Some thoughts on harmony

I have for many years (probably like 25) been thinking about the relation between harmony and maths. Almost 2 years ago I wrote down my current thouhgts about the subject.

I live on a remote island off the coast of Norway and I don't have any one out here to discuss the subject with. I have managed to build up enough courage to send it to this group, hoping that I may get some feedback.

I have created a folder under my name Jarl Mosand and I have uploaded a PDF file by the name of "The Harmony of Harmony". I hope some of you will take the time to read it. I am sorry for the poor English.

with regards
Jarl Mosand
Norway

--- In tuning@yahoogroups.com, "jarlmosand" <jarlmos@...> wrote:
>
> I have for many years (probably like 25) been thinking about the relation between harmony and maths. Almost 2 years ago I wrote down my current thouhgts about the subject.

Your thoughts are definitely along the lines of this group.

> I live on a remote island off the coast of Norway and I don't have any one out here to discuss the subject with. I have managed to build up enough courage to send it to this group, hoping that I may get some feedback.

The real conversations these days are happening on Facebook, on something called the Xenharmonic Alliance. Some online resources are
here:

http://xenharmonic.wikispaces.com/
http://x31eq.com/
http://tonalsoft.com/enc/encyclopedia.aspx

Hello Jarl, and welcome to the list!

I've taken some time to read through your document, and think it's
great that you've independently stumbled on the same sort of ideas
that we talk about around here. For example, you go onto express how
the prime factorization of a JI interval can lead to its
characterization as a point in a vector space - what we call "interval
space." You use the notation [-4, 4, -1] for the syntonic comma, and
we've been doing the same sort of thing here as well - we typically
notate it in a "ket" as |-4 4 -1>, and call such things "monzos,"
after Joe Monzo who's a theorist that used to frequent this list.

So here's a question: if you're representing intervals as a point in a
vector space (let's call it V), have you ever looked at the space of
all linear functionals on V - that is, the space V* which is the dual
space of V? For example, consider the covector <12 19 28|, written in
a "bra" to denote that it is in fact a covector, and then what it
might mean when you apply this covector to elements in interval space.
(Covectors acting on vectors in interval space are often called "vals"
around here).

Also, as a last note, many of the things you wrote about intervallic
"mood" are very interesting, but I admit that lately I've come to
believe that there is a potent source of musical emotion, mood, or
general feeling which is intonation-independent and isn't quite fully
understood. Consider these listening examples here, which are Bach
retunings:

http://soundcloud.com/mikebattagliamusic/sets/the-categorical-experiments/

While it's definitely true that the more harmonically accurate tunings
differ considerably in "mood" from the less accurate ones, it also
seems to be true that there is something that a "major third" is which
is independent of whether it's intoned as 5/4 (as is the case in
31-EDO) or 9/7 (as is the case in 22-EDO), so long as the scalar
structure is reasonably in place. So I'd encourage you to think about
what some of that might mean.

Anyway, aside from that, there's still obviously something important
about just ratios, and a remarkable amount of mileage to be cranked
out of just the notion of putting them into a vector space. You might
also want to consider the yahoo "tuning-math" group, where a lot of
research in this area continues to take place, as well as the
Xenharmonic Alliance group which Gene just linked you to.

-Mike

On Sat, Dec 31, 2011 at 9:17 AM, jarlmosand <jarlmos@...> wrote:
>
> I have for many years (probably like 25) been thinking about the relation between harmony and maths. Almost 2 years ago I wrote down my current thouhgts about the subject.
>
> I live on a remote island off the coast of Norway and I don't have any one out here to discuss the subject with. I have managed to build up enough courage to send it to this group, hoping that I may get some feedback.
>
> I have created a folder under my name Jarl Mosand and I have uploaded a PDF file by the name of "The Harmony of Harmony". I hope some of you will take the time to read it. I am sorry for the poor English.
>
> with regards
> Jarl Mosand
> Norway

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
as well as the
> Xenharmonic Alliance group which Gene just linked you to.

I just mentioned it. And as I'm not a moderator, I don't think I can do any more than that.

Oh sorry, I thought you had sent a link to the facebook group too.

I'm on mobile so I can't get links now, but a simple Facebook search for
"Xenharmonic Alliance" should reveal where all the action is.

Sent from my iPhone

On Dec 31, 2011, at 12:46 PM, genewardsmith <genewardsmith@...>
wrote:

--- In <tuning%40yahoogroups.com>tuning@yahoogroups.com, Mike Battaglia
<battaglia01@...> wrote:
as well as the
> Xenharmonic Alliance group which Gene just linked you to.

I just mentioned it. And as I'm not a moderator, I don't think I can do any
more than that.

Jarl:

I have read part of your The Harmony of Harmony. Would like to comment
on the miner third. I have seen a few sources written, in the 1800’s, of
the in inverted theory based on the inverted harmonic series. How ever
none of then came up with the Fmin chord as your have from the Cmin, as I
recall [40 years ago].

The problem with this theory is that it dose not fit the theory of how we
hear, as far as I know. Another is that the Fmin chord in the key of Cmin
would not function as a tonic. And if it was the real tonic then you
could not end a peace with a Cmaj chord as is sometimes done.

The root of the chord usually sets the function of the chord [tonic,
dominant, or subdominant] and the third sets the quality [maj or min] of
the chord.

Another way to look at the minor chord is say that the miner third is a
mistuned major third. Reference Paul Hindemith, The Craft Of Musical
Composition.

The way I see it, is to look at the chord as three separate intervals. The
main one is the fifth 2:3, and the thirds, which set the quality, 4:5 and
5:6. If the notes fall in the upper part of one harmonic series, then the
intervals are most blinding. If the thirds do not fall in the same
harmonic series the root and the fifth do, then is not as blinding.

What i have read has been interesting, I will read more of you paper.
ƒg

On Sat, Dec 31, 2011 at 9:17 AM, jarlmosand <jarlmos@...> wrote:

> **
>
>
> I have for many years (probably like 25) been thinking about the relation
> between harmony and maths. Almost 2 years ago I wrote down my current
> thouhgts about the subject.
>
> I live on a remote island off the coast of Norway and I don't have any one
> out here to discuss the subject with. I have managed to build up enough
> courage to send it to this group, hoping that I may get some feedback.
>
> I have created a folder under my name Jarl Mosand and I have uploaded a
> PDF file by the name of "The Harmony of Harmony". I hope some of you will
> take the time to read it. I am sorry for the poor English.
>
> with regards
> Jarl Mosand
> Norway
>
>
>