"Binde – Call and To" for Alto Flute: Reading a Score That Thinks Like a Foundry

 

"Binde – Call and To": Reading a Score That Thinks Like a Foundry

The first impression: this is not a score, it's a drawing of a casting

Open the page and the eye doesn't find a staff. It finds a foundry drawing. One of  sprues, vents, a parting line, a locating key, a long tubular cavity running the width of the page. The header confirms the intent rather than hiding it: "Sustained Tone / Negative Mould Cavity / For One Pitch Band."   I am presenting, in the driest possible technical language, that a held tone is being treated as an object to be cast in metal, not a note to be read off a stave.

This is the governing idea of Binde – Call and To, and everything else on the page...those ratio ladders, the cent deviations, the exponential timeline, the pseudo-taxonomic labels radiate outward from that single conceit: sound as a poured, cooled, and vented material.

For a performer used to five lines and a clef, that's disorienting on purpose. My score asks you to stop reading pitches and start reading a process: how a tone is introduced (sprue), how pressure escapes as it fills (vents), where two pours meet and risk a flaw (the interference region), and where the mould finally releases the object (the parting line). The alto flute, in this reading, isn't playing melody... it's acting as the crucible.

The harmonic ladder: just intonation as architecture, not ornament

Center-top, a bracketed staircase of ratios climbs from the simplest interval to the most complex:

3:2 → 5:4 → 7:5 → 11:7 → 13:8 → 17:8 → 17:10 → 23:12 →
29:15 → 31:16 → 37:20 → 41:24 → 43:22 → 47:24 → 53:28 → 59:30

Each rung is a just-intonation interval built from a higher prime than the last.  This is a Stern-Brocot-like tree of rational tunings, not a scale in the tempered sense. The numbering to the left of each bracket (1, 5, 6, 8, 9, 13, 14, 17, 18, 19...) doesn't track scale degrees; it tracks prime limit.  How far up the harmonic series you have to reach to justify that particular ratio. It's the same lineage of thinking found in Harry Partch's 43-tone just-intonation gamut, Ben Johnston's extended just-intonation string quartets, and the Helmholtz-Ellis notation used by Marc Sabat and Wolfgang von Schweinitz ... all of whom needed a way to notate pitches that standard accidentals can't express.

That lineage explains the strange fanning diagrams in the top corners: two mirrored bursts of flats and sharps radiating from a single point, each stamped with its own micro-fraction (13/1.7/5 on the left, a denser mirrored fan on the right). These aren't key signatures in the traditional sense, however they're spectral fans, harmonics of a fundamental laid out as a bouquet of accidentals, the way spectralist composers (Grisey, Murail, and later Haas) notate the overtone series when it needs to be played rather than merely implied. Here the fan sits at both extremes of the piece, framing it: the work opens and closes inside a harmonic field, not a key.

The two isolated fractions, that of 13/56 on the left and 29/128 on the right,  sit like coordinates rather than time signatures. Read against the ratio ladder above them, they mark where in the harmonic lattice the two long lens-shaped tones underneath them are drawn from: the 13th and 29th rungs of the climb, at denominators of 56 and 128. In performance terms, these are the two most harmonically remote sustained tones in the piece.  These are the ones that will require the most careful lipping and breath-pressure control to locate and hold.

The four lenses: tones as optical events

Running through the piece are four dark, vertically elongated lens or vesica shapes.  They present as almond forms shaded from black at the core to pale at the edges, like an eye, or like two overlapping circles' zone of intersection. They sit directly above the casting-cavity diagram at four points along the horizontal timeline, and a large, faint oval traces the entire page, containing everything else inside it as if the whole score is itself one enormous lens.

Read together with the ratio-ladder and the fraction markers, these lenses are best understood as pitch bands rendered as depth-of-field.  The shading gradient standing in for the tone's stability. Dense black at the center: a pure, locked pitch. Pale, feathering edges: the tone drifting, destabilizing, opening into beating. This is a visual vocabulary borrowed less from music notation than from optics and lens-grinding diagrams.  It is appropriate, since the piece is already speaking in the language of another craft (foundry work) to describe sound. The player is being shown, quite literally, how "in focus" each sustained tone should be at its core versus its decay.

The black ring near the right-hand lens signals a torus, an eye seen head-on and reads as the piece's single moment of pure resonance: a tone with no directional drift at all, a closed loop rather than an elongated band. It's the calmest object on the page, and its placement just before the final sprue and locating key suggests it functions as the work's still point before release.

