Modulo Notation Features


A Modulo Notation stave has only two stave lines. To allow a greater range of notes to be represented, temporary so-called stave segments (rectangles with rounded corners) can be added above or below the stave.

Temporary Stave Segments

Stave segments (rectangles with rounded corners) can extend the range of a stave. Stave segments should not be made longer than necessary. However, when two stave segments (at the same level) are closer together than approximately six stave units (a note head, for comparison, is two stave units tall), they should be replaced with one continuous stave segment.

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

Staves can be brought closer together by only showing the upper or lower part of a stave segment (cf. macfarlane.pdf).

Bar Lines

There are only three types of bar lines: normal bar lines, double bar lines, and ending bar lines. Bar lines are always only four stave units tall. That is, they are never used for connecting staves.


A clef in Modulo notation indicates the Do-range (octave) for a stave. A clef only affects one stave. A clef should always be provided for each stave at the beginning of each new line of music. Whenever there is a clef change, the clef turns into an arrow shape to show whether pitches go up or down with respect to the latest clef on the same stave. A clef at the beginning of a new line of music will point up or down, too, if the change happened to occur at that point. Courtesy clefs are not used. See chromatic.pdf 1a

When a clef change occurs on a stave, all previous specifiers on that stave and within the measure will cease to be valid. All kinds of arcs (slurs, ties, pointers) will not cross the clef. Instead, arcs will be split in the same way as when a line of music has a line break. A clef should not be inserted between stems in a beat.


Traditional All'Ottava with a dashed line is not used in Modulo notation. Instead, clefs (or possibly asterisks) should be used.


A key signature, in the form of a key symbol, simply states the SaLaTa note name that begins a "natural scale" ( = major scale). The key symbol text, within its characteristic brace, is always placed above the clef at the beginning of a line of music. The key symbol only affects one stave. A key symbol doesn't imply a tonic, it just specifies a portion of seven notes along a continuous chain of n7 steps ( = perfect fifths). The key symbol text can also have one of the prefixes d, b, n (d = dark, b = bright, n = natural). Consult chromatic.pdf and macfarlane.pdf for examples.

Whenever there is a key symbol change, the key symbol text will be written in italics. A key symbol at the beginning of a new line of music will have its text in italics, too, if the change happened to occur at that point. Courtesy key symbols are not used. When the key symbol changes on a stave, all previous specifiers on that stave and within the measure will cease to be valid. A key symbol should not be inserted between stems in a beat.

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), and down-comma (filled figure 9). A specifier only affects subsequent notes of the same color and 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 nDo, 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 a microtonal sign 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.

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 write Ta and Do together on the same stem, write a small slash (not much bigger than a note head), and write the specifier (or microtonal sign, or asterisk) to the left, or to the the right of the slash, depending on which of the two note heads should be affected.

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 a question mark (?). The use of key signatures could then, of course, always be resumed later on in the composition.

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 thus be written inside parentheses below the title. For example:

Hear the Birds' Twitter

(Do n7 mode)

Do n7 mode is the same as G Mixolydian in traditional nomenclature (cf. the section on Terminology below).


Pitch Set = a set of pitches.
Mode = pitch set + instructions on how to use those pitches. For example, indicate the tonic, etc.
Scale = a practical tool to describe a pitch set, or a mode, or a key.
Key = a pitch set comprised of seven contiguous note names taken from the sequence of seven steps (chain of perfect fifths).

Examples of Pitch Sets:
nDo Natural (Do Ro Mo Fa Sa La Ta)
nDo Pentatonic (Do Ro Mo Sa La)

Examples of Modes:
nDo n0 mode • C major mode
nDo n7 mode • G mixolydian mode
nFa n9 mode • D natural minor mode
nFa n9 melodic mode • D melodic minor mode

When we write "nFa n9" to describe a mode, as in the example above, we mean the key of nFa, where step 9 (Ro) is made the tonic.

Examples of Scales:
nDo natural scale • C major scale (pertains to pitches)
nDo n0 scale • C major scale (pertains to mode)
nFa n9 scale • D natural minor scale (pertains to mode)
nFa n9 melodic scale • D melodic minor scale (pertains to mode)

Examples of Keys:
Key of nDo • Key of C major, or Key of A minor
Key of nFa • Key of F major, or Key of D minor

Time Signatures

A time signature, or meter, is written inside square brackets. It could contain any text that describes the meter, but it would normally only consist of a digit that indicates the number of beats per measure, for example: [3]. It is also possible to show how the beats within a measure should be grouped together. For example, [2+2] would be the same as 2/2 in traditional notation (cf. Alla breve, traditionally written as a C with a vertical line through it). [3+2] or [2+3] could be specified when there are five beats per measure, and so on.

The meter should only be provided above the topmost stave in a system of staves. A meter should not automatically be repeated when a new line of music starts. A new meter would be placed above the beginning bar line of a measure. Here are some examples:

[?] The number of beats per measure is not defined and can vary.
[=] The number of beats per measure is not defined and can vary. Continue with measures having the same duration as the last measure before this meter (that is, if there was a preceding measure). The duration of a measure is constant, regardless of the number of beats per measure.
[!] The number of beats per measure is not defined and can vary. Continue with beats having the same duration as a beat in the last measure before this meter (that is, if there was a preceding measure). Measures can thus have durations that differ.
[3] There are three beats per measure. Continue with measures having the same duration as the last measure before this meter (that is, if there was a preceding measure).
[3!] There are three beats per measure. Continue with beats having the same duration as a beat in the last measure before this meter (that is, if there was a preceding measure).
[3+2] There are 3+2 beats per measure. Continue with measures having the same duration as the last measure before this meter (that is, if there was a preceding measure).
[3+2!] There are 3+2 beats per measure. Continue with beats having the same duration as a beat in the last measure before this meter (that is, if there was a preceding measure).

