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Object-oriented vs. Functional Modelling of Musical Arithmetic in Python

Classical vs. Functional Modelling of Musical Arithmetic in Python

I'm currently building a music theory library in Python, called Ophis.

In [1]:
import ophis

This is an attempt create a utility that "understands" music theory and can manipulate music information, to be used as a base for other applications. This would be handy for all sort of things, from music theory educational apps to AI composition.

In this notebook, we'll look at how I originally implemented basic musical arithmetic in Ophis, the problems with that approach, and why I am moving from a classical to a functional design.

A Classical OOP Design

My first approach in implementing this was classically object oriented, and influenced by an essentially Platonic ontology.

The idea was that musical building blocks would be, as much as possible, similar to integers.

In [2]:
# A `Chroma` is the *idea* of a note letter name 
#     Example: "A" or "D FLAT"
# 35 chromae are initialized to constants on load, 
#   representing all 7 letter names, 
#   with sharps, flats, double sharps, and double flats.

ophis.wcs # Western Chroma Set, 
          # the complete list of all initialized chromae

One of the main ideas here is that there is one and only one representation of the idea of C SHARP or F NATURAL . Moreover, the chromae can be inspected, and know how to represent themselves.

In [3]:
In [4]:
In [5]:

Chromae also carry all the logic needed for musical manipulation and mathematical representation.

In [6]:
In [7]:
In [8]:

A Pitch is a Chroma with an octave designation. Using the special __call__ method on Chroma, and the __repr__ method on Pitch, I was able to make their interactive representation is intuitive.

# in Chroma class

def __call__(self, octave):
    return Pitch(self, octave)

# in Pitch class:

def __repr__(self):
    return + "(" + self.octave + ")"
In [9]:
# The "standard Python" way to create a pitch. 
ophis.Pitch(ophis.GFLAT, 2)
In [11]:
# The Ophis canonical way.


Intervals (without octaves) and QualifiedIntervals (with octaves) have a similar relationship to each other as Chroma and Pitch.

Rather than initializing every possible musical interval, the qualities (major, minor, perfect, augmented, diminished) are initialized and callable, to create an intuitive API.

In [12]:
ophis.Major(2) # A Major second.
In [13]:
ophis.Perfect(4, 2) # A Perfect fourth, plus 2 octaves.

Function caching is used to ensure that only one of any interval is created. (Some experimental benchmarking showed that this would matter in large scores.)

In [14]:
id(ophis.minor(2).augmented()) == id(ophis.Major(2))

And, of course, you can use both types of intervals to manipulate chromae and pitches.

In [15]:
ophis.G + ophis.Major(2)
In [16]:
ophis.A(2) + ophis.Perfect(5)
In [17]:
ophis.FSHARP(1) + ophis.Major(2, 2)

All this lets you do complicated musical manipulation and representation.

In [18]:
(ophis.FFLAT + ophis.Perfect(5)).diminish().unicode

Obviously, all this is only the beginning of what is needed for a music theory library. But it is a beginning. The next submodule will build up Duration and TimeSignature, leading to the creation of Measure and eventually Score. My current plan is to use pandas.DataFrame for multi-voice scores, as that would allow cross-voice analysis in a way that multi-dimensional lists would not.

Problems Appear

So that's great, but...

I can't but help wonder if some of this is overwrought.

A number of interrelated concerns occured to me while working on this implementation.

Logic is hard to reason about

The math of moving from note to note is riddled with off-by-one and modulo arithmetic problems.

  • An interval representing no change (from a note to itself) is called a unison, represented with a 1. A difference of one step is called a second, and so on.
  • The first scale degree is 1. (Not zero indexed.)
  • We frequently think about scales as having eight notes, but in reality they only have seven. When this is zero indexed, the notes go from 0-6. This is fine for arithmetic, but when thinking as a musician it is jarring.

Because of this difficulty in clear thinking on my part, I often found myself using the guess-and-check method for remembering when to add or subtract a one.

I wrote rigorous tests along the way to keep these errors out, so everything ends up fine in the end. However, this made for slow and sometimes demoralizing progress, and I would hate to have to go back and reason about this code after being away from it.

Incorrect assumptions about logical order

The first attempt to implement basic Chroma functionality assumed that Interval — the relationship between two chromae — would depend on Chroma. It turns out this is exactly backwards. Interval is logically prior to Chroma. There is no way to define abstract named pitches without their relationships already existing.

Practically speaking, discovering this simply meant I had to re-order some code. But this challenged my thinking about what the fundamental building blocks of music theory actually are.

Convoluted logic and utility data structures

Here's an example, the augment method from the Chroma class.

def augment(self, magnitude=1, modifier_preference="sharp"):
    """Return a chroma higher than the one given.

        magnitude (:obj:`int`, :obj:`Interval`,
                   or obj with an ``int`` value; optional): 
            the distance to augment by. 
            Integer values are interpreted as half steps. 
            Defaults to 1.
        modifier_preference (:obj:`str`, 
                             ``'sharp'`` or ``'flat'``;
            Defaults to ``'sharp'``. 


