Yahoo Tuning Groups Ultimate Backup tuning Re: [MMM] Fwd: The tuning group at Yahoo.

---This group appears to have degenerated into trivialities.

Robert,
Agreed...in fact, honestly, many of the discussions such as "should I express my scales in fractions or cents or both and why?" or a book's worth of discussion of "why does a major triad sound better than a minor one" seems quite excessive.

Personally, I've tried to stick with new tunings I have worked on and give examples. I never intended, for example, threads about my scales to be de-railed and turned into topics like those above. If someone doesn't like the form my scale is in they can ask "can someone repost this as fractions?" and then have someone reply with the list rather than spend 10+ messages arguing why I'm being "ignorant" for not posting my scale in a way they want it.
-----------------------------------------------------
Pardon my anger, but I really don't give beyond one message's worth about why the way I notated my scale is weird vs. the traditional way...I just want to know what people like/don't about it and how it can be made to be better and/or expanded so far as musical theory.

Robert, if you or anyone else think I am one of those responsible for this excess of "trivialities", please give your best sage advice how to stop my threads from being de-railed into such things. I certainly don't come in intending that to happen.

I am just trying to develop something, and not meaning to start nasty long chains about topics that are often both overly subjective and tangential to what I originally was discussing. BTW, I started my own tuning group as well for the reason of avoiding this, but no one joined.

-Michael

--- On Sun, 2/1/09, robert thomas martin <robertthomasmartin@...> wrote:

From: robert thomas martin <robertthomasmartin@...>
Subject: [MMM] Fwd: The tuning group at Yahoo.
To: MakeMicroMusic@yahoogroups.com
Date: Sunday, February 1, 2009, 1:22 AM

--- In MicroMadeEasy@ yahoogroups. com, "robert thomas martin"

<robertthomasmartin @...> wrote:

This group appears to have degenerated into trivialities. It might have

quantity but it appears that it lacks quality. A pity since it has

carried the burden of supporting microtonality for so long.

--- End forwarded message ---

🔗Carl Lumma <carl@...>

🔗djtrancendance@...

---Great attitude, Michael. And you know what? I could tell.
---I could tell because it's been explained to you about seven
---times and you still haven't even acknowledged that you've
---read one of those messages.
    Sounds like you are more interested in starting a fight than solving the problem, in only one sentence did I find evidence you are interested in solving the problem that was not simply personal accusations. For the record I DID ask you "what can I do to help fix this", but instead of a clear answer I got a bunch of personal accusations with no obvious productive point (minus a hint of "shut
up!!!!")
--I bet this
will shock the shit out of
you, but neither
Kraig
---nor I nor Dave
Seidel nor anyone on this
list or MMM that
I
---have seen even know
what your scale is.
    You don't need to use words like "shock" and "shit"...something much more useful would be something like "I don't understand the cents values in the scale you posted and would APPRECIATE it if you converted it to fractions"
not messages that lecture on "why cents are stupid" and stuff like that.
    Instead of writing essays, it would be a lot easier for me to respond if people just asked simple questions of me (and expected sometimes I can't answer them 100% to their liking).

1.6875              27/16                905.8650025961624
1.75                  21/12                968.8259064691249
1.83333             22/12               1049.3629411845993
1.9375               31/16               1145.0355724642502

2
2/1 1200

For the record, when I say 1.6875, I mean 1.6875 and not 1.666666666. Some of the ratios are slightly off intentionally to help them mix in other keys.

***************
And if that still doesn't cut it...then I don't know what's left and it would help if someone just directly informed me. Because, as I will say again, I simply want help developing this scale and opinions on what does/doesn't work well about it. Just don't say I'm not trying to listen or make any of this understandable, because that's an outright lie. If I'm not perfect, that does not mean I am "intentionally not perfect".

-Michael

--- On
Sun, 2/1/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
To: tuning@yahoogroups.com
Date: Sunday, February 1, 2009, 11:30 AM

Michael Sheiman:

> Pardon my anger, but I really don't give beyond one

> message's worth about why the way I notated my scale is

> weird vs. the traditional way...

Great attitude, Michael. And you know what? I could tell.

I could tell because it's been explained to you about seven

times and you still haven't even acknowledged that you've

read one of those messages.

> I just want to know what people like/don't about it and

> how it can be made to be better and/or expanded so far as

> musical theory.

Then you'll need to communicate with them. That means making

compromises on things like language. It means empathizing

with others. Pretty basic stuff, Michael.

I bet this will shock the shit out of you, but neither Kraig

nor I nor Dave Seidel nor anyone on this list or MMM that I

have seen even know what your scale is. And as long as you

continue with your pigheaded attitude, none of us probably

will. So by all means, continue to pass messages back and

forth with Robert about how nothing here is of value instead

of reading the messages, and you'll do just great as the

advocate for microtonal music you said you wanted to be!

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, djtrancendance@... wrote:
>
> ---Great attitude, Michael. And you know what? I could tell.
> ---I could tell because it's been explained to you about seven
> ---times and you still haven't even acknowledged that you've
> ---read one of those messages.
> Sounds like you are more interested in starting a fight
> than solving the problem, in only one sentence did I find
> evidence you are interested in solving the problem that was
> not simply personal accusations. For the record I DID ask
> you "what can I do to help fix this", but instead of a clear
> answer I got a bunch of personal accusations with no obvious
> productive point (minus a hint of "shut up!!!!")

I already sent you the answer several times. How many times
would you like me to send it? I sent one most recently at 9pm
last night. You must have ignored it on your way to post your
most recent missive this morning.

> Anyhow, here is my >>best attempt<< to convert my tuning into all
>forms:
> 1                      1                      0
> 1.05555            19/18                93.603005289
> 1.125
> 9/8                   203.91000173077487
> 1.1875              19/16                297.5130161323026
> 1.25                 10/8                  386.3137138648348
> 1.3125
> 21/16                470.78090733451234
> 1.375                11/8                  551.3179423647566
> 1.4375              23/16                628.2743472684155
> 1.5                   3/2                    701.9550008653874
> 1.5625              25/16
>                772.6274277296696
>
> 1.6875              27/16                905.8650025961624
> 1.75                  21/12                968.8259064691249
> 1.83333             22/12               1049.3629411845993
> 1.9375               31/16               1145.0355724642502
>
> 2
> 2/1                   1200
>
>     For the record, when I say 1.6875, I mean 1.6875 and not
> 1.666666666. Some of the ratios are slightly off intentionally
> to help them mix in other keys.

As you can see, this came out a garbled and useless mess.
However, I will take my time to reformat it so it is useful

!
Michael's scale (finally).
14
!
19/18
9/8
19/16
5/4
21/16
11/8
23/16
3/2
25/16
27/16
7/4
11/6
31/16
2/1
!

Is this really so hard?

>And if that still doesn't cut it...then I don't know what's
>left and it would help if someone just directly informed me.

How can I be more direct?

-Carl

🔗Michael Sheiman <djtrancendance@...>

Carl said:

Michael's scale (finally).

19/18

9/8

19/16

5/4

21/16

11/8

23/16

3/2

25/16

27/16

7/4

11/6

31/16

2/1

---Is this really so hard?
It wouldn't be if yahoo mail didn't reformat my alignment!
Next time I will have to just post the scales on the same row and forget trying to align them into a table.
************************************

BTW, you turned all my x/8 format fractions into reduced ones IE 7/4.
There is a REASON I left some fractions unreduced, it hints in part how they were derived.
Ugh...this is in fact my scale IE I created it....please at least let me take some ownership for how it is presented.

******* If anyone beside Carl thinks I am "purposefully ignoring other people on the list because I'm too proud", please send me a personal message and I will listen. In the meantime I am sick and tired of all this blaming...I am JUST trying to improve my scale here and do NOT think I deserve this much crap just for TRYING to help.
**********

And for the record, Chris posted the first version of the scale here (in cents), not me, so if anyone completely "didn't get" the scale they'd have to say both of us did a terrible job for presentation. Personally I agree with Chris: Carl, if you don't think my work is perfect TOUGH; I tried my best, let's move on already.

-Michael

🔗Carl Lumma <carl@...>

🔗djtrancendance@...

--First of all, this is a very simple JI scale and there's
--nothing in it you can claim as original.
I'm not completely surprised, after all JI is also built from harmonic series inevitably a lot of the same ratios are going to pop up.

Side question (and general question to the group): is any scale with uses JI ratios or rational numbers, regardless of their order, "automatically" rendered unoriginal?

----------
I have not heard of this combination in JI (not on this list or anywhere else), but again I believe you that it existed before I ran across it...where can I read a formal explanation of this scale, I am interested to look into it (and try to figure out why it hasn't become a standard: it sounds a decent bit better than 12TET to my ears)?
---------

---Second of all, if
you want others to read and understand your
work, I suggest
---you avail yourself of the common tongue.
I am TRYING. The only person here who seems to be complaining so much about my efforts is you. I simply did not have time to reduce everything to fractions before, and I certainly don't see why you take this sort of thing as my being a snob. And, yes, I will write everything in fraction form in the future...you really didn't need to drum up all that drama if or use charged terms like "common tongue" if just plain old "PLEASE POST YOUR SCALES AS FRACTIONS: IT MAKES IT EASIER FOR EVERYONE" was your point in the first place.

-Michael

--- On Sun, 2/1/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
To: tuning@...m
Date: Sunday, February 1, 2009, 5:17 PM

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

>> !

>> Michael's scale (finally).

>> 14

>> !

>> 19/18

>> 9/8

>> 19/16

>> 5/4

>> 21/16

>> 11/8

>> 23/16

>> 3/2

>> 25/16

>> 27/16

>> 7/4

>> 11/6

>> 31/16

>> 2/1

>> !

>> Is this really so hard?

> It wouldn't be if yahoo mail didn't reformat my alignment!

> Next time I will have to just post the scales on the same row

> and forget trying to align them into a table.

Please provide only the ratios. We can easily convert

them to whatever other format we desire. Especially if

you use the format above, which can be copied and pasted

directly into a text file and opened in Scala. If you're

viewing this on the web, hit View Source under Message Options

on the right to see the exact formatting. Or consult:

http://www.xs4all. nl/~huygensf/ scala/scl_ format.html

> BTW, you turned all my x/8 format fractions into reduced ones

> There is a REASON I left some fractions unreduced, it hints

> in part how they were derived.

We can figure that out too.

> Ugh...this is in fact my scale IE I created it....please at

> least let me take some ownership for how it is presented.

First of all, this is a very simple JI scale and there's

nothing in it you can claim as original. Second of all, if

you want others to read and understand your work, I suggest

you avail yourself of the common tongue.

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗Michael Sheiman <djtrancendance@...>

Re-statement.
I think I finally see what Carl means by my tuning's being a "very simple JI scale" when I converted my scale into x/16 fractional format and fixed two of the notes that sounded "off".

Here was my result (ALMOST a straight JI series)

Michael's scale (finally).

17/16 1.0625

18/16

19/16

20/16

21/16

22/16

23/16

24/16

25/16

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

27/16

28/16

29/16
X11/6X

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

31/16

2/1

***********************************************************************************
The one thing that differs this from a straight JI series is the fact that
A) 30/16
and
B) 26/16
are MISSING from the series.
And, guess what, if you put them in everything sounds MUCH worse (at least to my ears).

Is there any theory which explains why those two notes in the series are best left out and/or do your have your own ideas why? Please share...I'm listening.

