Music Theory Powerpoint Presentation

[John Moriarty]

I've put together a rough Powerpoint describing the basics of some subjects pertaining to music such as acoustics, consonance, tunings, isomorphic layouts and music notations, and dynamic tonality. I know that at the moment it could use a few (a bunch) more diagrams, but I was interested in getting feedback on the general layout of the presentation as a whole as well as any simple proof reading help anyone would be willing to do. I plan eventually to simply narrate the presentation and put it on Youtube. Thanks for any feedback. John M

[Michael Johnston]

Can't open the 'x' MS things. Why not save as .ppt for preliminary purposes?

Cheers!
Michael
--
MICHAEL'S MUSIC SERVICE 4146 Sheridan Dr, Charlotte, NC 28205
704-567-1066 ** Please call or email us for your organ needs **
http://michaelsmusicservice.com "Organ Music Is Our Specialty"

[John Moriarty]

Thanks for letting me know, I think this file should work...

[Ken on Google Rushton]

Good stuff,
On first read-through it explains many of the points more clearly than Jim P. does. I'll does more indepth later today.
I've posted four and will be posting more pictures to the wikipedia commons (under MusicScienceGuy) that may help. If you have access to Visio I can give you the original.
Ken. 

[John Moriarty]

I did some general editing and figured I'd put this version out so anyone who was planning on helping with editing could work with the latest. Let me know if any of the graphics don't work and the like.

[Ken on Google Rushton]

Hi john,
I've reviewed about half of it, - all that I have time for. 
Below are my comments.

In summary, it's a very good start, but needs to be simplified and examples added.

Ken.

Add pictures, like my picture of where the harmonics are.
Page 3 An audio demo, of first a note, say from an organ, then filtered to show each harmonic, is very very effective.  You’ll save many words with it.
Page 4 change envelop to “time envelop”
- Again, an audio demo, together with a diagram will really help.
- I have a diagram of the dissonances.
Page 5 – have to use shorter phrases with smaller words.
- e.g. “So, given that the goal when picking the intervals in one’s tuning (choice of what pitches to include) is the maximization consonance, most cultures will pursue the inclusion the same intervals. They may do so by different means, but the goal is the same.”
 => could become: "Musicians base music on what sounds good; is where the harmonics fit together consonantly, or interestingly.
– when the instruments produce different harmonics, the intervals between notes will be different."
6. What is a hexachord?
I would not list all the tuning systems. The list is distracting.
7. What the heck is a “generator” (I know, but does the reader know?)
8. Is there a way to simplify the Stack and Reduce method. Add an audio demo?
Pages 9-11. The stack and reduce method is pretty simple arithmetic – why not just use that ?
13: simplify! “The relation of isomorphic layouts with tuning theory…etc.” => we can use 2 dimensions, we are no longer stuck with one dimension.  … and that changes everything.
14 I dislike “Isomorphic”, I favour “consistent” “simple” “easy-to-learn” etc. Mention that the technical term is “isomorphic”, then lean on the favour “consistent” “simple” and “easy-to-learn”.
Page 15 I would drop. Page 16 says it much better.
Page 16-21, Mention that we (or whoever) has reviewed all the ways to layout notes consistently, and find that the W/H is really clear – the reader will be happy with this explanation and is ready to go on.
Then mention that we’ve found that 19 buttons is really all that is needed.
Then show the array and relate it to a piano.

Does this help?

Ken.

[Enrique Prieto]

On Sun, Nov 1, 2009 at 11:03 PM, John Moriarty <jlmo...@gmail.com> wrote:

I did some general editing and figured I'd put this version out so anyone who was planning on helping with editing could work with the latest. Let me know if any of the graphics don't work and the like.

John great job but I think you should change the title “real” for introduction, overview, fundamental, background to something, I think the term music theory now is a very wide term that should be narrowed, the books and teaching of music notation are also included into the music theory term and when you purchase a book title music theory you get it all mixed without differentiation. Somehow it should be fixed.

Enrique.

[John M]

> Add pictures, like my picture of where the harmonics are.
> Page 3 An audio demo, of first a note, say from an organ, then filtered to
> show each harmonic, is very very effective. You'll save many words with it.

