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Essays arrive in groups rather than one at a time. The most recent group is below in full, and every earlier one after it, newest first.

Essays arrive in groups rather than one at a time, and a group usually opens up a subject not covered before. Between one group and the next nothing changes, so a reader who has seen the most recent group has seen everything.

17 September 2026

18 essays on pitch and tuning, form and structure, harmony and voice leading, intervals and chords, timbre and acoustics, scales and modes, perception and the listener and rhythm and metre

Counted in beats, the abandoned chord comes back sooner and by steps. The piece in standard tuning with its G major, open chord given more and more of the piece, searched twice: once minimising the mean departure from just in cents, once minimising the mean beat rate. The vertical axis is how far that chord sits from just at each optimum. Counted in cents it stays at 13.29 cents until it holds exactly 44 beats — the same as the rest of the piece — and then drops to zero in one step. Counted in beats it drops at 30.4 beats to 4.96, then at 47.4 beats to 3.91, then at 73.1 beats to 0.00 cents. At the piece's own 8 beats the two counts agree exactly: the corner does not move, and what the beats change is where the steps are.

Pitch and tuning

Counting beats moves the price of a chord, not the tuning

The search that found a guitar piece's best tuning counted every cent of error alike, and the obvious objection is that a cent of a third beats faster than a cent of an octave. Counted in beats instead, every piece gets exactly the same tuning back. What changes is how much of the piece the abandoned chord has to hold before it is rescued — thirty beats instead of forty-four, arriving in three steps instead of one.

6 figures

Two shapes asking fifteen pairs of strings for different things. Every pair of the six strings, and the difference in cents between the two strings' offsets that would make the interval each shape puts on that pair exactly just. The piece's chords fall into two families that never disagree with themselves: E major, open and A major barred at 5 (44 beats), and G major, open (8 beats). They disagree on 13 of the 15 pairs: E2–A2 is asked for 1.96 and -13.69; E2–D3 is asked for 0.00 and 1.96; E2–G3 is asked for -13.69 and 0.00; E2–B3 is asked for 1.96 and -13.69; A2–D3 is asked for -1.96 and 15.64; A2–G3 is asked for -15.64 and 13.69; A2–E4 is asked for -1.96 and 13.69; D3–G3 is asked for -13.69 and -1.96; D3–B3 is asked for 1.96 and -15.64; D3–E4 is asked for 0.00 and -1.96; G3–B3 is asked for 15.64 and -13.69; G3–E4 is asked for 13.69 and 0.00; B3–E4 is asked for -1.96 and 13.69. The ring on each row is where the piece's cheapest tuning actually puts the pair. It sits on the first family's demand every time, which is what abandoning the other chord means: no weighting of the error can put a ring on two different places.

Pitch and tuning

The chord a tuning gives up is a fingering

A guitar piece's best tuning makes two of its chords exactly just and abandons the third by thirteen cents, and no way of counting error — cents, beats, squared cents, or only the beats slow enough to hear — brings the third chord back. Fingered as a barre chord in the shape the other two already use, it comes back completely, and the whole piece is exactly just. The conflict was never between chords. It was between hands.

5 figures $A louder final chord stands higher and still stands for a fraction of a second. How far a final chord stands above the listener's running impression at the instant it is released, against how long it lasts. The chord is a struck six-note tonic; "a step louder" is the hammer velocity doubled, which raises its loudness 7.12 phons above the tutti's. At the tutti's level, after 1.2 s of silence, the impression is 8.09 dB below the chord and the chord stands highest, 5.14 dB, at 54 ms; a step louder, straight out of the tutti, the impression is 7.12 dB below the chord and the chord stands highest, 4.51 dB, at 36 ms; a step louder, after 1.2 s of silence, the impression is 15.21 dB below the chord and the chord stands highest, 9.46 dB, at 38 ms. Every curve returns to zero by half a second: the impression climbs to whatever level the chord is played at, so a louder mark is not a stand that lasts but a deeper fall to climb out of, and a silence and a mark add as depths.$ Form and structure

A louder final chord is a deeper silence and a brighter sound

A final chord marked a step louder than the passage was supposed to stand above a listener's running impression for as long as it sounded, since the impression can climb no higher than the chord. It climbs exactly that high, and the stand closes in half a second as it always did. What a louder mark actually buys is depth — about seven phons, the same depth a second of silence buys — and a spectrum whose balance point sits most of a whole tone higher, which, unlike the stand, lasts for the whole chord.

5 figures

Form and structure

An exit is worth nothing until the tutti is given up

Six parts entering a five-chord passage have a best schedule when each enters once and stays, and letting parts leave and come back was supposed to improve it. Searched over every set of sounding parts at every chord, it improves it by exactly nothing, with or without the chord before still masking — as long as all six must be playing at the end. Let one part be missing from the final chord and the weakest entrance gains 1.4 decibels; let two be missing and it gains 1.9, by a relay in which the parts with least room come in, are heard for one chord, and give way.

5 figures

Checkpoints sharpen the middle of a form and leave its top vague. A piece of 480 seconds divided 7 times, with how many proportions between 1 : 1 and 3 : 1 a listener tells apart at each level: timed, counted in 2-second units, and counted with a second count of 16-second phrases that can mend a lapse in the first. 480 s: 2.1 timed, 2.2 counted, 3.9 with 0 per cent of lapses shared and 2.5 with 50 per cent of lapses shared; 240 s: 2.1 timed, 2.5 counted, 7.1 with 0 per cent of lapses shared and 3.1 with 50 per cent of lapses shared; 120 s: 2.1 timed, 3.1 counted, 13.2 with 0 per cent of lapses shared and 4.0 with 50 per cent of lapses shared; 60 s: 2.1 timed, 4.1 counted, 19.4 with 0 per cent of lapses shared and 5.4 with 50 per cent of lapses shared; 30 s: 2.1 timed, 5.4 counted, 18.1 with 0 per cent of lapses shared and 7.2 with 50 per cent of lapses shared; 15 s: 5.2 timed, 12.2 counted, 12.2 with 0 per cent of lapses shared and 12.2 with 50 per cent of lapses shared; 7.5 s: 5.2 timed, 10.3 counted, 10.3 with 0 per cent of lapses shared and 10.3 with 50 per cent of lapses shared. With the two counts failing independently, the level of 60 seconds goes from 4.1 to 19.4, and the whole piece only from 2.2 to 3.9.