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Kraig Grady <kraiggrady@...>

🔗Michael Sheiman <djtrancendance@...>

---but i think that
---it only sounds correct with certain harmonics left out is something for
---others to play with/contemplate
I found this odd as well. It ALMOST simplifies to harmonics 17-32 of JI, but not quite...and was created by taking multiple harmonic series which just happen to sum up to nearly that scale.
Also, I tried adding the extra 2 notes in the JI series, and it makes smooth transposition (IE the equivalent of "key of c" to "key of c#", in case I am using the term transpose incorrectly) fail as well....whereas in my tuning with the removed notes such an operation no longer sounds good.

Another note, 12TET itself ALSO gets very near the JI 17/16, 18/16....but not quite (4/3, for example, is one of the notes estimated in 12TET, but NOT in the x/16 series).

Again this seems to say there is something special about JI harmonics in "x/16" form that makes them pleasing to the ear, but at the same time certain ones that need to be eliminated (in BOTH scales) to make the scale work.
-Michael

--- On Mon, 2/2/09, Kraig Grady <kraiggrady@...> wrote:

From: Kraig Grady <kraiggrady@...>
Subject: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
To: tuning@yahoogroups.com
Date: Monday, February 2, 2009, 12:52 AM

Ratios and cents are both useful. and we can also now conclude this is

an original 'scale' as far as i know. I will assume it is a scale

because the creator says they hear it as such. (i for one, am caught up

with too many things to be helpful why this might be) but i think that

it only sounds correct with certain harmonics left out is something for

others to play with/contemplate

For scales that are more limit based, i do think along with both ratio

and cents. Euler's generalized lattice and the variation there of are

also useful. as i use on my centaur scale just because it is easy to see

many of your simplest harmonies right off. but i do use them all.

http://anaphoria. com/centaur. html

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_

Mesotonal Music from:

_'''''''_ ^North/Western Hemisphere:

North American Embassy of Anaphoria Island <http://anaphoria. com/>

_'''''''_ ^South/Eastern Hemisphere:

Austronesian Outpost of Anaphoria <http://anaphoriasou th.blogspot. com/>

',',',',',', ',',',',' ,',',',', ',',',',' ,',',',', ',',',',' ,

🔗Mark Rankin <markrankin95511@...>

10/8 = 5/4
22/12 = 11/6

-- Mark Rankin

--- On Sun, 2/1/09, djtrancendance@... <djtrancendance@...> wrote:

From: djtrancendance@yahoo.com <djtrancendance@...>
Subject: Re: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
To: tuning@yahoogroups.com
Date: Sunday, February 1, 2009, 12:48 PM

---Great attitude, Michael. And you know what? I could tell.
---I could tell because it's been explained to you about seven
---times and you still haven't even acknowledged that you've
---read one of those messages.
    Sounds like you are more interested in starting a fight than solving the problem, in only one sentence did I find evidence you are interested in solving the problem that was not simply personal accusations. For the record I DID ask you "what can I do to help fix this", but instead of a clear answer I got a bunch of personal accusations with no obvious productive point (minus a hint of "shut up!!!!")
--I bet this will shock the shit out of you, but neither Kraig
---nor I nor Dave Seidel nor anyone on this list or MMM that I
---have seen even know what your scale is.
    You don't need to use words like "shock" and "shit"...something much more useful would be something like "I don't understand the cents values in the scale you posted and would APPRECIATE it if you converted it to fractions" not messages that lecture on "why cents are stupid" and stuff like that.
    Instead of writing essays, it would be a lot easier for me to respond if people just asked simple questions of me (and expected sometimes I can't answer them 100% to their liking).

Anyhow, here is my >>best attempt<< to convert my tuning into all forms:
1                      1                      0
1.05555            19/18                93.603005289
1.125                9/8                   203.91000173077487
1.1875              19/16                297.5130161323026
1.25                 10/8                  386.3137138648348
1.3125              21/16                470.78090733451234
1.375                11/8                  551.3179423647566
1.4375              23/16                628.2743472684155
1.5                   3/2                    701.9550008653874
1.5625              25/16                772.6274277296696
1.6875              27/16                905.8650025961624
1.75                  21/12                968.8259064691249
1.83333             22/12               1049.3629411845993
1.9375               31/16               1145.0355724642502
2                       2/1                   1200

For the record, when I say 1.6875, I mean 1.6875 and not 1.666666666. Some of the ratios are slightly off intentionally to help them mix in other keys.

************ ***
And if that still doesn't cut it...then I don't know what's left and it would help if someone just directly informed me. Because, as I will say again, I simply want help developing this scale and opinions on what does/doesn't work well about it. Just don't say I'm not trying to listen or make any of this understandable, because that's an outright lie. If I'm not perfect, that does not mean I am "intentionally not perfect".

-Michael

--- On Sun, 2/1/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
To: tuning@yahoogroups. com
Date: Sunday, February 1, 2009, 11:30 AM

Michael Sheiman:

> Pardon my anger, but I really don't give beyond one
> message's worth about why the way I notated my scale is
> weird vs. the traditional way...

Great attitude, Michael. And you know what? I could tell.
I could tell because it's been explained to you about seven
times and you still haven't even acknowledged that you've
read one of those messages.

> I just want to know what people like/don't about it and
> how it can be made to be better and/or expanded so far as
> musical theory.

Then you'll need to communicate with them. That means making
compromises on things like language. It means empathizing
with others. Pretty basic stuff, Michael.

I bet this will shock the shit out of you, but neither Kraig
nor I nor Dave Seidel nor anyone on this list or MMM that I
have seen even know what your scale is. And as long as you
continue with your pigheaded attitude, none of us probably
will. So by all means, continue to pass messages back and
forth with Robert about how nothing here is of value instead
of reading the messages, and you'll do just great as the
advocate for microtonal music you said you wanted to be!

-Carl

🔗Carl Lumma <carl@...>

🔗djtrancendance@...

--Because harmonics get closer together as you go up the series,
---sometimes it is a good idea to omit some of the higher identities
---to get a more even scale.
Agreed, critical band is an issue.
   But if that were the only issue...wouldn't the harmonics I would eliminate would be focused on the top of the scale rather than scattered among the middle-top and top of the scale?
   ********
   If I have it right I agree with Kraig; something peculiar is happening between those harmonics and this is likely not something simple and likely needs much further investigation....
   This happens in the same way that something peculiar makes a major triad sound clearer than a minor one despite their having the same amount of
mathematical consonance.

One
guess I have...is the notes I eliminated from the harmonic series cause conflicts between their overtones and scale notes on the next few octaves.

Another guess is...again my scale is symmetric about 3/2, just like 12TET is when summarized using JI intervals (as shown in my "proof of 12TET" example. When I tried, the x/16 harmonics not included in my scale appear to be the ones not symmetrical about 3/2. Meaning, if you take my scale up to 3/2 (all the fractions multiplied by one) and then multiply those same fractions by 3/2 you get the second half of the scale plus a few notes...and the harmonics I miss appear to be the same ones NOT included in that process.
*****
If there's something I am missing I would be interested to know...but I have the general impression critical band issues alone do not explain not just why notes from JI are omitted, but why it has to be certain
notes (every other combination of omitting notes I have tried kills the ability to transpose). BTW, if you are wondering "transpose what? you gave us the tuning but not the scales"...I am going to send a copy of the tuning AND the scales in my next major posting.

-Michael

🔗Chris Vaisvil <chrisvaisvil@...>

I'm getting a picture, that the key, regardless of how they are generated,
the difference tones are part of the key - and that a "harmonious" scale, at
least for public consumption, would be one where the intervals created
difference tones that reinforced the consonance of the interval. I'm sure
I'm not the first one to think of this.

Also, it seems apparent when listening to something like a major chord
played on a string section there is an array of frequencies beyond the root
sines and harmonics that occur from the interaction of said sines and
harmonics. This would seem to point back to Sethare's harmonic series -
octave relationship.

I am unsure if the dissonance curve graph found here is derived from
difference tone calculation or some other device. I.E. can someone identify
exactly what "y" is on figure 3. Perhaps I'm being dense but "If this timbre
is sounded at various intervals, the dissonance of the intervals can be
calculated by adding up all of the dissonances between all pairs of
partials." doesn't explain what "y" is to me. How does one mechanically "add
up all of the dissonances".

http://eceserv0.ece.wisc.edu/~sethares/consemi.html

It would seem that this dissonance curve would explain scales
mathematically, but since this is not being used that must be a draw back
I'm not aware of - and I'm guessing there is something subjective buried in
this.

Or am I totally wet?

On Mon, Feb 2, 2009 at 2:38 PM, Carl Lumma <carl@...> wrote:
>
> > Again this seems to say there is something special about JI
> > harmonics in "x/16" form that makes them pleasing to the ear,
> > but at the same time certain ones that need to be eliminated
> > (in BOTH scales) to make the scale work.
> > -Michael
>
> Because harmonics get closer together as you go up the series,
> sometimes it is a good idea to omit some of the higher identities
> to get a more even scale. Another general rule is to omit
> identities which are high primes, like 23.
>
> -Carl
>
>

🔗djtrancendance@...

What I have generally learned through practice is that keeping overtones from clashing IE Sethares' method only solves PART of the problem, even though it is an important factor.

The importance of Sethares' theories is they virtually eliminate the problem of clashing overtones' sound worse than they do with sine waves.

A few obvious examples: the major and minor chord have virtually the same dissonance level according to Sethares' formula, yet sound dramatically different far as "musical consonance", even in the form of pure sine wave!
As Carl seemed to have said, the human ear seems "trained" to accept overtones which get closer together at higher frequencies...the same way they do in a major vs. minor chord.
The other seems to be periodicity IE if many partials are spaced the same number of frequencies apart then the beating itself will be harmonic.

Yet another issue I've discovered
through experimentation...is the mind seems to like certain rational intervals. x/16 IE 17/18, 18/16 work well but 16/15 and 17/15 work less well together DESPITE x/15 formed harmonic intervals having lower levels of dissonance than their x/16 counterparts!
***********************************

Far as Sethares' formulas, when you solve for Y, Y is an "accumulated dissonance" variable. That is you compare the consonance of a partial to every other partial, minus the comparisons of the partials done in reverse (IE if you have compared partial 1 to 3 and added it to the total dissonance, don't re-add it when you get to partial 3 and try to compare it to partial 1).

A nice way to use Sethares' theories would be:
A) make a scale that sound AS GOOD as Just Intonation-based scales using pure sine waves.
B) don't worry about overtones...Sethares' dissonance formula can be used in inverse to find which
harmonic/overtone structure in an instrument would match the scale. Then you just have to re-sample the instrument using software which performs the alignment of overtones and play songs using such instruments.

My problem so far...is I haven't found any scales that, played pure sine-waves, that sound on par with those based around JI intervals. If someone can find them, Lord bless them because that would be a truly awesome thing that would make Sethares' tuning theories sound 100% good to most 12TET ear-ed people instead of 75-80% good.

-Michael

🔗massimilianolabardi <labardi@...>

Hi Chris,

you mean what is the vertical scale labelled "sensory dissonance" in
the plots?

It should be a measure of the dissonance of intervals performed by
instruments with non-trivial harmonics content, just based on the
critical bandwidth concept. I have remade the calculations (good
track for them is in the paper cited in one of my previous posts

/tuning/topicId_80116.html#80162

where I was also commenting on such curves).

