Composition Controls

Choose the program to be used to generate the composition.

rule type

The neighbor configuration for the WolframTones automaton

Each Rule Type in effect defines a completely different region of the computational universe. It is the first number in the Type.Rule.Seed specification for a WolframTones composition.

In a one-dimensional cellular automaton (Wolfram automaton), the new color of a particular cell depends on previous colors of a certain "neighborhood" of cells on the step before. The Rule Type specifies this neighborhood. Rule Type 7 (r=1) corresponds to Wolfram's "elementary cellular automata" (such as Rule 30), in which the new color of a cell depends on the previous colors of the cell and its immediate ("range 1") neighbors. Rule Type 31 (r=2) corresponds to range-2 Rules in which the color of a cell depends on previous colors of the cell its neighbors out to distance 2. Rule Type 15 (r=3/2) allows dependence on cells up to distance 2 on the left, and 1 on the right. General Rule Types allow dependence on noncontiguous neighbors. For Rule Type rt, the offsets of the neighbors are determined by Sort[(Quotient[#, 2](-1)^Mod[#, 2])&[Position[Reverse[IntegerDigits[rt, 2]], 1]]].

rule

The Rule number of the WolframTones automaton

The Rule number defines the program to use for the WolframTones automaton. It is the second number in the the Type.Rule.Seed specification for a WolframTones composition.

The Vary button searches for a new "nearby" Rule number.

The Show Variations button shows five variations using progressively more distant Rules.

The successive binary digits in the Rule number specify what color a cell will be when its neighbors have each possible arrangement of colors on the step before. The Rule number appears as the first argument to the Mathematica CellularAutomaton function. Even very similar Rule numbers can give very different behavior.

For all Rule Types, Rule numbers start at 0. The maximum meaningful Rule number is determined by the Rule Type. The general formula for Rule Type rt is 2^2^DigitCount[rt, 2, 1] - 1. For Rule Type 7 (r=1), the maximum number is 255; for Rule Type 15 (r=3/2) it is 65535; for Rule Type 31 (r=2) it is 4294967295. WolframTones automatically reduces Rule numbers to the correct range.

seed

The Seed number for the WolframTones automaton

The Seed number specifies the initial condition for the WolframTones automaton. It is the third number in the Type.Rule.Seed specification for a WolframTones composition.

The Vary button searches for a new "nearby" Seed, in which the colors of two cells are reversed.

The Show Variations button shows five variations in which progressively more cells are changed.

The number of binary digits in the Seed number specifies how many cells are in the WolframTones automaton; their values specify what the initial colors of the cells should be. With Seed s, the number of cells is Floor[Log[2, s]]. The values of the cells are Rest[IntegerDigits[s, 2]]. The number of cells determines the Height of the WolframTones automaton. (Changing the Seed number can therefore change the setting for Height, and vice versa.) The last (least significant) binary digit in the Seed number corresponds to the lowest musical note.

Seed number 2^h gives a Height-h WolframTones automaton with all cells white. Seed number 2^h + 2^Round[h/2] puts one black cell in the center.

height

The number of cells in the WolframTones automaton

The Height determines the number of cells to be used in the WolframTones automaton, or the number of different note levels in the musical score.

The Height determines the position of the first 1 in the binary digits of the Seed number, so that the Height slider is linked to the Seed number. If you increase the Height slider, the "newly created" cells in the Seed will be assumed white. If you decrease the Height slider, cells will be dropped at the "top" of the Seed. Note that since WolframTones automata are drawn left-to-right rather than top-to-bottom, their "height" corresponds to "width" in Wolfram's cellular automata in A New Kind of Science. The Show Evolution window shows evolution for a system with a large number of cells; it is not affected by Height.

cyclic boundaries

Whether the cells in the WolframTones automaton are taken to wrap around cyclically

Cyclic Boundaries determines what happens outside of the array of cells shown in the WolframTones "score." With Cyclic Boundaries on, the cells just wrap around, as if arranged cyclically on a circle. With Cyclic Boundaries off, the WolframTones automaton acts as if it has an infinite number of cells, but only some are shown.

With Cyclic Boundaries on, the WolframTones automaton is taken to have a total number of cells equal to the Height. The cells are assumed to be arranged so that (in a top-to-bottom orientation) the left neighbor of the leftmost cell is the rightmost cell, and vice versa. With Cyclic Boundaries on, the complete automaton has only a finite number of possible states--so that its evolution must eventually repeat. (See A New Kind of Science.) However, since the number of states is 2^Height, the repetition period can be extremely large. The only place where it is often small is in Signalling-style compositions. With Cyclic Boundaries off, cells outside the region defined by the Height are always assumed initially to be white.

show evolution

A large-scale view of the evolution of the WolframTones automaton

Pressing Show Evolution brings up a window showing a large-scale evolution of the current WolframTones automaton. The evolution is oriented to go from top to bottom (as in A New Kind of Science).

Show Evolution is always 250 cells wide, and uses a random initial condition. It gives a global view of typical behavior in the current WolframTones automaton, but will not show the specific pattern generated by the Seed actually used for the current composition. Press the Show Evolution button again to get a different random initial condition. Note that with Cyclic Boundaries on, the behavior of the automaton in the region of Height cells may be significantly different from the much larger Show Evolution case.

Specify how musical instruments should be used to render the composition.

instruments

Instruments to use for each Role in rendering the WolframTones composition

WolframTones supports all standard general MIDI instruments (with the exception of SFX "sound effects").