Form and structure

Checkpoints sharpen the middle of a form, not its top

A listener who counts bars loses the count somewhere in a long section and is thrown back on timing the whole of it. A listener who also counts phrases can mend the lapse at the last phrase. If the two counts fail independently, the level a minute long goes from four distinguishable proportions to nineteen; the whole eight-minute piece goes only from two to four, because thirty phrases are long enough to lose a count as well. And if a fifth of lapses take both counts at once, three quarters of the gain is gone.

5 figures

The content errs slow and the bass errs fast. Passages of eight bars built at three harmonic rhythms, each with a bass that states every new chord's root and moves to another chord tone on a beat 50 per cent of the time. Two readings are asked the chord rate: one from how much the pitch-class content changes across a grid, one from how completely the bass's moves land on it. At two chords a bar the content reading names the rate 63 per cent of the time, too fast 0 and too slow 37; the bass reading 100, 0 and 0. At one chord a bar the content reading names the rate 67 per cent of the time, too fast 0 and too slow 33; the bass reading 18, 80 and 2. At a chord every two bars the content reading names the rate 98 per cent of the time, too fast 2 and too slow 0; the bass reading 0, 100 and 0. The two readings miss in opposite directions and at opposite ends of the tempo range: the content reading at fast harmonic rhythms, by naming a multiple, and the bass reading at slow ones, by naming its own arpeggiation.

Harmony and voice leading

The bass errs fast where the content errs slow

Asked how often the chords change, a reading built on pitch-class content names a slower multiple and never a faster rate. Give the passage a bass that states each new root and moves between chord tones inside a chord, and a reading built on the bass's moves errs the other way: it names a faster grid and never a slower one. At two chords a bar the bass is right every time; at a chord every two bars it is never right. Six ways of combining the two readings each trade one end of the range for the other.

5 figures

Put back beside its notes, the crowd names the bass at every dynamic. A just major third on complex tones, drawn on one axis of harmonic numbers of the fundamental its ratio implies: the partials of the two played notes, and the products of those partials that clear threshold, at 55 and 80 dB. At 55 dB the products alone name 3 times the fundamental with 0 empty slots; the products and the notes together name 1 times it with 4 empty slots, and the notes alone name it with 9. At 80 dB the products alone name 1 times the fundamental with 0 empty slots; the products and the notes together name 1 times it with 0 empty slots, and the notes alone name it with 9. The soft reading on a higher note exists only when the loud notes are set aside. Taken together, the products do not decide which fundamental is named; they decide how many holes its template has.

Intervals and chords

The played notes already name the ghost bass

The products of a just third's partials, fitted on their own, name a note a twelfth above the bass when the interval is soft and drop to the bass when it is loud. Put the two played notes back beside them and the drop disappears: the notes and their products name the bass at every dynamic, because the notes' own partials are harmonics of it already. What the dynamic changes is not which note is implied but how complete its harmonic series is — nine holes from the notes alone, four when soft, none when loud.

5 figures

A harder strike buys beats only if the drop does not deepen with it. The beats a mistuned octave on A3 delivers on a string that decays in two stages, against how hard both notes are struck, with the aftersound's drop below the strike 20 dB at 80 dB and changing by a stated number of decibels for each decibel of strike. -0.5 dB per dB: 70 dB 2.5, 75 dB 5.7, 80 dB 8.9, 85 dB 11.9, 90 dB 12.2, 95 dB 11.6, 100 dB 10.9; 0 dB per dB: 70 dB 4.7, 75 dB 6.9, 80 dB 8.9, 85 dB 11.0, 90 dB 12.3, 95 dB 12.2, 100 dB 11.8; +0.5 dB per dB: 70 dB 7.2, 75 dB 8.1, 80 dB 8.9, 85 dB 9.8, 90 dB 10.7, 95 dB 11.2, 100 dB 11.9; +1 dB per dB: 70 dB 9.6, 75 dB 9.2, 80 dB 8.9, 85 dB 8.4, 90 dB 8.1, 95 dB 7.8, 100 dB 7.5. Where the drop stays put, a harder strike keeps buying beats to about 90 dB; where it deepens by a decibel per decibel, every strike past 70 dB costs beats.

Intervals and chords

A firm touch buys beats until the aftersound sinks with it

A piano string decays twice, and a mistuned octave's countable beats were found to rise with how hard the note is struck — on the assumption that the aftersound always starts twenty decibels below the strike. It need not. The moment the count shuts is set by the level the aftersound starts at and nothing else, so a harder strike buys beats only if its aftersound does not sink with it. If the drop deepens by more than 0.85 decibels for each decibel of strike, the firm touch costs beats instead.

6 figures

No seventh chord can be spaced to last as long as a triad. Every inversion and spacing within 2 octaves over C3, struck at 80 dB, for two triads and five seventh chords: the bar is the longest any spacing keeps every pair's partial coincidence, and the tick is the bound set by the chord's worst pitch-class distance — the longest any presentation of that distance lasts. major triad: 1.26 s over 12 voicings, bound 1.26 set by the minor third; minor triad: 1.26 s over 12 voicings, bound 1.26 set by the minor third; dominant seventh: 0.66 s over 32 voicings, bound 0.64 set by the tone; major seventh: 0.42 s over 32 voicings, bound 0.38 set by the semitone; minor seventh: 0.69 s over 32 voicings, bound 0.64 set by the tone; half-diminished seventh: 0.69 s over 32 voicings, bound 0.64 set by the tone; diminished seventh: 0.86 s over 32 voicings, bound 0.87 set by the tritone. Every seventh chord contains a distance worse than any a triad contains, except the diminished seventh, whose distances are only minor thirds and tritones.

Timbre and acoustics

A seventh chord cannot be spaced to last like a triad

A struck triad keeps the partial coincidences of all its intervals for at most 1.26 seconds, whichever way it is spaced. Run the same census over every inversion and spacing of five kinds of seventh chord and none gets near: the dominant, minor and half-diminished sevenths top out at about two thirds of a second, the major seventh at 0.42. The diminished seventh, which theory calls the least stable of them, lasts longest at 0.86 — because it is the only one with no tone or semitone among its pitch-class distances, and the worst distance a chord contains sets a ceiling no spacing can lift.

