Musical Logo Widget
This widget creates musical logos using a simple Markov process. You specify the allowed transitions between any melody note (row) and its successor (column). The computer generates the logo by randomly selecting from the pool of transitions allowed by your settings. An "ear training" setting is provided in the count-off dropdown menu which challenges you to sing along with the logo after just one hearing. The traditional solfège (or solfeggio) syllables are displayed and can be incorporated into the exercise.
The mathematical model behind this melody-generating widget is known as a Markov process or Markov chain. Markov processes describe systems that unfold probabilistically as opposed to deterministically. Also germane to Markov processes is the notion that the future state of the system is determined exclusively by the current state, that is, with no knowledge of or reference to the system's past history.
Each row of the GUI matrix represents a single pitch of a C major scale which could appear in a logo. You itemize the notes that are allowed to follow the current note by clicking in the desired columns. Since a common compositional device in musical composition is theme and variation, Markov processes are simultaneously a natural fit (variation) and an anathema (no reference to prior states). The author's motivation was not so much to create a tool for composition but rather a tool to dislodge him from his compositional habits.
Using the widget to generate sight-singing exercises was a natural outgrowth of the widget's ability to compose melodies that ranged from mundane to unusual. If you're new to ear training or solfège singing do not be afraid to start with a very small set of choices as shown in snapshot 1. A simple way to create a blank slate from which to start is to click the "one pitch" button as shown in snapshot 2. From this setting gradually add additional pitches and rhythms. The ear training mode can be found listed in the "count-off" dropdown menu. In this mode the logo is played twice. It is assumed you will either sing the logo the second time, or for those vocally challenged, transcribe the melody to score paper.
The "ti→ do" preset tries to force the melody to a resolution if it hits the leading tone (ti syllable). This preset also eliminates the tritone (fa→ ti) transition; see snapshot 3.
The rhythms are purposely specified as fractions of a whole number to allow you to hear the melodies in 4/4, 2/4, or cut time as you prefer—a hemi-demi-semi-quaver by any other name would sound as sweet.
With some judicious choices you can force a specific logo out of the widget. Snapshot 4 uses the "GuitarMuted" instrument setting to produce logos reminiscent of the famous Maxwell House Coffee logo of the 1960s. Snapshot 4 is the famous "NBC" logo. Snapshot 5 is the opening motif of Beethoven's Fifth Symphony. Notice in the NBC logo of snapshot 5 the key center is no longer C major but more naturally heard as F major. Unfortunately, the widget is not aware enough to rename the syllables from do-la-fa to the more appropriate sol-mi-do. In music pedagogy circles this is known as the fixed-do system. Alternatively, in a movable-do system you would honor the tonal functionality of the pitches and relabel them sol-mi-do as you sing the pitches.
After generating a logo, you can replay the logo by hitting the triangular-shaped play button provided in the lower-left corner of the piano-roll display. Curiously enough, if you play any one logo repeatedly you might hear it as changing in detail. 2500 years ago the Greek philosopher Heraclitus observed that "you cannot step into the same river twice". And so too it is with these logos. You will subjectively hear the logos change as they transition from new and novel on their first playback to old and familiar on subsequent playbacks. They go from unexpected and startling to anticipated and inevitable. Initial novelty quickly becomes old hat. Foreground details move to the background, and vice-versa. It was this phenomena that led the author to conceive of this widget as an ear training exercise generator. Until you can sing a melody, have you really heard it? Does not singing demand a more intimate relationship with the notes than mere passive listening? Singing along with the melody adds a third layer of familiarity, a third layer of depth. As John Donne observed—in a slightly self-deprecating frame of mind—while noticing his depth of insight growing, "And I, which was two fools, do grow to three". Or perhaps more to the point is the "new knowledge of reality" that Wallace Stevens speaks to in his poem "Not Ideas About The Thing, But The Thing Itself".
"Musical Logo Widget"
Wolfram Demonstrations Project
Published: March 7 2011