In essence, if an interval has two harmonics that are as close in
frequency as to lay in the critical bandwidth, the sensory dissonance
of such interval is increased. The calculation is done for each
combination of harmonics, and the amount of dissonance is increased
proportionally to the product of amplitudes of the harmonics
concerned.

If you wish I can share my Mathematica file, but it is not commented
and it is difficult even for myself to remember what is what...

Cheers

Max

I am unsure if the dissonance curve graph found here is derived from
> difference tone calculation or some other device. I.E. can someone
identify
> exactly what "y" is on figure 3. Perhaps I'm being dense but "If
this timbre
> is sounded at various intervals, the dissonance of the intervals
can be
> calculated by adding up all of the dissonances between all pairs of
> partials." doesn't explain what "y" is to me. How does one
mechanically "add
> up all of the dissonances".
>
> http://eceserv0.ece.wisc.edu/~sethares/consemi.html
>
>
> It would seem that this dissonance curve would explain scales
> mathematically, but since this is not being used that must be a
draw back
> I'm not aware of - and I'm guessing there is something subjective
buried in
> this.
>
> Or am I totally wet?
>

🔗djtrancendance@...

What becomes obvious to me...is that Sethares exclusively uses dyads for the formula when, ultimately, using combinations of 3-4 notes at once for comparison my yield different result. I think Carl briefly mentioned something about that a while ago.

For example, what about 9 or 8 tone JI scales? Surely there's some type of dissonance comparison that could get fairly close to "proving" those as well, at least to some extent. A 9-note scale under my 14-note tuning has a few centers (3-4) that are by no means located on Sethares' chart that sound like "sweet spots" nonetheless.

BTW Max, I think I understand your "why detuning a 5th matters more than any other interval" argument. The slope around the dip at the 5th on Sethares' curve is VERY high, thus
causing any detuning error to make a very quick move upward along that slope/derivative.

Realistically, though, I think detuning any interval off, and not just the 5th, can matter a lot. And I have my doubts any dissonance formula can fully explain musical consonance.
For example, Sethares formula can't give extra credit to three notes with may be dissonant vs. each other but have periodic distortion between them that makes them more tolerable to the human ear.

Again, I think its a very cool idea but, as you seem to be saying, it is not an all-inclusive formula that explains "everything".

-Michael

--- On Mon, 2/2/09, massimilianolabardi <labardi@...> wrote:

From: massimilianolabardi <labardi@...>
Subject: [tuning] Re:
[MMM] Fwd: The tuning group at Yahoo.
To: tuning@yahoogroups.com
Date: Monday, February 2, 2009, 1:38 PM

Hi Chris,

you mean what is the vertical scale labelled "sensory dissonance" in

the plots?

It should be a measure of the dissonance of intervals performed by

instruments with non-trivial harmonics content, just based on the

critical bandwidth concept. I have remade the calculations (good

track for them is in the paper cited in one of my previous posts

http://launch. groups.yahoo. com/group/ tuning/message/ 80162

where I was also commenting on such curves).

In essence, if an interval has two harmonics that are as close in

frequency as to lay in the critical bandwidth, the sensory dissonance

of such interval is increased. The calculation is done for each

combination of harmonics, and the amount of dissonance is increased

proportionally to the product of amplitudes of the harmonics

concerned.

If you wish I can share my Mathematica file, but it is not commented

and it is difficult even for myself to remember what is what...

Cheers

Max

I am unsure if the dissonance curve graph found here is derived from

> difference tone calculation or some other device. I.E. can someone

identify

> exactly what "y" is on figure 3. Perhaps I'm being dense but "If

this timbre

> is sounded at various intervals, the dissonance of the intervals

can be

> calculated by adding up all of the dissonances between all pairs of

> partials." doesn't explain what "y" is to me. How does one

mechanically "add

> up all of the dissonances" .

> http://eceserv0. ece.wisc. edu/~sethares/ consemi.html

> It would seem that this dissonance curve would explain scales

> mathematically, but since this is not being used that must be a

draw back

> I'm not aware of - and I'm guessing there is something subjective

buried in

> this.

> Or am I totally wet?

🔗Chris Vaisvil <chrisvaisvil@...>

This may be heresy, but... is 12-TET not in the end -the- best compromise?
For 12 notes that is.

I wonder if we would not be better off finding another tuning system
entirely instead of trying to re-compromise 12-TET.

I will admit that I found Lucy tuning to be significantly different, and I
see the "sweeteners" in my Perterson Tuner... but these seem to be special
cases of 12-TET. JI injections into the de facto common tuning system.

If one looks at Western music historically there has been an continuous
march to increased tolerance to dissonance. While contemporary classical
music has taken this to such extremes (dodecophonic music comes to mind,
sound clusters music (Carl Ruggles I am most familiar with, the extreme
polytonality of Charles Ives, etc)) that it has by a large degree left its
audience behind this acceptance is markedly evident in popular music. Think
of the increased tolerance to dissonance (and sheer noise) compared to the
popular music of the 1900's, 10's, 20's, 30's, 40's, and 50's of which we
have recordings. Compare lots of Techno to say Les Paul and Mary Ford.

I wonder if we are at a unique time in history when an alternate system all
together could obtain significant traction. And in proposing this - I wonder
if "ultimate consonance" is really the holy grail. Perhaps the true holy
grail is a real application, not just demonstration, of alternate tuning, by
which I mean say, 22-TET, something that actually adds more possibilities.

There seems to be a lot of history behind the selection of 12-TET - and
evolution that included what was to me some surprising alternatives (19 and
53 TET).

I would think the constraints must be:

1. It would have to be sung by the general population - no super sopranos
need apply.
2. Have to have a prayer in being executed on existing, or somewhat modified
existing instruments.
3. Have a reasonable relationship to current practice 12-TET.

We have lots of flexible tools - and lots of examples of alternate tunings
from around the world.

I know I'm not the only to think of this - thanks to the tuning and MMM list
there are many fine examples of music in alternate tuning.

My point here - perhaps abandoning 12-TET should be a conscience goal
instead of a matter of trying fix the holes in the dyke.

🔗djtrancendance@...

--This may be heresy, but... is 12-TET not in the end -the- best compromise? For 12 notes --that is.
I think 12TET falls enough behind JI that it is a problem.
So in my book 12TET is a "good" compromise as opposed to a great one.

A great one for 12-tone, would be chock-full of pure JI intervals and not have any crap like 3rds that are 12+ cents off of their JI equivalents. There would likely be intervals "slightly" off JI pure, but they would at least be balanced enough so no interval is more than 5 cents off it's purest form.
************************
So my personal opinion is that
1) My "proof of 12TET" scale (based on Just Intonation) beats 12TET by a considerable margin and gets much closer to diatonic JI far as what 7-note scales can
be created from it.
2) My 14 note scale is basically #1, but swaps the minor-like interval steps (IE 4/5 followed by 3/2) with major ones (this was inspired from the argument "why do major triads (even with pure sine tones" sound better than equally mathematically consonant minor triads?)".

So I think it #2 is pretty close to the consonance of #1 (if not better than it), but allows the additional option of 9-note scales (which I will explain in an upcoming post).
************************
I also think Lucy Tuning and Sethares' theories are very cool for things like jazz, blues, classical and some electronica. To me they sound 80% convincing as tonal wheras 12TET sounds more like 90% and JI diatonic more like 95% convincingly "tonal".
Wilson's scales in general I think are more like 92% convincing with 2 tones and more like 85% with 7 tones.

But far as things like
pop and rock, which really often put high demands on musical consonance, I seriously suspect something smarter may need to be produced to "beat 12TET".

-Michael

🔗Michael Sheiman <djtrancendance@...>

From the last post, I made a hilarious typo:

"Wilson's scales in general I think are more like 92% convincing with ???2?? tones and more like 85% with 7 tones."

I meant Wilson's scales sound 92% convincing with 6 tones, not 2.
-Michael

--- On Mon, 2/2/09, djtrancendance@... <djtrancendance@...> wrote:

From: djtrancendance@... <djtrancendance@...m>
Subject: Re: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
To: tuning@yahoogroups.com
Date: Monday, February 2, 2009, 2:42 PM

A great one for 12-tone, would be chock-full of pure JI intervals and not have any crap like 3rds that are 12+ cents off of their JI equivalents. There would likely be intervals "slightly" off JI pure, but they would at least be balanced enough so no interval is more than 5 cents off it's purest form.
************ ********* ***
So my personal opinion is that
1) My "proof of 12TET" scale (based on Just Intonation) beats 12TET by a considerable margin and gets much closer to diatonic JI far as what 7-note scales can
be created from it.
2) My 14 note scale is basically #1, but swaps the minor-like interval steps (IE 4/5 followed by 3/2) with major ones (this was inspired from the argument "why do major triads (even with pure sine tones" sound better than equally mathematically consonant minor triads?)".

So I think it #2 is pretty close to the consonance of #1 (if not better than it), but allows the additional option of 9-note scales (which I will explain in an upcoming post).
************ ********* ***
I also think Lucy Tuning and Sethares' theories are very cool for things like jazz, blues, classical and some electronica. To me they sound 80% convincing as tonal wheras 12TET sounds more like 90% and JI diatonic more like 95% convincingly "tonal".
Wilson's scales in general I think are more like 92% convincing with 2 tones and more like 85% with 7 tones.

But far as things like
pop and rock, which really often put high demands on musical consonance, I seriously suspect something smarter may need to be produced to "beat 12TET".

-Michael

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> I'm getting a picture, that the key, regardless of how they are
> generated, the difference tones are part of the key - and that
> a "harmonious" scale, at least for public consumption, would
> be one where the intervals created difference tones that
> reinforced the consonance of the interval. I'm sure I'm not the
> first one to think of this.

As recently discussed ad nauseum, difference tones are not
significant in common practice music theory, or in microtonal
extensions thereof. You can get a majority consonance judgments
right by doing arithmetic with difference tones, which is why,
no, you are not the first person to think of this. But you can
also get a majority of consonance judgments right by doing any
number of basic arithmeticy things involving simple ratios, since
they occur in so many places in music settings: the spectra of
the human voice and most musical instruments, harmonic templates
in the human brain, and between combination tones created in the
ear, to name a few.

"Keys" in tonal music are largely a matter of the grammer of the
diatonic scale. You have to be able to explain things like why
only the Ionian and Aeolian modes are capable of being keys...

> How does one mechanically "add
> up all of the dissonances".
>
> http://eceserv0.ece.wisc.edu/~sethares/consemi.html

See:
http://eceserv0.ece.wisc.edu/~sethares/paperspdf/consonance.pdf

> It would seem that this dissonance curve would explain scales
> mathematically, but since this is not being used that must be
> a draw back I'm not aware of - and I'm guessing there is
> something subjective buried in this.

The drawback is that it doesn't work. :)

Actually, it partly works, and some people do use it (notably
Sethares himself).

-Carl

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> This may be heresy, but... is 12-TET not in the end -the- best
> compromise? For 12 notes that is.

If all of society had to pick only one 12-note tuning to use
in all music for the next hundred years, 12-ET is probably
the best choice.

> If one looks at Western music historically there has been an
> continuous march to increased tolerance to dissonance.

I don't think that's true. Most music (in terms of people-hours
it's listened to, or dollars spent on it, etc.) today and in the
past is very simple and very consonant. It has been argued that
music is marching higher up the harmonic series -- 3-limit in
the medieval period, 5-limit in the classical, and the 7-limit
in African-American music -- but that doesn't mean higher
dissonance, and it's a debatable interpretation of history at
any rate. I was listening to some 15th-century Italian music
the other day, and it was remarkably similar to modern folk
music. One of the galliards in particular could have been put
on a CD of square dancing music and nobody would notice.
So if music is changing, at least it seems to be a matter of
expansion rather than linear evolution.

