38 rules

Clefs, ledger lines, and tessitura

How many ledger lines are too many, and when should the clef change instead?

Ledger lines are a legibility budget. Their geometry is fixed, their count is a deterministic function of pitch and clef, and past a threshold a reader stops decoding them at speed. These rules cover that threshold, the alternatives — a clef change or an octave sign — and the clearance a ledgered note needs from its own accidental, flag and beam.

Breaks the readingCheckable from the score alone
A clef change must never fall inside a beamed group, and must be handled deliberately across a tie, slur, or system break
A clef change is never placed in the MIDDLE of a beamed group — beam groups are engraved as one visual unit, and mixing two clefs' worth of noteheads under one beam (with two different staff-position interpretations for the same physical notehead position) is not a recognized notation at all; a clef change must fall on a beam-group boundary. Where a clef change falls immediately before or after a tie or slur, the arc is drawn using each note's own (post-change) staff position, exactly as engraved without any clef change — the clef change affects only how a given staff position is READ, never the physical arc geometry between two noteheads' drawn positions. Where a clef change coincides with a system break, the courtesy-clef (clef-change-courtesy-clef-end-of-system) and repeated-clef (clef-repeated-every-system) rules both apply together — the courtesy clef announces it at the end of the old system, and the new system opens already in the new clef.
Breaks the readingCheckable from the score alone
A single note at 5 or more ledger lines fails legibility regardless of context or duration
Independent of run length or musical context, any single notehead requiring 5 or more ledger lines (ledgerLineCount(pitch, clef) >= 5) has crossed the point every cited authority treats as a legibility failure, not merely a stylistic preference. This is a harder, unconditional ceiling layered on top of ledger-line-sustained-threshold, which only fires on a RUN of 4+ notes — this rule fires on any single occurrence, including an isolated climactic note that ledger-line-sustained-threshold deliberately tolerates at 4 ledger lines.
Breaks the readingCheckable from the score alone
A tessitura/range violation must be checked in the correct pitch space — written for a player, sounding for the audience — and the two are never interchangeable
Every range or tessitura judgment (comfortable range, extreme range, 'this is unsingable/unplayable') is properly a statement about either WRITTEN pitch (what the player must read and, for a wind player, finger — the player's physical/reading comfort) or SOUNDING pitch (what the audience hears — relevant for balance, register clash between instruments, and doubling checks), and a rule must be explicit about which space it operates in. For a transposing instrument, comparing a WRITTEN-pitch range table against a SOUNDING note (or vice versa) produces a wrong-by-exactly-the-transposition-interval result — silently plausible-looking but incorrect.
Breaks the readingCheckable from the score alone
Alto clef is the viola's primary clef and is correct wherever the viola's normal register sits
Alto clef (C clef on the middle line, so middle C sits on the staff's third line) is the viola's standard clef because the instrument's core comfortable register (roughly C3 to C5, tessitura table below) straddles the bass/treble boundary in a way neither clef serves well — alto clef puts the bulk of that range on the staff with minimal ledger lines in either direction. Outside the viola, alto clef appears in Gradus's curriculum context wherever open-score fugue writing puts an inner voice (alto-range vocal part, or an instrumental line in that tessitura) on its own stave, and in trombone parts written unusually high (rare, and usually tenor clef is chosen first — see clef-choice-tenor-clef).
Breaks the readingNeeds both
Ledger lines on chords and on seconds — displaced notehead side and ledger extension
When two chord tones are a second apart, the upper notehead is displaced to the right of the stem (Gould, Behind Bars p.20-22, notehead-displacement chapter) rather than both noteheads sharing the stem's exact x-position. When such a displaced pair sits on ledger lines, EVERY ledger line that either notehead needs must extend far enough horizontally to pass under/over BOTH noteheads — the displaced (right-shifted) notehead is not left dangling off the end of a ledger line sized only for the primary (left) notehead.
Breaks the readingNeeds both
Stems on ledgered notes must lengthen enough to visibly reach the staff
A note's stem is normally about 3.5 staff-spaces long (one octave). When a notehead sits on or beyond a ledger line, the stem must extend further so that it visibly bridges the gap between the ledgered notehead and the staff proper — the stem should reach at least to the staff's near edge, and conventionally continues to (or toward) the middle staff line for notes with several ledger lines, so the eye can track the note's relationship to the staff via the stem.
Breaks the readingCheckable from the score alone
The public API's `transposition` field documentation states the wrong direction relative to what the code actually implements
By the code's own arithmetic (see the detection field below), `transposition` is the number of semitones the WRITTEN pitch sits ABOVE concert/sounding pitch (written = concert + transposition) — the standard way orchestration texts describe transposing instruments (a Bb clarinet's transposition value is positive because its written C sounds a concert Bb, a whole step BELOW the written note, i.e. written sits above sounding).
