Daily Archives: February 22, 2012

assignments_musth4 musicTheory4

(musTh 212) Rhythm and Meter Assignment Number 2

Due Monday, 2/27/12.

Exercises from Chapter 6 of the Kostka (pp. 122 – 124):

  • Part A, 3 and 4
  • Part B, 1 – 5

For the questions about polytempo in Part A, the equation and explanations from the tempo modulation post will be all you need to solve for all the tempi in question 3. For question 4, the wording is a little confusing. Here are some hints:

  • 4a: first find the quarter note tempo of half = 96. Then treat the triplet eighth and the sixteenth note as the same rhythmic value (they equal each other from old to new). The new tempo will be slower than the old quarter note tempo (but faster than the old half note tempo).
  • 4b: focus on the common denominator rhythmic value between the dotted half note and the half note tied to an eighth note. If you plug and chug you are likely to end up with a faster tempo, but realize that if the new shorter duration equals the old longer duration, then the tempo is slowing down.** Adjust your ratio accordingly; the answer is a whole number, and slower than the original tempo.
  • 4c: the same is true of this ratio. What used to take x units now takes x+1. The new tempo is slower than the previous tempo.**

**Consider a two simple examples:

  • The tempo is quarter = 120.
  • To change to the new tempo, an old eighth note now equals a triplet eighth note. It used to take two subdivisions to complete one beat, but now it takes three subdivisions of the same length to complete one beat. Therefore, the tempo is slowing down.
  • 120(2/3) = 80. The old grouping was two (eighth notes); the new grouping is three (triplet eighth notes, that are the same duration as the old eighth note).
  • The tempo is quarter = 120.
  • The old half note equals the new quarter note. The old grouping is four eighth notes and the new grouping is two eighth notes, but the eighth notes are note equal across tempi. What took two beats now takes one beat, which is twice as long as the old beat 120(1/2)=60. Remember, if the old duration is equal to a new duration of shorter rhythmic value, then the tempo is slowing down. Adjust your ratio accordingly.
lectureNotes_musth4 musicTheory4

(musTh 212) Tempo Modulation and Polytempo

Last year’s post walks you through the basics. Look it over and make sure you understand the formula and how to use it for both tempo modulation (metric modulation to some) and polytempo. Just to include it here and reiterate:

The formula can be stated in a simple, easy to remember way:

original_tempo * (original_grouping_number / new_grouping_number) = new_tempo

For the ratio to work, the rhythmic value of both the original and new groupings must be the same. In other words, compare groupings of sixteenth notes to sixteenth notes, eighth notes to eighth notes, etc.

If you are trying to solve for polytempi, you will always compare to subdivisions of the stated reference tempo (the given metronome marking). You can always subdivide the reference tempo into the necessary rhythmic subdivisions to compare to the other tempi. In the Carter String Quartet No. 1, the reference tempo is for the quarter note in the cello part. The quarter note can be divided into sixteenth notes to compare to the second violin, into triplet eighths to compare to the first violin, etc.

If you are ever confused about which grouping goes first in the ratio, consider whether you are speeding up or slowing down. If you are speeding up, the smaller number will come second, making the ratio greater than one and increasing the original tempo via multiplication. If you are slowing down, the smaller number will be first, making the ratio smaller than one and decreasing the original tempo via multiplication.

lectureNotes_musth4 musicTheory4

(musTh 212) Rhythm and Meter in Post-Tonal Music

I want to include a chapter 6 clean-up to make sure all are clear about the major concepts. This post from last year summarizes the topics very briefly, except for polytempo and tempo modulation.

computerMusic3 lectureNotes_cm3

(maxmsp) Simple Additive Synth, patcher aesthetics…

I’ve uploaded a much-improved version of my simple additive synthesizer (2 oscillators). The patcher makes extensive use of send and receive objects, which function to both clean up the spaghetti tangle of patch cords, and provide a means for self-commenting code.

The core of the patcher is a two-oscillator additive synth, with function controls for amplitude envelopes.

MIDI input and other user interface controls, aside from the function editors, are located at the top of the patcher. A MIDI keyboard is used to supply the pitch (as a MIDI note number later converted to a frequency in Hz), and to trigger the attack and release sections of the envelopes. Note numbers from noteon messages are sent via stripnote to the s noteNumber object. noteNumber is received by both oscillator patches. Stripnote also passes the noteon velocity, which is sent to each function editor via s noteOn and used to bang (start) the function. Since each function editor makes use of a sustain point (indicated by the white halo around the dot), a next message is needed to move to the release portion of the envelope. All incoming velocities are sent from notein to the select object. Noteoff velocities of 0 are selected, and the resulting bang is sent via s noteOff to each function editor to trigger a next message. Notice how the send and receive objects are self-commenting the patcher? Since you have to label a send/receive destination, you can use a label that indicates what is being sent. I’ve color-coded all the send/receive objects so you can easily find the connections.

The ratio (multiplier) for the second oscillator frequency can be set with a float, sent via s partialRatio. Overall partial amplitude is addressed similarly via partialAmp. To the far right of the top portion there is also an input to set the overall time length of the function editors (via adrLength). Since the sustain will last as long as you hold down a key, this length only really applies to the attack, initial decay, and release times. The integer is sent to the setdomain $1 message, and the whole message is sent to each function editor.

There are two continuous controllers being used to set the detune amount, and the portamento time (portTime). The top integer of this portion can be used to tell ctlin to listen to a different controller number (119 and 120 work with my nanoKontrol). The cc input is scaled to an appropriate range (0. – 1. for detune, meaning a max of one half step; 0. – 1000. for portamento in ms), and then sent.

The first oscillator is very straightforward. noteNumber is converted from MIDI to frequency (Hz), packed with the current portamento time, and the message is sent on to line~ and eventually to the frequency input of a saw~. The function editor receives noteOn, noteOff, and adrLength messages. Its output is pairs of numbers in line~ format, sent to a line~, and then on to a *~ to control amplitude.

The second oscillator has the exact same function editor controls, but is more involved with regards to frequency. noteNumber and detune are added together and eventually sent to mtof. mtof can convert fractional MIDI note numbers to the appropriate microtune frequency. The detune amount is added to the note number, and the bang message is triggers the + operation when ever the detune amount changes. This allows you to update the partial frequency with detune information even while holding a note.

The detuned frequency is then sent to a multiplication object to be multiplied by the partial ratio. From there, the rest of the patcher is similar until you get to the extra *~ object for scaling the overall partial amplitude (since partials usually have less amplitude than fundamentals).

The output of both scaled saw~ objects are sent via an audio send object (send~) to the same receive~ destination, and then to gain~ object and ezdac~. It’s important to note that audio send~ and receive~ objects must be spelled out in full, not abbreviated as s~ and r~.