> While contemporary classical music has taken this to such
> extremes (dodecophonic music comes to mind,

This movement is by now mostly dead, even in academic circles,
and it never can claim to have been widely enjoyed.

> I wonder if we are at a unique time in history when an alternate
> system all together could obtain significant traction. And in
> proposing this - I wonder if "ultimate consonance" is really the
> holy grail.

One nice thing about tunings like 22-ET is that they contain
all three of these possibilities:

1. greater consonance in traditional chords (triads)
2. more consonances to choose from (e.g. 7-limit and 11-limit)
3. more and much greater dissonances available

In other words, a triple play.

> 2. Have to have a prayer in being executed on existing, or
> somewhat modified existing instruments.

It's easy to put 22 on a guitar by refretting. A relatively
cheap mod. Most MIDI keyboards can do 22 or any other
tuning in seconds, but to get the conceptual part of the
instrument right, new keyboard layouts are unfortunately
required.

> My point here - perhaps abandoning 12-TET should be a conscience
> goal instead of a matter of trying fix the holes in the dyke.

I think that is the conscience goal around here!

-Carl

🔗Michael Sheiman <djtrancendance@...>

🔗Carl Lumma <carl@...>

Michael wrote:

>> Because harmonics get closer together as you go up the series,
>> sometimes it is a good idea to omit some of the higher
>> identities to get a more even scale.
>
> Agreed, critical band is an issue.

It's not about the critical band, actually. Every 12-ET
semitone is smaller than a critical band, but we can still
pick chords in 12-ET that straddle CBs. Rather, scale
evenness is an issue in its own right. The more even a
scale is, the more likely it is to be Rothenberg-proper,
for one thing. Rothenberg propriety is explained here:
/tuning/topicId_79449.html#79883

See also this message:
/tuning/topicId_78031.html#78038

> But if that were the only issue...wouldn't the harmonics
> I would eliminate would be focused on the top of the scale
> rather than scattered among the middle-top and top of the
> scale?

Yes.

> Another guess is...again my scale is symmetric about 3/2,
> just like 12TET is when summarized using JI intervals (as
> shown in my "proof of 12TET" example. When I tried, the x/16
> harmonics not included in my scale appear to be the ones not
> symmetrical about 3/2.

Hm, not sure how you're getting that. In harmonics 16-32,
there are seven notes that could be involved in such a
symmetry -- three that match when transposed by 3/2, three
that match when transposed by 2/3, and one that matches both
directions (3/2 itself, matching to 1/1 and 9/8). Of the
two notes you left out, one participated no matches (13/8)
and the other participated in one match (15/8), which is
about what we'd expect if we randomly removed two notes
(since 6:16 match once, 9:16 never match, and 1:16 match
twice).

Here's the longhand for that:

17/16
9/8 ! 27/16 ; 3/2
19/16
5/4 ! 15/8 ; 5/3
21/16 ! 63/32 ; 7/4
11/8
23/16
3/2 ! 9/8 ; 1/1
25/16
13/8 ! not used
27/16 ! 81/64 ; 9/8
7/4 ! 21/16 ; 7/6
29/16
15/8 ! not used 45/32 ; 5/4
31/16
2/1

-Carl

🔗Michael Sheiman <djtrancendance@...>

> My point here - perhaps abandoning 12-TET should be a conscience

> goal instead of a matter of trying fix the holes in the dyke.
---I think that is the conscience goal around here!

    I'd actually say a bit of both.
1. "Fixing the holes"
    Far too many times have I composed in 12TET and become frustrated trying to, say, make 13th chords sound good and/or figure out why many inversions of 5 or 6-note chords sound awful.
   I still believe...there is likely a tuning that compromises consonance IE has many "mostly consonant" intervals rather than the bizarre combination of very consonant and fairly off (IE 3rds) intervals in 12TET. It bugs me complex music theory is often needed just to find many sweet-sounding chords over 3 notes "wide" in any given key in 12TET....I think it scares a lot of people away from songwriting.
2. "Making Theory Wider"
   Things like 9 and 8-note micro-tonal scales that sound not so much like consonant than 12TET harmonically seem to indicate there's a way to get more than 7-notes and still be well within the general human perception of "good consonance". Would there be fresh new melodies inspired in 9-tone scales not available in 7-tone even to the best 7-tone composers? Of course!   That's why I'm often so pig-headed about trying to get a tuning which allows 9-tone scales to work.

--- On Mon, 2/2/09, Carl Lumma <carl@lumma.org> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
To: tuning@yahoogroups.com
Date: Monday, February 2, 2009, 5:31 PM

--- In tuning@yahoogroups. com, Chris Vaisvil <chrisvaisvil@ ...> wrote:

> This may be heresy, but... is 12-TET not in the end -the- best

> compromise? For 12 notes that is.

If all of society had to pick only one 12-note tuning to use

in all music for the next hundred years, 12-ET is probably

the best choice.

> If one looks at Western music historically there has been an

> continuous march to increased tolerance to dissonance.

I don't think that's true. Most music (in terms of people-hours

it's listened to, or dollars spent on it, etc.) today and in the

past is very simple and very consonant. It has been argued that

music is marching higher up the harmonic series -- 3-limit in

the medieval period, 5-limit in the classical, and the 7-limit

in African-American music -- but that doesn't mean higher

dissonance, and it's a debatable interpretation of history at

any rate. I was listening to some 15th-century Italian music

the other day, and it was remarkably similar to modern folk

music. One of the galliards in particular could have been put

on a CD of square dancing music and nobody would notice.

So if music is changing, at least it seems to be a matter of

expansion rather than linear evolution.

> While contemporary classical music has taken this to such

> extremes (dodecophonic music comes to mind,

This movement is by now mostly dead, even in academic circles,

and it never can claim to have been widely enjoyed.

> I wonder if we are at a unique time in history when an alternate

> system all together could obtain significant traction. And in

> proposing this - I wonder if "ultimate consonance" is really the

> holy grail.

One nice thing about tunings like 22-ET is that they contain

all three of these possibilities:

1. greater consonance in traditional chords (triads)

2. more consonances to choose from (e.g. 7-limit and 11-limit)

3. more and much greater dissonances available

In other words, a triple play.

> 2. Have to have a prayer in being executed on existing, or

> somewhat modified existing instruments.

It's easy to put 22 on a guitar by refretting. A relatively

cheap mod. Most MIDI keyboards can do 22 or any other

tuning in seconds, but to get the conceptual part of the

instrument right, new keyboard layouts are unfortunately

required.

> My point here - perhaps abandoning 12-TET should be a conscience

> goal instead of a matter of trying fix the holes in the dyke.

I think that is the conscience goal around here!

-Carl

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

"I'd actually say a bit of both.
1. "Fixing the holes"
Far too many times have I composed in 12TET and become frustrated trying
to, say, make 13th chords sound good and/or figure out why many inversions
of 5 or 6-note chords sound awful."

Mike, this is why composers who do make it work (first) obtain renown. As
I've said before, you are after the harmony of late romanticism (or,
arguably jazz). There are theory books out there that explain how people in
the past did it.

An easy way to study extended chords is find some midi's of said composers
and study how the chord progressions work. I've been on IRC channels with
guys picking apart music modules the same way.

On Mon, Feb 2, 2009 at 9:20 PM, Michael Sheiman <djtrancendance@yahoo.com>wrote:

> > My point here - perhaps abandoning 12-TET should be a conscience
> > goal instead of a matter of trying fix the holes in the dyke.
> ---I think that is the conscience goal around here!
>
> I'd actually say a bit of both.
> 1. "Fixing the holes"
> Far too many times have I composed in 12TET and become frustrated
> trying to, say, make 13th chords sound good and/or figure out why many
> inversions of 5 or 6-note chords sound awful.
> I still believe...there is likely a tuning that compromises consonance
> IE has many "mostly consonant" intervals rather than the bizarre combination
> of very consonant and fairly off (IE 3rds) intervals in 12TET. It bugs me
> complex music theory is often needed just to find many sweet-sounding chords
> over 3 notes "wide" in any given key in 12TET....I think it scares a lot of
> people away from songwriting.
> 2. "Making Theory Wider"
> Things like 9 and 8-note micro-tonal scales that sound not so much like
> consonant than 12TET harmonically seem to indicate there's a way to get more
> than 7-notes and still be well within the general human perception of "good
> consonance". Would there be fresh new melodies inspired in 9-tone scales
> not available in 7-tone even to the best 7-tone composers? Of course!
> That's why I'm often so pig-headed about trying to get a tuning which allows
> 9-tone scales to work.
>
>
>
> --- On *Mon, 2/2/09, Carl Lumma <carl@...>* wrote:
>
>
> From: Carl Lumma <carl@lumma.org>
> Subject: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
> To: tuning@yahoogroups.com
> Date: Monday, February 2, 2009, 5:31 PM
>
> --- In tuning@yahoogroups. com<http://mc/compose?to=tuning%40yahoogroups.com>,
> Chris Vaisvil <chrisvaisvil@ ...> wrote:
> >
> > This may be heresy, but... is 12-TET not in the end -the- best
> > compromise? For 12 notes that is.
>
> If all of society had to pick only one 12-note tuning to use
> in all music for the next hundred years, 12-ET is probably
> the best choice.
>
> > If one looks at Western music historically there has been an
> > continuous march to increased tolerance to dissonance.
>
> I don't think that's true. Most music (in terms of people-hours
> it's listened to, or dollars spent on it, etc.) today and in the
> past is very simple and very consonant. It has been argued that
> music is marching higher up the harmonic series -- 3-limit in
> the medieval period, 5-limit in the classical, and the 7-limit
> in African-American music -- but that doesn't mean higher
> dissonance, and it's a debatable interpretation of history at
> any rate. I was listening to some 15th-century Italian music
> the other day, and it was remarkably similar to modern folk
> music. One of the galliards in particular could have been put
> on a CD of square dancing music and nobody would notice.
> So if music is changing, at least it seems to be a matter of
> expansion rather than linear evolution.
>
> > While contemporary classical music has taken this to such
> > extremes (dodecophonic music comes to mind,
>
> This movement is by now mostly dead, even in academic circles,
> and it never can claim to have been widely enjoyed.
>
> > I wonder if we are at a unique time in history when an alternate
> > system all together could obtain significant traction. And in
> > proposing this - I wonder if "ultimate consonance" is really the
> > holy grail.
>
> One nice thing about tunings like 22-ET is that they contain
> all three of these possibilities:
>
> 1. greater consonance in traditional chords (triads)
> 2. more consonances to choose from (e.g. 7-limit and 11-limit)
> 3. more and much greater dissonances available
>
> In other words, a triple play.
>
> > 2. Have to have a prayer in being executed on existing, or
> > somewhat modified existing instruments.
>
> It's easy to put 22 on a guitar by refretting. A relatively
> cheap mod. Most MIDI keyboards can do 22 or any other
> tuning in seconds, but to get the conceptual part of the
> instrument right, new keyboard layouts are unfortunately
> required.
>
> > My point here - perhaps abandoning 12-TET should be a conscience
> > goal instead of a matter of trying fix the holes in the dyke.
>
> I think that is the conscience goal around here!
>
> -Carl
>
>
>

🔗Michael Sheiman <djtrancendance@...>

---Hm, not sure how you're getting that. In harmonics 16-32,
---there are seven notes that could be involved in such a
----symmetry -
I'm going to have to get back to this...but you have a point.
Basically I built this scale from the 7-note scale
9/8 * 10/9 * 11/10 * 12/11 * 10/9 * 11/10 * 12/11
Which involves more-or-less multiplying the first half of the scale by 3/2 to get the second half (meaning the greatest discrepancy you get is something like 9/8 vs. 10/9 IE more or less symmetrical). I then built on that and took both ends of the harmonic series under 8/8 (IE 7/8,6/8....13/9, 14/9) and slid them a few octaves to fit in position. Then I took the ones near an x/16 fraction and rounded them to that fractions.
But, you are right, the several of the results don't match symmetrically, even if the were generated based on harmonic series derived from 8/8 and 10/9.