Misleads the readerNeeds both
A beamed note reaching into ledger-line territory must not let the beam collide with the ledger
When one or more notes of a beamed group extend into ledger-line territory while others in the group sit on or near the staff, the beam's slant and the stem-length rule together must keep the beam stroke itself clear of every ledger line the group's extreme notes pass through. This is a straightforward corollary of the general beam-slant and stem-length engraving rules (see the Beaming chapter and the Stems and Flags chapter) applied at the specific case of a group whose outer note is ledgered.
Misleads the readerCheckable from the score alone
A clef change does not by itself require (or forbid) restating the key signature
A clef change and a key-signature change are independent events — changing clef alone never requires the key signature to be restated at that point (since the key signature already repeats at the start of every SYSTEM regardless, per clef-repeated-every-system, a mid-system clef change with no accompanying key change simply carries on with the same key, unrestated, since it was never in question). The key signature IS restated at a mid-system clef change only if the key is ALSO changing at that same point, in which case both the new clef and the new key signature are engraved together, new-clef-then-new-key, at that point in the score.
Misleads the readerNeeds both
A courtesy (small) clef at the end of a system announces the next system's new clef
When the clef is about to change at the start of the NEXT system, a small courtesy clef (in the new clef, at reduced size, matching the change-clef convention above) is printed at the very end of the current system, after the last note, giving the reader advance notice before the page/line turn.
Misleads the readerNeeds the rendered page
A flag on a ledgered note must clear every ledger line it passes near
An eighth-note-or-shorter note far enough from the staff to sit on ledger lines still carries its flag at the stem's far end, well clear of the staff — but on notes just barely into ledger territory (1-2 ledger lines), a flag whose curve swings back toward the notehead side can visually clip the nearest ledger line if the stem is not lengthened enough. The standard fix is the same stem-lengthening rule that already applies to all ledgered notes (see ledger-line-stem-length-extension below): a sufficiently long stem keeps the flag's curve entirely clear of every ledger line beneath/above it.
Misleads the readerNeeds both
A ledger line drawn for one voice must not collide with a notehead or stem belonging to another voice sharing the stave
In a stacked or SATB texture where two voices share one stave, a ledger line drawn to reach one voice's extreme note extends across the FULL horizontal width the ledger convention specifies (see ledger-line-geometry-length-thickness-spacing) — which can pass directly behind or through a notehead belonging to the OTHER voice if that voice's note falls at a similar x-position and pitch level. Engraving practice requires the ledger line to visually read as belonging to its own voice's note without appearing to strike through the other voice's notehead.
Misleads the readerNeeds the rendered page
A mid-passage change-clef is engraved smaller than a system-opening clef
A clef sign appearing mid-system (a change clef) is drawn at a visibly reduced size relative to the full-size clef that opens each system — conventionally around two-thirds to three-quarters of the normal clef glyph size — signaling to the reader that this is a same-passage change rather than a new system's opening clef.
Misleads the readerCheckable from the score alone
A mid-system clef change is placed immediately BEFORE the barline it precedes, not after
When a clef changes partway through a system (not at a system break), the new clef sign is engraved at the END of the measure it will govern — immediately before the barline — rather than at the start of the following measure after the barline. The barline itself, and any following key-signature or time-signature change, comes after the new clef sign. This positions the new clef where the reader's eye naturally looks just before crossing into new material.
Misleads the readerNeeds both
A notehead in the space just past the staff or just past an existing ledger line gets no line of its own
Ledger lines are drawn only at LINE-levels beyond the staff (spaced a third apart, i.e. 2 diatonic steps), never at the intervening SPACE-levels. A notehead that lands in the first space beyond the staff edge, or in the space between two already-drawn ledger lines, needs no additional line stroke of its own — it reads by simple proximity to the nearest already-visible reference line (the staff's own edge line, or the last ledger line drawn for a note further out). This falls directly out of the count formula in ledger-line-count-formula (floor(steps/2) is unchanged between a space-note and the line-note just below it), and is the precise meaning of what several older texts call the 'partial ledger line' case.
Misleads the readerNeeds the rendered page
Accidental clearance is wider when the note sits on ledger lines
An accidental placed to the left of a ledgered notehead must clear not only the notehead but the ledger line(s) passing through/near it — the accidental's glyph bounding box must not overlap the ledger-line stroke. Because the ledger line already occupies horizontal space at the notehead's exact y-level, engravers give the accidental slightly more left-clearance on ledgered notes than the ordinary same-staff clearance.