        >>> C.augment()

        >>> C.augment(1, 'flat')

        >>> C.augment(minor(3))

        >>> D.augment(2)

        >>> E.augment()

        >>> E.augment(2, 'flat')

    value_candidates =  self.essential_set.chroma_by_value(
        int(self) + int(magnitude)
        letter_candidates = self.essential_set.chroma_by_letter(
            self.base_num + magnitude.distance
        solution, = value_candidates & letter_candidates
        return solution
        return value_candidates.enharmonic_reduce(modifier_preference)

If it isn't obvious, here's what it does:

  • Calculate the integer value of the target Chroma and find the set of Chroma objects which have the integer value we're looking for.
  • Try:
    • Calculate the letter name of the target Chroma and find the set of Chroma that have the name value we're looking for.
    • Find and return the union of the integer-value set and the note-name value set.
  • Except:
    • Return a member of the integer-value set, basing the selection on some logic (defined elsewhere) that prefers sharps to flats or flats to sharps in certain instances.

This works, but it isn't at all how a musician thinks about this operation. Moreover, it depends on the essential_set, the collection of all initialized chromae. (Referred to above as wcs, the Wesern Chroma Set.) It would be bad enough if this was just used to keep the pool of initialized chromae, so that methods returning C Sharp always returned the same C Sharp. But it doesn't just do that. An inordinate amount of musical knowledge and logic crept into the ChromaSet class that defines the essential_set. While I'm positive that some of this is due to bad coding on my part, I think the bulk of it is due to bad conceptualization.

The final problem with this is that it is non-obvious. This code is hard to read and reason about, because it isn't clear what is actually happening.

Fragile Primitives

Python doesn't really allow you to protect object attributes or module-level constants. There are some things you can do to ensure object attributes aren't reassigned accidentally (and I've done them), but (as far as I can tell) module-level constants cannot be protected.

This is a problem, since the fundamental building blocks of music theory in the current implementation are initialized as constants. The object representing C Sharp is created and assigned to the name CSHARP. If that name gets reassigned, you are basically hosed. This could lead to hard-to-trace errors and frustrating interactive sessions.

Poor isomorphism to numbers

One of the design goals of Ophis is to be able to treat musical concepts as numbers. That's why the arithmetic operators are implemented and everything has an integer value. I wanted it to be easy for math utilities to operate on pitches and intervals. This would enable things like advanced theoretical analysis and machine learning.

But, they aren't numbers. They just aren't.

You can't (meaningfully) have a Chroma with a float, decimal, or fractional value. This means that microtones are not presently accounted for and will require an extension, the logic of which I can only guess at.

You also can't meaningfully multiply or divide values. Offhand, I'm not sure why you would want to do so, but I can imagine approaches to musical analysis where it would be needed.

Further, even with supported integer-based operations, using any standard math tool requires notes from a score to be converted into numbers, manipulated or analyzed, and converted back. There's no direct access to Ophis "primitives" in Numpy, SciKitLearn, or anything else.

These problems piled up over time as I implemented the basic logic and worked out the implications. Technical debt accumulates through a process of small compromises and justifications. By the time I became aware of the scope of the problem, I had two thoughts:

  • Re-architecting everything would take too long to be worthwhile. I would probably get disheartened and give up.
  • I can refactor the internals in the future to make things a bit clearer and cleaner. In the meantime, good documentation would make the code maintainable.

So, my plan was to just keep moving. But then, thinking about the isomorphism problem, I realized another poorly-mapped isomorphism.

Poor isomorphism between Chroma and Intervals

Or really, no explicit isomorphism at all. And this is a problem because these are really the same thing.

I had implemented the Interval class, and written all the logic for how intervals are inverted, augmented, and diminished. This requires understanding of the interplay between interval distances (third, fourth, sixth) and their qualities (Major, minor, Perfect), and how many half-steps each are. And of course there's that zero-indexing stuff to think about (second = 1, third = 2).

Then I implemented the Chroma class, and wrote almost the same logic (but just a bit different) for how pitches are augmented and diminished (pitches aren't inverted). This requires an understanding of the interplay between note letter names (C, D, E), how those letter names map to a zero-indexed numerical representation (C = 0, D = 1, E = 2), and how modifiers like sharp and flat affect the total number of halfsteps from C (the origin point in modern music theory).

But these are, as I said, exactly the same thing.

Every note can be represented as an interval from C. And not only can it be represented that way, but that is exactly how it was already defined. There is no other reasonable way to (numerically) define notes.

Here's an example in case this isn't clear:

  • E Natural is a Major Third away from C.
  • In our zero-indexed representation intervals, a Third is 2.
  • A Major Third is 4 half-steps.

Those two numbers, (2, 4), are an integral part of the definition of E Natural; without them, you can't do any of the manipulation that makes the Chroma meaningful.

In [19]:
print(ophis.Major(3).distance, int(ophis.Major(3)))
print(ophis.E.base_num, int(ophis.E))
2 4
2 4

Obviously, this holds for every other Chroma as well.

In [20]:
print(ophis.Perfect(5).distance, int(ophis.Perfect(5)))
print(ophis.G.base_num, int(ophis.G))
4 7
4 7
In [21]:
print(ophis.Augmented(6).distance, int(ophis.Augmented(6)))
print(ophis.ASHARP.base_num, int(ophis.ASHARP))
5 10
5 10

Further, it turns out that these two numbers are the only things you need to know in order to do any standard musical manipulation you might want to do.