5 figures

The ceiling is thirteen bars, and every one of them has a name. Every bar of the six schemes read by the key-finder at a key cost of 3 and a bass weight of 3, with the chord in every bar given exactly — no segmentation is involved. 175 of 188 bars have both the key and the degree right, 93.1 per cent. The misses: 7 in the thirty-two-bar song's bridge, where the chain III7 is read in E major, III7 is read in E major, VI7 is read in E major, VI7 is read in D major, II7 is read in D major, II7 is read in D major, V7 is read in D major; 4 bars of the rondo's A minor episode read as C major; 2 next to a change of key; and 0 of any other kind.

Scales and modes

The ceiling is thirteen bars with names

The key-finder's two cues stop buying anything at about 93 per cent of scheme bars read right, and the obvious suspect was the chord segmentation feeding it. The reading was never given a segmentation: every bar arrives with its true chord. What the ceiling is made of can be listed instead, and it is thirteen bars of 188 — seven in a bridge of secondary dominants, four in a minor episode whose chords C major also owns, and two at the edges of a modulation. No weight of any cue moves one of them.

5 figures

A staccato is the direct sound's, and the room takes it within a fifth of the critical distance. A note on 130.8 Hz held 0.4 s and damped, in a room of 2 s reverberation, heard at distances from 0.02 to 5 times the critical distance: how long after the release the note takes to fall 10 dB and 20 dB. To fall 10 dB: 24 ms at the source, 333 ms far away; 0.02: 24 ms, 0.05: 25 ms, 0.1: 25 ms, 0.15: 26 ms, 0.2: 28 ms, 0.3: 35 ms, 0.5: 103 ms, 0.75: 187 ms, 1: 234 ms, 1.5: 281 ms, 2: 302 ms, 3: 318 ms, 5: 328 ms; doubled by 0.38 of the critical distance. To fall 20 dB: 49 ms at the source, 667 ms far away; 0.02: 49 ms, 0.05: 51 ms, 0.1: 60 ms, 0.15: 117 ms, 0.2: 198 ms, 0.3: 308 ms, 0.5: 436 ms, 0.75: 520 ms, 1: 568 ms, 1.5: 614 ms, 2: 635 ms, 3: 652 ms, 5: 661 ms; doubled by 0.14 of the critical distance. Where the direct sound and the room are equal, the damper's work is already hidden: the room's copy is only 20 dB below the direct sound at a tenth of the critical distance, and a 20 dB fall reaches it there.

Timbre and acoustics

Only the player hears a staccato end

A damper stops a string in a seventh of a second, and in a hall the room goes on for two. A listener hears both, mixed in proportion to how close they sit, and the question was at what distance the short part stops mattering. The answer is closer than any seat. A damped note's twenty-decibel fall has doubled in length by a seventh of a hall's critical distance — 77 centimetres in a two-second concert hall — and by a quarter of it in a jazz club. The end of a staccato is something the pianist hears and the front row does not.

5 figures

Perception and the listener

The arch belongs to hearing, not to the series

A chord delivers most of its partials in the middle of the compass and loses them in the bass and the treble, and every spectrum that showed that arch was built on whole multiples of a fundamental. Give the same amplitudes to a bell's eight modes and to a stiff string's stretched partials and the arch is still there, peaking within a major third of where the harmonic series peaks. What the spacing changes is the detail: a bell crowds its tierce and quint into a quarter of a critical band in the bass and loses them, and a stiff string's stretch buys the bass back.

5 figures

Rhythm and metre

A late dancer needs the landmarks, not the rhythm

A listener who joins an additive-metre dance part-way recognises it far more reliably with the downbeat accented. Strip the stream down to its landmarks — the onsets that begin a bar or a long beat, with every other onset removed — and the listener does as well or better: knowing a hundred metres, 23 per cent are recognised within the present against 14 with every onset. Unmarked, the landmarks still beat every onset with the long beats accented. Neither half does it alone; what identifies a metre from a late entry is where its long beats sit relative to its bar.

5 figures

Against a pulse, the bell pattern is the quickest of its orders to place. The bits of position a listener is still missing, averaged over the first cycle heard, for each cyclic order of the gaps 1 1 2 2 2 2 2 in 12 steps, heard alone, against a pulse every three steps and against a pulse every four, at perfect memory, half-life 3 steps, half-life 1.5 steps. 2 2 2 1 2 1 2: alone 1.08, 1.23, 1.73; against a pulse every 3 steps 0.69, 0.75, 0.96; against a pulse every 4 steps 0.63, 0.67, 0.85. 2 2 2 2 1 1 2: alone 1.22, 1.63, 2.02; against a pulse every 3 steps 0.60, 0.73, 0.92; against a pulse every 4 steps 0.83, 1.07, 1.36. 2 2 1 2 2 1 2 (the standard bell pattern): alone 1.25, 1.45, 1.82; against a pulse every 3 steps 0.54, 0.56, 0.67; against a pulse every 4 steps 0.55, 0.57, 0.68. Alone, the bell pattern is not the quickest order to place at any memory. Against either pulse it is the quickest at every memory.

Rhythm and metre

Against a pulse the bell pattern is the easiest to place

Heard alone, the standard bell pattern is not the quickest order of its own gaps to place in its cycle, for a listener with any memory. Heard against a pulse every three steps or every four — which is how anyone hears it — it is the quickest, at every memory and at every alignment of pulse and bell, and by a wide margin: at a memory of a quarter of the cycle, 0.56 bits unplaced over the first cycle against 0.73 for either rival against a pulse in threes. Six of eight named timelines do the same. A timeline's order of gaps looks chosen for how it sits against the beat, not for how it sounds alone.