Misleads the readerCheckable from the score alone
An instrument name that implies transposition, left at the field's 0 default, silently produces an un-transposed part
When an instrument's name unambiguously implies a transposing instrument (e.g. 'Clarinet in Bb', 'Horn in F', 'Trumpet in Bb', 'Alto Saxophone', 'English Horn'), its `transposition` field should be auto-inferred from that name exactly as `clef` already is — leaving it at its 0 default silently produces a part written and sounding at the same pitch, which is wrong for every one of those instruments. This is a distinct, arguably higher-risk fault than supplying the wrong SIGN on an explicit value (transposition-field-sign-convention-mismatch): it requires no incorrect value at all, only silence — the schema's own default path, and therefore the path of least resistance for an agent author who does not already know the instrument transposes.
Misleads the readerNeeds the rendered page
Below-staff ledger lines and below-staff text (lyrics, dynamics) compete for the same vertical band
Dynamics and lyrics are conventionally placed in the space immediately below the staff — exactly where below-staff ledger lines also live. When a note carrying a below-staff ledger line also carries a dynamic marking or lyric at that same beat, the text must be pushed further down (below the lowest ledger line reached at that beat, plus the ordinary text-to-notation clearance) rather than colliding with or sitting directly on top of the ledger lines.
Misleads the readerCheckable from the score alone
Changing clef too often costs more than the ledger lines it saves
A clef change interrupts a reader's established pitch-reading frame and forces a brief re-orientation; authorities uniformly caution against changing clef merely because a passage's median pitch briefly crosses a threshold, if the passage then immediately crosses back. As a concrete guardrail: a clef change should not be introduced for an excursion that returns within roughly one bar (or, for the more forgiving octave-sign alternative, see octave-sign-preferred-over-ledger-threshold) — clef changes are for passages that GENUINELY settle into a new register for a meaningful span (conventionally several bars or more), not for every local peak or trough in the line.
Misleads the readerNeeds the rendered page
Ledger-line length, thickness, and spacing relative to the staff
A ledger line is drawn only as long as necessary to pass through (or just past) its notehead — conventionally extending about a quarter of a notehead's width beyond the notehead on each side, never a full staff-width line. Its thickness matches the ordinary staff-line weight (a hairline), NOT the heavier barline weight. Vertical spacing between successive ledger lines, and between the staff's own edge line and the first ledger line, equals the staff's own line-to-line distance exactly — ledger lines are a literal continuation of the staff grid, not an independently-spaced element.
Misleads the readerNeeds both
Octave signs interacting with ties, slurs, and system breaks are a known hazard
Three specific hazards recur with octave signs: (1) a tie or slur that begins inside an octave-sign span and ends outside it (or vice versa) requires the reader to track a pitch relationship across a register-shift boundary, which is legitimate but must be engraved so the arc's shape does not visually suggest the two notes are the interval they would be WITHOUT the octave transposition; (2) an octave-sign span that crosses a system break needs either a full bracket restatement at the top of the new system or an unambiguous 'loco'/continuation cue — a bare assumption that the reader remembers the previous system's still-active bracket is unsafe; (3) a tie that crosses the octave sign's own START or END boundary (the note right before the bracket begins, tied to the first note inside it) is especially error-prone because the tie's two endpoints are notated at genuinely different absolute pitches once the sounding transposition is applied, which is correct notation but must not be mistaken by the audit engine for a 'tie between mismatched pitches' violation.
Misleads the readerNeeds both
Octave-sign bracket placement, termination, and the loco marking
An 8va bracket is drawn above the staff (8vb below) starting at the first affected note, with a dashed horizontal line continuing for the full duration of the transposed passage, and a downward (8va) or upward (8vb) hook at the bracket's END marking exactly where the transposition stops. Where the bracket ends and normal-register notation resumes, the word 'loco' may optionally be printed to make the return-to-normal explicit — this is most needed when the bracket's terminal hook could be visually ambiguous (e.g. right at a system break, or immediately followed by a further register excursion).
Misleads the readerCheckable from the score alone
Sustained passage ledger-line ceiling before a clef change or octave sign is required
A SUSTAINED passage — four or more consecutive notes in one voice each requiring 3 or more ledger lines — should be re-clef'd or wrapped in an 8va/8vb bracket rather than engraved on ledger lines throughout. A single note or a brief 2-3-note excursion may go to 4 ledger lines without triggering a rewrite. (A single note at 5 or more ledger lines, regardless of run length, is a separate and harder failure — see ledger-line-absolute-ledger-ceiling.)
Misleads the readerCheckable from the score alone