In [22]:
g_or_p5 = (4,7) # Tuple representing G or a Perfect Fifth
e_or_maj3 = (2,4) # Tuple representing E or a Major Third

# Add tuples element wise.
sum_of_tuples = (
    g_or_p5[0] + e_or_maj3[0], 
    g_or_p5[1] + e_or_maj3[1]

sum_of_tuples # (6,11)
(6, 11)
In [23]:
g_augmented_by_maj3 = ophis.G.augment(ophis.Major(3))
e_augmented_by_p5 = ophis.E.augment(ophis.Perfect(5))

In [24]:
print(ophis.B.base_num, int(ophis.B)) 
6 11
In [25]:
z = ophis.Perfect(5) + ophis.Major(3)
In [26]:
print(z.distance, int(z)) 
6 11

So any chroma and any interval can be represented by a two-tuple, while manipulations originally implemented as methods in different classes can be a unified set of pure functions that accept tuples as arguments.


But two-tuples don't provide all the additional information you need to notate pitches or otherwise make them understandable as music.

So we need some "translation" functions. This still involves a lot of "magic number" coding, but hopefully it can be condensed into a small set of mappings that are easy to reason about.

In [27]:
import bidict # efficient two-way indexing of dicts

primary_map = [
    # half steps, scale degree / interval number, 
    # interval name, letter name, Perfect? 
    #                             (False=Major) 
    (0,  1, "unison",  "C", True),  #0
    (2,  2, "second",  "D", False), #1
    (4,  3, "third",   "E", False), #2
    (5,  4, "fourth",  "F", True),  #3
    (7,  5, "fifth",   "G", True),  #4
    (9,  6, "sixth",   "A", False), #5
    (11, 7, "seventh", "B", False)  #6

# Split primary map into bidicts for each value.
#     For faster, more sensible referencing.
#     This feels wrong and I need a better way.
#     Maybe something with named tuple...

hs_map = bidict.bidict(
    {x:item[0] for x, item in enumerate(primary_map)}
interval_map = bidict.bidict(
    {x:item[1] for x, item in enumerate(primary_map)}
interval_name_map = bidict.bidict(
    {x:item[2] for x, item in enumerate(primary_map)}
name_map = bidict.bidict(
    {x:item[3] for x, item in enumerate(primary_map)}
quality_map = {
    x:item[4] for x, item in enumerate(primary_map)

# How to translate between 
# diatonic intervals and modified intervals.
interval_quality_map = {
    True: bidict.bidict({ # Diatonic is Perfect
        -2 : 'double diminished', 
        -1 : 'diminished', 
         0 : 'Perfect',
         1 : 'Augmented', 
         2 : 'Double Augmented'
    False: bidict.bidict({ # Diatonic is Major
        -2 : 'diminished', 
        -1 : 'minor', 
         0 : 'Major', 
         1 : 'Augmented', 
         2 : 'Double Augmented'

modifiers = bidict.bidict({
    -2 : 'doubleflat',
    -1 : 'flat',
     0 : 'natural',
     1 : 'sharp', 
     2 : 'doublesharp'
In [28]:
import functools

# Single Dispatch:
#     two functions with the same signature.
#     The type of the first argument determines 
#     which function is executed.
#     This way, if a tuple is passed in, 
#         a string is returned,
#     and if a string is passed in, 
#         a tuple is returned.

def chroma(x):
    return None

def _(xy):
    x,y = xy
    name = name_map[x]
    modifier = modifiers[y - hs_map[x]]
    return " ".join([name, modifier])

def _(letter, modifier):
    x = name_map.inv[letter]
    mod_diff = modifiers.inv[modifier]
    y = hs_map[x] + mod_diff
    return x,y

def interval(x):
    return None

def _(xy):
    x,y = xy
    name = interval_name_map[x]
    q_mod = y - hs_map[x]
    q = interval_quality_map[quality_map[y]][q_mod]
    return " ".join([q, name])

def _(q, n): # quality, number
    x = n - 1
    is_perfect = quality_map[x]
    q_mod = interval_quality_map[is_perfect].inv[q]
    y = hs_map[x] + q_mod
    return x, y
def augment(a, b):
    return tuple(map(sum,zip(a,b)))

def diminish(a, b):
    return tuple(y - b[x] for x,y in enumerate(a))
In [29]:
'C natural'
In [30]:
'diminished third'
In [31]:
chroma('D', 'sharp')
(1, 3)
In [32]:
interval('Major', 3)
(2, 4)
In [33]:
chroma(augment(chroma('C', 'sharp'), interval('minor', 3)))
'E natural'
In [34]:
%timeit chroma(
    augment(chroma('C', 'sharp'), interval('minor', 3))
22.3 µs ± 1.4 µs per loop (mean ± std. dev. of 7 runs, 100000 loops each)
In [35]:
In [36]:
%timeit ophis.CSHARP.augment(ophis.minor(3))
101 µs ± 3.95 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)

A functional approach:

  • simplifies the math and logic
  • preserves important isomorphisms
  • requires much less code
  • executes much faster

The only downside is that the API for interactive use is a little less elegant, but not so much as to be a problem.