I've managed to stumble upon several of these audio examples across
the net but haven't bookmarked their sites. Is there a central
location where there are many such demonstrations?

> Page 5 - have to use shorter phrases with smaller words.

> - e.g. "So, given that the goal when picking the intervals in one's tuning
> (choice of what pitches to include) is the maximization consonance, most
> cultures will pursue the inclusion the same intervals. They may do so by
> different means, but the goal is the same."
> => could become: "Musicians base music on what sounds good; is where the
> harmonics fit together consonantly, or interestingly.

> - when the instruments produce different harmonics, the intervals between
> notes will be different."

I guess it comes down to whether I am merely trying to expose the
audience to the applications of this theory or explain it, because
there is meaning lost in your simplification. Also the phrase
"musicians base music on what sounds good", although quite obvious, is
still disputed. There is still argument that music is 100% cultural
and therefore non-western societies use alternate tunings due purely
to cultural differences, not in the mathematically definable and
psycho acoustically proven locations of consonance and dissonance in
the intervals played by different timbres. If I don't mention the fact
that it is still argued that those who use alternate tunings do so for
strictly cultural reasons then I will have musicologists jumping down
my throat.

6. What is a hexachord?

My understanding is that by definition it is any combination of six
pitches, while certain hexachords were the basis of early theory
describing solfeggio's creation and progression which is linked to
tuning theories based on that. I'll have to find the link…

>7. What the heck is a "generator" (I know, but does the reader know?)

I didn't think that the use of the word generator requires any more
understanding in the context of tuning theory than it would anywhere
where a generator "generates" something else. How do you think I can
specify its meaning?

> 8. Is there a way to simplify the Stack and Reduce method. Add an audio
> demo?

> Pages 9-11. The stack and reduce method is pretty simple arithmetic - why

>not just use that ?

I've always been partial to visual diagrams displaying pitch linearly
and then relating them to the two dimensional diagrams. Do you really
think its unnecessary? I suppose I could add some strictly math stuff
but I do think the visual aid is necessary.
As for audio demonstrations, I'd need visual at the same time to show
where the locations of the pitches I'm playing are.

>Page 15 I would drop. Page 16 says it much better.

Are those the right page numbers? How so?

> Page 16-21, Mention that we (or whoever) has reviewed all the ways to layout

> notes consistently, and find that the W/H is really clear - the reader will

>be happy with this explanation and is ready to go on.

Again, a deeper understand of the application of tuning theory in the
form of the stack and reduce method to isomorphic layouts would be
lost. I'd prefer to somehow get the same information across, just
maybe more efficiently if you have any ideas.

>Does this help?

I think so!

>  John great job but I think you should change the title “real” for
> introduction, overview, fundamental, background to something, I think the
> term music theory now is a very wide term that should be narrowed, the books
> and teaching of music notation are also included into the music theory term
> and when you purchase a book title music theory you get it all mixed without
> differentiation. Somehow it should be fixed.

The title was moreso poking fun at the inconsistent and convoluted
charactoristics of the current musical cannon than it was an attempt
at a re-definition of the term "music theory". Though I certainly
would consider anything that has a berring on music whatsoever part of
that theory, I do recognize that the title may have to change :-P
As far as narrowing the definition of music theory, who decides where
the line is drawn? What makes something that pertains to music not
definable as part of its theory?

John M

[Paul W Morris]

Hi John M,

I only had time to glance through it. Sorry I can't offer more
feedback. It looks like a good start towards making a lot of
complicated material more accessible, especially on all the abstract
tuning theory.

I did notice what appears to be an error on slide 14, the first one on
isomorphic layouts where you say, "all isomorphic layouts are
inherently and by definition two dimensional." However, the Janko
layout is isomorphic and has a simple one-dimensional, linear pitch
axis.

I agree with Enrique that the title should probably be less broad,
more specific. Music theory encompasses a very broad range of things.
A subtitle is a good way to make it more specific.