5 figures $A timed expectation would erase a slow cycle's cost, and a listener cannot time a slow cycle that well. Bits of position a listener with a 3.5-second memory is still missing over the first cycle of son clave, against how long the cycle takes, for a newcomer with no expectation, a listener timing the cycle with the Weber fraction a duration that long is judged with, and a listener timing it to ten per cent. a newcomer, no expectation: 2 s 0.94, 8 s 0.97, 24 s 1.41, 40 s 2.02, 60 s 2.47; timing as well as listeners do: 2 s 0.68 (w 0.150), 8 s 0.69 (w 0.150), 24 s 0.85 (w 0.150), 40 s 1.90 (w 0.375), 60 s 2.38 (w 0.375); timing the cycle to ten per cent: 2 s 0.47, 8 s 0.48, 24 s 0.55, 40 s 0.73, 60 s 1.02. At ten per cent even a sixty-second cycle is placed about as well as a newcomer places a two-second one. At the precision a listener actually has for durations of half a minute or more, the expectation is worth a tenth of a bit.$ Rhythm and metre

An expectation cannot rescue a cycle too slow to time

A listener who knows a piece arrives with an expectation of where in the cycle they are, and the size of that expectation was the number the last essay said nobody had. It can be given one: a listener who has been timing the cycle carries a spread of their Weber fraction times the cycle, which is the same number of steps at any tempo. Timed to ten per cent, a forty-second cycle would be placed better than a newcomer places a two-second one. But forty seconds is judged in the band where the Weber fraction is nearer forty per cent, and there the expectation is worth a tenth of a bit.

5 figures

Counted over what arrives, the balanced bass is not the roughest register. The mean roughness of the I – vi – IV – V – I arrivals with each chord played as loud as the written register's, relative to the written register, counted over every partial and over the partials that stand above what the rest of the chord masks. Every partial: 70 −2 octaves, 7.48 −1 octave, 1.00 as written, 0.20 +1 octave. Delivered partials only: 6e-9 −2 octaves, 2.83 −1 octave, 1.00 as written, 0.19 +1 octave. Over every partial the lowest register is 343 times rougher than the highest; over what arrives it is the smoothest of the four, and the roughest is −1 octave, 2.8 times the written register.

Perception and the listener

A bass chord low enough to balance has already hidden its tenor

Played as loud as the written register, a progression two octaves down is 343 times rougher than the same progression an octave up — if every partial on the page is counted. Count only the partials that stand above what the rest of the chord masks and that register is the smoothest of the four, with nothing left that beats. The balance is not what does it: the extra thirteen decibels move no voice by more than two partials. The register had already buried the tenor at the written dynamic.

6 figures

A wrong bar costs the same whichever instrument it is on. What moving one degree of a measured slendro by 10 cents, flat or sharp, adds to the roughness per second of a two-instrument texture — a ringing part at 0.15 s a note over a damped one four times slower — on the ringing instrument and on the damped one. The ensemble in tune scores 7.47. Degree 1 (0¢): ringing 0.142 flat and 0.202 sharp, damped 0.163 and 0.185, of which beating 0.178; Degree 2 (231¢): ringing 0.119 flat and 0.068 sharp, damped 0.096 and 0.090, of which beating 0.093; Degree 3 (474¢): ringing 0.106 flat and 0.021 sharp, damped 0.069 and 0.057, of which beating 0.063; Degree 5 (717¢): ringing 0.079 flat and 0.072 sharp, damped 0.075 and 0.078, of which beating 0.077; Degree 6 (955¢): ringing 0.023 flat and 0.018 sharp, damped 0.019 and 0.022, of which beating 0.020. Over all ten errors the ringing instrument's cost 0.85 and the damped one's 0.85, and the wrong bar beating against the other instrument's right one comes to 0.86 on either — as much as the whole, because the intervals the error changes add as often as they save. One error costs about 1.1% of the texture's roughness.

Scales and modes

A wrong bar beats the same on either instrument

The ringing instrument carries a gamelan scale's standing, so a tuning error on it was predicted to cost more than the same error on the damped instrument. Put in the beating the model lacked, and the prediction fails: moved ten cents, a degree costs the same 0.85 summed over the scale on either instrument, because almost all of the cost is the wrong bar beating against the right one on the other instrument, and a beat belongs to both of the bars that make it. Moving a whole instrument costs exactly what its five degrees cost separately, and it takes nothing from the scale's standing.

6 figures

Harmony and voice leading

A bass that holds through a change marks the barline

At two chords a bar the chords change on the barline and on the half-bar alike, so a reading of where they change is at chance, and the metre ties the two. The bass has one more piece of evidence: a change inside the bar can be voiced over the note already sounding, and a change on the barline is voiced over its root. Hold the bass through one mid-bar change in six and the metre and bass together place the barline in 85 per cent of eight-bar passages; one in three, 97. The convention cannot be stronger than that, and the chord changes, asked first, only get in the way.

6 figures

Before that

Everything published earlier, newest first. Titles only — the cards are on the full listing.

16 September 2026

4 essays on pitch and tuning, timbre and acoustics, perception and the listener and scales and modes

A tuning is right for some chords and wrong for the rest — pitch and tuning
A damper cannot reach into the room — timbre and acoustics
The error that moves straight ahead — perception and the listener
The two parameters turn out to have a ceiling between them — scales and modes

15 September 2026

20 essays on timbre and acoustics, intervals and chords, form and structure, pitch and tuning, rhythm and metre, harmony and voice leading and scales and modes

A bow holds the number a blow hides — timbre and acoustics
The room is the slower of the two — timbre and acoustics
A damper changes the clock, not the colour — timbre and acoustics
A minor triad can be spaced to last — intervals and chords
Three harmonics of the bass arrive before the bass — intervals and chords
The ghost bass drops a twelfth at a forte — intervals and chords
One note in the compass loses its pizzicato — timbre and acoustics
A count is not an estimate — form and structure
A form is sharp at the bottom and vague at the top — form and structure
A golden section is a coin toss with six coins — form and structure
The ceiling everybody names is the loose one — form and structure
One tuning has no comma to place — pitch and tuning
The quartet settles at two pitches, not four — pitch and tuning
Repetition buys least where it is needed most — rhythm and metre
The change reading follows the chords, not the bar — harmony and voice leading
Asked for the rate, it answers a multiple — harmony and voice leading
The tempo moves a scale further than the touch — scales and modes
The scale belongs to the ringing instrument — scales and modes
Given the bar in octaves, the degree comes back — scales and modes
A sharper cue is worth nothing to a reading that moves — scales and modes

13 September 2026

15 essays on form and structure, harmony and voice leading, intervals and chords, pitch and tuning, rhythm and metre, scales and modes and timbre and acoustics