Where to Go From Here

The quick functional implementation demonstrated here doesn't include all the things that the OO approach currently has.

Foremost, this version needs to include modulo arithmetic.

In [37]:
augment((7,11),(1,1)) # Should be (0,0), in musical logic.
(8, 12)
In [38]:
# This result is meaningless.
chroma((8,12))  # KeyError
KeyError                                  Traceback (most recent call last)
<ipython-input-38-114c113c80ec> in <module>()
      1 # This result is meaningless.
----> 2 chroma((8,12))

/Users/adamwood/amwenv/lib/python3.5/ in wrapper(*args, **kw)
    742     def wrapper(*args, **kw):
--> 743         return dispatch(args[0].__class__)(*args, **kw)
    745     registry[object] = func

<ipython-input-28-f2a6c2b4cc47> in _(xy)
     13 def _(xy):
     14     x,y = xy
---> 15     name = name_map[x]
     16     modifier = modifiers[y - hs_map[x]]
     17     return " ".join([name, modifier])

/Users/adamwood/amwenv/lib/python3.5/site-packages/bidict/ in proxy(self, *args)
     94         attr = getattr(self, attrname)
     95         meth = getattr(attr, methodname)
---> 96         return meth(*args)
     97     proxy.__name__ = methodname
     98     proxy.__doc__ = doc or "Like dict's ``%s``." % methodname

KeyError: 8

Additionally, I need to include octave designations. The arithmetic is almost included for free with the functional approach, but the translation functions don't support it.

In [39]:
# Maj Second (or D) and min 3, with a third term for octave designation
augment((1,2,1), (2,3,2)) 
(3, 5, 3)
In [40]:
# F, 2 octaves above Middle C
chroma((3,5,3)) # ValueError
ValueError                                Traceback (most recent call last)
<ipython-input-40-3c4313b92e77> in <module>()
----> 1 chroma((3,5,3)) # F, 2 octaves above Middle C

/Users/adamwood/amwenv/lib/python3.5/ in wrapper(*args, **kw)
    742     def wrapper(*args, **kw):
--> 743         return dispatch(args[0].__class__)(*args, **kw)
    745     registry[object] = func

<ipython-input-28-f2a6c2b4cc47> in _(xy)
     12 @chroma.register(tuple)
     13 def _(xy):
---> 14     x,y = xy
     15     name = name_map[x]
     16     modifier = modifiers[y - hs_map[x]]

ValueError: too many values to unpack (expected 2)

The translation functions and associated dictionaries need to be extended to include multiple representations such as Unicode, ASCII, and Lilypond.

Finally, I might also do some experiementation with a hybrid approach that would keep the OO API intact. However, that might get too complicated.

Is Functional Really Better?

I don't know.

The difference in execution speed can probably be resolved by cleaning up the OO implememenation and importing the tuple-based arithmetic instead of the union-of-sets approach. I suspect that this would also make the OO code easier to read and reason about.

I'm not at all convinced that there is something inherently wrong with object oriented code. However, I do think that a classical paradigm promotes a "different things are different things" mentality. In some cases this is probably helpful. In music, at least in this case, it obscured a fundamental sameness between two important concepts. Functional programming forced me to recognize that sameness. Someone else might have recognized it anyway, and written a good OO implementation first.

If there is a generalizable lesson here, I think it might this: Think through a few different approaches and paradigms. Try coding up more than one logical implementation in the domain. See how that sheds light on the underlying problems and data structure.

Also, don't be afraid to redesign things. Especially if you don't have any users yet.

Emacs for Technical Writing

I've been thinking about switching to Emacs for a long time. I had a sense that it would fit my personality, and that the ability to automate tasks and customize the environment would boost productivity. But it always seemed a bit out of reach. I thought I would probably need to take several weeks to really learn it, and I never seem to have that kind of time.

But I recently made the switch, and am now using Emacs as my primary editor and terminal.

This is my fourth editor. When I first started writing code and using plaintext for prose, I used Notepad++. When I had enough of an idea about what I wanted in an editor, I switched to Sublime. Then about a year or so ago I switched to Atom because it is Free and Open, and provided a very similar experience to Sublime.

But Emacs was always there, in the back of my mind. Finally, two things shifted the balance for me:

  • better reStructured text support in Emacs (specificially, proper syntax highlighting)
  • the dawning realization of Atom's (well, Electron's) performance problems

There are a couple Atom plugins for highlighting ReST, but neither one works right 100% of the time. I would write some oddball directive and all of the sudden half the document was grey or red. Then I'd open a new .rst doc and try the samwe thing and it would be fine. Or portions simply wouldn't highlight at all. I found it maddening. I thought about learning enough about the Atom plugin development and syntax highlighting to try to fix the problem myself, but that seemed like a bad use of my time and learning bandwidth.

Looking around for editors with good ReST support, I found Emacs listed. I use ReST and Sphinx every day now, and I'm currently on my fourth Sphinx-using writing gig. Okay... I guess I'll finally take the time.

