New Release: Agua y Arena

I’ve released a new track called Agua y Arena. The title means “water and sand” in Spanish, and the track is about my liking for the natural landform of beaches. It’s not about any particular beach in a country or city, nor is it about any events that may take place on one. It’s about how I generally feel about the physical composition of beaches – sand, pebbles, gravel and sea water – and about my positive feelings towards this artwork of nature. It’s not about women in bikinis.

Production

Agua y Arena was drafted in Cubase around 2010, and later developed in Ableton Live. My current preferred DAW is Logic Pro, but since this track was already developed extensively in Ableton, I finished it up in Ableton.

Agua y Arena Ableton screenshot

I kind of hate Ableton because it’s not easy to edit MIDI on it, but one of its advantages is that you can use the Packs. Packs are similar to traditional sample libraries but they offer more than just samples. In addition to one-shot samples and loops, Ableton Packs also provide MIDI files and sampler instrument settings which makes it easy (and fun) for you to test different stylistic ideas quickly. And the sound quality is great.

The percussion part in this tracks was produced with the Afoxê Percussions instrument that came with the Latin Percussion Pack. Here’s my Afoxê part from Agua y Arena:

Afoxê is a genre of music originating in Brazil, apparently. I’ve used a combination of 5 instruments – Tumba, Agogo, Cabasa, Pandeiro and Surdo. When you load the instrument from the Pack, it also contains Tambourine and it comes with a MIDI performance apparently modeled after typical percussion performances in this musical genre. Here’s how the original MIDI performance sounds like:

Other Individual Tracks in this tune

Let me show you the other instruments I’ve used in this tune, one at a time.

Here’s the Piano Chords track. I used it to play the Dmaj9 chord in the intro:

…as well as to provide chord changes in the chorus section (Em7 – Bm7 – Bm7/A – F#7(b5) – F7(b5):

Here’s the Bass track:

I like how I added vibrato to this part. The red curves going up and down in the image indicate the increase/decrease in the vibrato amount.

Here’s the Kick track. Oops, this isn’t very illuminating when heard on its own:

Here’s the Synth Lead track:

This sound was made with the Analog synthesizer instrument in Ableton. It’s a combination of two sawtooth waveforms, each detuned by 4 cents from the original pitch and away from each other. (As the result, you have a 8-cent detuned sound.) Combining and detuning make a sound thicker, or more colloquially, “phatter”. I passed the sound through a high-pass filter, set the cutoff frequency to 185Hz and boosted the resonance amount at that frequency.

Agua y Arena synth lead w captions

Here’s the Piano Melody track:

This piano was done with an instrument in the Grand Piano Pack. When it comes to piano sounds, I definitely prefer the ones in the Ableton Pack to the ones in Logic Pro.

Here’s the Hihat track:

Here’s the Breakbeat track:

This was played with the Drum Rack instrument containing chopped drumbeat that I took from an old sample CD many years ago. (Yup, I’m old enough to have bought sample CDs.)

Agua y Arena breakbeat w caption a

The Drum Rack allows you to assemble your own drum kit by adding the components (e.g. kick, snare) of your choice. On top of that, it has Macro Control with which you can simultaneously manipulate the behaviors of all the samples by turning a knob. For example, I assigned the Sample Length parameter of all my samples to a knob and gradually shortened the playable length of samples in some places. That’s why the breakbeat part sounds excessively chopped up sometimes. Please listen again:

Here’s the Synth Chords track:

There’s also the Crash Cymbal track, but let’s not waste time listening to just crash cymbals.

Streaming and Stores

As of this writing, Agua y Arena is in the following sites and stores:

And will be in Google Play soon too. Thanks for visiting!

Solutions for Kangaroo Math Questions – 2017 Benjamin Q29

This is part of a series of posts about the International Kangaroo Mathematics Contest. I think the Kangaroo exams are a great source of teaching/learning because their questions demand creative and logical thinking. My students love them. Surprisingly, though, there aren’t a lot of websites out there that show you how to solve those questions. So I thought it would be nice to share some of my suggested solutions here. The past exams and answer keys are available at the IKMC website, by the way.

In this post, I’ll show you how to solve Question 29 on the 2017 Benjamin exam.

Question 29

Julia has four different colored pencils and wants to use some or all of them to paint the map of an island divided into four nations, as in the picture. The map of two nations with a common border cannot have the same color. In how many ways can she color the map of the island?

(A) 12     (B) 18     (C) 24     (D) 36     (E) 48

Source: International Kangaroo Mathematics Contest

I’ll write the solution below, but I’ll leave some space before that so you don’t accidentally see it while trying to solve it on your own.

(empty space)












(end of empty space)

Solution

Let’s simplify the map like this, and call it Variation A.