--- On Mon, 2/2/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: [MMM] Fwd: The tuning group at Yahoo.
To: tuning@yahoogroups.com
Date: Monday, February 2, 2009, 6:09 PM

Michael wrote:

>> Because harmonics get closer together as you go up the series,

>> sometimes it is a good idea to omit some of the higher

>> identities to get a more even scale.

> Agreed, critical band is an issue.

It's not about the critical band, actually. Every 12-ET

semitone is smaller than a critical band, but we can still

pick chords in 12-ET that straddle CBs. Rather, scale

evenness is an issue in its own right. The more even a

scale is, the more likely it is to be Rothenberg-proper,

for one thing. Rothenberg propriety is explained here:

http://groups. yahoo.com/ group/tuning/ message/79883

See also this message:

http://groups. yahoo.com/ group/tuning/ message/78038

> But if that were the only issue...wouldn' t the harmonics

> I would eliminate would be focused on the top of the scale

> rather than scattered among the middle-top and top of the

> scale?

Yes.

> Another guess is...again my scale is symmetric about 3/2,

> just like 12TET is when summarized using JI intervals (as

> shown in my "proof of 12TET" example. When I tried, the x/16

> harmonics not included in my scale appear to be the ones not

> symmetrical about 3/2.

Hm, not sure how you're getting that. In harmonics 16-32,

there are seven notes that could be involved in such a

symmetry -- three that match when transposed by 3/2, three

that match when transposed by 2/3, and one that matches both

directions (3/2 itself, matching to 1/1 and 9/8). Of the

two notes you left out, one participated no matches (13/8)

and the other participated in one match (15/8), which is

about what we'd expect if we randomly removed two notes

(since 6:16 match once, 9:16 never match, and 1:16 match

twice).

Here's the longhand for that:

17/16

9/8 ! 27/16 ; 3/2

19/16

5/4 ! 15/8 ; 5/3

21/16 ! 63/32 ; 7/4

11/8

23/16

3/2 ! 9/8 ; 1/1

25/16

13/8 ! not used

27/16 ! 81/64 ; 9/8

7/4 ! 21/16 ; 7/6

29/16

15/8 ! not used 45/32 ; 5/4

31/16

2/1

-Carl

🔗Michael Sheiman <djtrancendance@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Carl,
>
> This stuff is =not- obvious to me.

Ok, well... for my part I'd like to apologize if, since I'm
often doing this at work when I should probably be doing
something else, I get a bit short. I try to explain things
as directly and correctly as possible, but please let me know
if there's anything I can do better. Lucky for me, the real
heavy-hitters of this list have retired, so all my mistakes
are currently going unnoticed. :)

> I have been a member if the list since it first started
> (I think) or for quite a while anyway.

It goes back to the mid '90s. I joined in '97. Anyway,
it's currently in an interesting period. Microtonality is
booming. The digital music revolution (both in terms of
mp3s commoditizing music listening and digital recording and
synthesis commoditizing music making) is largely to thank
for that. It's grown beyond the ability of mailing lists to
contain, which is very good.
The theory is now to the point where beginners can no longer
stumble onto new ground -- or at least, it's very unlikely.
It's not nearly as bad as something like physics in this
regard, but as with physics, though there are plenty of big
open questions, they all require substantial background
before they can even be understood.
A new generation of musicians are starting to get involved.
We may be nearing critical mass as far as getting a microtonal
rock band soon. As you may know, even with the density of
12-ET musicians available, forming a band can be hard.
There are now several generalized keyboards on the market,
one or two even at affordable prices. I must say, however,
that I am a bit surprised at many keyboardists' and
microtonalists' resistance to the idea.

Who knows what the future holds?

> Back on topic
>
>> "Keys" in tonal music are largely a matter of the grammer of the
>> diatonic scale. You have to be able to explain things like why
>> only the Ionian and Aeolian modes are capable of being keys..."
>
> in my experience this is totally incorrect as I have used every
> classic mode in improvisation.

Sure, improvise all you want. But in Western tonal music
theory, ONLY the Ionian or Aeolian modes are used.

> In its simplest terms a tonal center can be defined by simple
> repetition without -any- defined scale at all.

Indeed. But in Western tonal music, a "key" means a little
bit more. You can hear the transition between the medieval
and Ars Nova modal styles and the tonal style of the
Renaissance. And again the transition between the tonal
style of the romantic period and the modal style of jazz.
Something is going on here.

-Carl

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Carl,

I'm not sure what your definition of a tonal center is but my impression is
that it is not as broad as mine. Tonal centers started as melodic, not
harmonic. And this is very, very old. Harmonization has been a matter of
progression through the ages as you seem to indicate in your response - and
that this started in earnest in what 1,000 AD or so? And certainly other
cultures have a sense of tonal center - this is not at all a western music
monoply. And "keys" are not certainly essential to defining a tonal center.

You would think you'd know that modes were used regularly, in a tonal
context, regularly as late as the Renaissance. And this stuff -has- been
analyzed and codified into theory and taught. I won't argue that modes fell
into disuse - but that doesn't change the fact it exists.

And in fact, if we are discussing going beyond 12 -TET (and I just saw yet
another 12-TET scheme in my in box) I think we will have to think out of the
box harmonically. I think the 7 modes are familiar compared to a theoretical
full fledged 22 TET harmonic usage.
Triadic harmony really is rather simple to understand even applied to modes.

I should add that historically, besides the acceptence of incresed
dissonance, modulation to more and further keys also evloved. However key
(in your context) != tonality Tonality is not limited to major and minor -
in fact there are several versions of minor, and beyond that - modal usage
(with harmonization) existed in european folk music well into the 20th
century (and I'd guess to today) - as captured by the likes of Bela Bartok.
In fact it was popular past time amoung european composers to go out "into
the field" with a note book to write down the music of the "common folk" -
but I'd think you'd know this? This must be boring for most people on this
list and way off topic.

=> I certainly would like to see microtonal music gain popularity - just for
the sake of variety if nothing else. However, my Korg comes with various
versions of just and mean tone - not say, 17, 19, or 22 edo. My hats off
that it does come with anything at all. Its my first synth that even has the
possibility to reprogram notes.

==>Ok, I joined the tuning list in a recent membership drive - or perhaps I
have it backwards and MMM is more recent. Nonetheless the flames existed and
put me off.

> > Back on topic
> >
> >> "Keys" in tonal music are largely a matter of the grammer of the
> >> diatonic scale. You have to be able to explain things like why
> >> only the Ionian and Aeolian modes are capable of being keys..."
> >
> > in my experience this is totally incorrect as I have used every
> > classic mode in improvisation.
>
> Sure, improvise all you want. But in Western tonal music
> theory, ONLY the Ionian or Aeolian modes are used.
>
> > In its simplest terms a tonal center can be defined by simple
> > repetition without -any- defined scale at all.
>
> Indeed. But in Western tonal music, a "key" means a little
> bit more. You can hear the transition between the medieval
> and Ars Nova modal styles and the tonal style of the
> Renaissance. And again the transition between the tonal
> style of the romantic period and the modal style of jazz.
> Something is going on here.
>
> -Carl
>
>
>
>
>

🔗Carl Lumma <carl@...>

🔗Daniel Forro <dan.for@...>

🔗Carl Lumma <carl@...>

🔗Michael Sheiman <djtrancendance@...>

---It should not hurt for me to tell you that harmonic series scales, with and without
----omitted notes, are well-traveled territory (as well-traveled
---as anything microtonal can be, anyway), from Wendy Carlos to
---Denny Genovese, Jules Siegel, Hukwe Zawose, etc. etc.
Right, but far as I know very few of those (at least that I know of) have produced any scales made from combinations of JI intervals that were convincing enough to make many non-microtonal fans want to listen to their works. Granted, that's a constant challenge for micro-tonalism...but one which becomes more appealing as people realize how likely you are to wind up composing something someone has already composed something exactly like in 12TET.

---You don't seem to have a model that explains why you omitted those
---tones,
   Not mathematically, at least. I started with
8/8 * 9/8 * 10/9 * 12/11 (5th) * 10/9 * 11/10 * 12/11 (octave)
and then built around the harmonic series starting at the first 9/8 and the second 10/9...and then approximated to the nearest x/16 fraction.
   What historical theories do I have to back this up? Essentially none. :-)
   I created it via "cross-talk" between which direction my ears were telling me to go to move each note to fit better (up or down), which matching note was nearest on one of the two harmonic series mentioned above, and trying to space each note more close to evenly apart to avoid critical band issues.

---and for now I'm fairly confident that what you're
---experiencing is some form of bias...
----http://en.wikipedia .org/wiki/ List_of_cognitiv e_biases
----Which is nothing reflective of you, but rather is quite
----unavoidable when doing unblinded tests on oneself. :)
    Right but, on the other hand, Chris, for example, actually grabbed the first version of my scale and was impressed enough by it (unlike with my other scales) to compose something with it. And then that thing he composed got rated well, by you and many people at Trax In Space. Sure, sure...a lot of it is that he's a good composer...but surely if the scale was bad I doubt it could have done so well among even non-micro-tonal listeners.

    Maybe you or someone else could pick the scale apart mathematically and reformat it into something better sounding?   That's why I posted the new "x/16 scale challenge" thread...I actually want to see what you experts in theory can do to make something that sounds better than my scale using somewhat similar constructs.

---But experimenting is definitely the best way to go about
---microtonal music-making, and I hope you'll continue.
Well thank you! Even though I am sure guys like you can find hundreds of possible improvements, it means a lot that I am contributing something. And, don't worry...in the odd case I get anywhere special I'm not going to withhold anything from the public, start charging for it, or name it after myself...that's just not in my ethics or style at all. :-)

-Michael

🔗Daniel Forro <dan.for@...>

Yes, Carl, you are right, there must be something special with Ionian an Aeolian besides the fact, that their root notes are located as neighbors of original four modes used in European music - Ionian is to the left from Dorian, Aeolian to the right from Mixolydian.

When I analyzed those old modes and ordered all of them from the most major sounding to the most minor sounding, I have realized that Ionian is in the middle of major modes, and Aeolian in the middle of minor. Locrian can be omitted as a very special one with diminished fifth which is difficult to use not only harmonically but even melodically.

MAJOR: Lydian - Ionian - Mixolydian / MINOR: Dorian - Aeolian - Phrygian

Golden middle way? Maybe. For sure they sound neutral, not so special and typical like the other ones, but maybe just because we are used to it. In this sense they allow more melodic alterations, and harmonically they have all main chords with "normal" pure fifth. (Lydian's subdominant can't be used as well as Phrygian dominant).