Benefits of Emacs

I've quickly discovered that Emacs is:

  • not that hard to get going with
  • enormously helpful

Here are a few of the benefits I have noticed in just the first couple weeks, while barely scratching the surface.

Less Pain

I have moderate-to-severe pain in my back, around my right shoulder blade. This seems to be largely caused by my constant trackpadding. Moving to a keyboard-centric interface has greatly reduced my pain. (I suspect that if I switch to a split keyboard and maybe get a foot pedal I can make more progress on this front. I also think I should take the time to learn to type properly.)

It is, of course, possible to use a keyboard to navigate in Atom and most other editors. I could have installed Emacs keybinding for Atom. But it was too easy not too. Emacs served a forcing function because mouse navigating simply isn't possible. (I am even running Emacs in my terminal, rather than as a standalone app, so I can't even mouse on the menu.)

Less Distraction

You can run a shell inside Emacs. Since I can switch from the file I'm working on to the shell inside the same window, I don't need to swipe over to another screen. This

Registering Functions Against Object Methods in Python

My big side project right now is a music theory library in Python, called Ophis. Among many other concerns, I'm trying to make the API as natural and easy to use as possible. This often means finding ways of creating objects other than ClassName(args).

Ophis has the classes Chroma and Pitch. A chroma is a note name without an octave (the idea of C), while a pitch is a chroma with a specified octave (middle C).

The problem with this is that the conventional way of referring to a pitch would then be:

ophis.Pitch(ophis.C, 0)

You can see, Ophis has already initialized all the note names (chromae) you would need. We could do that with pitches...

C0 = Pitch(C, 0)
C1 = Pitch(C, 1)

# later, in user code...


...but I think we all know the problem with that. It requires initializing several hundred pitch objects that may never be used. Most songs don't use every note. And every physical note has multiple names because of enharmonic spelling (F♯ == G♭).

So, what if the API looked like this?


That's cool. Pretty easy to do, too.

class Chroma:


  def __call__(self, octave):
    return Pitch(self, octave)

What if we went deeper?

Once you realize this is a good idea, the next thing you realize is.... what about chords?

ophis.Chord(ophis.C, Major)

Well, that looks pretty similar, doesn't it?

So, um... okay...

class Chroma:


    def __call__(self, x):
          return Pitch(self, x)
        except TypeError:
          return Chord(self, x)

There are problems with this.

  • Definitions for Pitch and Chord are in modules that get loaded after Chroma. This doesn't create any errors (because the function isn't run on load), but still feels wrong.
  • It is brittle. If I change the name of Pitch or Chord, I have to go back and change it here. The tightly-wound nature of music terminology means I have long-since given up the idea of loose coupling, but I'm trying to make these types of dependencies only go up the conceptual ladder, not back down it.
  • What if I want to add more things to this method? Eventually I'm going to end up creating a series of type checks.

When I was working through this, I didn't see any way around a series of type checks, but I thought I could solve the first two problems with some creative coding.

I decided I could register functions into a dict, stored on the class. The keys for the dict would be types, and the values would be the functions to run when __call__ is called with that particular type as an argument. These functions could be registered at the point when the type that the function is supposed to return is created.

Something like...

class Chroma:


    _callable_funcs = dict()

    def __call__(self, x, x_type=None):

        if callable(x):
            self.__class__._callable_funcs[x_type] = x
            return self.__class__._callable_funcs[type(x)](self, x)

# This code has not been tested.

I got (a version of) this to work, and I was feeling pretty darn proud of myself for thinking of this solution, and implementing it.

Then I had this feeling like this was all very familiar. Maybe I had read about this type of thing?

I quickly discovered three things:

Unfortunately, I have two problems:

  • The @singledispatch decorator only looks at the first argument of a function call. The first argument of a method call is always self. So, out of the box, this dosn't work for instance methods.
  • @singledispatch was added in v3.4, making it still a little newish. Since I'm writing a utility library for others to use, and not my own application, it seems unwise to rely on something that everyone might not have.

But, now I can do two things:

  • See if anyone has already figured out a way to apply @singledispatch to a method. (Someone has.)
  • Potentially re-implement @singledispatch myself, for backwards compatibility.



    from functools import singledispatch
    # A re-implementation of @singledispatch
    # has been left as an exercise for the reader
    # because I haven't done one yet.

def method_dispatch(func):
    An extension of functools.singledispatch,
    which looks at the argument after self.
    dispatcher = singledispatch(func)
    def wrapper(*args, **kw):
        return dispatcher.dispatch(args[1].__class__)(*args, **kw)
    wrapper.register = dispatcher.register
    update_wrapper(wrapper, func)
    return wrapper


class Chroma():


    def __call__(self, x):
        return self


import chroma as ch

class Pitch:

    def __init__(self, chroma, octave=0):
          self.chroma = chroma
          self.octave = int(octave)

ch.Chroma.__call__.register(int, Pitch)

# In user code:

ophis.C(0) == ophis.Pitch(ophis.C, 0)
# True

And finally, to encourage this usage...

class Pitch:


        return "".join([
            self.chroma.__repr__()], "(",
            self.octave.__repr__()], ")"

# At a terminal...

>>> ophis.Pitch(ophis.C, 0)

Feels Pythonic, yes?