Also, I see you forgot to mention the MNP website on the References page ;-)

Cheers!
Paul

[John M]

> I did notice what appears to be an error on slide 14, the first one on
> isomorphic layouts where you say, "all isomorphic layouts are
> inherently and by definition two dimensional."  However, the Janko
> layout is isomorphic and has a simple one-dimensional, linear pitch
> axis.

The Janko layout with only two rows is not isomorphic, because to play
the major scale of a top row key is different than playing one of a
bottom row key. Once the third row is introduced, it becomes
isomorphic and two dimensional.

> Also, I see you forgot to mention the MNP website on the References page  ;-)

!
Will fix that this very moment....

Ken-
I've reconsidered my use of a one dimensional axis to explain the
stack and reduce method. Basically, I like to think about it that way
and later on it would probably be beneficial to view tunings as two
dimensional representations of combinations of pitches that exist in
the single dimensional concept of pitch, but it is too complicated to
start out with. As Jim P put it, you have to understand it to
understand it. I'll get to some serious editing, get rid of some of
the too busy diagrams, and hopefully introduce some new simpler ones
tonight.

Thanks for the feedback so far guys, I appreciate it.

John M

[Doug Keislar]

John M wrote:

I did notice what appears to be an error on slide 14, the first one on
isomorphic layouts where you say, "all isomorphic layouts are
inherently and by definition two dimensional."  However, the Janko
layout is isomorphic and has a simple one-dimensional, linear pitch
axis.
    

The Janko layout with only two rows 

Technically, that is not really a Janko layout.  We could call it a 6-6 layout or a double-whole-tone layout (a term that is a
superset of the specific design of Janko's).

is not isomorphic, because to play
the major scale of a top row key is different than playing one of a
bottom row key. 

True.  (And more generally, not just a major scale, but any pattern that includes notes from more than one whole-tone scale.)  Still, there is a maximum of only two possible forms of any set of pitches, instead of the traditional keyboard's 12.  A limited isomorphism.

Once the third row is introduced, it becomes
isomorphic and two dimensional.
  

I don't understand why you consider a three-row version two-dimensional, but not the two-row version.  Can you please explain your rationale?

Doug

[John M]

> A limited isomorphism.

I would definitely assert that the adjective "isomorphic" is an
absolute one, such as is unique or pregnant, to which there can be no
degrees. Most any layout conceivable would contain your definition of
"limited isomorphism". For a simple example, on the the piano the C,
F, and G major triads are the same shape. Is that "limited
isomorphism"? Consider a randomly located group of pitches across any
dimensional space. As long as the pitches are in fixed locations, then
that layout has "limited isomorphism" because, if anything, unisons in
succession are always played the same way.

In fact, the only "layout" that I can think of that would not have
"limited isomorphism" would be an interface where the locations of
every pitch changed after every single interaction by the user, and is
that really a layout any more?

> Can you please explain your rationale?

It all depends on how one defines the layout itself and how many axis
then arise from that definition. I would not define every possible
movement on a two row janko layout not as a combination of left-right
and up-down movements but instead as simply a number of movements from
left to right. From that definition would arise one axis, moving from
left to right.

On a three row janko layout the definition of all movements could no
longer be defined as movements along a single axis and would have to
include a second.

Note that any two dimensional layout, like one dimensional layouts,
are only limited approximations of the real thing because a true
representation would extend to infinity along each of its axis. My
conceptualization of the two-row layout would extend infinitely in one
dimension while the three-row would extend infinitely in two.

If you wanted to, you could *define* the two row janko layout the same
way you *define* your three row, as combinations of left-right and up-
down movements, which would require two axis, and therefor the "real"
representation of this two row janko keyboard would extend not just
infinitely to the right and left, but up and down as well.
A two row janko *can* be defined as two dimensional, while a three
must *has to be*.
I'm sure this all could be derived mathematically but I've no idea
how.

John M

PS. I'm making progress in completely overhauling the powerpoint, I'll
put it up reasonably soon.

[Paul W Morris]

Hmmm... I do think it is useful and intelligible to speak
comparatively of some instruments as being more isomorphic than others
(or closer to the ideal of isomorphism than others, if you want to
split hairs on semantics). It seems pretty clear that a two row 6-6
keyboard is more isomorphic than a traditional keyboard, and less
isomorphic than a 3 row 6-6 keyboard.

