Modulo Notation Features


A Modulo Notation stave has only two stave lines. To allow a greater range of notes to be represented, temporary stave segments can be added above or below the stave. A left hand stave and a right hand stave can often be replaced by a single stave if a compact notation is considered more important than keeping left and right hand separated. See macfarlane.pdf.

One could also let the distance between the RH stave and the LH stave in a grand stave be precisely such that a temporary stave segment placed between the staves could belong to either stave. In this case the LH clef and the RH clef must be consistent in such a way that they refer to the same Do-range (octave) for the stave segment between the staves (which can be used for either LH or RH).

Temporary Stave Segments

Temporary stave segments extend the range of a stave. Stave segments should not be made longer than necessary, but when two stave segments at the same level are closer together than six stave units (a note head, for comparison, is two stave units tall), they should be replaced with one continuous stave segment. The (currently suggested) distance of six stave units is measured between where the horizontal lines of the first stave segment end, and where the lines of the second stave segment begin.

Stave segments should never extend past a bar line. Instead, start a new segment in the measure that follows.

If all of the topmost stave segments above a stave, and along one complete line of music, do not contain any visible objects (such as stems, slurs etc.) higher than the note head of Pa, replace all those stave segments with compressed stave segments (cf. macfarlane.pdf). Stave segments below the stave should be treated conversely. The compressed stave segments will make it possible to bring staves closer to each other; or to place lyrics closer to the stave.

Bar Lines

There are only three types of bar lines: normal bar lines, double bar lines, and ending bar lines. Bar lines should never extend between staves. Although not strictly a bar line, there is also a delimiter used in polyrhythms. It should consist of four vertically aligned points: two between the stave lines, one just above the upper stave line, and one just below the lower stave line.


A traditional treble clef makes the stave begin with Do4. A clef that looks like a horn indicates that the stave begins with Do3. The third type of clef looks like a lyre and indicates that the stave begins with Do5. For clefs having an associated number, the number directly indicates the Do-range (= octave) of a stave. See chromatic.pdf 1b, which shows all available clefs.

When the Do-range disposition changes (by a change of clef or all'ottava), any previous specifiers (accidentals) continue to affect note heads along the same vertical position on the stave, regardless of the fact that the notes now sound in a different Do-range.


The All'Ottava number indicates how many prime zero intervals (octaves) to transpose (+ = up, - = down), followed by the usual dashed line with a vertical dash at the end (cf. chromatic.pdf 1b).

When the Do-range (octave) disposition changes due to All'Ottava, any previous specifiers continue to affect note heads on the same vertical position on the stave, regardless of the fact that the notes now sound in a different Do-range.

Key Signatures

Key signatures simply state the SaLaTa note name that begins a "natural scale" ( = major scale). The key signature is usually placed above a clef and has a characteristic brace. A key signature doesn't imply a tonic, it just specifies a portion of seven notes along a continuous chain of n7 steps ( = perfect fifths). The signature can also have one of the prefixes d, b, n (d = dark, b = bright, n = natural). Consult chromatic.pdf and macfarlane.pdf for examples.

The first occurrence of a "foreign note" (that is, a note that is not diatonic to the key signature), is marked with a specifier (accidental) that stays valid until the end of a measure. There are two types: up-comma (filled figure 6), down-comma (filled figure 9). A specifier only affects subsequent notes at the same vertical position on the stave.

There is never a specifier of the above kind being applied to a note that belongs to the key signature. The system is relative to the key in the key signature. This means that you can specify which note the foreign note is closer to (in accordance with Pythagorean tuning). If the key signature is nDo (C major), for example, the note Pa (between Do and Ro) can have either an up-comma to show that it is closer to Ro (that is, Pa = bPa = C#), or a down-comma to show that it is closer to Do (that is, Pa = dPa = Db).

Although extremely rare: What if you want to have bFa instead of nFa (that is, E# instead of F) when the key signature is Do, for example? The microtonal signs that push notes up or down by commas (> and <) can be used for this. Consequently, bFa (E#) would be written as a Fa with a > in front of it, in the key of Do.

The signs > and < push notes up or down a comma according to Pythagorean tuning (cf. the Nydanalyzer). For example, if a note is originally bPa (C#), and you put a < in front of it, it should instead be interpreted as dPa (Db). These microtonal signs (cf. chromatic.pdf 3b and 3c) will only affect intonation. The microtonal signs (> and <) are totally independent of the ordinary specifier system (comma signs). A microtonal sign is only valid for the one note head that it targets, and thus has no effect on subsequent note heads.