Further Reading

Intersection of Non-Empty Sets in Python

Suppose you generate several sets on the fly, and you want to find the elements that are in all the sets. That's easy, it's the intersection of sets.

# One syntax option
result = set_one & set_two & set_three

# Another option
result = set.intersection(set_one, set_two, set_three)

But let's suppose that one or more of your sets is empty. The intersection of any set and an empty set is an empty set. But, that's not what you want. (Well, it wasn't what I wanted, anyway.)

Suppose you want the intersection of all non-empty sets.

List comprehension

If the sets are in a list, you can remove the empties. Then unpack the list into the set.intersection() function.

list_of_sets = [set_one, set_two, set_three]

# Empty sets evaluate to false,
# so will be excluded from list comp.
non_empties = [x for x in list_of_sets if x]

solution_set = set.intersection(*non_empties)

The asterisk before non_empties unpacks the list into a series of positional arguments. This is needed because set.intersection() takes an arbitrary number of sets, not an iterable full of sets. (It's the same asterisk as in *args in function definitions.)

(Note: You could use a filter instead of a list comprehension, but Guido thinks a list comprehension is better. I agree.)

With iterable unpacking (tuple unpacking)

In my case, I was generating the sets in my code, and the solution set always contained only one item. And I wanted the item, not a set with the item. So...

# initialize an empty list
list_of_sets = []

# each time I create a set,
# append set to list when it is created,
# instead of naming them individually
list_of_sets.append( thing_that_generates_a_set() )

# drop the empties, find the intersection
# and unpack the remaining single element
solution, = set.intersection(*[x for x in list_of_sets if x])

The comma after solution turns the assignment into a tuple unpacking. If you unpack a collection of one, you get the single item.

By the way, if you end up with more than one item in your collection, and only want the first item, you can do:

first_item, *_ = some_collection

The * indicates a variable number of positional arguments (it's the same asterisk as in *args and in passing the list to set.intersection() above), and the underscore is used as a convention for "not using this stuff."

# you could have done this instead

first_item, *stuff_i_will_not_care_about = some_collection

I'll be using that *_ below, in the actual code.

Why would you ever do this?

The generalized problem

From a pool of items, there are three attributes to select for. Specifying any two of them should produce one and only one result.

More specifically...

Musical intervals.

A musical interval has:

  • a quality (Major, Minor, Perfect, Augment, or Diminished)
  • a number (Unison (1), Second (2), Third (3) ... Octave (8))
  • a distance of half_steps (for example, a major third is 4 half steps)

If you know any two of these, you can select the correct one.

Some actual code

class Interval():

  # ... all sorts of things removed ...

  instances = set()
  # all instances of Interval

  def get_intervals(cls, *, quality=None, number=None, half_steps=None):
      """Return a set of intervals."""

      candidate_sets = []

      candidate_sets.append({x for x in cls.instances if x.quality == quality})

      candidate_sets.append({x for x in cls.instances if x.number == number})

      candidate_sets.append({x for x in cls.instances if x.half_steps == half_steps})

      candidate_sets = [x for x in candidate_sets if len(x) > 0]

      return set.intersection(*candidate_sets)

  def get_interval(cls, quality=None, number=None, half_steps=None):
      """ Return a single interval."""

          interval, = cls.get_intervals(quality=quality, number=number, half_steps=half_steps)

      ## if there was not one and only one result
      except ValueError:

          # only select by half_steps
          candidates = [x for x in cls.instances if half_steps == x.half_steps]

          # select the first one,
          # based on quality priority:
          # Perfect, Major, Minor, Dim, Aug
          interval, *_ = sorted(candidates, key=lambda x: x.quality.priority)

        return interval

In the actual code, there's a bunch of other things going on, but this is the general idea.

Another approach

For my specific use case, another approach is simply to not create a set for the unspecified attribute.

if quality is not None:
    candidate_sets.append({x for x in cls.instances if x.quality == quality})

if number is not None:
    candidate_sets.append({x for x in cls.instances if x.number == number})

if half_steps is not None:
    candidate_sets.append({x for x in cls.instances if x.half_steps == half_steps})

In my working code, I actually do both. This allows for a potentially meaningful result even if something is specified incorrectly. I could have decided to let bad input cause explicit failure, but I think I'd rather not in this case.

So... what's the point?

This post looks like a tutorial on list comprehension. Or maybe set operations. But really this post is about problem solving while writing code.

The code solution to this problem is really easy... but only if you've figured out the problem you need to solve.

I started with the following problem:

Find the intersection of all non-empty sets, from an arbitrary pool of sets, not knowing which ones would be empty.

So I started Googling variations on that theme. But there aren't any "intersection of just the good sets" functions. Then I tried to start writing a question for Stack Overflow, and as soon as I had written the title, I knew the answer.

Starting with a collection of sets, drop the empty sets and find the intersection of the remaining sets.

As soon as I broke my one problem into two steps, the problem was immediately solved:

  1. Create a new collection without the empties. (List comp.)
  2. Find the intersection of that list.

At the same moment I realized these steps, it also become clear that the original group of sets should be a collection, not just several unrelated objects.