If you wanted to get tediously detailed and make this argument
quantitatively you could catalog how many different shapes are needed
for each interval on a given instrument. The numbers would give you
some way to measure and compare each instrument's relative
isomorphism.

But back to the question of whether isomorphism requires a two
dimensional instrument... Consider a one row xylophone with bars
pitched a half step apart. Or a stringed instrument with one string.
These would be isomorphic and one dimensional.

On the other hand, a guitar has a two dimensional fretboard, but is
not strictly isomorphic since all six strings are not the same
interval apart (there is one exception, at least as the strings are
typically pitched).

The confusion seems to lie in whether a 6-6 or a Janko keyboard should
be understood as one dimensional or two dimensional. This comes down
to whether you mean this to refer to its pitch axis or to its key
layout. If you have 3 or more rows the key layout is clearly 2D, but
I'd say that its pitch axis is still 1D. Here's why:

Pitch increases or decreases as you move left to right, but moving up
or down doesn't change the pitch. Ah, but what about diagonals?
Consider that moving one key diagonally up and to the right, or
diagonally down and to the right, results in the same pitch. So it's
the moving right, and not the moving up or down, that is relevant.
The pitch axis is a simple, linear 1D from left to right. The
additional rows of keys don't increase the complexity of the pitch
axis, they just allow for more fingering possibilities and greater
isomorphism.

You can see this when comparing it with a guitar fretboard or Wicki
accordion where the pitch layout is 2D and more complex. On these
instruments the pitch increases both as you move either right or up.
Here moving diagonally up-right and diagonally down-right are not
equivalent in terms of pitch.

Am I making sense?

Good clarification Doug about the 6-row Janko layout being a
particular subset of 6-6 keyboard layouts.

John, thanks for adding the MNP website to your references page, and
glad the powerpoint is coming along.

Cheers,
Paul M

[John M]

> If you wanted to get tediously detailed and make this argument
> quantitatively you could catalog how many different shapes are needed
> for each interval on a given instrument.  The numbers would give you
> some way to measure and compare each instrument's relative
> isomorphism.

Fair enough =)

> But back to the question of whether isomorphism requires a two
> dimensional instrument...  Consider a one row xylophone with bars
> pitched a half step apart.  Or a stringed instrument with one string.
> These would be isomorphic and one dimensional.

Good point. I guess that for an instrument to be isomorphic across a
temperament it must be two dimensional, but to be isomorphic within a
tuning only requires one dimension.

> The confusion seems to lie in whether a 6-6 or a Janko keyboard should
> be understood as one dimensional or two dimensional.  This comes down
> to whether you mean this to refer to its pitch axis or to its key
> layout.  If you have 3 or more rows the key layout is clearly 2D, but
> I'd say that its pitch axis is still 1D.  Here's why:
>
> Pitch increases or decreases as you move left to right, but moving up
> or down doesn't change the pitch.  Ah, but what about diagonals?
> Consider that moving one key diagonally up and to the right, or
> diagonally down and to the right, results in the same pitch.  So it's
> the moving right, and not the moving up or down, that is relevant.
> The pitch axis is a simple, linear 1D from left to right.  The
> additional rows of keys don't increase the complexity of the pitch
> axis, they just allow for more fingering possibilities and greater
> isomorphism.

I think this proves that whether or not a layout is isomorphic or two
dimensional depends on how you define it. You are looking at the janko
layout in terms of half steps, whereas if you look at it in terms of
musically relevant intervals things change.
Look at Dan Lindgrens proposed keyboard:
http://home.swipnet.se/nydana/keyboard1.pdf
It could be defined as having a janko keyboard layout, if you define
the janko layout correctly. And then, depending on the tuning, going
up and to the right would bring you a different result than down and
to the right.
This is because up and to the right is not a half step but instead an
augmented unison, while down and to the right is up a minor second.

