Plogger Method — Complete Reference

Introduction

The Plogger Method is the foundational pedagogical system developed by Marianne Ploger at the Blair School of Music, Vanderbilt University. It is the Musical Operating System of the Adaptable Musician's Framework (AMF) — the layer on which all chamber work (Melody, Harmony, Voicings, Rhythm) and synthesizer work rest. The method's lineage descends directly from Nadia Boulanger through Ploger, and the textbook carries a foreword by Charles Rochester Young.

This reference synthesizes the complete three-book system — Textbook, Practice Manual, and Workbook — into a single navigable document for AMF practitioners.

Six Core Philosophical Premises

System Architecture

The Adaptable Musician's Framework (AMF) is the overall system name. Its layers:

Three Books

• Textbook — Core concepts, explanations, and chapter content
• Practice Manual — Structured daily exercises and protocols
• Workbook — Written exercises and ear training drills

Four Practice Sections (Daily Session Structure)

Core Pedagogical Principles

• Hear/Sing Before You Play — Audiation precedes physical execution at every stage
• Few exercises, multi-layered — Deep fluency in a small set beats shallow exposure to many
• Plogger as dual presence — The method functions as both content and the lens through which all content is perceived
• Three Stages labeling — Every practice activity is explicitly tagged as Stage 1, 2, or 3
• Anchor song thread — A single song is learned across all chambers simultaneously
• Genre-agnostic — The system applies equally to classical, jazz, folk, pop, and all other genres

Ch.1 — Three Stages of Learning

All skill acquisition proceeds through three distinct stages. Conflating them — performing Stage 2 behavior during Stage 3, or skipping Stage 2 entirely — is the single most common cause of permanent plateaus.

Stage 1 — Roughing In

First contact with new material. Errors are normal and expected — do not stop to correct them. The sculptor analogy: you are roughing out the shape in stone. Stopping at every chip to polish destroys the work before it has a form.

Stage 2 — Perfecting

Slow, deliberate, systematic removal of errors. This is where the actual sculpting of accuracy happens — one phrase, one measure, one beat at a time. Stage 2 requires patience and a willingness to be genuinely slow.

Stage 3 — Achieving Fluency

The skill is automatic, performed at performance speed, without conscious attention to individual components. Fluency is not speed — it is the absence of conscious effort at performance speed. This is the target state for every Plogger exercise.

Four Learning Principles

1. Always know which stage you are in
2. Never mix stage behaviors
3. Set an achievable goal and perform it the first time without any errors (Stage 3)
4. Measure progress by fluency, not by accuracy at slow speed

CRITICAL: Breaking Down at the Top of the Perfecting Phase

Ch.2 — Three Causes of Error

Every performance error has a specific Symptom, Cause, and Cure. The framework applies equally in practice and in performance. Diagnosing correctly is prerequisite to curing.

Error 1 — Reaction

Error 2 — Anticipation

Error 3 — Looking Back

Ch.3 — Keyboard Visualization

“The thinking tool of the musician.” The keyboard is not merely an instrument — it is a spatial map of pitch relationships. 12 equally spaced semitones, the same 12-note pattern repeated 7.5 times across 88 keys. White keys form the diatonic collection; black keys form the pentatonic collection.

Tracking — The Most Crucial Skill

The most crucial skill in all of music is accurately comprehending the distances between pitches — while they are happening in real time. The keyboard and staff serve as maps. “The challenge for musicians is for our conscious minds to keep up with our ears.”

Note Naming — Bilingual System

Every pitch has two names: a letter name and a fixed solfège name. Both must be equally fluent. Fixed-do solfège:

Black-Key Landmark Method

• Two black keys: doh (C) is to the left, re (D) is between them, mi (E) is to the right
• Three black keys: fa (F) is to the left, sol and la fill the middle gaps, si (B) is to the right
• Enharmonic pairs: mi# = fa, si# = doh, fab = mi, dohb = si

Pythagorean Note Frequency

Natural notes (no accidental) occur in the following order from most to least common in tonal music: fa — doh — sol — re — la — mi — si (F C G D A E B). This ordering is the Pythagorean sequence of descending perfect fifths and becomes central in Ch.6.