Put the comma closest to the note head if, for instance, a < and a comma both affect the same note head.

Courtesy specifiers (that is, the same specifier is yielded more than once within the measure) are allowed. Whenever there is a change of key signature, all and any previous specifiers are automatically canceled.

A specifier only affects note heads of the same kind. For example, if Ta (= B) has a specifier, any subsequent notes Do will not be affected although the vertical position on the stave is the same. If you want to write Ta and Do together on the same stem, put them instead on separate stems and join them with a horizontal bracket; a specifier (or microtonal sign) can now be fitted between the note heads if necessary (thus only affecting the second note head). Written this way, both note heads could have individual specifiers (or microtonal signs) if necessary.

In the event that you want to stop using key signatures and specifiers at some point in a composition, simply write a new key signature brace in which the note name is replaced with X. The use of key signatures could then, of course, always be resumed later on in the composition.

It is okay to change key signatures more often than you would in traditional notation. If all information from traditional notation is to be preserved, the original key signature could be added in parentheses.

The fact that specifiers are relative to the key signature makes all keys equal. So, for example, in the MacFarlane Spring Song excerpt (macfarlane.pdf), you have a Bb that is reset to B in traditional notation. In Modulo Notation, that B (Ta) gets an up-comma; which is very logical actually, because it shows that Ta is closer to Do (B is a leading-tone to C in traditional notation). Unlike traditional notation, the same behavior now applies to all keys.

The key signature shows what section, in the sequence of seven steps (chain of perfect fifths), will be mostly used. Since the key signature doesn't say anything about the mode, or where the tonal centre is, this will have to be deduced by analyzing the music. One can nevertheless always specify the mode as part of the song title, in the way that classical music often does. The mode could be written in parentheses below the title, and does not have to be limited to only "natural" or "d3" mode. For example:

Hear the Birds' Twitter

(Fa n7 mode)


Accidentals are referred to as specifiers. See Key Signatures.

Time Signatures

The table below shows some examples of how traditional time signatures could be translated.

12/8, 3/8, 2/16, 3/16
22/1, 2/2, 2/4, 4/8, 5/8, 6/8, 7/8, 9/8, 4/16, 6/16
33/1, 3/2, 3/4, 9/16
44/2, 4/4, 8/8, 12/8, 8/16, 12/16
66/2, 6/4

Time signatures could also be written as sums. For example, 5 could be written as 3+2 or 2+3. Alla breve (traditionally written as a C with a vertical line through it, or 2/2) could be written as 2+2

If the number of beats varies from measure to measure, time signature numbers could be separated with slashes. For example, 2/3 would mean that the time signature for an individual measure could be either 2 or 3.

If the number of beats varies from measure to measure, but all measures are equal with respect to duration, then the time signature numbers could be separated with equals signs. For example, 2=3 would mean that there could be either 2 or 3 beats per measure, but that each measure takes up the same amount of time regardless. If a BPM (beats per minute) figure is added, it could be preceded by, for example, |3|=> (which is then followed by a small note, an equals sign, and the BPM figure). This would indicate what the BPM figure would be if the number of beats within a measure happens to be equal to 3. This clarification is necessary because the BPM may now vary from measure to measure.

When time signature 1 replaces 5/8, then each measure could contain one beam that is broken up into two fractions. The first beam fraction could contain three stems, and the second could contain two stems. Alternatively, two stems in the first fraction could be followed by three in the second fraction. Traditional time signatures 5/8, 7/8, 8/8, 8/16 and 9/8 can be treated in a similar way.


The traditional whole-note lacks a stem. A stem, however, is useful for gathering note heads into chords; or when you want to assign note heads to different parts with opposing stem directions (different parts can be played with left and right hand, respectively, on some instruments). It will also be clear which note heads are affected by diagonal tremolo bars across a stem.

Giving each note a stem also frees stemless note heads to instead be used as grace notes. Consequently, notes with clearly defined durations will always have stems. Stems also make note heads more noticeable. And lastly, note heads of ordinary size and shape can be used for all notes.