The mould itself: sprues, vents, and the interference region

The long horizontal cavity is the spine of the piece, and its foundry vocabulary maps cleanly onto breath and tone production:

• Sprue A / Sprue B — the two points where molten metal (breath, tone) enters the mould. These sit at the absolute start and end of the piece: the first attack and the final release.
• Locating Key (appearing at both ends) — the mechanism that ensures the two halves of a mould align correctly. Structurally, this is the piece's rhyme: whatever gesture opens the work should be recognizable, if inverted, at its close.
• Parting Line — the seam where the two halves of the mould separate once the metal cools. In performance terms, this is the fingering/embouchure "seam". It becomes the point of maximum instability, where a shift in air support could visibly (audibly) crack the tone.
• Vents 1, 3, 4, 5, 6, 7, 8, 9, 11 — small outlets that let trapped air/gas escape as the metal fills the cavity, preventing a flawed casting. The absence of Vent 2 and Vent 10 from the labeled sequence is almost certainly deliberate: two silent, ungoverned moments where nothing bleeds off.  These are points of maximum internal pressure. These are strong candidates for the piece's two most exposed, breath-strained passages.
• The Interference Region — the single most important annotation on the page: "Pitch bands overlap. This band: +14.2¢. Neighbour: −11.7¢. (Attack may occur before it begins.)" This is the score's plainest instruction, and its most radical one. Two tones.  One pulled 14.2 cents sharp, the other 11.7 cents flat.  Theses are meant to beat against each other, and the performer is warned that the next attack may need to begin before the written interference has finished resolving. It's an instruction about overlap and impatience: don't wait for silence or stability before moving on.

The four small glyphs strung along the ticks beneath the cavity are tuning-fork-like marks paired with accidentals and small directional arrows.  They function as micro-cues: local reminders, at specific timepoints, of which direction to bend a pitch (the arrow) and by how much (the fraction beneath it). They're the score's closest approach to conventional performance directions, scattered sparsely rather than continuously, which keeps the player oriented without overriding the ear.

Time that grows like a shell: the golden-ratio timeline

Beneath the cavity runs a timeline from Datum 0.0 to 2,377.9, in units the score never names (most plausibly milliseconds, though a performer could just as reasonably read them as a proportional map of an 8-second span, since the final box states the whole structure resolves against "Event Duration of 8.000 seconds.")

The intervals aren't linear. From roughly the fourth marker onward, each value is close to 1.287–1.289 times the one before it.  It is a steady exponential growth rate, distinct from but reminiscent of the golden ratio proportioning found in Bartók's and Nancarrow's rhythmic structures, and of Xenakis's architectural approach to musical time (unsurprising, given Xenakis trained as an architect and thought about sound the way this score thinks about casting). The practical effect for a performer: events are packed close together at the start and spread increasingly far apart as the piece proceeds. The piece opens dense and closes dilated. Whatever happens in the first second happens many times faster than whatever happens in the last.

The four triangular fans at the very bottom of the page, growing from sparse lines to dense cross-hatching and back to sparse again, visualize this directly.  They are density maps of event-frequency across the timeline, confirming that the piece has a real accelerando/decelerando shape underneath its static, technical-drawing surface.

The closing tally of "Stack Total: ± 58.4 cents against event duration of 8.000 seconds" reads as the piece's summary statistic: across the whole eight-second unit the drawing represents, the cumulative pitch drift the performer is asked to carry (and resolve) totals just under 60 cents, a little over half a semitone. It's a small number for a page this dense and a reminder that Binde is a piece of fine tolerances, not large gestures.

The specimen labels: what "Vespa novedecimus" and "Apus undecimus" are doing here

Flanking the mould at each Sprue are two boxed labels, styled like museum specimen tags:

• Left: Vespa novedecimus — "nineteen-wasp" — 19/80, catalog 0295
• Right: Apus undecimus — "eleven-swift" — L.P./M.C., catalog 0292

These are invented Latin binomials, but they're not decorative Latin, they're coded. Novedecimus (nineteen) and undecimus (eleven) point straight back to the harmonic ladder: 19-limit and 11-limit just intonation, the two outer edges of the tuning system the ratio-tree climbs through. A wasp and a swift (one earthbound and stinging, one aerial and fast) stand in as characters for the two harmonic "species" that anchor either end of the piece, the way a naturalist's chart pairs an image with a name and a catalog number. It's a small but telling gesture: the piece wants its abstractions (11-limit, 19-limit) to also be creatures, with a body, a behavior, and a number in a ledger.  19/80 and 0295 on one side, an unresolved fraction, "L.P./M.C.," and 0292 on the other. Whether L.P./M.C. is read as a pressing/edition mark or as a tempo direction (lento poco / molto cantabile), it deliberately leaves the right-hand creature less fully catalogued than the left and swifter, harder to pin down, true to its name.

