reply, that's fine by me.  I'm just thinking aloud waiting
>>for Paul's reply myself.
>>
>>I'm not sure why you're subtracting these beat rates here.
>>    
>>
>
>Sorry if I'm behind, but . . . subtracting beat rates? It seems Yahya 
>is merely calculating beat rates here (and correctly, I might add), 
>not subtracting any.
>
>  
>
>>As I think Paul was trying to say, beats are amplitude
>>modulation, which is sort of a second order sound wave.
>>They represent changes in the amplitude of a sound,
>>    
>>
>
>a pitch
>
>  
>
>>not
>>a sound
>>    
>>
>
>a pitch.
>
>  
>
>>in and of themselves.  AM is used for synthesis
>>and can create new pitches, called sidebands, but they
>>aren't at the frequency of the beats.
>>    
>>
>
>They're at the frequency of the original sine waves in Yahya's 
>example, if what you're modulating is a sine wave whose frequency is 
>the average of the two. You've just turned the equivalence of beating 
>with AM around, and applied it backwards, which is of course 
>perfectly valid to do.
>
>  
>
>>Perhaps sidebands
>>could be evoked from beating in an acoustic musical
>>instrument,
>>    
>>
>
>I think you've gotten a bit confused. The sidebands "created" by the 
>AM applied to the heard frequency would be identical to the original 
>frequencies in the musical instrument; the AM itself would be 
>identical to the beating heard.
>
>
>
>
>
>________________________________________________________________________
>________________________________________________________________________
>
>Message: 25        
>   Date: Mon, 17 Oct 2005 20:52:34 -0000
>   From: "wallyesterpaulrus" <[email protected]>
>Subject: Re: Beats (was No doubt about Lehman's Bach scale)
>
>--- In [email protected], "Yahya Abdal-Aziz" <yahya@m...> wrote:
>
>  
>
>>When ANY two frequencies sound simultaneously, so do two
>>other frequencies - their sum and difference.
>>    
>>
>
>Yahya, this is not true in general. It's not true when the sound is 
>amplified or reproduced *linearly*, i.e., with no distortion. 
>Meanwhile, when there is a quadratic distortion of the signal, you 
>get not only the sum and difference, but also the 2nd partials of 
>each of the two frequencies. Shall I show the math?
>
>  
>
>>>As I think Paul was trying to say, beats are amplitude
>>>modulation, which is sort of a second order sound wave.
>>>      
>>>
>>Combining two pure sinusoidal waves of frequencies A and B
>>results in sinusoidal waves with components of frequencies
>>A-B and A+B. 
>>    
>>
>
>This is false, in general, as I wrote above. It's only true in the 
>presence of distortion. A quadratic nonlinearity is the simplest kind 
>of distortion, and results in not only A, B, A-B, and A+B, but also 
>2*A and 2*B as well. Perhaps I should review the math?
>
>  
>
>>If the upper and lower sidebands aren't at the 
>>frequencies of the combination tones, what frequencies 
>>are they at?
>>    
>>
>
>They are at the frequencies corresponding to A and B in your example.
>
>
>
>
>
>________________________________________________________________________
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>
>
>You can configure your subscription by sending an empty email to one
>of these addresses (from the address at which you receive the list):
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>------------------------------------------------------------------------
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>
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>
>
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>
>  
>

-- 
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

From: Gene Ward Smith (2005-10-17)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

--- In [email protected], "monz" <monz@t...> wrote:

> As i said, i really think the main reason so many
> microtonalists think of blues as "septimal" is because
> of the fact that *all* of the chords are dominant-7ths,
> and the 7ths are not felt as dissonances in need of
> resolution, which leads the ear into perceiving the
> harmony *in a general sense* as a bunch of 4:5:6:7 ratios.

I think this is correct. Septimally constructed chords and melodies
tend to sound vaguely bluesy or jazzy.

From: Gene Ward Smith (2005-10-18)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

--- In [email protected], "monz" <monz@t...> wrote:
>
> Hi Gene,
> 
> 
> I guess you missed this. I asked you directly to
> furnish me with a scale, because i was inspired to
> start composing some Orwell Blues! Please do!

I wasn't sure what you were asking, and still am not, but here is
Orwell[9]:

! or9.scl
Orwell[9] in 1728/1715 (0,-1) tuning
9
!
156.143810
271.228762
427.372572
542.457524
698.601334
813.686286
928.771238
1084.915048
1200.000000

From: wallyesterpaulrus (2005-10-18)
Subject: Re: blues (was: "pentatonic hearing" (was: Otonal / Utonal))

--- In [email protected], "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In [email protected], "monz" <monz@t...> wrote:
> >
> > Hi Gene,
> > 
> > 
> > I guess you missed this. I asked you directly to
> > furnish me with a scale, because i was inspired to
> > start composing some Orwell Blues! Please do!
> 
> I wasn't sure what you were asking, and still am not, but here is
> Orwell[9]:
> 
> ! or9.scl
> Orwell[9] in 1728/1715 (0,-1) tuning
> 9
> !
> 156.143810
> 271.228762
> 427.372572
> 542.457524
> 698.601334
> 813.686286
> 928.771238
> 1084.915048
> 1200.000000

You guys should hear Igliashon Jones's Orwell[9] piece (in 31-equal, 
only a touch different than the above). It seems to be gone from his 
Soundclick page now. Igs?