A beam represents a beat. Every beam has a smallest time unit being represented by a stem without any dot or triangle (or number in italics greater than 9). Any courtesy number on a beam tells us how many of those smallest units will fit within the beat. A dot next to a stem represents a note/chord or rest whose duration equals two time units. A triangle means three time units, and so on. Ties are never used within a beat.

It is easy to understand how long each note in a beam is supposed to be. For example, if a beam has a stem with a triangle followed by a stem with a dot, then just count 1 2 3 1 2

Multiple beams to subdivide a beat is never used in the new notation.

Beams can be broken up into smaller fractions to show how notes belong together rhythmically (cf. chromatic.pdf 2c). It could also be done to prevent beams from obscuring other objects. In the latter case, a dashed arc that encompasses all notes in the group could show that the beam was split for this reason only. The dashed arc would not imply legato. A beam is always cut off with a vertical cut.

Beams/beats can be concatenated by so-called connectors, to create groups of notes (cf. rhythm.pdf and chromatic.pdf 2c). The lines that are used for this could also have a slant. The part of a stem that sticks out on the other side of the beam could be extended. If two adjacent beams should be connected, and one of the beams has stems that go in the opposite direction, the connector could go from the extended stem of one of the beams, and then only embrace the (nearest) note head of the other beam. This is basically the same approach as when a beam is connected to a single note that represents one whole beat (that is, one without a beam).

A minimum of one whole beat should be used in anacrusis (upbeat). If the beam would not be complete, note values would become undetermined. Another possibility is to use a beam courtesy number and simply leave out the first part of a beam.

Ties and Slurs

Tied notes do not repeat the original note head. Instead only a stem without a note head is shown.

Slur arcs would only indicate legato.

An arc that finishes with an arrowhead is called a pointer. It means that notes that can be tied should be tied. Any remaining notes should be slurred. If the pointer arc embraces a number of notes, those should all be kept sounding until the note or chord that the arrowhead points to is reached.

Phrasing slurs should rather be replaced with ampersand marks (&) between longer phrases. Such ampersands should preferably be placed below staves. They could be seen as a replacement for lyrics that would otherwise indicate phrases. To signal that the application of ampersand marks has ended, write three small and vertically aligned points instead of an ampersand mark. If the ampersands are used for phrases, slurs can be devoted solely to indicate legato. Legato in itself turns something into a phrase, but when the ampersands are employed, they do not infer legato.

For the unusual combination of tied, normal, and slurred notes: in the chord that a pointer points to, mark the notes with asterisks that should be neither tied nor slurred. Explain what the asterisk means in a message above the stave.


The type of rests that lasts for one, or more, undivided beats has a short stem-like feature that can be synchronized with the stem direction of a part. This makes it easier to see which part the rest belongs to.

Multi-measure rests look like this (the digit indicates the number of measures):


Multi-measure rests should be placed between the two stave lines.

Arpeggiated Chords

In traditional notation an arpeggiated chord can be written as successive notes with individual ties that all end up at the completed chord. In Modulo notation it is possible to use only the tools already provided: so, on each successive stem, all sounding note heads accumulated thus far would be shown. Between the stems there would then be pointers (arcs with arrowheads). A simpler approach would be to write out the successive note heads on individual stems, and draw a slanted undulating line between the first and the last note head (slightly below the note heads if stems are upwards directed). The completed chord would thus not be shown, only the note heads that make up the chord, on their individual stems. The time value associated with the last stem decides for how long the resulting chord will sound.

Small Note Heads

Small note heads in traditional notation have sometimes been used for:

A small note head in Modulo Notation looks somewhat like the left or right half of an ordinary note head (cf. chromatic.pdf 1e). This makes small note heads clearer than if they were simply miniature note heads.

Asterisks are recommended to make a leading voice distinct from other note heads in a chord, instead of employing small note heads. Small note heads should never be used for grace notes.

Grace Notes

Grace notes (cf. chromatic.pdf 1c and macfarlane.pdf) will be written as ordinary note heads without stems, to which a slur is added. The long grace note should not be used. The short grace note borrows time from the foregoing note/chord. Various text messages can be added to describe whether grace notes should be played very fast or moderately fast.

Grace notes can alternatively be written out explicitly in the form of ordinary beamed notes. Use the L-shaped symbols from traditional notation if it should be marked out which notes to play with left and right hand, respectively (allows a series of grace notes to be written on the same stave instead of being split between the RH and LH stave).