I’ve put numbers 1, 2, 3, 4 to represent the colors available, and I began by applying them clockwise.

Now I’ll keep the colors 1 and 2 fixed and swap 3 and 4 and get a new combination, and call it Variation B:

Let’s go back to Variation A, keep the colors 1 and 3 fixed, and swap the colors 2 and 4. We’ll call it Variation C:

Let’s go back to Variation A again, keep the colors 1 and 4 fixed and swap 2 and 3, you’ll get Variation D:

Take Variation D, keep the colors 1 and 2 fixed, and swap 3 and 4. You’ll get Variation E:

Take Variation D again, keep the colors 1 and 3 fixed, and swap 2 and 4, you’ll get Variation F:

Let’s put all of them together and check if we’ve done it right so far. They are all different, right?

These are all possible options when we have the color 1 at the left-top, and we use all 4 colors available. But remember we can use the same color for the nation at the left-top and the one at the bottom-right? We can, because they don’t share a common border.

That means, we also have these options:

We can have Variation A’ which is very similar to Variation A but different because of that bottom-right nation. Same goes for B, C, D and so on.

Therefore, in total, we have 12 ways to color the map when we have the color 1 at the left-top.

Now, how many colors can be used for the top-left? 4 colors. So the total number of ways she can color the map is:

12 × 4 = 48

Answer is (E) 48.

How was your attempt? Got that right? I was quite lost on this one at first, but then I got an idea when I was cueing up in a supermarket. Hope you enjoyed this post. Thanks for visiting.

Solutions for Kangaroo Math Questions – 2017 Benjamin Q28

This is part of a series of posts about the International Kangaroo Mathematics Contest. I think the Kangaroo exams are a great source of teaching/learning because their questions demand creative and logical thinking. My students love them. Surprisingly, though, there aren’t a lot of websites out there that show you how to solve those questions. So I thought it would be nice to share some of my suggested solutions here. The past exams and answer keys are available at the IKMC website, by the way.

In this post, I’ll show you how to solve Question 28 on the 2017 Benjamin exam.

Question 28

John wants to write a natural number in each box in the diagram so that each number above the bottom row is the sum of the two numbers in the boxes immediately underneath. What is the  largest number of odd numbers that John can write?

(A) 4     (B) 5     (C) 6     (D) 7     (E) 8

Source: International Kangaroo Mathematics Contest

I’ll write the solution below, but I’ll leave some space before that so you don’t accidentally see it while trying to solve it on your own.

(empty space)












(end of empty space)

Solution

Note the following rules regarding adding odd/even numbers:
Odd + Odd = Even (1 + 1 = 2, also 3 + 3 = 6 and so on)
Odd + Even = Odd (1 + 2 = 3, also 3 + 4 = 7 and so on)
Even + Even = Even (2 + 2 = 4, also 4 + 4 = 8 and so on)

This means the following:

  • Bottom boxes are odd–odd–odd–odd numbers:
    • 2nd-bottom row will be even-even-even
    • Rest will all be even, therefore you have 4 odd numbers
  • Bottom boxes are odd–odd–odd–even numbers:
    • 2nd-bottom row will be even-even-odd
    • 3rd-bottom row will be even-odd
    • Top row will be odd, therefore you have 6 odd numbers
    • Even-odd-odd-odd at the bottom will have the same result
  • Bottom boxes are odd–odd–even–even numbers:
    • 2nd-bottom row will be even-odd-even
    • 3rd-bottom row will be odd-odd
    • Top row will be even, therefore you have 5 odd numbers
    • Even-even-odd-odd at the bottom will have the same result
  • Bottom boxes are odd–even–even–even number:
    • 2nd-bottom row will be odd-even-even
    • 3rd-bottom row will be odd-even
    • Top row will be odd, therefore you have 4 odd numbers
  • Bottom boxes are even-even-even-even numbers:
    • The rest will all be even, therefore 0 odd numbers
  • Bottom boxes are odd–even–odd–even numbers:
    • 2nd-bottom row will be odd-odd-odd
    • Rest will all be even, therefore 5 odd numbers
    • Even-odd-even-odd at the bottom will have the same result
  • Bottom boxes are odd–even–even–odd numbers:
    • 2nd-bottom row will be odd-even-odd
    • 3rd-bottom row will be odd-odd
    • Top row will be even, therefore 6 odd numbers
  • Bottom boxes odd–odd–even–odd numbers:
    • 2nd-bottom row will be even-odd-odd
    • 3rd-bottom row will be odd-even
    • Top row will be odd, therefore 7 odd numbers
    • Odd-even-odd-odd at the bottom will have the same result

At this point, we have tried all possibilities for the bottom boxes.

Answer is (D) 7.

How was your attempt? Did you get it right? I’ll post solutions for Q29 and Q30 in the following posts. Thanks for visiting.