None will play no Instrument in a specified Role. You can give the same Instrument for multiple Roles. If you want to hear what a single Role sounds like, just set the Instruments for the other Roles to None. All the Instruments listed (including bells and drums) support the full range of pitch levels, although some of them will not sound good outside of a particular range. Note that in ordinary usage of the WolframTones site, all compositions are transmitted in MIDI form, so that the final rendering is done on the local computer or phone. Particular compositions or Instruments may sound different on different rendering devices.

roles

Which parts of the underlying WolframTones automaton pattern will be played by each Instrument

Each successive Role listed effectively "picks off" certain black cells from the underlying automaton pattern to be played as notes, leaving other black cells for subsequent Roles. The notes used by different Roles are shown in different colors in standard WolframTones "scores."

Different Roles in effect represent different algorithms for picking out features in the automaton pattern. WolframTones includes many such algorithms; different ones are typically chosen for different musical styles.

None plays no notes. Polyphonic plays all notes that satisfy certain basic WolframTones criteria; it typically plays many notes at a time. Lead n plays one note at a time, allowing several choices for how the note should be picked out from black cells in the underlying pattern. Chords n plays a few notes at a time. Bass n plays one note at time, placing it at a lower pitch level. When Polyphonic is listed as a Role, it effectively "uses up" all remaining notes, so that no Roles listed below get any notes to play.

percussion

What drumming should be added to a composition

WolframTones includes a large number of algorithms for deriving drumming from underlying automaton patterns. Each algorithm in effect specifies a different procedure for determining what configuration of notes in each beat should produce what drumming.

Different styles of music typically involve characteristically different drumming patterns. In WolframTones all Percussion choices are nevertheless in principle available for all styles--though "crossing" drumming patterns can lead to unusual results.

None gives no drumming. Metronome gives one pulse per beat. Most choices of Percussion do not just repeat fixed drumming loops; instead they derive the drumming locally at every beat using special WolframTones algorithms. Each algorithm typically produces a certain number of drum sounds in the course of each beat. In most styles of music, it's good to have the Notes Per Beat align with the number of drum sounds per beat. Many WolframTones drumming algorithms use a sequence different drumming patterns at different beats, effectively defining measures that span multiple beats.

Specify what Musical Pitch space should be used.

musical scale

What type of Musical Scale should determine the sequence of Musical Pitch levels

The successive Height levels in a WolframTones "score" are mapped to a sequence of Musical Pitch levels. Once the overall Musical Pitch has been determined, the successive Height levels are taken to correspond to successive notes in a given type of Musical Scale. The overall Musical Pitch determines the root note of the scale. The type of Musical Scale is determined by specifying the subset of the 12 semitones in an octave that it includes. The Play Scale button plays the currently selected Musical Scale using the first instrument listed under Instruments.

The WolframTones Musical Scale menu lists all standard named scales, in all major standard musical traditions. The most common scales traditional to Western music are Major and Minor. Any subset of semitones in the octave in principle specifies a Musical Scale. The menu field will be blank if there is no standard name for it. Any ordinary octave-based scale in the 12-tone system can be specified by a number between 2048 and 4095: a semitone is included where there is a 1 in the corresponding position in the sequence of binary digits (IntegerDigits[s, 2, 12]), and is excluded if there is a zero. (Such "code numbers" for musical scales are analogous to Wolfram's rule numbers for cellular automata.) The usual Major scale has number 2773. Note that you can edit the explicit number given under Musical Scale. (Numbers below 2048 or above 4095 either repeat standard scales, or correspond to musical scales that do not repeat in each octave.) When you specify a Musical Scale, the notes it contains are repeated in successively higher octaves until enough notes are available to cover the Height specified for the score. WolframTones automatically adjusts the names of notes depending on the root note specified by the Musical Pitch. Standard conventions are used to determine whether notes will be denoted as sharps or flats.

musical pitch

The Musical Pitch of the lowest note in the WolframTones score

The Musical Pitch specifies the pitch of the root note in the Musical Scale. Successive pitch numbers correspond to successive semitones, with 60 being Middle C (the C note in the center of a piano keyboard).

The Musical Pitch slider spans four octaves: from three below Middle C to one above. WolframTones uses standard MIDI equal temperament, in which successive semitones correspond to frequencies that differ by a factor of 2^(1/12). When you change Musical Pitch, the names of notes available in the Musical Scale change, with sharp and flat designations being made according to standard conventions.

Specify the speed and length of the composition.

tempo

The rate at which notes should be played

The grouping of notes into beats helps determine the "feel" of the rhythm of a composition. Different parts of a beat are generally treated slightly differently, particularly with respect to drumming.

The product of Beats per Minute and Notes per Beat determines the time allocated to each horizontal position in the array of cells in the WolframTones score, corresponding to each step in the evolution of the underlying WolframTones automaton. How "fast" or "busy" a composition will seem depends both on its Tempo settings, and on the distribution of lengths of notes that it contains. The Beats per Minute slider is set up to give the traditional metronome sequence of tempos. You can also edit the explicit numerical values for the Tempo settings.

duration

The total Duration of the composition.

Changing the Duration of a composition changes the number of steps in the evolution of the underlying WolframTones automaton.

The number of automaton steps is equal to the product of the Duration (divided by 60 to convert to minutes), the number of Beats per Minute, and the number of Notes per Beat. Each step in the automaton evolution defines a column in the WolframTones score. When there are too many steps, the later steps are typically truncated when the score is displayed.