Horizontal brackets can be used if two stemless note heads should be played simultaneously. A dotted line could connect consecutive short grace notes if the interval between them is very big.


It is recommended that a normal-size note head, without a stem, is written in parentheses after the principal trill note, to represent the auxiliary trill note. There can also be slurred note heads without stems after a trill note (cf. macfarlane.pdf).


Tremolo should be written in the same style as trills, but with "tr" being replaced by "tm" (a wavy line could also be added). If necessary, tremolo bars across the stem can indicate the number of repetitions: one tremolo bar = 2 tones, two bars = 4 tones, three bars = 8 tones. In traditional notation a beam is supposed to be seen as one of the tremolo bars when calculating the note value. This is, however, not relevant in the new notation. Furthermore, tremolo bars between stems should not be used. All repeated notes are carried out within the duration that the note would have had without the tremolo bars.


Traditional tuplets and their associated rules are not used.

BPM Tempo Indication

A small note with a black note head, followed by an equals sign and a number, would be all that is needed to indicate tempo. The note always represents a beat. The figure indicates how many beats there are per minute. There is no longer any need to use notes having a specific note value for this kind of tempo marking.

Note Heads

How to arrange note heads in chords having an upwards directed stem:

Place the lowest note head on the left side of the stem. If the interval to the next note head is two steps (one step equals a semitone in traditional notation), always place that note head on the right side of the stem; then continue placing note heads on the left side of the stem. If the interval becomes two steps once again, somewhere higher up on the stem, make sure that the note head is again placed on the right side.

When a chord starts with a note head on the left side of the stem and the interval to the next note head is instead one step, that second note head should likewise always be placed on the right side of the stem, but in addition to that, the note head itself should always be rotated 90 degrees (that is, use a note head that is mirrored with respect to the y-axis). Any additional note heads can then be placed on the left side until possibly an interval of one or two steps should occur again.

Note heads on the left side of the stem are, by the way, never rotated. In the event that there are two successive 1-step intervals, the latter note head is placed on a separate stem to the right of the first stem (any stem flag should be copied over to the new stem). Continue after this on the left side of the first stem if there are any additional note heads. The two stems are then connected by a horizontal square bracket to show that they are to be played simultaneously.

How to arrange note heads in chords having a downwards directed stem:

Place the highest note head on the right side of the stem. If the interval to the next note head is two steps, always place that note head on the left side of the stem; then continue placing note heads on the right side of the stem. If the interval becomes two steps once again, somewhere lower down on the stem, make sure that the note head is again placed on the left side.

When a chord starts with its topmost note head on the right side of the stem and the interval to the next note head is instead one step, that second note head should likewise always be placed on the left side of the stem, but in addition to that, the note head itself should always be rotated 90 degrees. Any additional note heads can then be placed on the right side until possibly an interval of one or two steps should occur again. Note heads on the right side of the stem are, by the way, never rotated. In the event that there are two successive 1-step intervals, the latter note head is placed on a separate stem to the right of the first stem (any stem flag should be copied over to the new stem). Continue after this on the right side of the first stem if there are any additional note heads. The two stems are then connected by a horizontal square bracket to show that they are to be played simultaneously.

With the above approach, the visual recognition of intervals will be facilitated. The slant of the note head, and whether it is placed on the left or right side of the stem, gives an indication of what kind of interval it is. Note heads on the same side of the stem are at least three steps away from each other. Note heads on the opposite side of the stem are either 1-step or 2-step intervals; the slant of the note head will tell which one it is.

If two note heads, such as, for example, Ta and Do, are placed next to each other on the same stem, it would be difficult to know which of the two note heads a comma-sign or microtonal sign is meant for. The solution to this is to put a small slash ( / ) ahead of the two note heads. Any sign placed on the left side of the slash will affect the first note head ( , / ). Any sign placed on the right side will affect the second note head ( /, ). Both note heads could be addressed if, for example, the first should have a microtonal sign, and the second a comma-sign ( < /, ).

Note heads being used mutually by two parts:

Two parts, with stems that go in opposite directions, should always share the same note head in the new notation when the interval is 0 steps and each stem only has one note to represent. This is made possible because note heads no longer are associated with note value indications (cf. dotted note heads, and solid vs. hollow note heads, in traditional notation). When at least one of the stems has more than one note to represent, note heads should never be shared.