A proportion is only as fine as its two durations — form and structure
A return is shorter than its first hearing — form and structure
A final chord stands out for a twentieth of a second — form and structure
The chords mark the barline by changing there — harmony and voice leading
A rough arrival is rough because of its spacing — harmony and voice leading
A combination-tone bass needs a forte — intervals and chords
An open triad lasts as long as its tenth — intervals and chords
An open string pulls the quartet flat — pitch and tuning
A guitar tuned by harmonics hides a comma — pitch and tuning
A string that decays twice is counted early — pitch and tuning
Knowing every metre is slower than knowing none — rhythm and metre
The bell pattern is slowest only to a perfect memory — rhythm and metre
A scale is committed to how long its instrument rings — scales and modes
A room keeps a pizzicato from giving its note away — timbre and acoustics
A dancer who comes in late needs the downbeat marked — rhythm and metre

12 September 2026

17 essays on pitch and tuning, intervals and chords, timbre and acoustics, scales and modes, harmony and voice leading, rhythm and metre and form and structure

Counted in the decay, or not at all — pitch and tuning
The third sound magnifies cents, not hertz — intervals and chords
The tone on the root changes hands at the fifth — intervals and chords
A major triad's combination tones are its own notes — intervals and chords
The bass line under a passage in thirds — intervals and chords
The tuning a string quartet cannot change — pitch and tuning
The cello cannot hear its own tempering — pitch and tuning
An inversion lasts as long as its outer sixth — timbre and acoustics
A doubled pizzicato gives its note away early — timbre and acoustics
Two cues meet in a corner — scales and modes
A bass line is not a list of roots — scales and modes
The smoothness is in the skips — scales and modes
The chords never move the barline — harmony and voice leading
The chords are a weak witness to the barline — harmony and voice leading
The other censuses keep evenness, not locating — rhythm and metre
The accent buys two units, however loud it is — rhythm and metre
Room is used up by whoever enters first — form and structure

9 September 2026

20 essays on form and structure, intervals and chords, pitch and tuning and scales and modes

An entrance is a change of colour — form and structure
The release is on the wrong side — form and structure
A part that leaves is not a part that arrives — form and structure
The chord that has room for an entrance — form and structure
An interval is two posteriors subtracted — intervals and chords
Which end the mistuning is on — intervals and chords
The setting is not the preference — intervals and chords
An orchestra is given a note — pitch and tuning
Who listens to whom when an orchestra tunes — pitch and tuning
The unison is the coarsest thing in the room — pitch and tuning
A consensus with nothing to hold it — pitch and tuning
One fluctuation or two — pitch and tuning
How hard the note was struck — pitch and tuning
A note lasts until the next one starts — scales and modes
The notehead that is not a note — scales and modes
Leaps do not fall where offbeats do — scales and modes
One number for a page — scales and modes
A boundary beside a fifth — scales and modes
The best seven of the twelve — scales and modes
The unequal scale that is easier to name — scales and modes

8 September 2026

20 essays on instruments and their design, perception and the listener, intervals and chords, harmony and voice leading, timbre and acoustics, rhythm and metre and form and structure

Which notes go brassy first — instruments and their design
The throat that decides both — instruments and their design
The interval between two quills — instruments and their design
A bar and its pipe are one object — instruments and their design
Where a woodwind actually sounds from — instruments and their design
Where a wrong head gives itself away — perception and the listener
A subito piano is four seconds longer in the bass — perception and the listener
A clarinet keeps what a string loses — perception and the listener
A short note is heard more in tune than it is — intervals and chords
A tonic bought with the function — harmony and voice leading
A fourth decision, and two that were never made — harmony and voice leading
Eighty-one chords, one number — harmony and voice leading
A fifth on a piano is not a fifth a second later — timbre and acoustics
An orchestrator doubles a line, not a chord — instruments and their design
The blend arrives before the note does — timbre and acoustics
A twenty-five is a nine until its last unit — rhythm and metre
The longest silence is not a third axis — rhythm and metre
A general pause is spent by the note after it — form and structure
Where the note is costs more than which note it is — rhythm and metre
Every member of a beat family is the same depth — intervals and chords

5 September 2026

50 essays on instruments and their design, perception and the listener, rhythm and metre, timbre and acoustics, form and structure, harmony and voice leading, intervals and chords, scales and modes and pitch and tuning

The resonator at the far end — instruments and their design
The mouth that decides nothing — instruments and their design
The cutoff that is a list — instruments and their design
The partials the tube makes itself — instruments and their design
The turn is half the angle — perception and the listener
A smaller head in the same hall — perception and the listener
A blown note does not start late, it starts slowly — perception and the listener
Eleven partials is one too many — perception and the listener
How long a limping bar can be — rhythm and metre
The cycle that outruns the memory — rhythm and metre
The frontier and the ruler — rhythm and metre
The parent nobody measured — rhythm and metre
The hair runs the wrong way — instruments and their design
What the rosin is worth — instruments and their design
What the second register is for — instruments and their design
What the tongue actually removes — rhythm and metre
Read at two different heights — perception and the listener
A part entering is not a change of level — perception and the listener
A staccato is a dynamic mark — perception and the listener
The listener is given the top voice, and the bass as a sine — perception and the listener
A low chord stops being rough by stopping being a chord — perception and the listener
A section has a loudest member, not a colour — timbre and acoustics
The blend table has a row for every note — timbre and acoustics
A soft chord has to fade in — form and structure
The fourth player is a spectrum, not a decision — instruments and their design
A bar's partials are the odd numbers, squared — instruments and their design
One cut cannot place two partials — instruments and their design
The tube shuts on the partial the arch placed — instruments and their design
The four ways a marimba loses what its arch placed — instruments and their design
The bars a key is made of — harmony and voice leading
The key-finder with no tonic — harmony and voice leading
The surprise of nothing happening — harmony and voice leading
Where the chord actually lands — harmony and voice leading
The long note and the strong note — harmony and voice leading
Three beats at most, and only in the middle of the keyboard — intervals and chords
The scale least committed to its own instrument — scales and modes
A boundary costs the same wherever it is put — scales and modes
The part of the error a key cannot touch — intervals and chords
One cup and seven lengths — timbre and acoustics
The top that falls while the note lasts — timbre and acoustics
The middle nobody could have guessed — timbre and acoustics
The collapse belongs to the bass — timbre and acoustics
A standard moves the page, and not the seam — pitch and tuning
A standard is a point, and a performance is a band — pitch and tuning
The partial that gets louder as it goes sharp — instruments and their design
The rate that does not rise with the partial — instruments and their design
Twelve violins are more punctual than one — rhythm and metre
An attack time is not an attack — perception and the listener
A rest needs a dry room — form and structure
Four parts are easier to read than two — harmony and voice leading