So, the moral of the story is...

If you can't find the solution to your specific problem, restate your problem as a series of steps.


I hate the word verbiage.

First, we need to deal with the fact that it is the wrong word. Most of the time, when people say verbiage, they really mean verbage --- that is, the wording. Verbiage, properly, means excessive wordiness, not the specifics of word choice.

But this isn't what I hate about it. I would hate it just as much if it meant precisely what every one uses it to mean. My problem is with the idea itself. I hate what people are saying when they say verbiage.

Every time I have ever heard the word verbiage, the person has been talking about the precise way that something is worded. The context is always about improving something.

  • Can you make this more clear by fixing up the verbiage?
  • After you get the first draft of the design done, ask Adam to help you clean up the verbiage.
  • Maybe we can change the verbiage on this form to make it more user friendly.

Without fail, a request to work on the verbiage is symptomatic of a deeply flawed design and engineering process. We got to this point because people were decorating, not designing, and now we are going to try to get out of it by changing the words the user sees.

This causes more problems, of course.

The reason the words aren't clear and precise in the UI is that the mental model developed by the engineering team is either confused or just plain wrong. In order to make the application easy to use, our Verbiage Specialist has to overlay a new mental model --- often, the one that should have been used in the first place. This new mental model, and the collection of verbages that go with it, will be imprecise and incomplete because the Verbiage Engineering Team can't tell the developers to restructure the database and rename all the application's variables. The result is that the UI becomes temporarily easier to use, but at the cost of taking on additional Verbiage Debt. Somewhere deep in an internal wiki or Confluence page is a OVM (Object-Verbiage Mapper) glossary telling you that dev:event_property => user:"Device Status". But nobody reads internal wiki pages, so the problem just gets worse.

You cannot fix an application by redecorating the UI. Fixing the verbiage is just redecorating + technical debt. If you find yourself fixing up the verbiage, the problems are much deeper.

So how do you avoid Verbiage Debt?

Stop treating writers as Verbiage Technicians and think of them as Verbiage Architects. (I'm sure there's a good word for this already.) Your Verbiage Team, along with your Pictures of Things Engineers, need to be involved from the beginning with the design of your application, and they need to be fully-fledged members of the engineering team --- not hired hands, consultants, helpers, or otherwise after-the-facters.

Building software has more to do with creating mental models than it does with writing code. Humans create mental models in language and pictures.

Your language and pictures people are as important as your coders.

Designing vs. Decorating

My wife spent some time in an Interior Design master's degree program. One of the things that frequently frustrated her was the conflation, by people outside the industry, of interior design and interior decorating.

  • "Oh, so like, you're learning how to pick out furniture and stuff."
  • "Can you help me pick paint colors in my bedroom?"
  • "That's cool, like that show on HGTV."

Decorating is primarily about aesthetics --- how things look. Design is about function --- how things work. There is certainly overlap between the professions, but their focus and concern is very different.

At least, though, nearly everyone in the industry --- and certainly everyone at her school --- understood the difference. Since my wife was there the school has actually changed the name of the program to Interior Architecture, to make the focus more clear.

I'm not sure the software industry as a whole understands the difference between decorating and design. Part of the problem is that we don't use the word "decorator," to describe people with graphics skills and no sense of the underlying software. Everyone is a "designer." The best we have done is to try to make distinctions between "UX Design" and "Graphic Design."

In fact, I think the push in the last decade or so to use the word "UX" is an attempt to make the distinction. Unfortunately, I don't think it has helped. Like Tech Writers calling themselves "Documentation Specialists," the change in label has been driven as much by a desire for a cooler resume as by any real change in practices. The distinction we need to make is not between "graphics" and "UX," and certainly not between "UX" and "UI" (as if those are, you know, actually different things, really). The distinction we need to make is between design and decoration.

Have you ever sat in a redesign review that solved exactly none of the problems of the original design? The new thing looks better, but it functions the same. Decorating

Have you ever been involved in a process where some non-engineer Product Manager drew pictures of screens and buttons, and then someone with Photoshop skills and no coding experience turned that into a mockup? Decorating.

Have you ever been asked, after the graphics person has completed an entire set of screen mockups, to "help with some of the verbiage" in order to make things more clear? Decorating.

Any process that separates out the work of contributors --- first the engineers do something and then hand it off to the graphics person and then the tech writer writes about it later --- will tend toward decorating. Design requires people to actually talk to each other, preferably in the same room. Design requires that a person drawing and labelling a form input understand the conceptual model the form is interacting with.

I suggest we stop futzing with labels for types of people and buzzwords that feel helpful but aren't. This problem cannot be solved by finding an even cooler replacement word for "UX," and then blogging about how "UX is dead, we're doing XZ now." Just keep "design" and "decoration" in your head as an evaluative tool. Look at how things are being done and ask yourself --- it this designing or is it decorating? Then, if there's too much decorating, don't spend a lot of energy convincing people about the difference. Just begin to change the process.

And don't let someone with Photoshop skills redesign an app they don't understand and have never used.

