I’ve been vaguely wanting to write again––ideas pop up now and again, say, in the car––”I should write about that!”––but then I get home, my habits take over, and the idea is lost.  So I guess I am following some wisdom I learned from who-knows-where and dipping my toe in the water, just to see how it feels, and maybe it will become a habit, or maybe not.

I have enough experience with myself to know that when I set out to create some Great Opus––usually a series of blog posts or videos, or anything ending in “number 1”, or anything where I give too much service to imagining the great and important impact that this thing will have––I do the first bit and then literally never work on it again.  Commitmentphobe.  So this is not that.  I am not Starting Blogging Again, I’m just blogging again.

Which is weird, isn’t it?  You’d think feeling like something is going to make a splash on the world would be motivating, not demotivating.  The only thing I am consistently motivated to do is practice piano (ironically, I didn’t practice at all today, but that does not make me the least bit skeptical of my statement since it has been so consistent for so many years).  I suppose that’s not true––I have successfully made short-term commitments to meditate, exercise, what have you, and kept them.  I guess my reading of this is that I am deeply process-oriented, not results-oriented.  Even in practice––I will happily practice my scales for an hour, but I have tried to make a commitment to master some piece of music by a certain date, or finish a book of sightreading exercises, and those, too, fall through.

About writing… I wonder if I could make a commitment to––shut up.  The result doesn’t matter to me, so why make a commitment!?  I think this gets at the truth of it.  I don’t actually care whether I finish that series of videos, or master that piece of music.  Sometimes I spend a lot of time telling myself what I ought to care about, and

Yeah see I’m done with this post now.



Don’t heal too fast

Heart, please — don’t heal too fast
Lest the pulse in my chest won’t last
How I feared this favor, now caressed
Were it here when I tenderness asked
— No need

Happy does not know your depths
I concede, I’ve tread water without rest
A smile forever will never fall
— in love —
I thought no sweetness here, I confess

I feel truer when thee bleed
When giving of love is what I need
For myself —
So clear submerged undersea
Pain cleanse, love breathe
This too shall pass, but I ask
Heart, please —

don’t heal too fast


Modes, Scales, and Families

I have a natural curiosity for mathematical things, but I’ve made the decision to put as much focus as I can on music.  So, naturally, I’ve been studying the math of music.

From the perspective of a musician, it may seem frivolous to study music mathematically. After all, does all this left-brain stuff really help you express yourself?  I think it does. By investigating musical structures systematically, we can build our intuition, our understanding of how the pieces fit together, and then more ideas are available to us.  It also allows us to hear others music in a more detailed way, with more language available for our minds to describe, and thus understand, patterns.

Today I wanted to share some of the investigations I’ve been making into modes and scales, from a mathematical perspective rather than a sonic perspective.   Some of this stuff is well-known to musicians, and other bits of it are rather novel, as far as I know.

Natural Modes

Here I’ll quickly review modes.  Play a C major scale, all the white keys starting on C.  Now play another scale starting on A with all the white keys.  This, as you may know, is the minor scale.  It has all the same notes as C major, but because it starts in a different place it sounds different.  This is how modes are generated — we use the same notes but start in a different place.

We always refer to the key of a mode by the note it starts on.  So the two scales we just played are “C major” and “A minor” — they have the same notes, but they started in different places, and we refer to them by their starting position.  In “C major”, C is the key, and “major” is the mode.

The modes that have the same notes as a major scale are called “natural modes” (I’m defining this right now, I don’t think this is standard jargon).  There are 7 of them (because there are 7 different places to start!).  Play all the white keys starting on each of these notes and you will get the different modes:

  • Start on C: major (aka “ionian” if you want to be pretentious)
  • Start on D: dorian
  • Start on E: phrygian
  • Start on F: lydian
  • Start on G: mixolydian
  • Start on A: minor (aka “aeolian” for the grandiloquent)
  • Start on B: locrian

It is a bit hard to hear how these sound when you play them next to each other — our mind aligns to the key of C major and it just sounds like we are playing runs in C major.  To hear how these sound, and also to exercise your music math skills, transpose all these modes so they start on C.  So look at the pattern of whole and half steps, e.g. minor goes whole-half-whole-whole-half-whole-whole, and then do that same pattern starting on C.  It looks like this:

Step structure of the minor mode of C

Do this for all the modes above, starting on C. Doing it this way you will get a feel for how each of the modes sounds.