When note heads from two parts are close to each other:

When two parts, with stems that go in opposite directions, have note heads that cannot be written strictly one above the other (for example, Ta with a down-stem and Pa with an up-stem), the note head of Ta should be placed to the left of note head Pa.

Stave Braces

Braces are used to group staves together (in a grand stave or a score). Modulo uses special braces (cf. chromatic.pdf 1f). As shown, braces can be joined together with vertical lines. It's also possible to insert a wedge (<) halfway down the brace when an instrument designation affects a whole group of staves. An important distinction is that braces are also applied at the right side of a stave. The reason for this is to make it clearer that the staves belong together, since bar lines are not drawn out between staves.


A small flageolet circle and ordinary note heads should always be used instead of the traditional notation rhombic note head. See chromatic.pdf 1d. If individual note heads should be targeted, consider also using asterisks.

Accent Marks

It is recommended that accent marks (>) are drawn in such a way that the lower line becomes horizontal. This avoids the possibility of having microtonal intonation signs and accent marks confused (cf. chromatic.pdf 2c).

Microtonal Notation

The new intonation signs, > and < etc. (cf. chromatic.pdf 2b, 2c) assume Pythagorean tuning (cf. the Nydanalyzer), and conform to 53-ET. The intonation signs allow you to pinpoint any of the 53 notes per octave associated with 53-ET. The pierced intonation signs, that represent 11 cents, make 106-ET possible - that is, you can also access the notes that fall right between the dots on the Nydanalyzer.

The Pythagorean 53-ET intonation scheme is the default system. Other tuning schemes where, for instance, bPa is considered lower in pitch than dPa, could also be employed, but then this should ideally be explicitly declared.

Strictly quarter tone music, that would assume equal-tempered tuning, could use >> for quarter tone up, and << for quarter tone down.


Asterisks can be used as a multipurpose tool. It's possible, for example, to mark out a melody line that is hidden inside chords. The function of the asterisk should thus be explained in a text message above the stave, for example, like this: * prima voce

Tone Clusters

Tone clusters can be written as two separate chords that are joined by a horizontal bracket (cf. ”Note Heads” above). A more condensed way to write a tone cluster (and likely unique to Modulo notation) could be to have two triangular note heads on a stem, and let those note heads point towards each other. All notes in between the two note heads are then assumed to be included.

Breath Marks

A breath mark should be written as a sign that resembles a drop instead of a comma sign. This is suggested because comma signs may be frequently used in Modulo Notation as specifier/accidental signs. The pointy part of the drop should point downwards.

Jump Instructions

Modulo Notation has its own system to manage jumps between various sections in the music (cf. chromatic.pdf 1g). This system has the capability to replace the following notions in traditional notation: repeat bars, prima/seconda volta brackets, and measure repeat signs. It will also replace various Italian terms and instructions related to Segno and Coda. Any degree of complexity can be expressed with the new system without ambiguity.

The new system consists of jump instructions and anchors. A jump instruction has an arrow pointing in the direction to jump, followed by a number that indicates an anchor. For example: <-3, or ->5.

The anchor is a number followed by a colon. The anchor shows the point from which to continue playing after the jump. For example: 3:

Jump instructions and anchors always appear at a double bar line, and are written in a bold typeface, above the stave.

In the event that a jump instruction collides with an anchor, the anchor is written above the jump instruction.

Jump instructions are always carried out in numerical order: start with 1, then 2, and so on.

If there is more than one anchor at the same place, separate anchors with comma signs (this applies to jump instructions, too), like so: 3,4,6:

Instead of writing, for example, 2,3,4,6:, it's possible to just write 2-4,6:

If a portion should be repeated an arbitrary number of times (not all verses in a song may have to be sung), then the jump instruction should look like this: <-5+

and it means that one is supposed to jump to anchor 5 as many times as one wishes. After the last jump to anchor 5, one would start looking for the next jump instruction (in this case, number 6).

There is also a jump instruction that looks like a T rotated 90 degrees clockwise, followed by a number. It means: jump to the end of the piece/movement. In traditional notation it corresponds to "Fine".

Traditional notation also has something called vi- -de, indicating that a portion could be left out. In the new system, this can be achieved by putting the jump instruction (-> followed by a number) in parentheses. The corresponding anchor should then also be put in parentheses.