Tenor clef is correct for cello, bassoon, and trombone whenever their line rises into the upper-middle register
Tenor clef (C clef on the fourth line, so middle C sits on the staff's fourth line from the bottom) is the standard clef for cello, bassoon, and tenor trombone parts when the line's tessitura rises out of bass clef's comfortable range but does not yet justify treble clef — roughly, when a sustained passage would otherwise sit at 2+ ledger lines above the bass staff. This is exactly the case Sean named by name in the assignment brief: 'cello thumb position' and 'high bassoon' are the textbook triggers for a tenor-clef switch.
Misleads the readerCheckable from the score alone
The `transposition` field has no validity range check today and should be bounded to real instrument values
Real orchestral transposition intervals span a known, bounded set — from roughly a minor third down (Eb alto sax family, transposition +9 by the code's convention, or written a minor third+octave arrangements for some Eb instruments) to about a major sixth or minor seventh in either direction for the most extreme common transposing instruments (e.g. contrabassoon sometimes notated with an octave transposition, bass clarinet at -10 to -14 depending on octave convention). A `transposition` value far outside this range (e.g. +40, or a non-integer) is never a real instrument and is almost certainly an authoring mistake — a typo, a confusion between semitones and some other unit, or a garbled agent-generated value.
Misleads the readerCheckable from the score alone
The concrete decision rule for switching clef mid-stream versus tolerating ledger lines
Combine the three preceding rules into one decision procedure: (1) compute the ledger-sum for the CURRENT clef over the excursion; (2) compute the ledger-sum for the best alternative clef over the same excursion (clef-choice-general-criterion); (3) if the alternative's sum is not meaningfully lower, stay on the current clef and tolerate the ledger lines (up to the absolute ceiling in ledger-line-sustained-threshold); (4) if the alternative is meaningfully better AND the excursion's duration exceeds the octave-sign span limit (octave-sign-preferred-over-ledger-threshold), prefer a clef change; (5) if the alternative is meaningfully better but the excursion is brief, prefer an octave sign over a clef change (clef-change-frequency-cost's thrashing concern favors this); (6) never introduce a clef change for an excursion of only 1-2 notes under any circumstance — ledger lines or, at most, an accidental awkward moment, are always preferable to a same-passage clef round-trip that short.
Misleads the readerCheckable from the score alone
The correct clef minimizes ledger lines across the WHOLE passage, not at a single note
Clef choice is a passage-level optimization, not a note-level one: the correct clef for a line is whichever of the available clefs minimizes the total ledger-line burden (sum, or equivalently mean, of ledgerLineCount across every note in the passage) — not whichever clef happens to put any one note, including the first note, directly on the staff. A passage whose FIRST note sits comfortably in treble clef but whose overall tessitura centers a fourth below the staff should still be notated in a lower clef if that reduces the passage's aggregate ledger burden.
Misleads the readerNeeds the rendered page
Ties and slurs arcing near ledgered notes must clear the ledger lines, not just the noteheads
A tie or slur whose endpoint sits on a ledgered note must curve clear of that note's ledger line(s), not merely clear of the notehead itself — the arc's control point nearest the ledgered endpoint needs extra vertical clearance proportional to the endpoint's ledger-line count.
Falls short of best practiceCheckable from the score alone
A transposing instrument's WRITTEN key signature must be transposed along with its notes
When an instrument transposes, its part is conventionally notated with a key signature appropriate to its OWN written pitch (transposed the same interval as the notes), not the concert-pitch key signature — a Bb clarinet playing a concert-C-major passage is written in D major (up a whole step), key signature and all, not written in C major with clarinet notes that happen to sound a step low. This keeps every note's relationship to its own staff position, and to the accidentals implied by its key signature, internally consistent for the player reading only their own part.
Falls short of best practiceNeeds the rendered page
Above-staff and below-staff ledger lines follow identical geometry
There is no engraving distinction in length, thickness, or spacing between ledger lines drawn above versus below the staff — the same continuation rule applies symmetrically in both directions. The only real differences are contextual: stems on below-staff notes point up (per the middle-line stem-direction pivot, see the Stems and Flags chapter) so they reach toward the staff, and below-staff ledgers are far more likely to collide with a lower stave in a grand staff or open-score system, while above-staff ledgers are more likely to collide with a slur, tie, or dynamic hairpin arcing above.
Falls short of best practiceCheckable from the score alone
Baritone and sub-bass clefs are historical curiosities, not live choices for Gradus's repertoire
Plain bass clef (F clef on the second-from-top line) is correct for essentially all of Gradus's low-voice and low-instrument writing. The baritone clef (F clef on the middle line, or historically a C clef on the top line) and sub-bass clef (F clef on the top line) are 18th-century-and-earlier notations essentially never used in modern engraving, choral writing, or the instrumental repertoire Gradus teaches (bass, cello, trombone, tuba, bass voice). They should never be a candidate clef in any Gradus rule or renderer.