[Keislar, Doug]

Here are a couple of fine points regarding "limited" isomorphism:

1. I believe that the only layout that has no limits to its isomorphism is one that extends infinitely in all directions.
Real, finite instruments have edges where one can no longer continue transposing the pitch pattern without a change of shape.
This is true of Wicki-Hayden, as well as of Janko.
In an equal temperament, at least, and on an instrument having a sufficient number of redundant keys that repeat pitches, you might be able to find another place on the instrument to play the same pitches (with the desired shape) untransposed without going off the edge of the instrument.
I don't think that's true in the general case, where the tuning system might have no enharmonic equivalents that are exactly equal in pitch, and/or where the instrument might provide no redundant positions for a given pitch. At some point you come to the edge and you can't move the pattern to the next logical transposition.
And even on an instrument with redundant pitches and equal temperament (say, a Janko piano), you can always still find some shape that can't be transposed (without changing the shape), if the shape extends across the instrument to include keys on opposite edges of the keyboard. I'm not saying that this is necessarily a practical concern, although that depends on the layout.

2. On a two-row 6-6 layout, there are at most two different shapes for any set of pitches (as I mentioned before), but furthermore these two different shapes are closely related: they're mirror images of each other. Maybe one wouldn't call that mirroring isomorphic, but it certainly is a form of similarity, and it does simplify learning.

None of this is meant to suggest that a two-row 6-6 layout is "as isomorphic" as a Janko or Wicki-Hayden layout. Just that isomorphism might not be an all-or-nothing proposition.

Doug

[Paul W Morris]

Ah, Dan Lindgren's proposed keyboard... I think I'd put it in a
different category from both Von Janko's design (which was a piano
replacement that used 12-TET), and the Wicki-Hayden layout.
Lindgren's seems like a variation on Bosanquet's layout (from 1875):
http://improvise.free.fr/bosanquet/bosanquet.html

I think Lindgren's would have to be understood to have a 2D pitch
layout, since as you mention moving on the vertical axis does make a
slight difference in pitch, the slight difference between enharmonic
"equivalents" (unless it is tuned to 12-TET). But its vertical axis
mostly just provides for these slightly different intonations. And
you wouldn't typically go beyond a couple rows since triple sharps and
flats are so uncommon. (Compare this with the Wicki-Hayden layout
which really exploits the vertical dimension so that it quickly takes
you up and down octaves. Then it's the left and right that becomes
less useful after you get over into double and triple sharps and
flats.)

Paul M

[John M]

> Ah, Dan Lindgren's proposed keyboard... I think I'd put it in a
> different category from both Von Janko's design (which was a piano
> replacement that used 12-TET), and the Wicki-Hayden layout.

Why? If you are going to say that Dan's (and the bosanquet) layout are
inherently different from the Janko layout merely because they define
each interval more specifically as musically relevant intervals
therefor opening up the layout to tunings outside their original
intent, then the layout that the thummer/jammer employs is not really
the W/H layout (I assume neither Kaspar nor Brian specifically
intended their layouts to have the ramifications they do in our newly
coined syntonic temperament). Maybe this is a good distinction to
make, that these layouts that allow for dynamic tuning across a
certain range are deviating away from their original definition
(number of steps in an equal temperament of 12) and therefor should
not be referred to by the same name. But I doubt the distinction is
really necessary.

John M

[Paul W Morris]

I guess I wasn't clear on how I'm thinking of these (mostly comparing them in terms of how they implement 1D or 2D pitch layouts):

1D PITCH AXIS/LAYOUT  

       Most 6-6 Keyboards, including the Janko Keyboard

       

2D PITCH LAYOUT  

        A. Uses 2nd dimension for subtle differences, "enharmonic equivalents" 

                      Bosanquet and Lindgren keyboards

        B. Really exploiting 2D layout for larger pitch range in smaller space

                      Wicki-Hayden layout, Harmonic table layout, etc.

Hope that clarifies.  I imagine that the layouts that distinguish between enharmonic equivalents were designed to be used with a variety of tuning systems.  But they probably weren't thinking of dynamically changing tuning systems during a performance.

(BTW, you've been using the phrase "musically relevant intervals" but seems to me that all intervals are musically relevant, so you might need a better phrase for what you're getting at with this...)  