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

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.

Metronome marks, or BPM figures, can be the same as in traditional notation.


Stems can be of three kinds: note/chord stems, tie stems, or rest stems. A stem always has a basic stem value that can also be augmented with dots and triangles, or numbers. Those attributes will indicate the duration of a stem.

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 one beat. A stem that makes part of a beam can have stem value attributes (dots, triangles, or numbers in italics greater than 6). A stem without such an attribute represents the smallest possible division of the beat. Stems that do have stem value attributes are multiples of that smallest time unit. A dot associated with a stem represents a note/chord/tie/rest whose duration equals two time units. A triangle means three time units, and so on. If there is a courtesy numeral on a beam, it tells us how many of those smallest time units will fit within the 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 and a stem with a dot, then just count 1 2 3 for the first stem, and 1 2 for the second.

The traditional method of adding secondary beams 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). A beam is always cut off with a vertical cut. An isolated stem that constitutes a fraction of a beam, and isn't grouped together with another beam, should have a beam stub that is horizontal.

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 numeral, and simply leave out the first part of a beam.

In traditional notation there can be beam breaks in secondary beams. This makes it easier to read notes, as they become arranged into smaller groups. In Modulo notation, beam breaks will also create smaller groups. However, if you don't want to split up a beam that has many stems, adding a courtesy numeral can help. Let's say that you have a beam with eight stems, then courtesy numeral 8 could be placed at the midpoint of the beam. Now you know that half of the stems are on the left side of the numeral, and the remaining four stems are on the right side. In case all those stems just repeat the same note, the numeral also directly tells you how many times to strike the note, so that you don't have to count how many notes there are.

Ties and Slurs

Tied notes do not repeat the original note head(s). Instead only a stem without any note heads is shown.

Slur arcs will only indicate legato.

An arc that finishes with an arrowhead is called a pointer. It means that any note(s) that the pointer points to, and that are able to simply continue the sound of a previous note, should not be struck anew. 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.


A stem with a horizontal dash (and no note heads), represents a rest. The whole-beat rest has a very short stem. Its stem direction should be synchronized with the stem direction of a part. This makes it easier to see which part the whole-beat 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).


It is recommended that a normal-size note head, without a stem, is written inside 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.


Successive beams can be tied together with so-called connectors to create rhythm groups (cf. rhythm.pdf and chromatic.pdf 2c). Connected beams and their connector brace lines should be aligned.

A connector brace that connects two stems with the same stem direction, but where the stem direction has flipped, will naturally have to be turned upside down. A brace that connects two stems with opposing stem directions would be S-shaped.

Connectors create rhythm groups out of beams. If whole-beat stems should be included in a group, use "rhythm separators". A rhythm separator has four equidistant points arranged vertically (two points between the stave lines, one point above, and one point below). A separator divides a measure into separate rhythm groups. If not all stems within a measure should belong to a group, use instead a "rhythm enclosure" with an opening and a closing square brace: [ ]. A brace should be as tall as a separator, and likewise be centered on the stave. The horizontal lines in such braces should open up to an angle of about 45 degrees. With these braces it is now possible to group any set of stems – also when a group passes across a bar line. A group defined by braces can be further divided with separators, if needed.

A whole-beat stem can still be part of a connected group of beams if it is converted to a beam that has a note-stem followed by a tie-stem.

Beat Containers

A beat container is a way to simplify complex syncopated rhythms. It consists of a square horizontal brace that looks like a traditional tuplet brace. There is a small gap in the brace where a numeral is placed. The numeral indicates the number of beats that are being claimed. Then, within that brace, any number of beats can be written. The brace is valid for all parts on a stave. For example, if the numeral is 2, and you see three beats within the extension of the brace, it means that you should play those three beats during the time period of the original two beats. That is, each of the three beats is played a little faster than normally.

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 one or two steps (one step equals a semitone in traditional notation), 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 one or two steps once again, somewhere higher up on the stem, make sure that the note head is again placed on the right side; then continue placing note heads on the left side of the stem once again.

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. The stems are then connected with an upside-down Y-shaped stem extension. It is possible to give the combined stem a stem value symbol (dots and triangles, etc.). The Y-shape could also be connected to a beam. Continue after this on the left side of the first stem if there are any additional note heads.

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 one or two steps, 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 one or two steps once again, somewhere further down on the stem, make sure that the note head is again placed on the left side; then continue placing note heads on the right side of the stem once again.

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. The two stems are then connected with a Y-shaped stem extension. Continue after this on the right side of the first stem if there are any additional note heads.

With the note head coloring, the visual recognition of intervals will be facilitated. The color 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 color of the note head will tell which one it is.

If two note heads, such as, for example, Do and Pa, 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.

Vertical adjustment of note heads:

In order to provide a better correlation between a note head's pitch and its vertical position on the stave, black note heads that touch stave lines can be slightly moved away from the line, by approximately 0.3 stave units (two stave units equals the height of a note head). White note heads that touch lines can be embedded in the line, by moving them approximately 0.1 stave units up or down. If the note heads are not too big, these white note heads will not protrude on the other side of the line.

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

An alternative sign that can be used exactly like an asterisk, is N. Examples can be found in chromatic.pdf 1b

Tone Clusters

Tone clusters can be written with double stems, connected by a Y-shaped stem extension (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 chromatic notes 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) inside parentheses. The corresponding anchor should then also be put inside parentheses.