3 September 2026

20 essays on instruments and their design, timbre and acoustics, rhythm and metre, pitch and tuning, form and structure, intervals and chords, perception and the listener, harmony and voice leading and scales and modes

What a cup does to the support — instruments and their design
The bell is tuned for the cup — timbre and acoustics
A hole is a short tube — instruments and their design
Three exciters and three wires — instruments and their design
The bow is not a point either — instruments and their design
The pitch that does not wobble — instruments and their design
A note starts twice — rhythm and metre
The instrument that cannot be moved — pitch and tuning
Two players on one note — timbre and acoustics
The dissonance arrives and the dynamic does not — form and structure
A beat is never one beat — intervals and chords
The hall through a head — perception and the listener
An equal note cannot be masked — perception and the listener
The cue that settles it — perception and the listener
A page has two decibels — perception and the listener
The listener who forgets — harmony and voice leading
Two surprises and one event — harmony and voice leading
A reader does not read notes — scales and modes
A rest is a diminuendo — form and structure
The passage that separates two players — rhythm and metre

1 September 2026

20 essays on instruments and their design, pitch and tuning, rhythm and metre, timbre and acoustics, intervals and chords, perception and the listener, harmony and voice leading, form and structure and scales and modes

A note takes a number of periods to speak — instruments and their design
The higher note speaks sooner and takes longer — pitch and tuning
The hardest place is also the latest — rhythm and metre
A family resemblance in the heights — instruments and their design
The vent a cone cannot place — instruments and their design
The flare that makes a series harmonic — timbre and acoustics
The crossing belongs to the felt — timbre and acoustics
A woodwind cannot be pulled to a new standard — pitch and tuning
The beat a tuner can actually use — intervals and chords
The mean survives the window — intervals and chords
A position and a width — perception and the listener
The exchange rate nobody has — perception and the listener
Expectation is a curve, not a list — harmony and voice leading
A loud chord is a smaller chord — harmony and voice leading
The reading was a step response — form and structure
A subito piano is a rate, not a level — form and structure
A family of readings — rhythm and metre
How many bars an ensemble needs — rhythm and metre
How much of the reading arrives late — scales and modes
The page is read by an eye — scales and modes

30 August 2026

40 essays on instruments and their design, timbre and acoustics, pitch and tuning, intervals and chords, perception and the listener, rhythm and metre, form and structure, scales and modes and harmony and voice leading

Only two shapes make a series — instruments and their design
What the mouthpiece is actually for — timbre and acoustics
A horn has one length per partial — pitch and tuning
The hand goes in, and the note jumps — pitch and tuning
Two dials the player turns together — instruments and their design
The corner does not come back a corner — timbre and acoustics
Sixteen sweeps against sixteen — intervals and chords
A room with directions in it — perception and the listener
The spectrum that will not fuse — perception and the listener
A low note cannot start on time — rhythm and metre
The shape a wall leaves behind — rhythm and metre
The dynamics are in the score already — form and structure
A final chord is not made loud by adding to it — form and structure
The notes in between — intervals and chords
It was never the strings that stopped the climb — pitch and tuning
The axis that is not a time axis — scales and modes
The number every claim here has been quoting — scales and modes
A modulation and a borrowing are one number apart — scales and modes
A count and a correlation — harmony and voice leading
Surprise is a number — harmony and voice leading
Who plays what and how loud is one question — form and structure
The ranking survives the dynamic and the chord does not — harmony and voice leading
A dynamic mark changes what a note is — timbre and acoustics
A resonance has a strength as well as a frequency — pitch and tuning
The cutoff a maker can actually measure — instruments and their design
The hardest place on the fingerboard — instruments and their design
An echo is prevented by the crowd around it — perception and the listener
The partials that do not die together — perception and the listener
Four terms, and only one of them binds — timbre and acoustics
A roughness with a rate of its own — intervals and chords
A beat has a depth, and six essays held it at one — intervals and chords
The quantity a rival account says is not there — intervals and chords
The parameter that did not decide the answer — form and structure
A detector whose resolution the performance sets — form and structure
A chord, given a key and a predecessor — harmony and voice leading
The passage built to make them disagree — harmony and voice leading
Which notes have to be played early — rhythm and metre
The margin the dynamic program already had — scales and modes
How much music a page holds — scales and modes
A cycle that says where it is — rhythm and metre

28 August 2026

20 essays on rhythm and metre, instruments and their design, perception and the listener, form and structure, timbre and acoustics, pitch and tuning, intervals and chords, scales and modes and harmony and voice leading

A note is heard after it starts — rhythm and metre
The players who have to be early — instruments and their design
Playing louder is playing earlier — perception and the listener
Loud is relative, and it comes down slowly — form and structure
A quantity resting against a wall — rhythm and metre
Which player on which note — timbre and acoustics
Every partial beats at its own rate — pitch and tuning
A section against another section — timbre and acoustics
How much an anchor would have to be worth — intervals and chords
The listener the model was never run for — scales and modes
Where the two ears stop agreeing — perception and the listener
The hand that changes the bore — pitch and tuning
The fourth top is the maker's — intervals and chords
The same note is a different width — instruments and their design
The pulse that was assumed — timbre and acoustics
What the climb was a search for — pitch and tuning
A key-finder that keeps the order — harmony and voice leading
The cadence as evidence — harmony and voice leading
The level the tempo chooses — form and structure
The notations invented for the overflow — scales and modes

27 August 2026

15 essays on perception and the listener, timbre and acoustics, intervals and chords, pitch and tuning, instruments and their design, harmony and voice leading, rhythm and metre, scales and modes and form and structure