(Another way to think of this if you know your major scales already, is that for dorian you play a Bb major scale starting on C, for phrygian you play a Ab major scale starting on C, and so on.)

For expert mode, do it starting on all the keys (I do this as part of my daily practice).  Obviously don’t burn yourself out though, learn a little at a time.

It turns out there’s a best order to do this in: it goes lydian, major, mixolydian, dorian, minor, phrygian, locrian.  Doing it in this order will show you something about the relationship between the different modes (I’m not going to give it away!).

Scale Fragments

After we get going here, we’ll see that there are actually 21 different 7-note modes.  It took me a long time just to learn the names of the 7 natural modes, and the other modes we will study often don’t even have agreed-upon names.  So first I’m going to give a scheme for naming modes, which also helps you think about them.

We will focus our attention on “4 note scales”.  In the natural modes, there are only four of these that ever appear.  Their names come from the most common natural mode that they are the first four notes of.

  • Major (maj)
    •  major_component
  • Minor (min)
    •  minor_component.png
  • Phrygian (phr)
    • phrygian_component.png
  • Lydian (lyd)
    • lydian_component.png

It’s of course about the pattern of whole and half steps, not about the specific key we’re starting on.  Every natural mode can be made by putting two of these guys together, with an appropriate step in between.  For example, the minor mode:

Fragment anatomy of the minor mode of C

Thus I might refer to the minor mode as “minor phrygian” or “min-phr“.

Notice how there is a whole step between the two components.  You put in whatever step between the two fragments that will make the last note the same as the first one.  It’s usually a whole step, but it will be a half step when lydian is one of the components, because there’s an extra half step between its first and last notes.  For example:

The fragment anatomy of the minor-lydian mode of C.

This mode (which is not a natural mode, by the way!) has a half step between its two fragments.

(Theoretically the lydian-lydian mode should have a 0th step between its two components.  Instead we just fuse the two identical notes into one, and you get the six-note whole tone scale.)

With this vocabulary, we can refer to the 7 modes in a way that makes them easier to understand:

  • Major: maj-maj
  • Dorian: min-min
  • Phrygian: phr-phr
  • Lydian: lyd-maj
  • Mixolydian: maj-min
  • Minor: min-phr
  • Locrian: phr-lyd

Play each of these modes, concentrating on their fragment anatomy.

This anatomy suggests more modes than the natural ones, for example the min-lyd mode we saw above, which doesn’t appear as one of the natural modes.  What’s up with that?

Melodic Minor Modes

In standard music theory, the min-lyd mode we saw above is one of the modes of the melodic minor scale, and it does not fit into the scheme of natural modes (i.e. it won’t be all the white keys starting from any key).   The melodic minor scale is a major scale with a flatted third:

The C melodic minor scale.

And it sounds really cool (very classical sounding when played as an ascending scale, and becomes much more jazzy when you start building riffs out of it).  The melodic minor scale has 7 of its own modes, just like the major scale.   You can find these by playing the melodic minor scale above starting on each of its consecutive degrees, just like we did for the natural modes.  The colloquial names I’ll give for these are from Mark Levine’s excellent book “The Jazz Piano Book”:

  • Start on C: min-maj  (“melodic minor’)
  • Start on D: phr-min
  • Start on Eb: lyd-dim* (“lydian augmented”)
  • Start on F: lyd-min (“lydian dominant”)
  • Start on G: maj-phr
  • Start on A: min-lyd (“half-diminished”)
  • Start on B: dim*-lyd (“altered”)

Notice that there’s a new fragment that we haven’t seen before in a few of these scales, the diminished (dim) fragment:

  • Diminished (dim)
    • diminished_component.png

Like the lydian fragment, it does not have a perfect fourth between its first and last notes. Whenever there is a diminished fragment as part of a mode, the two components should be separated by an extra half step.  Because we’re only looking at scales with whole and half steps right now, and usually fragments are separated by a whole step, that means that the diminished fragment is always paired with a lydian fragment to cancel it out — otherwise we’d end up with a minor 3rd somewhere in our scale (which happens, e.g. in the harmonic minor scale, we’re just not considering that at the moment).

