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Water Usage and Washing Machines

Earlier this month (9/4) our dishwasher started leaking, and I disconnected it. The new dishwasher comes in about a week, but I was curious whether I would see an increase in our water usage from handwashing the dishes. After downloading the data, though, there were more interesting slope changes:

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Diatonic modes as progressive flattening

Most tunes are built around a diatonic scale. The most well known diatonic scale is the major scale, C D E F G A B, but all seven cyclic permutations of those notes are named scales:
  • C D E F G A B: major (I)
  • D E F G A B C: dorian (II)
  • E F G A B C D: phrigian (III)
  • F G A B C D E: lydian (IV)
  • G A B C D E F: mixolydian (V)
  • A B C D E F G: minor (VI)
  • B C D E F G A: locrian (VII)

Even though seven of these are possible, the only ones you generally run into in traditional music are major (I), minor (VI), mixolydian (V), and dorian (II).

Another way to think of these is as adding flats:

  • no flats: C D E F G A B (I, major)
  • add a flat seventh: C D E F G A Bb (V, mixolydian)
  • add a flat third: C D Eb F G A Bb (II, dorian)
  • add a flat sixth: C D Eb F G Ab Bb (VI, minor)
  • add a flat second: C Db Eb F G Ab Bb (III, phrigian)
  • add a flat fifth: C Db Eb F Gb Ab Bb (VII, locrian)
You'll notice that IV (lydian) is missing. Following the pattern, this would give us:
  • flat first: Cb Db Eb F Gb Ab Bb (IV, lydian)
And then, I guess:
  • flat fourth: Cb Db Eb Fb Gb Ab Bb (I, major)

This is correct, except that we switched down to Cb once it came time to flat the first.

The problem is that the major scale (I) isn't actually a great place to start: if we instead start with the lydian scale (IV) everything works:

      C  Db D  Eb E  F  F# G  Ab A  Bb B
IV    1     2     3     4  5     6     7
I     1     2     3  4     5     6     7
V     1     2     3  4     5     6  7
II    1     2  3     4     5     6  7
VI    1     2  3     4     5  6     7
III   1  2     3     4     5  6     7
VII   1  2     3     4  5     6     7

You can see that starting with the lydian scale each scale degree in turn is flattened: 4, 7, 3, 6, 2, 5. For more symmetry, each note to be flattened is a fifth down from the previous note to be flattened.

If we follow this pattern, flattening one note at a time, we can run through all the modes of all the keys:

       A  Bb B  C  Db D  Eb E  F  F# G  Ab A  Bb B
C IV            1     2     3     4  5     6     7
C I             1     2     3  4     5     6     7
C V             1     2     3  4     5     6  7
C II            1     2  3     4     5     6  7
C VI            1     2  3     4     5  6     7
C III           1  2     3     4     5  6     7
C VII           1  2     3     4  5     6     7
B IV         1     2     3     4  5     6     7
B I          1     2     3  4     5     6     7
B V          1     2     3  4     5     6  7
B II         1     2  3     4     5     6  7
B VI         1     2  3     4     5  6     7
B III        1  2     3     4     5  6     7
B VII        1  2     3     4  5     6     7
Bb IV     1     2     3     4  5     6     7
Bb I      1     2     3  4     5     6     7
Bb V      1     2     3  4     5     6  7
Bb II     1     2  3     4     5     6  7
Bb VI     1     2  3     4     5  6     7
Bb III    1  2     3     4     5  6     7
Bb VII    1  2     3     4  5     6     7
A  IV  1     2     3     4  5     6     7
A  I   1     2     3  4     5     6     7
A  V   1     2     3  4     5     6  7
A  II  1     2  3     4     5     6  7
A  VI  1     2  3     4     5  6     7
A  III 1  2     3     4     5  6     7
A  VII 1  2     3     4  5     6     7

Turning this on it's side, it's really quite a pretty pattern:

Stepping back, this makes it easy to think about what notes to expect in a mode:

  • major: no extra flats
  • mixolydian: one extra flat
  • dorian: two extra flats
  • minor: three extra flats

I find this framing much more useful than the cyclic permutation approach of thinking about starting the major scale on different notes.

(This also gets more elegant if we rename "F#" to "F" and "F" to "Fb". Then the lydian scale is C D E F G A B and all the other scales add flats from there.)

full post...

Dual Bagpipes

A standard bagpipe has a single bag feeding multiple pipes. The player keeps the bag inflated with their mouth, and maintains the bag at a constant pressure with their left arm. The chanter and drones all respond differently to varying amounts of pressure, so that constant pressure is really important.

But what if we added a second bag, under the player's other arm, which powered the drones? Now the player can intentionally modulate the pressure on the drone bag to make the drones vary rhythmically:

Alternatively, instead of chaining the bags you could pipe the player's air into both of them directly, allowing them to vary the pressure on the chanter as well. My impression is that this is less useful, because when pipers play with just their chanter I've always seen them keep a steady pressure instead of using variation in pressure to add expression. Or maybe bagpipe culture is just anti-expression, and the instrument is actually quite capable? Or am I paying too much attention to British Isles piping and other traditions do involve varying bag pressure for rhythmic accentuation?

full post...

Brendin Lange is a Scammer

In Spring 2016 we contracted with Brendin Lange to put dormers on our house. He took the deposit, did a single day of interior demolition, and then disappeared with the money. Since then I've spoken to several other people who he's also ripped off. I wanted to write this up publicly so other people can consider our experience when deciding whether to work with him.

Other people I've talked to with similar experiences:

  • Someone who says Brendin Lange took his $5k deposit and disappeared.
  • Someone who says Brendin Lange defrauded him for $2k.
  • Someone who says Brendin Lange owes him $36k, and that Lange has also defrauded many other people he knows.

He's operated under many business names:

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Load Testing a Battery

I wrote earlier about how I was putting together a battery backup. I wanted to measure its capacity to see how it compared to the rating. It uses a lead-acid AGM battery rated at 100Ah, though the capacity will generally be higher or lower depending on how much current you draw.

To tell how full an AGM battery is, you let it rest for at least four hours and then measure the voltage. This isn't all that accurate, but it should be enough to keep from drawing the battery down too far. You can also measure the voltage under load, but this is even less reliable.

I tested with a box fan on "high", which drew about 70W (75W counting the inverter), and recorded the voltage every so often:

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Charging Shelf

A few months ago I made a set of built-in shelves for our living room. Recently I was noticing that people tended to leave their laptops and phones in awkward places while charging, so I decided to make a set of charging shelves:

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