The title: Binde – Call and To

Binde is the German first-person verb "I bind." or, as a noun, a tie, a bandage, a ligature. Paired with the fractured English "Call and To" (very likely a deliberately severed "call and response," with the answering half withheld or left as pure direction.  A "to," a vector without a destination), the title mirrors the score's own logic: everything here is a binding-together of two things that don't quite resolve into each other.  Think two pitch bands that beat rather than merge, two mould-halves joined at a parting line that will eventually split them apart again, a call sent out with its response deliberately incomplete. The title isn't decoration; it's the same interference-region logic the score notates in cents, translated into two languages that don't finish each other's sentences.

Influences, in brief

Binde doesn't sit inside any single tradition, but it's legible against several:

• Harry Partch / Ben Johnston / Marc Sabat & Wolfgang von Schweinitz: For the extended-just-intonation ratio ladder and the HEJI-style fanned accidentals.
• Alvin Lucier: For treating audible beating between two close, deliberately mistuned frequencies as the actual subject of the piece, not an error to be corrected.
• Éliane Radigue: For the patience of the "sustained tone" framing, and the idea that a single held pitch can be a whole compositional world if you listen closely enough to its interior drift.
• Iannis Xenakis: For the architectural, almost engineering-schematic approach to time and material, and the exponential (rather than metric) handling of the timeline.
• Gérard Grisey / Tristan Murail (spectralism): For treating the harmonic series itself, rendered as a literal spectrum/fan, as compositional material.
• Industrial and technical draftsmanship more broadly (sand-casting and mould-making diagrams, specifically) as the score's actual notational language, borrowed wholesale rather than referenced in passing.

None of these are quotations; Binde doesn't sound like any of them individually. It's closer to a piece that took the diagrams several of these traditions produce as supporting material and made the diagram itself the score.

A performer's guide

For a flautist approaching Binde – Call and To on alto flute, a few practical anchors:

1. Treat the ratio ladder as your tuning reference before you touch the cavity diagram. Locate 13/56 and 29/128 on the ladder first (rungs 13 and 29).  These will be the two hardest tones in the piece to place by ear alone, and they're worth finding on a tuner or drone before rehearsal.
2. Read the four lens shapes as focus, not volume. A dense black center asks for a tone with almost no vibrato and rock-steady air support; the pale, feathering edges are an invitation to let pitch and timbre soften and drift.  Don't fight the decay into instability, lean into it.
3. The interference region is the emotional center of the piece, not a technical footnote. +14.2¢ against −11.7¢ is roughly a 26-cent gap It is audible, deliberate beating, not tuning error. Don't correct it. And take the instruction "attack may occur before it begins" literally: the next gesture is permitted, even expected, to overlap the unresolved beating rather than wait for it to settle.
4. Pace by the exponential timeline, not a metronome. Events compress hard in the first third of the eight-second unit and stretch out dramatically by the close. If you're using the timeline as a literal proportional map, expect the opening to feel almost rushed and the ending to feel suspended, spacious, nearly stalled. That asymmetry is structural, not a performance choice to smooth over.
5. Vents 2 and 10 are the pressure points. Because every other vent is marked and these two are conspicuously silent, treat the passages around them as the places where breath control is most exposed.  There is no scheduled release, so the player has to find their own.
6. Let the specimen labels inform character, not just tuning. The 19-limit "wasp" material (left/Sprue A) can be played with more grounded, articulated weight; the 11-limit "swift" material (right/Sprue B) invites more air, more velocity, less definition at the edges.

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Binde – Call and To asks a flautist to stop thinking of the alto flute as a melodic instrument for the duration of the piece, and to think of it instead as the thing pouring metal into a mould requiring patient, precise, alert to where the pressure needs to escape, and willing to let two close, unequal pitches sit in the same space without ever quite becoming one.