Transpose each of these modes into C (or wherever you like) to get a feel for how they sound.

Scale Families

If you make any mode randomly out of whole and half steps, chances are it’ll be either a natural mode or a melodic minor mode.  They account for two-thirds of all the possible modes.  There is one more type of mode that we haven’t covered, and is very uncommon in western music (which makes me itch for opportunities to use it!).  I’m not sure what to call it, right now I’m calling them “exotic” modes alongside the “natural” and “melodic” modes.  It looks like this:

The phr-maj mode of C, a member of the “exotic” family.

These modes are strange because they have two half steps in a row (separated by an octave in the the above version, but notice it has B,C,and Db).  This means many of its chords have major seconds as intervals, and it’s quite weird and foreign sounding.

But I am interested in it because together with natural and melodic modes, we have now covered all the seven note scales.  No matter what scale you make, as long as it has seven notes and no interval greater than a whole step, it will be a mode of one of these three families.   Why?

Let’s consider what it takes to make 7 intervals cover 12 half steps.  If every interval were a whole step, the scale would span 14 half steps, which is 2 too many. So we need to shrink it by two half steps: change exactly two of the whole steps into half steps.  The different families come from the different places we can do that.

Put your focus on the two half steps in the scale.  They can either be separated by 2 whole steps, 1 whole step, or none.  They can’t be separated by 3, e.g.:


Because you can just rotate it around


And now we can see that they’re actually just separated by two.

So when you have your scale, it should just have two half steps in it.  If they are separated by two whole steps, it’s a natural mode; if they’re separated by one, it’s a melodic mode; and if they’re separated by none, then it’s an exotic mode.


There you have it, some interesting mathematical music stuff.  I have more — there are lots of neat symmetries between all these modes, but I’m tired of writing for today. Remember to follow me if you’re into this kind of thing (lower right).  I get a little burst of approval happiness every time I get a new follower, and it makes me want to write more! The same goes for sharing, of course. ;-)

Inner Prayers

The voice is a gift
and he gives it not to some but to all
to YOU all
the small and the large
the weak and the in charge
We all have that thing
we were born to say
you may not be able to access it today
but someday
let me hear you say someday
I will stand tall
I will take charge
Outward my inner prayer I will pray

I used to be ashamed of my voice
Couldn’t make the choice
to be heard
I had hurt
I had heart
but I couldn’t speak the words
Couldn’t sing the songs
that I knew all along
Every day a new invention
A hidden intention
Well this is my intervention
I make the choice to use my voice
I stand tall
I take charge
And outward this inner prayer I pray

I pray to come alive today
There ain’t no other way
My brothers can think what they may
Cause I know they also got something to say
Let my courage show you the way
And let yours be inspiration to another
This is the situation there’s no other
It is WE who light the world on fire
Who inspire the weak and the tired
To be strong and admired
To change ourselves from liars
mask wearers, fear bearers
Heart hiders, insiders
To fearless riders
carrying our word
be it simple or absurd
the truth is the word
OUR truth is the word
And today
I make the choice to use my voice
I stand tall
I take charge
And outward my inner prayers I pray

The Memory

On a day long ago was learned
a terrible lesson, my friend.
In the memory burned
Too swiftly to comprehend
And dry a great river turned.

What happened that echoing day?
To this little boy, full of passion
So much to give and to say
A life for beauty amassing…
Then for watching it fade away.

“I’m sorry,” he began to cry
Before giving his gift.
It became too much to try,
A burden too heavy to lift,
And he almost told it goodbye.

Someday, it is said, he will find
Holding the hand of a friend
The memory locked away in his mind
And the courage to give once again
With shame left far, far behind.


What would you have me do?

What would you have me do?
For your sake I’d hidden myself from you.
I knew inside so I built a wall,
Attached a mirror, so whatever you wished you would see as true.

Might you I ought to’ve cared for,
But I resolved not to pretend anymore.
A false heart I’d not caring call,
And when I did finally speak, it stopped feeling so awfully sore.

This sharpening pain I have made,
I hope is better than how I’ve betrayed.
All I really want is to bring down this wall.
I asked for love, truth asked of me, and I obeyed.