Falls short of best practiceNeeds the rendered page
Clef (and key signature) repeat at the start of every system, regardless of whether either changed
Unlike a clef CHANGE (which is a genuine mid-passage event), the PREVAILING clef and key signature are conventionally re-stated at the start of every system in a multi-system piece, whether or not anything changed since the previous system — a reader beginning a new line should never have to scroll/look back to know the current clef or key.
Falls short of best practiceCheckable from the score alone
Comfortable and extreme tessitura tables, as MIDI note numbers, for every voice type and instrument Gradus teaches
Every range/tessitura judgment in this chapter (sustained-ledger threshold interacting with clef choice, SATB voice-order sanity check, transposition range-space checks) is only mechanizable against a concrete numeric table. The tables below give MIDI note numbers (C4 = middle C = 60) for a COMFORTABLE range (the zone a passage should mostly live in without comment) and an EXTREME range (the outer bound beyond which a note is flagged as questionable for the given voice/instrument) for the six SATB choral voice types Gradus's chorale-harmony curriculum teaches, and for the instrumental families named in the brief. All figures are stated in SOUNDING/concert pitch throughout, with no exceptions (per transposition-written-vs-sounding-range-check's requirement to state the pitch space explicitly) — a written-pitch comparison for a transposing instrument must first convert via that rule's `soundingPitchOf()` helper. (The first draft of this table stated clarinet, horn, trumpet, and guitar in WRITTEN pitch while claiming 'sounding throughout' — corrected below; every row is now genuinely sounding pitch.)
Falls short of best practiceCheckable from the score alone
In multi-voice writing, each voice's clef changes independently — one voice changing clef never forces another to change
When two or more voices share a system (SATB grand staff, open-score fugue, stacked counterpoint), each voice's clef is chosen and changed entirely independently based on its OWN tessitura — a soprano voice moving into an unusually low passage does not drag the alto's clef along with it, and vice versa. The only shared-stave constraint is that voices sharing ONE physical stave (as in SATB's treble/bass pairing) necessarily share that stave's single clef; voices given their OWN stave (open score) are fully independent.
Falls short of best practiceCheckable from the score alone
Ledger-line count is a deterministic function of pitch and clef
The number of ledger lines a note needs equals the number of complete thirds (2 diatonic steps) its notehead sits beyond the nearest staff edge line, rounded down. A note in the first space beyond the staff needs zero ledger lines; a note a third beyond the staff needs one; a note a fifth beyond needs two, and so on. This is the arithmetic every engraving program (VexFlow, Verovio/MEI, LilyPond, Finale) implements identically because it falls directly out of the 5-line staff's own line/space alternation — it is not a matter of house style.
Falls short of best practiceCheckable from the score alone
Multi-voice ledger-line legibility budget is shared, not per-voice
In a texture where two or more voices share a stave (chorale SATB, second-species stacked counterpoint), a passage where BOTH voices simultaneously reach into ledger-line territory compounds legibility cost beyond what either voice alone would cost — two sets of ledger lines interleaved on one stave, on opposite sides of the shared noteheads, is harder to read than either voice's excursion in isolation. The sustained-passage threshold (ledger-line-sustained-threshold) should therefore be evaluated per-voice AND with a stricter combined threshold when two voices are simultaneously ledgered.
Falls short of best practiceCheckable from the score alone
The octave-treble clef (treble clef with a small 8 below) is the standard choral notation for the tenor voice
In choral (SATB) writing, the tenor voice is conventionally notated in treble clef with a small '8' below the clef sign — indicating the part sounds an octave lower than written — rather than in true tenor (C) clef or true bass clef. This 'octave-treble' or 'treble-8' clef lets sopranos, altos, and tenors all read from visually similar treble-clef notation while the tenor's SOUNDING pitch sits correctly an octave below what is written, which is the near-universal convention in choral octavo publishing.
Falls short of best practiceCheckable from the score alone
When an 8va/8vb/15ma/15mb bracket is preferable to continued ledger lines
Once a passage crosses the sustained-ledger threshold (ledger-line-sustained-threshold: 4+ consecutive notes at 3+ ledger lines), the preferred fix is an 8va (for above-staff excursions) or 8vb (for below-staff excursions) bracket over the passage, NOT a clef change, when the excursion is temporary (expected to return to the normal register within the same system or the next one or two). A clef change is preferred instead when the excursion is genuinely sustained across a longer span (see clef-choice-minimize-across-passage below) — octave signs are for a temporary register excursion inside music that otherwise belongs on the current clef; clef changes are for a genuine, lasting shift of tessitura.