A chord is not as loud as its notes — perception and the listener
Which instrument is underneath — timbre and acoustics
An interval is two errors — intervals and chords
The boundary that barely moves — perception and the listener
The pair tuned apart on purpose — pitch and tuning
The partial the lips cannot reach — pitch and tuning
The hammer that is heavier than its string — instruments and their design
The note the body will not let start — instruments and their design
The alternation a key-finder cannot follow — harmony and voice leading
Three decisions that constrain each other — harmony and voice leading
What the clave buys with its unevenness — rhythm and metre
The short note is sitting on the floor — rhythm and metre
The note that sounds twice — intervals and chords
The clef is an integer — scales and modes
A boundary at a stated level — form and structure

26 August 2026

15 essays on harmony and voice leading, scales and modes, form and structure, intervals and chords, instruments and their design, perception and the listener, timbre and acoustics, rhythm and metre and pitch and tuning

Why the exercise is in four parts — harmony and voice leading
The set with fewer modes than notes — scales and modes
The repeat that is not in the notes — form and structure
What the onsets left out — form and structure
Two keys at once — harmony and voice leading
How many boxes an octave holds — intervals and chords
The chord that is not played at once — intervals and chords
Three strings, and the note that comes back — instruments and their design
The hammer is not a point either — instruments and their design
How long a note has to be — perception and the listener
The beat that is not in the air — perception and the listener
The note that gets duller as it dies — timbre and acoustics
An instrument is not one timbre — timbre and acoustics
How unequal a beat is allowed to be — rhythm and metre
Blowing harder is playing sharper — pitch and tuning

24 August 2026

15 essays on scales and modes, pitch and tuning, rhythm and metre, timbre and acoustics, instruments and their design, harmony and voice leading, perception and the listener, form and structure and intervals and chords

The stave is not a ruler — scales and modes
Two names for one key — pitch and tuning
The time signature is a claim — rhythm and metre
The mark that is not a level — timbre and acoustics
What a tablature keeps — instruments and their design
Three notations, one progression — harmony and voice leading
The note that has a length — rhythm and metre
The part of the tune that is kept — perception and the listener
The twelfth, and where it comes from — form and structure
The pitch that moves the wrong distance — perception and the listener
The one note that decides the mode — scales and modes
The series has three tops — intervals and chords
A standard is a specification — pitch and tuning
The hole that spoils a note — instruments and their design
Where a phrase ends — form and structure

22 August 2026

15 essays on scales and modes, form and structure, instruments and their design, pitch and tuning, timbre and acoustics, rhythm and metre, intervals and chords and harmony and voice leading

A melody is a walk, not a set — scales and modes
The leap that pays itself back — form and structure
The shape that survives everything else — form and structure
The register where the series becomes a scale — instruments and their design
The note that is sharp because of where it goes — pitch and tuning
The sound a listener knows best — timbre and acoustics
What a choir does that a soloist cannot — timbre and acoustics
A degree is where it goes next — scales and modes
The ratio that stops being two — rhythm and metre
The rotation the necklace cannot see — rhythm and metre
The note has to start somewhere — instruments and their design
The series is not a chord — intervals and chords
The same distance, under two names — intervals and chords
Which notes are the chord — harmony and voice leading
The note that moved by a minor third — pitch and tuning

21 August 2026

15 essays on instruments and their design, timbre and acoustics, pitch and tuning, intervals and chords, harmony and voice leading, form and structure and scales and modes

The other instrument with a reed — instruments and their design
Two mechanisms, and the seam between them — instruments and their design
One voice over ninety players — timbre and acoustics
A note that is never at its pitch — pitch and tuning
The inversion that cannot end a phrase — intervals and chords
The root an ear supplies — intervals and chords
A chord is a register — intervals and chords
A stack that is not thirds — harmony and voice leading
An ending is a deceleration — form and structure
An ending that can be heard coming — form and structure
A silence long enough to be an ending — form and structure
The reed is a valve, not a vibrator — instruments and their design
A wind instrument is a thermometer — pitch and tuning
The bell decides what gets out — timbre and acoustics
A scale built downward from a fourth — scales and modes

20 August 2026

15 essays on scales and modes, pitch and tuning, perception and the listener, intervals and chords, harmony and voice leading and timbre and acoustics

The only sizes a fifth will make — scales and modes
Every universe has one, or none — pitch and tuning
Nothing in the census knows which note is home — scales and modes
What a tonic costs in seconds — perception and the listener
The mode with no fifth — intervals and chords
One dominant among seven — harmony and voice leading
Seven rotations that are not seven modes — scales and modes
Parallel and relative are two different maps — scales and modes
The third the model has no opinion about — intervals and chords
Three answers to how finely a pitch can be heard — perception and the listener
The spectrum that was supposed to explain the gamelan — timbre and acoustics
A tuning is not a table of cents — pitch and tuning
Three ways to measure how far a key is — harmony and voice leading
How much evidence a modulation needs — perception and the listener
The circle is a circle, and the map is not — scales and modes

19 August 2026

15 essays on rhythm and metre, pitch and tuning, perception and the listener, form and structure, instruments and their design and timbre and acoustics

The third pattern nobody played — rhythm and metre
Which of the two is the beat — rhythm and metre
The bell is not a polyrhythm — rhythm and metre
One player is not two clocks — rhythm and metre
A comma is a polyrhythm that never closes — pitch and tuning
The right period at the wrong phase — rhythm and metre
Syncopation is a number about the metre — rhythm and metre
The beat that is never sounded — perception and the listener
No term for an unequal beat — rhythm and metre
A metre has to be able to change its mind — form and structure
The deviations are not noise — rhythm and metre
Two players and no clock — instruments and their design
How late is a different note — perception and the listener
The first eighty milliseconds are a different room — timbre and acoustics
The model has nobody in it — instruments and their design

17 August 2026

15 essays on form and structure, perception and the listener, harmony and voice leading, intervals and chords and instruments and their design

How long until it comes back — form and structure
The form a first hearing cannot have — form and structure
The same thing somewhere else — form and structure
A return has to be remembered — perception and the listener
Where a repeat is changed — form and structure
What the rules cost — harmony and voice leading
Two criteria that are taught as one — harmony and voice leading
The resolution the metric cannot find — harmony and voice leading
A voice is a stream, and the ear decides which — perception and the listener
Which harmonics carry the pitch — intervals and chords
Two pipes for a note neither makes — instruments and their design
A pitch with nothing to match — perception and the listener
The bass a small loudspeaker does not make — instruments and their design
A dissonance is what has to be resolved — harmony and voice leading
The same chord is harsher when it is louder — intervals and chords

