Modulo Notation Features

Staves

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. It's also possible to have partial segments with the upper or lower half of the segment being left out to save some vertical space and thereby allow staves to be brought closer to each other (cf. macfarlane.pdf).

Stave segments should never extend past a bar line. Instead, start a new segment in the measure that follows. Segments should frequently be broken up into smaller segments to prevent them from being too long, as this could cause eye orientation difficulties otherwise. When doing such divisions, rhythmical groups could be given priority.

Bar Lines

There are only three types of bar lines commonly used: normal bar lines, double bar lines, and ending bar lines. Bar lines should never extend between staves.

Clefs

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 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.

Avoid putting a clef between tied notes.

All'Ottava

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 accidentals 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.

Avoid starting an All'Ottava between tied notes.

Key Signatures

A key signature, with its characteristic brace, simply states the SaLaTa note name that begins a "natural scale" (= major scale). The 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). See chromatic.pdf 3a, 3b, 3c, and macfarlane.pdf.

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

There is never an accidental 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 accidental 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 accidentals (that is, the same accidental is yielded more than once within the measure) are allowed. Whenever there is a change of key signature, all and any previous accidentals are automatically canceled.

An accidental only affects note heads of the same kind. For example, if Ta (= B) has an accidental, 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; an accidental (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 accidentals (or microtonal signs) if necessary.

In the event that you want to stop using key signatures and accidentals 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.

The fact that accidentals 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

See Key Signatures.

Time Signatures

It is recommended to always use numbers in time signatures. Avoid using c (=4/4) or c with a vertical line (=2/2).

Stem Flags

Stem flags (cf. chromatic.pdf 1c) should be on the left side of stems. Those are the default flag positions; but, a flag can nevertheless be flipped to the other side of the stem in tricky situations to avoid collisions with other objects (that is, a flag becomes mirrored in respect to the Y-axis). The reason why stem flags normally reside on the left side of stems, is to make room for augmentation triangles.

The whole-note stem is useful for grouping note heads into chords, or when you want to assign whole-notes to different parts with different stem directions (different parts can be played with left and right hand, respectively, on some instruments). Two parts with whole-notes can now share the same note head. It will also be clear which note heads are affected by diagonal tremolo bars across a stem.

Giving the whole-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. The whole-note stem also makes sure that a whole-note is not likely to be overlooked, since the stem draws attention to it. Furthermore, with the introduction of the whole-note stem, note heads of ordinary size and shape can be used also for the whole-notes.

The Maxima (=8/1) stem flag is made to look somewhat like the letter M. Likewise, the "Longa" (=4/1) reminds of an L; and the "Breve" (=2/1) is consequently shaped like the letter B. The Breve is seldom used these days, and the Maxima and Longa note values are hardly used at all, but are still provided for the sake of completeness.

Beams

Partial beams are cut off diagonally for aesthetic reasons (cf. chromatic.pdf 3c).

Ties and Slurs

Tie arches should look like arrows (cf. chromatic.pdf 2a and 3c, and macfarlane.pdf). The note or chord to which the arrow points should thus, ideally, not be struck anew. Ties will affect all notes on a stem, so only one tie arch is needed. If there are additional note heads in a chord that cannot be tied to any note head in the next chord (because the notes don't represent the same pitch), a slur arch (just one) can also be added.

For the unusual combination of tied, normal, and slurred notes: add asterisks to the chord at which the arrow points, to mark the notes that should be neither tied nor slurred, and explain what the asterisk means in a message above the stave.

Rests

Rest symbols are shown in chromatic.pdf (1c), below the corresponding stem flags.

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

<12>

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

Note Value Augmentation

Traditional notation note value dots are replaced with note value augmentation triangles (cf. chromatic.pdf 1d). Only one triangle is used, even if a stem has more than one note head. Any vertical line placed to the left of a triangle indicates another (hidden) triangle. Each additional triangle has a halving effect on the note value to be added, just like ordinary traditional augmentation dots have.

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 2e). This makes small note heads clearer than if they were simply miniature note heads.

When a small note head is fused with an ordinary note head (with two parts having stems in opposite directions), only the ordinary note head is written.

Asterisks are recommended to make a leading voice distinct from sub-voices instead of employing small note heads. Small note heads should never be used for grace notes.

Grace Notes

Grace notes (cf. chromatic.pdf 2b) will be written as ordinary note heads without stems, to which a slur is added. The long grace note is distinguished from the short grace note by adding a fermata sign just above the grace note. The short grace note borrows time from the foregoing note/chord. The long grace note borrows time from the note into which it slowly resolves with a heavy slur. Various text messages can be added to describe whether short 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.

Trills

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

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, slanted tremolo bars across the stem would determine the note value of each individual note in the tremolo (and from that, the number of tremolo notes can be deduced).

Tuplets

Tuplet numerals in the new notation represent the note value that the tuplet occupies (cf. chromatic.pdf 2d, 3c, and macfarlane.pdf). For example, 1:4 means that the tuplet lasts for the duration of a quarter note. However, the numeral 1 is always omitted, so instead we just write :4.

When the tuplet equals something more complex, like a note with an augmented note value, or the total note value of two tied notes, the smallest common denominator should be employed. Thus, if the occupied note value equals a dotted eight note, the numeral becomes 3:16 (that is, three sixteenth notes). Likewise, if the occupied note value equals a half note tied to an eight note, the numeral becomes 5:8.

With the new tuplet approach, the individual note values of the notes in the tuplet do not all have to be equal; any musical phrase could be turned into a tuplet - just remember to add a horizontal bracket when necessary.

BPM Tempo Indication

A small note symbol with a regular (oval) black note head should be used for tempo indication, followed by an equals sign and a BPM figure. Use Modulo Notation stem flags, if necessary.

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 2g). 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.

Flageolets

A small flageolet circle and ordinary note heads should always be used instead of the traditional notation rhombic note head. See chromatic.pdf 2c. 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 3c).

Microtonal Notation

The new intonation signs, > and < etc. (cf. chromatic.pdf 3b) 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.

A microtonal sign is only valid for one note head; and it does not apply automatically to a tied note head that follows.

Asterisks

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, 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 an ampersand (&) instead of a comma sign. This is suggested because comma signs may be frequently used in Modulo Notation as accidental signs.

Jump Instructions

Modulo Notation has its own system to manage jumps between various sections in the music (cf. chromatic.pdf 2f). 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.