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A clef change must never fall inside a beamed group, and must be handled deliberately across a tie, slur, or system break

A single note at 5 or more ledger lines fails legibility regardless of context or duration

A tessitura/range violation must be checked in the correct pitch space — written for a player, sounding for the audience — and the two are never interchangeable

Alto clef is the viola's primary clef and is correct wherever the viola's normal register sits

Ledger lines on chords and on seconds — displaced notehead side and ledger extension

Stems on ledgered notes must lengthen enough to visibly reach the staff

The public API's `transposition` field documentation states the wrong direction relative to what the code actually implements

A beamed note reaching into ledger-line territory must not let the beam collide with the ledger

A clef change does not by itself require (or forbid) restating the key signature

A courtesy (small) clef at the end of a system announces the next system's new clef

A flag on a ledgered note must clear every ledger line it passes near

A ledger line drawn for one voice must not collide with a notehead or stem belonging to another voice sharing the stave

A mid-passage change-clef is engraved smaller than a system-opening clef

A mid-system clef change is placed immediately BEFORE the barline it precedes, not after

A notehead in the space just past the staff or just past an existing ledger line gets no line of its own

Accidental clearance is wider when the note sits on ledger lines

An instrument name that implies transposition, left at the field's 0 default, silently produces an un-transposed part

Below-staff ledger lines and below-staff text (lyrics, dynamics) compete for the same vertical band

Changing clef too often costs more than the ledger lines it saves

Ledger-line length, thickness, and spacing relative to the staff

Octave signs interacting with ties, slurs, and system breaks are a known hazard

Octave-sign bracket placement, termination, and the loco marking

Sustained passage ledger-line ceiling before a clef change or octave sign is required

Tenor clef is correct for cello, bassoon, and trombone whenever their line rises into the upper-middle register

The `transposition` field has no validity range check today and should be bounded to real instrument values

The concrete decision rule for switching clef mid-stream versus tolerating ledger lines

The correct clef minimizes ledger lines across the WHOLE passage, not at a single note

Ties and slurs arcing near ledgered notes must clear the ledger lines, not just the noteheads

A transposing instrument's WRITTEN key signature must be transposed along with its notes

Above-staff and below-staff ledger lines follow identical geometry

Baritone and sub-bass clefs are historical curiosities, not live choices for Gradus's repertoire

Clef (and key signature) repeat at the start of every system, regardless of whether either changed

Comfortable and extreme tessitura tables, as MIDI note numbers, for every voice type and instrument Gradus teaches

In multi-voice writing, each voice's clef changes independently — one voice changing clef never forces another to change

Ledger-line count is a deterministic function of pitch and clef

Multi-voice ledger-line legibility budget is shared, not per-voice

The octave-treble clef (treble clef with a small 8 below) is the standard choral notation for the tenor voice

When an 8va/8vb/15ma/15mb bracket is preferable to continued ledger lines