16 August 2026

15 essays on pitch and tuning, harmony and voice leading, scales and modes, intervals and chords, timbre and acoustics and perception and the listener

A fraction of a comma — pitch and tuning
What a temperament cannot do — pitch and tuning
Somebody has to pay the comma — harmony and voice leading
A comma under the threshold — pitch and tuning
Where the chain was never closed — scales and modes
A spectrum chooses its own scale — intervals and chords
Roughness cannot choose a scale — intervals and chords
A dissonance has to last — intervals and chords
Where to put the third — harmony and voice leading
Where a room stops being a room — timbre and acoustics
How far away the room takes over — perception and the listener
A room does not decay evenly — timbre and acoustics
Every interval a different number of times — scales and modes
The same algorithm made a Cuban rhythm — scales and modes
Why seven — scales and modes

14 August 2026

15 essays on form and structure, harmony and voice leading, timbre and acoustics and rhythm and metre

A piece is mostly itself again — form and structure
The boundary is where the neighbourhood changes — form and structure
How much of this is new — form and structure
A phrase is a number of seconds — form and structure
One of these eight-bar phrases accelerates — form and structure
What makes an ending an ending — form and structure
An ending that exists so a bigger one can — form and structure
The bar above the bar — form and structure
The key plan is the form — form and structure
The chord that did not come — harmony and voice leading
How often the chord changes — harmony and voice leading
The room chooses the harmonic rhythm — timbre and acoustics
A cycle cannot cadence — form and structure
A process that enumerates its own form — rhythm and metre
A melody that can accompany itself — harmony and voice leading

13 August 2026

15 essays on instruments and their design, timbre and acoustics and pitch and tuning

A tube that skips every other partial — instruments and their design
A cone is not a cylinder — instruments and their design
The tube ends after it ends — instruments and their design
Above a certain note the holes stop working — instruments and their design
One hole doing a dozen jobs — instruments and their design
Where the hammer lands — instruments and their design
A hammer is not an impulse — instruments and their design
The bow makes a corner — instruments and their design
How much bow is allowed — instruments and their design
A bell has no fundamental — instruments and their design
What a drum is doing instead — instruments and their design
The body is the filter — timbre and acoustics
The other wolf — timbre and acoustics
A guitar cannot be in tune — pitch and tuning
An instrument points — timbre and acoustics

11 August 2026

15 essays on perception and the listener, timbre and acoustics, pitch and tuning, intervals and chords and rhythm and metre

The quietest thing audible, and why the volume knob is a tone control — perception and the listener
One sound hides another, and it hides upward — perception and the listener
A sound hides what came before it — perception and the listener
The ear builds objects, and sometimes offers a choice — perception and the listener
What makes two partials one note — timbre and acoustics
Two ears, and the whole of the difference is 655 microseconds — perception and the listener
The first wavefront wins — perception and the listener
How small a difference is audible — perception and the listener
The octave that is not two to one — perception and the listener
A memory for the note itself, and it is dated — pitch and tuning
The chord is still major, and that is why temperament works — perception and the listener
Counting produced the hierarchy — perception and the listener
Consonance is half learned, and this is the half — perception and the listener
The ear makes its own sound, and it is not the missing fundamental — intervals and chords
The beat has a preferred rate, and it is not the notation's — rhythm and metre

10 August 2026

12 essays on pitch and tuning, intervals and chords, scales and modes, harmony and voice leading, rhythm and metre and timbre and acoustics

A tuner counts beats, and that is the whole method — pitch and tuning
The pitch nobody agreed on, for four hundred years — pitch and tuning
Three is the largest agreeable number — intervals and chords
The ear sorts into boxes, and the boxes are the theory — intervals and chords
Two sizes of every step, which is why the names work — scales and modes
A scale without an octave, and the spectrum that asks for it — scales and modes
The progression that never comes home — harmony and voice leading
Two voices that stop being two — harmony and voice leading
A rhythm fast enough to be a chord — rhythm and metre
The beat is inferred, and sometimes wrongly — rhythm and metre
How long a room rings, and where the formula stops — timbre and acoustics
The first fifty milliseconds — timbre and acoustics

3–7 August 2026

34 essays on pitch and tuning, intervals and chords, scales and modes, harmony and voice leading, rhythm and metre and timbre and acoustics

Twelve fifths and seven octaves, which are not the same thing — pitch and tuning
Where to hide the comma, which is the only real question — pitch and tuning
The wolf at the end of the chain — pitch and tuning
A second comma, arriving by a different road — pitch and tuning
Keys that had characters, and could be measured — pitch and tuning
Nineteen, thirty-one and fifty-three — pitch and tuning
Two notes and a ratio, which is the whole of consonance — intervals and chords
Beats are arithmetic that anybody can hear — intervals and chords
Roughness can be computed, and the answer looks like a scale — intervals and chords
The note that is not there — intervals and chords
A third is rougher in the bass — intervals and chords
Seven of the twelve, chosen unevenly — scales and modes
The same seven, started later — scales and modes
Keys are neighbours, and the map is computed — scales and modes
Five notes, and no semitones — scales and modes
What a raised seventh is for — scales and modes
A scale is not a set of pitches — scales and modes
Three notes at once, and why these three — harmony and voice leading
The shortest move, which is what a chord change is — harmony and voice leading
A progression is a path, and the map can be drawn — harmony and voice leading
The interval that inverts to itself — harmony and voice leading
Chords as a space — harmony and voice leading
Rhythm is a circle, and the bar line is a choice — rhythm and metre
As evenly as possible, which turns out to be a famous rhythm — rhythm and metre
Two clocks at once, and where they agree — rhythm and metre
Swing is a ratio, and it is not two to one — rhythm and metre
Beats of unequal length — rhythm and metre
The milliseconds that are the groove — rhythm and metre
A string does everything at once — timbre and acoustics
The ear hears the list, not the shape — timbre and acoustics
The shape of a note, which is most of what an instrument is — timbre and acoustics
The room is part of the instrument — timbre and acoustics
A vowel is two resonances — timbre and acoustics
The piano is tuned wrong on purpose — timbre and acoustics

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