Who knows how tonal music and functional harmony would evolve if in some parallel world both extremes were accepted as standard, that means the most major Lydian with the most minor Phrygian. For sure distance between major and minor music would be bigger.

Daniel Forro

On 3 Feb 2009, at 12:42 PM, Carl Lumma wrote:

> Daniel-
>
> Thank you for the reference to Anton Reicha, with whom
> I was not familiar. That said, of course there are always
> exceptions. This does not change the basic assessment of
> the situation: there is something special about the ionian
> and aeolian modes, and a theory of scales, that might be
> employed to generate new scales for a new kind of tonal
> music, should be able to explain what it is.
>
> -Carl
>

🔗Chris Vaisvil <chrisvaisvil@...>

Carl,

Go back and read my message - I did not mention keys, it was you, whom I
quoted.

Key = tonal center = most used to denote harmonically defined tonal center
though divorce from melody isn't real.

And what on earth is your measure of success? I would consider Bartok as
quite well known for a 20th century composer. How many other better known
names would one pull from that hat? Copeland, Ives, Stravinsky,
Shostakovitch, Britten?
And I believe Beethoven did the same thing for that matter.

Carl, why do you respond with such loaded value judgments on what is
obviously a subjective matter? Frustrating!@

Back on subject - I think I remember an argument that major and minor were
chosen because they could more conclusively define a tonal center and form
better, more definitive, cadences. (But defining tonal centers, and what was
done, stylistically, was one of the major points of the course)

An interesting question - at least 3 variants of minor - only one of major.

Good night

Chris

On Mon, Feb 2, 2009 at 10:38 PM, Carl Lumma <carl@...> wrote:

> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > Carl,
> >
> > I'm not sure what your definition of a tonal center is but my
> > impression is that it is not as broad as mine.
>
> You said "key" and so did I. "Tonal center" may be different.
> The definition is hardly mine -- it's standard music theory 101
> at any conservatory.
>
> > You would think you'd know that modes were used regularly, in
> > a tonal context, regularly as late as the Renaissance.
>
> *Until* the Renaissance, as I said. And not again until
> the 20th century, as I said.
>
> > In fact it was popular past time amoung european composers to
> > go out "into the field" with a note book to write down the music
> > of the "common folk" - but I'd think you'd know this?
>
> They met with dubious success -- including Bartok -- mainly
> because these traditions do not use 12-ET. They are also
> not "Western" or "tonal" traditions, in which the term "key"
> was born. If you want to talk about tonal centers, I'm all
> ears. Key is something with a specific meaning.
>
> > This must be boring for most people on this list and way off
> > topic.
>
> It pertains to scale theory, which has been a *major* topic of
> discussion here, for good reason.
>
> -Carl
>
>
>

🔗Mike Battaglia <battaglia01@...>

🔗Daniel Forro <dan.for@...>

Yes, basically I agree with you.

Just small detail not to make more confusion in terminology: I use terms "modal harmony" and "functional harmony" in accordance with historical development of European music. Modal harmony was more simple, used mainly major and minor triads and because tonality in later sense didn't exist and tonal centre was not stabilized and clearly defined, also harmonic relations are more free (and sometimes unusual, surprising and difficult to analyze from the point of view of later functional harmony). There are strange chromatic connections, sudden jumps to "foreign" chords etc. Of course we can find here ome typical chord progressions in embryonal state, which were stabilized and commonly used later in functional harmony, like V - I in the end and so. Also this modal music doesn't know something like "modulation" in later sense, as I'm not aware about the only example when music would be let's say in Dorian with root note on D, and somewhere in the middle changed to Lydian on Gb. Despite the fact that chromatic scale was well known, and even used (there are nice examples even in late 14th century Ars subtilior, like Solage's Fumeaux fume), but not for modulations like this. Generally modal music disppeared very slowly somewhere between 1600-1630.

Functional harmony could start when tonality was developped, with clearly defined tonal centre, and certain chords progressions started to be used intentionally because they had different result emotionally, some made a feeling we are far from centre, therefore there's more tension, and when we came back to the centre, there was more peace. In this sense later also modulation to different key were used, to add even more - this process came to its peak in Wagner's Tristan und Isolde. And of course also chords started to be more complex - 7th, 9th in 17.-18. century to 13th in the middle of 19th century, and later even more complex with using more notes then 7 notes of diatonic scale.

I think also this is just historical view. Of course there is possible to use any historical or folklore modes and accompany them with functional harmony, but if we will keep the original mode, then possibilities will be limited even for some common basic diatonic chord progressions (depending on mode), nothing to say about more rich chromatic harmony, which will be almost restricted (like double dominants or subdominants or seventh chords, chains of double dominants or subdominants, chords or chromatic third relation, and such phenomenons like chromatic/enharmonic modulation). Chromatic note alterations would destroy original atmosphere of mode and move it in the direction to standard major/minor or chromatic, so it will not be taken as enrichment (which is the case of major/minor functional tonality), just as a return to major/minor. Also use of modulations will sound strange, as well as harmonizing of simple modal melody with rich functional harmony... But there is still some potential.

Opposite it's possible to take major/minor diatonic, pandiatonic or chromatic and use it over modal harmony. This is more promissing because melody can be more rich then harmony, which is often the case in music.

Another understanding of modality is in jazz, where complex chords are often used with old modes in melody part, or opposite chromatic melody is harmonized in modal way without traditional functional harmony relations.

Another variation on this theme showed us for example Messiaen - to create any scale and then create chords only from its notes. Even such simple scale like diminished will give interesting modal harmony far from traditional relations of functional harmony. (Here I would add that right in this he had some predecessors - Skriabin (who derived it probably from Chopin/Liszt) and Bartok (who found it in folklore)).

So functional harmony in the frame of modality has a lot of limitations, so much that I would not use a term "functional" for it. Examples you gave had nothing to do with functional harmony, it's pure modal harmony.

Daniel Forro

On 3 Feb 2009, at 2:07 PM, Mike Battaglia wrote:

> > Who knows how tonal music and functional harmony would evolve if in
> > some parallel world both extremes were accepted as standard, that
> > means the most major Lydian with the most minor Phrygian. For sure
> > distance between major and minor music would be bigger.
>
> They are all accepted as standard in circles outside of common
> practice theory. A lot of metal songs use phrygian mode. And a whole
> tone of classic rock songs are written in mixolydian, and dorian, and
> sometimes lydian.
>
> I think people are arguing over terminology, but the notion that the
> only modes with functional harmony are major/minor is an antiquated
> common practice idea that generally irritates me when it's taught as
> some inherent truth of the universe. Functional harmony can exist in
> all 7 diatonic modes, although some, like locrian, are a bit trickier
> to work out.
>
> Louie Louie is a good example - I IV v IV is the chord progression,
> and I hear it as being based in mixolydian mode, with the minor v
> chord having its own function that differs from the major V chord. Or
> any song that utilizes the bVII IV I progression - it's kind of like a
> double plagal cadence.
>
> Long live functional modal harmony!
>
> -Mike

🔗Mike Battaglia <battaglia01@...>

> Another variation on this theme showed us for example Messiaen - to
> create any scale and then create chords only from its notes. Even
> such simple scale like diminished will give interesting modal harmony
> far from traditional relations of functional harmony. (Here I would
> add that right in this he had some predecessors - Skriabin (who
> derived it probably from Chopin/Liszt) and Bartok (who found it in
> folklore)).

The half-whole diminished scale is glorious. A masterwork of temperament.

> So functional harmony in the frame of modality has a lot of
> limitations, so much that I would not use a term "functional" for it.
> Examples you gave had nothing to do with functional harmony, it's
> pure modal harmony.
>
> Daniel Forro

Well, perhaps it's a matter of terminology as to what is meant by
"modal" vs "tonal" and "functional" vs "modal".

They seem functional to me. Functional and exotic. The minor v chord
has its own function that differs from the major V chord. bVII has its
own function as well. There are a few ways to analyze those chord from
a common practice standpoint - you could say that bVII is some kind of
IV/IV chord, or you could say that the minor v chord is a borrowed
chord from a minor key. But why try to fit everything into the
major/minor system? It seems like a powerful and fairly intuitive
extension of common practice theory to throw out the fairly arbitrary
assertion that major and minor are the only two valid forms of
tonality. If you remove that axiom from the system, you'll find you
can use dorian and mixolydian and such as tonalities and that you can
find functional harmonies and chords with specific "functions" in
them.

Plus, it isn't like you're limited to only the notes in the mode
you're using -- how many common practice songs written in minor really
stick entirely to aeolian mode? They use V7 chords, they use harmonic
minor, they use melodic minor... I'm basically advocating the same
type of approach to writing with modes. Instead of writing a piece in
aeolian and using V7 chords occasionally and such, you can write a
piece in dorian and use V7 chords occasionally. Why not?

My personal view on the matter is that a certain type of aural space
is created when you have A B C D E F G A -- and a different type of
aural space is created when you have A B C D E F# G A. You can throw a
V7 chord in there and the G# will be incredibly dissonant and
unexpected and make you beg for that i chord. So being as these
feelings and emotions and shifting end up working pretty nicely when
thrown into certain sequences, such as V7-i (hence functional
harmony), what reason is there you couldn't feel out the "emotion
space" for something like dorian and proceed to write music in it?
Does common practice theory hold that all music written in different
modes than major and minor has to be pandiatonic?

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Daniel Forró <dan.for@...>

On 3 Feb 2009, at 4:05 PM, Mike Battaglia wrote:

> The half-whole diminished scale is glorious. A masterwork of > temperament.
>
>
Full agreement. Great atmosphere.
> Well, perhaps it's a matter of terminology as to what is meant by
> "modal" vs "tonal" and "functional" vs "modal".
>
> They seem functional to me. Functional and exotic. The minor v chord
> has its own function that differs from the major V chord. bVII has its
> own function as well. There are a few ways to analyze those chord from
> a common practice standpoint - you could say that bVII is some kind of
> IV/IV chord
>
It depends on the context. It can be like this when it's followed by IV. That's a basic principle of functional harmony. (Same like D major chord in C major. When it's before V, it will be double dominant. When it's before IV, it can be considered as chromatic third relation chord.)
Besides there's no law prohibiting to use such chord (with appropriate harmonic function) in the frame of major/minor functional harmony. Still it doesn't mean I will call such music modal music.
> , or you could say that the minor v chord is a borrowed
> chord from a minor key.
>
That's difficult to say, minor V chord doesn't exist in functional harmony. Even minor tonality use major V. Only Mixolydian has minor V, so in this case we would say more exactly it's taken from Mixolydian, but that means it's not functional, but modal harmony.
> But why try to fit everything into the
> major/minor system? It seems like a powerful and fairly intuitive
> extension of common practice theory to throw out the fairly arbitrary
> assertion that major and minor are the only two valid forms of
> tonality.
>
Of course, compositional practice was always ahead theory which accepted new principles as a norm with some delay after their stabilization .
Theory is usually only simplified generalized model derived ex post from practice. (There are some exceptions when theoretical concept came first, even in music. Don't we see a lot of examples here with tunings and scales?)
All rules of functional harmony are based on major/minor music, that's the reason why it's not possible to use it fully with older modal attitude.
> If you remove that axiom from the system, you'll find you
> can use dorian and mixolydian and such as tonalities and that you can
> find functional harmonies and chords with specific "functions" in
> them.
>
Yes, but reason why theory doesn't mix these two possible attitudes is partly historical, partly because it's difficult or in many case impossible to find harmonic functions for modal chord relations (and there's no reason to do so, it works differently than functional chord relations), or because we can use a lot of functional chord relations at all as they don't fit into the modal context.
> Plus, it isn't like you're limited to only the notes in the mode
> you're using -- how many common practice songs written in minor really
> stick entirely to aeolian mode? They use V7 chords, they use harmonic
> minor, they use melodic minor...
>
Sorry, but pure Aeolian mode and melodic/harmonic minor are totally different things, we have to see them historically. They came from different music era. Again you mix modal and functional attitude. Which is possible but that functional one will probably win as it's historically younger and still used.
> I'm basically advocating the same
> type of approach to writing with modes. Instead of writing a piece in
> aeolian and using V7 chords occasionally and such, you can write a
> piece in dorian and use V7 chords occasionally. Why not?
>
Of course that's easily possible in compositional practice, usually pure Dorian will be in melody, and V7 in harmony, and composer will usually avoid a meeting of Dorian 7th in melody with functional 7th in harmony because it's pretty dissonant (or he will intentionally emphasize it, why not). But thanks to using V7 you destroy one of typical intervals of Dorian and make from it melodic minor. You can even use very complex jazz chords or even some totally abstract 12tone chords for harmonizing very simple modal melody. Why not. But by crossing a border between old modality and modern major/minor attitude in the direction to historically later music you give up modality.
> My personal view on the matter is that a certain type of aural space
> is created when you have A B C D E F G A -- and a different type of
> aural space is created when you have A B C D E F# G A. You can throw a
> V7 chord in there and the G# will be incredibly dissonant and
> unexpected and make you beg for that i chord. So being as these
> feelings and emotions and shifting end up working pretty nicely when
> thrown into certain sequences, such as V7-i (hence functional
> harmony), what reason is there you couldn't feel out the "emotion
> space" for something like dorian and proceed to write music in it?
>
Yes, this is possible, but then we can't call such music "modal" in that historical sense.
> Does common practice theory hold that all music written in different
> modes than major and minor has to be pandiatonic?
>
>
I don't understand what you mean by this.

Daniel Forro

🔗Daniel Forro <dan.for@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Mike Battaglia <battaglia01@...>

>> , or you could say that the minor v chord is a borrowed
>> chord from a minor key.
>>
> That's difficult to say, minor V chord doesn't exist in functional
> harmony. Even minor tonality use major V. Only Mixolydian has minor
> V, so in this case we would say more exactly it's taken from
> Mixolydian, but that means it's not functional, but modal harmony.

I think you mean that the minor v chord is rare in common practice-era
functional harmony. It is used occasionally. But even so, to state
that it serves no potential function in music makes no sense, and it
certainly -exists- - we're talking about it, aren't we?

The whole point I'm making is that common practice theory places
arbitrary limitations on functional harmony. So if you respond that
certain chords just "can't be functional" or "don't exist in the
system," that basically reinforces what I'm saying. "Functional
harmony" is a real-life concept that exists outside of common practice
theory. It has to do with the colors that chords have and what chords,
when placed in sequence after other chords, "fit" in a certain way, or
lead you to expect a certain type of resolution.

Modern jazz fusion artists, like Robert Glasper, have made an entire
art form out of finding weird and unexpected chord progressions in
which the chords DO lead into each other for some strange reason. E7#9
Absus13 C#maj9. To say that they aren't "functional" is wrong, because
when you listen to his progressions you get the impression that they
do "function", but in a new and exotic way. To say that they make no
sense in common practice theory, on the other hand, is correct.

>> But why try to fit everything into the
>> major/minor system? It seems like a powerful and fairly intuitive
>> extension of common practice theory to throw out the fairly arbitrary
>> assertion that major and minor are the only two valid forms of
>> tonality.
>>
> Of course, compositional practice was always ahead theory which
> accepted new principles as a norm with some delay after their
> stabilization .
> Theory is usually only simplified generalized model derived ex post
> from practice. (There are some exceptions when theoretical concept
> came first, even in music. Don't we see a lot of examples here with
> tunings and scales?)
> All rules of functional harmony are based on major/minor music,
> that's the reason why it's not possible to use it fully with older
> modal attitude.

Functional harmony is something independent from common practice
theory. Common practice theory is an attempt to write down some of the
rules of functional harmony as commonly used in the 18th-19th
centuries and such. In my opinion, they tried to place restrictions on
functional harmony that don't really exist.

>> If you remove that axiom from the system, you'll find you
>> can use dorian and mixolydian and such as tonalities and that you can
>> find functional harmonies and chords with specific "functions" in
>> them.
>>
> Yes, but reason why theory doesn't mix these two possible attitudes
> is partly historical, partly because it's difficult or in many case
> impossible to find harmonic functions for modal chord relations (and
> there's no reason to do so, it works differently than functional
> chord relations), or because we can't use a lot of functional chord
> relations at all as they don't fit into the modal context.

What exactly do you mean by "modal chord relations" vs "functional
chord relations"? And what do you mean by the "modal context?" Perhaps
we're just differing on the terminology.

>> Plus, it isn't like you're limited to only the notes in the mode
>> you're using -- how many common practice songs written in minor really
>> stick entirely to aeolian mode? They use V7 chords, they use harmonic
>> minor, they use melodic minor...
>>
> Sorry, but pure Aeolian mode and melodic/harmonic minor are totally
> different things, we have to see them historically. They came from
> different music era. Again you mix modal and functional attitude.
> Which is possible but that functional one will probably win as it's
> historically younger and still used.

I used the word Aeolian because Carl earlier mentioned that the only
two modes you can label "keys" are Ionian and Aeolian. I'm making the
point that common-practice music is almost never written using pure
Aeolian mode - V7 chords and such are thrown in all the time. Hence
the invention of the harmonic minor scale. And they do love those
melodic minor melodies. So you could write music in a Mixolydian tonic
and still throw a V7 chord in there if you want. That's what they do
with minor as well. I've heard plenty of songs in which the I chord
seems to be a "stable" sounding dominant 7 chord. I7. No need for it
to be viewed as a V7/IV. Sometimes it has to do with the I7
approximating an otonal tetrad, I think, but even when the 7th is
tuned 9/5, it still can work as a root chord.

The "functional and modal" paradigm that I've been describing is
historically younger than both the renaissance modal attitude and the
common-practice attitude, and is currently "winning" and still in
formation. It's, as you said, an ex poste attempt to describe the last
hundred years of music (except for some of the 12-tone stuff, which I
hate anyway). No, it isn't as well established as common practice
theory, but it is what they teach in most jazz schools, and I find the
paradigm superior for analyzing all kinds of music, even common
practice.

>> My personal view on the matter is that a certain type of aural space
>> is created when you have A B C D E F G A -- and a different type of
>> aural space is created when you have A B C D E F# G A. You can throw a
>> V7 chord in there and the G# will be incredibly dissonant and
>> unexpected and make you beg for that i chord. So being as these
>> feelings and emotions and shifting end up working pretty nicely when
>> thrown into certain sequences, such as V7-i (hence functional
>> harmony), what reason is there you couldn't feel out the "emotion
>> space" for something like dorian and proceed to write music in it?
>>
> Yes, this is possible, but then we can't call such music "modal" in
> that historical sense.

What would you call it? Whatever you would call it, that's the
direction I see most modern music going into. Debussy, Ravel, film
scores, electronic music, the Beatles, post-bop... They all used modes
as various forms of tonic, or borrowed chords from different modes,
but they definitely use modes differently than Renaissance music or
Gregorian chant did. What it seemed like they were doing to me was
extending the concept of a "tonality" to other modes besides major and
minor. Some post-bop jazz composers, such as Wayne Shorter, would also
extend it to melodic minor modes as well, such as mixolydian b6 (C D E
F G Ab Bb C).

The prime innovation of modern music that I've seen is that they've
figured out how to run around functionally in modes, something which
was previously deemed "impossible." I've been calling it a "functional
modal" approach, but perhaps the term is misleading or contradictory
when viewed in a historical sense.

>> Does common practice theory hold that all music written in different
>> modes than major and minor has to be pandiatonic?
>>
> I don't understand what you mean by this.

If functional harmony can't exist for the modes, what does "modal
harmony" entail? Random chord clusters played over a drone? A
pandiatonic wash of notes?

-Mike

🔗chrisvaisvil@...

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Mike I certainly agree with everything you just said and so does this
article

http://en.wikipedia.org/wiki/Tonal_music

I think this will help address the confusion on the point of "tonal" music

On Tue, Feb 3, 2009 at 12:20 PM, Mike Battaglia <battaglia01@...>wrote:

> >> , or you could say that the minor v chord is a borrowed
> >> chord from a minor key.
> >>
> > That's difficult to say, minor V chord doesn't exist in functional
> > harmony. Even minor tonality use major V. Only Mixolydian has minor
> > V, so in this case we would say more exactly it's taken from
> > Mixolydian, but that means it's not functional, but modal harmony.
>
> I think you mean that the minor v chord is rare in common practice-era
> functional harmony. It is used occasionally. But even so, to state
> that it serves no potential function in music makes no sense, and it
> certainly -exists- - we're talking about it, aren't we?
>
> The whole point I'm making is that common practice theory places
> arbitrary limitations on functional harmony. So if you respond that
> certain chords just "can't be functional" or "don't exist in the
> system," that basically reinforces what I'm saying. "Functional
> harmony" is a real-life concept that exists outside of common practice
> theory. It has to do with the colors that chords have and what chords,
> when placed in sequence after other chords, "fit" in a certain way, or
> lead you to expect a certain type of resolution.
>
> Modern jazz fusion artists, like Robert Glasper, have made an entire
> art form out of finding weird and unexpected chord progressions in
> which the chords DO lead into each other for some strange reason. E7#9
> Absus13 C#maj9. To say that they aren't "functional" is wrong, because
> when you listen to his progressions you get the impression that they
> do "function", but in a new and exotic way. To say that they make no
> sense in common practice theory, on the other hand, is correct.
>
> >> But why try to fit everything into the
> >> major/minor system? It seems like a powerful and fairly intuitive
> >> extension of common practice theory to throw out the fairly arbitrary
> >> assertion that major and minor are the only two valid forms of
> >> tonality.
> >>
> > Of course, compositional practice was always ahead theory which
> > accepted new principles as a norm with some delay after their
> > stabilization .
> > Theory is usually only simplified generalized model derived ex post
> > from practice. (There are some exceptions when theoretical concept
> > came first, even in music. Don't we see a lot of examples here with
> > tunings and scales?)
> > All rules of functional harmony are based on major/minor music,
> > that's the reason why it's not possible to use it fully with older
> > modal attitude.
>
> Functional harmony is something independent from common practice
> theory. Common practice theory is an attempt to write down some of the
> rules of functional harmony as commonly used in the 18th-19th
> centuries and such. In my opinion, they tried to place restrictions on
> functional harmony that don't really exist.
>
> >> If you remove that axiom from the system, you'll find you
> >> can use dorian and mixolydian and such as tonalities and that you can
> >> find functional harmonies and chords with specific "functions" in
> >> them.
> >>
> > Yes, but reason why theory doesn't mix these two possible attitudes
> > is partly historical, partly because it's difficult or in many case
> > impossible to find harmonic functions for modal chord relations (and
> > there's no reason to do so, it works differently than functional
> > chord relations), or because we can't use a lot of functional chord
> > relations at all as they don't fit into the modal context.
>
> What exactly do you mean by "modal chord relations" vs "functional
> chord relations"? And what do you mean by the "modal context?" Perhaps
> we're just differing on the terminology.
>
> >> Plus, it isn't like you're limited to only the notes in the mode
> >> you're using -- how many common practice songs written in minor really
> >> stick entirely to aeolian mode? They use V7 chords, they use harmonic
> >> minor, they use melodic minor...
> >>
> > Sorry, but pure Aeolian mode and melodic/harmonic minor are totally
> > different things, we have to see them historically. They came from
> > different music era. Again you mix modal and functional attitude.
> > Which is possible but that functional one will probably win as it's
> > historically younger and still used.
>
> I used the word Aeolian because Carl earlier mentioned that the only
> two modes you can label "keys" are Ionian and Aeolian. I'm making the
> point that common-practice music is almost never written using pure
> Aeolian mode - V7 chords and such are thrown in all the time. Hence
> the invention of the harmonic minor scale. And they do love those
> melodic minor melodies. So you could write music in a Mixolydian tonic
> and still throw a V7 chord in there if you want. That's what they do
> with minor as well. I've heard plenty of songs in which the I chord
> seems to be a "stable" sounding dominant 7 chord. I7. No need for it
> to be viewed as a V7/IV. Sometimes it has to do with the I7
> approximating an otonal tetrad, I think, but even when the 7th is
> tuned 9/5, it still can work as a root chord.
>
> The "functional and modal" paradigm that I've been describing is
> historically younger than both the renaissance modal attitude and the
> common-practice attitude, and is currently "winning" and still in
> formation. It's, as you said, an ex poste attempt to describe the last
> hundred years of music (except for some of the 12-tone stuff, which I
> hate anyway). No, it isn't as well established as common practice
> theory, but it is what they teach in most jazz schools, and I find the
> paradigm superior for analyzing all kinds of music, even common
> practice.
>
> >> My personal view on the matter is that a certain type of aural space
> >> is created when you have A B C D E F G A -- and a different type of
> >> aural space is created when you have A B C D E F# G A. You can throw a
> >> V7 chord in there and the G# will be incredibly dissonant and
> >> unexpected and make you beg for that i chord. So being as these
> >> feelings and emotions and shifting end up working pretty nicely when
> >> thrown into certain sequences, such as V7-i (hence functional
> >> harmony), what reason is there you couldn't feel out the "emotion
> >> space" for something like dorian and proceed to write music in it?
> >>
> > Yes, this is possible, but then we can't call such music "modal" in
> > that historical sense.
>
> What would you call it? Whatever you would call it, that's the
> direction I see most modern music going into. Debussy, Ravel, film
> scores, electronic music, the Beatles, post-bop... They all used modes
> as various forms of tonic, or borrowed chords from different modes,
> but they definitely use modes differently than Renaissance music or
> Gregorian chant did. What it seemed like they were doing to me was
> extending the concept of a "tonality" to other modes besides major and
> minor. Some post-bop jazz composers, such as Wayne Shorter, would also
> extend it to melodic minor modes as well, such as mixolydian b6 (C D E
> F G Ab Bb C).
>
> The prime innovation of modern music that I've seen is that they've
> figured out how to run around functionally in modes, something which
> was previously deemed "impossible." I've been calling it a "functional
> modal" approach, but perhaps the term is misleading or contradictory
> when viewed in a historical sense.
>
> >> Does common practice theory hold that all music written in different
> >> modes than major and minor has to be pandiatonic?
> >>
> > I don't understand what you mean by this.
>
> If functional harmony can't exist for the modes, what does "modal
> harmony" entail? Random chord clusters played over a drone? A
> pandiatonic wash of notes?
>
> -Mike
>
>

🔗Marcel de Velde <m.develde@...>

🔗Charles Lucy <lucy@...>

🔗Daniel Forro <dan.for@...>

On 4 Feb 2009, at 2:20 AM, Mike Battaglia wrote:
> I think you mean that the minor v chord is rare in common practice-era
> functional harmony. It is used occasionally. But even so, to state
> that it serves no potential function in music makes no sense, and it
> certainly -exists- - we're talking about it, aren't we?
>
>
I use term "function" here only as technical term, for function of chord in the frame of functional harmony theory. That's the reason why this theory is called "functional", it is based on "functions" of chord in the tonality. Functions can be for example: Tonic, Subdominant, Dominant, Mediants III and VI, then II, VII for diatonic harmony, and additionally Double Subdominant, extra-key Subdominants, Double Dominant, extra-key Dominants, extra-key VII, Lydian function (B minor chord in C minor), Phrygian function (Db major triad in C major, when used as a Subdominant substitution before Dominant, it's called Napolitan sixth chord), chords of chromatic third relation, extra-key chords, Substitution chords... for extended tonality (chromatic).

In this theory chords don't exist just as isolated chords, but they work in context thanks to their function. For example C major triad is Tonic in C major, but as well Subdominant in G major, Mediant in A minor, Phrygian chord () in B minor or major etc. When we re-value a function of chord, we can easily modulate to the other key.

Of course minor V exists and is used, and we can determine its function in concrete musical context, but this function doesn't belong to dominant class functions. For example when it stays before II, it can be considered as Double II. (I have solution how to indicate this minor chord on Vth step in major scale when its function is not totally explainable. We can use just V without function, as it is not Dominant function or some other.)
There's another beautiful example in the end of Janacek's Taras Bulba symphonic poem: B7 on A - Gm - F7 - C9add. Can be analyzed as chord of chromatic third relation - minor V - S7 - T. That C in the function of T is very surprising, everybody would expect after Gm and F7 - Bb as a Tonic. He changed direction and didn't used dominant, but subdominant resolution. That's called creativity! I don't think he heard something about blues...

Minor chords in major tonality generally have tendency to Subdominant class, as minor Subdominant is often used, its effect with following Tonic or Dominant class chord is much stronger than major Subdominant.

This classical approach to harmony works and can explain harmony until Wagner and lot of music which followed later, but it is not quite suitable for music style which let's say Debussy started, where chords are connected freely and any chord can follow any other one.
> The whole point I'm making is that common practice theory places
> arbitrary limitations on functional harmony. So if you respond that
> certain chords just "can't be functional" or "don't exist in the
> system," that basically reinforces what I'm saying. "Functional
> harmony" is a real-life concept that exists outside of common practice
> theory. It has to do with the colors that chords have and what chords,
> when placed in sequence after other chords, "fit" in a certain way, or
> lead you to expect a certain type of resolution.
>
Exactly so.
> Modern jazz fusion artists, like Robert Glasper, have made an entire
> art form out of finding weird and unexpected chord progressions in
> which the chords DO lead into each other for some strange reason. E7#9
> Absus13 C#maj9. To say that they aren't "functional" is wrong, because
> when you listen to his progressions you get the impression that they
> do "function", but in a new and exotic way. To say that they make no
> sense in common practice theory, on the other hand, is correct.
>
>
I didn't write they are not functional, just they can be hardly analyzed from the point of the traditional (an rather limited) functional harmony. Because its rules were created years before such weird and unexpected chord sequences came into the use.
>
> Functional harmony is something independent from common practice
> theory. Common practice theory is an attempt to write down some of the
> rules of functional harmony as commonly used in the 18th-19th
> centuries and such. In my opinion, they tried to place restrictions on
> functional harmony that don't really exist.
>
>
Definitely yes.
> What exactly do you mean by "modal chord relations" vs "functional
> chord relations"? And what do you mean by the "modal context?" Perhaps
> we're just differing on the terminology.
>
>
Modal chord relations are chord progressions which we can find in modal music, that means until beginning of 17th century. Typical is using of old modes, chords have no harmonic function in later sense (but some of later functional progressions can be traced, like D - T in the end of compositions, where T is usually major even in minor mode), chords were connected freely, and sometimes very strange chromatic progressions appear, especially in the end of this period (chromatic madrigal by Venosa, Lasso, Marenzio...). Feelings were expressed mainly by change of mode. Composers didn't use modulations or transpositions during one composition.

When music started to work with contrast major/minor, also harmony developped into functional harmony very quickly. Feelings were expressed by intentional work with tension and peace which was possible because chords can belong to Tonic function class (maximum peace), Subdominant function class (little tension) and Dominant function class (maximum tension), later also chromatic extra-key chords came into the game. Chords became more and more complex (until 13th chord in the half of 19th century), which helped also to this process, as some chords were more dissonant, some were consonant. Composers could use also modulations to different key as a powerful expression tool.
> I used the word Aeolian because Carl earlier mentioned that the only
> two modes you can label "keys" are Ionian and Aeolian. I'm making the
> point that common-practice music is almost never written using pure
> Aeolian mode - V7 chords and such are thrown in all the time. Hence
> the invention of the harmonic minor scale. And they do love those
> melodic minor melodies. So you could write music in a Mixolydian tonic
> and still throw a V7 chord in there if you want. That's what they do
> with minor as well.
>
All this is done often, yes.
> I've heard plenty of songs in which the I chord
> seems to be a "stable" sounding dominant 7 chord. I7. No need for it
> to be viewed as a V7/IV. Sometimes it has to do with the I7
> approximating an otonal tetrad, I think, but even when the 7th is
> tuned 9/5, it still can work as a root chord.
>
>
Yes, I7 is quite normal in blues, rock'n'roll, jazz...
> The "functional and modal" paradigm that I've been describing is
> historically younger than both the renaissance modal attitude and the
> common-practice attitude, and is currently "winning" and still in
> formation. It's, as you said, an ex poste attempt to describe the last
> hundred years of music (except for some of the 12-tone stuff, which I
> hate anyway). No, it isn't as well established as common practice
> theory, but it is what they teach in most jazz schools, and I find the
> paradigm superior for analyzing all kinds of music, even common
> practice.
>
I would be last one who wouldn't agree with this, I compose this way since I've started to make music.

Using it for analysis of historical modal or functional music is possible, but a-historical from musicological point of view. Almost same like if somebody will try to analyze Bach's or Mozart's works from the point of dodecaphony. Despite finding many unusual chromatic melodic motifs and harmonies we can't say they were dodecaphonists.
> What would you call it?
>
Something like extended or free tonality, or modality (in modern sense).
> Whatever you would call it, that's the
> direction I see most modern music going into. Debussy, Ravel, film
> scores, electronic music, the Beatles, post-bop... They all used modes
> as various forms of tonic, or borrowed chords from different modes,
> but they definitely use modes differently than Renaissance music or
> Gregorian chant did. What it seemed like they were doing to me was
> extending the concept of a "tonality" to other modes besides major and
> minor. Some post-bop jazz composers, such as Wayne Shorter, would also
> extend it to melodic minor modes as well, such as mixolydian b6 (C D E
> F G Ab Bb C).
>
> The prime innovation of modern music that I've seen is that they've
> figured out how to run around functionally in modes, something which
> was previously deemed "impossible." I've been calling it a "functional
> modal" approach, but perhaps the term is misleading or contradictory
> when viewed in a historical sense.
>
In music everything is possible, theory is always delayed to practice. Everything can work well. I tried everything in my works what you describe and much more, and didn't need a theoretical confirmation or permission for it.
Extended tonality is only one of styles or streams in 20th century music, not the main one.
> If functional harmony can't exist for the modes, what does "modal
> harmony" entail? Random chord clusters played over a drone? A
> pandiatonic wash of notes?
>
> -Mike
>
Such combination is possible, but then it is not modal harmony in historical sense.

Daniel Forro