Paul M

[John Moriarty]

-Gmail won't let me send the PowerPoint in its "package and go" format with the videos/sounds because it contains an executable, so I'll just have to attach the presentation at its bare minimum and if you want the whole thing I can maybe get it to you some other way- I would describe a musically relevant interval as one describing tonal function with no specific reference to actual size in cents or steps in an equal temperament: Augmented unison, minor third, major sixth, etc. This would be opposed to any interval that does not inherently describe tonal function and requires a reference to a single tuning for context: Half step, semitone, whole tone, or third step, etc. Maybe one wouldn't want to refer to the formers as a "musically relevant intervals" as to keep from implying that the others are "unmusical", but I think one could argue that one is relevant to far *more* than the other, and maybe even that the other *is* somewhat unmusical. I'm not sure if I understand the reasoning behind your distinctions of 2D layouts. Both of the examples "really exploit" their 2D nature, one just does so for a larger harmonic context, and the other more-so for range. One could analyze the efficiencies of each and find that the W/H layout is far more efficient when considering the two together, that is, range and harmonic context. One would likely also find the W/H layout to be outright superior in efficiency when taking into account, as you said, that for a given tonic one would not be using double or triple sharps and flats in common practice tonal music. But they are still simply two different two dimensional layouts, defined by alpha and beta, that the have specific properties and tuning ranges that arise from each. John M

[jason....@gmail.com]

Hi brothers in music notation:-)

Check out the NN app on ITunes...just put Numbered Notes into the search box.

At this point the App plays basic songs and introduces the idea....more changes and improvements coming soon.

All feedback is welcome and appreciated!

Thanks, Jason

www.NumberedNotes.com

 
Sent from my iPhone

[Michael Johnston]

> Check out the NN app on ITunes...just put Numbered Notes into the search
> box.

How about a demo vid? There are several of these high quality demos on
Youtube and that would give you and us some good exposure. Besides, I do
not have an IPhone to try it on.

[jason....@gmail.com]

Yes, great idea!

Sent from my iPhone

On Nov 12, 2009, at 6:49 AM, Michael Johnston <mic...@michaelsmusicservice.com

[Paul W Morris]

Hi John, Just getting around to replying to your post, see below.
I've been out of town and behind on email...

On Fri, Nov 6, 2009 at 5:14 AM, John Moriarty <jlmo...@gmail.com> wrote:

> I would describe a musically
> relevant interval as one describing tonal function with no specific
> reference to actual size in cents or steps in an equal temperament:
> Augmented unison, minor third, major sixth, etc.

> This would be opposed to
> any interval that does not inherently describe tonal function and requires a
> reference to a single tuning for context: Half step, semitone, whole tone,
> or third step, etc.

> Maybe one wouldn't want to refer to the formers as a
> "musically relevant intervals" as to keep from implying that the others are
> "unmusical",

Or from implying that they are "irrelevant".

It seems that "specificity in tonal function" is what you're talking
about, rather than musical relevance. Whether a name for an interval
was musically relevant would depend on the context and how it's being
used. That these interval names (half step, etc) are used and are
meaningful in their use speaks to their relevance.

> I'm not sure if I understand the reasoning behind your distinctions of 2D
> layouts. Both of the examples "really exploit" their 2D nature, one just
> does so for a larger harmonic context, and the other more-so for range.

That's just the distinction I'm getting at. One uses the 2nd
dimension to allow for small differences in pitch between "enharmonic
equivalents". The other uses it as a second vector for larger
differences in pitch.

You're right they're still logically the same when viewed in the
abstract ("still simply two different two dimensional layouts, defined
by alpha and beta"), but when viewed in terms of practice and use, a
musician would use the second dimension rather differently in each, I
think.

Cheers,
Paul M

PS. Here's what we're talking about, from an earlier post of mine:

1D PITCH AXIS/LAYOUT

Most 6-6 Keyboards, including the Janko Keyboard


2D PITCH LAYOUT

A. Uses 2nd dimension for subtle differences, "enharmonic equivalents"

Bosanquet and Lindgren keyboards

B. Uses 2D layout for larger pitch range in smaller space