Docs as Code


  • Docs are written in plain text formats such as Markdown or reStructured Text.
  • Docs are stored as flat files, not database entries.
  • Docs are authored in a code editor of the writer's choice, not a monolithic authoring application.
  • Docs are kept under version control.
  • Doc versions are organized in parallel to product versions.
  • Docs are built and deployed from source in an automated process that mirrors product deployment.
  • Docs are automatically tested for internal consistency and compliance to style guides.
  • Whenever reasonable, writers use the same tools and processes as developers.
  • Writers are integrated into the development team.


  • Writers have more control over their authoring environment.
  • Less friction in the authoring process.
  • Elimination of inconsistencies between docs and product.
  • Less need for human proofreading.
  • Coordinated releases of docs with product.
  • Developers are more likely to contribute to docs.
  • Writers and developers have more awareness of and respect for each others' work.
  • Authoring and deployment tools are mostly free; hosting requires less overhead.

DocOps Isn't Just the Fun Part

Somewhere in the last year I decided I was into DocOps.

What that really meant for me is that I am into Docs-as-code, which is a related trend, but not quite the same. I care about things like single-source documents (DRY), version control, plain text editing, style linting, and automated deployment. I write little Python or Bash scripts to pipe tools together and customize the output of static site generators. I'm learning a lot, having a lot of fun, and finally weaving together a number of different skill sets and interests I've picked up over the years (writing, coding, project management).

When I was the only writer at a startup, this was all really effective. I could fool myself into thinking I was doing DocOps. And maybe I was, but only in that particular context.

But now I work at a big, hulking enterprise company. And all of the sudden it is clear that DocOps isn't just the fun technology bits, just like how DevOps isn't just about knowing how to deploy Docker on Kubernetes. It's about dealing with people and dealing with organizations.

I just want to stand up my docs somewhere. "Give me SSH access to a directory with a public URL." At the startup I just made a decision and had live docs published my second or third day there. At the enterprise? Not so simple. My tooling has to go through security checks. Engineers have to sign off on deployment processes. Customer service has a vested interest in how documents are delivered. Can we integrate to Salesforce knowledge base? How do I pip install from behind a firewall?

If I'm into DocOps, this is what I'm into. Not just hacking on writing tools (as much fun as that is), but also being effective in an organization. I was very effective in a startup, where hacking on things was how the organization operated. Now I have to level up and learn how to be effective at scale.

The Real Reason I Love Static Site Generators

There's a lot to like about static site generators like Jekyll, Nikola, and Sphinx.

  • Hosting is much simpler, and can usually be done for free.
  • Static sites are inherently more secure than dynamic ones.
  • Very fast page load times.
  • Authoring in a code editor that I have control over.
  • Markdown and reStructured Text are both faster to type than HTML or rich content in a WYSIWYG editor.
  • Version control.
  • The ability to manage the build and deploy process like code.

There are probably more benefits I'm not thinking of at the moment. When I first started using Jekyll, my main motivation was wanting to simplify hosting and exert control over authoring. I discovered the other benefits along the way, and they have really changed my professional life.

But I've realized there's one thing that has come to matter the most to me:

Static sites revive and make real the notion of a document on the web.

In database-backed CMSes, the pretty URL is a noble lie. Content is smeared around in a database and accessed through ?id=1234 parameters or internal query mechanisms. This is fine, and really the only way to handle massive amounts of content.

But the web was built to serve documents, not database results. In an age where content-as-data is on such hyperdrive that people think a single-page app blog system is a reasonable idea, it is calming to use a technology that works the way the web was always supposed to work.

And this has as much to do with the mental model as with the technology. (Maybe more.) The individual documents that make up a static site are handled as documents before being processed to HTML. If I want to change the content on some blog post, I edit a file on my local computer. I don't have to log in and use an application. It is transparent, and there's a direct relationship between a single file in my source and a single URI on my site. Now it feels like the URI actually identifies a resource, and is not just a cleverly-disguised search pattern.

I understand why we moved past the web of documents. But if you're producing documents, maybe it's the right model.

File Names

There are only two hard things in Computer Science: cache invalidation and naming things.
-- Phil Karlton

I cannot help you with cache invalidation.
-- Adam Michael Wood

I recently saw a question about file names in the Episcopal Communicators Facebook Group:

Question about file names.

This is a question about filenames for websites.

When we first developed our website, our consultant told me that when we put a file on there, it's important to give the file a date and a unique and descriptive name.

While that works for some files, it doesn't for others. It caused me to end up with a lot of old files on my website.

What I changed was that I stopped changing file names. So instead of mileage_rates_2016.pdf, I just call it mileage_rates.pdf. That way every link is correct, everywhere on the site.

However, when we link to outside websites, like the wider church's site, we end up with obsolete links. Case in point: the Manual of Business Methods:

We had full_manual_updated_09-30-2013.pdf.

And now the link is full_manual_updated_012815_0.pdf

Is there any need to give dates to files like this? It's important for the organization to archive old versions, but is there any need to have unique names so that websites like ours end up with older versions?

I summed a few file name best practices, but... I have a lot to say about this topic. File naming is one of those weird little things I have irrationally strong feelings about, and the ubiquity of bad file naming practices is a constant source of rage in my life.

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