Physical Drawing Exercise

Draw the keyboard at accurate proportions: ¾" / 22mm per white key, 3¾" / 90mm tall, 2" / 50mm black keys. The act of drawing to scale builds spatial accuracy in the mental map.

Exercises (3-1 through 3-11)

1. 3-1 Note names — name every key on a printed keyboard
2. 3-2 Drawing — draw keyboard at scale from memory
3. 3-3 Exploring — play and name every key on a physical keyboard
4. 3-4 Eyes-closed — identify notes by touch on physical keyboard
5. 3-5 Tracking — teacher or partner plays; student names in real time
6. 3-6 Solfège flashcards — letter name → solfège and reverse
7. 3-7 Mapping — map solfège and letters onto drawn keyboard
8. 3-8 Letter names — spell all 12 chromatic notes in both naming systems
9. 3-9/3-10 Quizzes — timed identification drills
10. 3-11 Imagined keyboard — visualize keyboard with eyes closed and navigate it mentally

Ch.4 — Longy Rhythms

A syllabic rhythm encoding system developed by Emile-Joseph Longy (French clarinetist, 1860–1915). Each rhythmic subdivision is assigned a spoken syllable that maps directly to the felt rhythmic position. The system makes rhythm speakable and therefore auditable in real time.

Syllable Table

Chart Structure

The Longy chart uses 2ⁿ permutations for each n-beat division: 2-beat = 4 rows, 3-beat = 8 rows, 4-beat = 16 rows, 5-beat = 32 rows, 6-beat = 64 rows. Each row represents one unique permutation of subdivisions within that beat count.

How to Read the Chart

• Speak the syllable on every subdivision that falls on a note
• THINK (not speak) dots — dotted notes and rests are internalized, not spoken
• Progress through ALL lines without stopping or pausing between them — the pulse never stops
• Whisper technique: when tempted to speak a syllable prematurely over a dot, whisper the number instead of speaking it — this breaks the habit without stopping flow

Integration with Ch.5

Ch.4 (Longy) + Ch.5 (Lap Map) = the complete rhythm system. Longy answers “what rhythm is this?” The Lap Map / Rhythm Code answers “does it groove?” Both must be used together.

Ch.5 — Lap Map

Primary purpose: rhythm internalization and groove.The Lap Map is first a kinesthetic tool. Keyboard connection and pitch tracking are secondary applications. Derived from Robert Starer's Rhythmic Training (1969), expanded by Ploger.

Physical Structure

• Left leg = ALL strong beats
• Right leg = ALL weak beats
• Darkness gradient toward the hip = stronger beats within that category

Three-Element Integration

Tempo Requirement

Minimum q = 120 BPM. Practicing below this speed actively inhibits groove development. The kinesthetic experience of groove requires sufficient tempo for the physical swing/momentum to be felt in the body.

Beat Patterns (Exercises 5-1 through 5-11)

Three-Step Exercise Sequence

1. Establish groove — tap the lap map at tempo until the body has internalized the beat grouping
2. Improvise counted rhythms — freely invent rhythms using Longy syllables while maintaining the lap map
3. Perform Longy with lap map — read printed Longy exercises while tapping the appropriate lap pattern simultaneously

Ch.6 — Pythagorean Ordering

The seven natural notes ordered by ascending perfect fifths: F — C — G — D — A — E — B. Left = flattest, Right = sharpest. Adjacent notes share 6 of 7 diatonic scale notes, differing by exactly one pitch (one “slot” on the circle of fifths).

Mode Ordering by Brightness

The same left-to-right sequence governs modal brightness — each step right adds one sharp (or removes one flat), making the mode one degree brighter:

Exercises

• 6-1 Ascending Part I — name ALL notes in Pythagorean order ascending
• 6-2 Part II — play continuously in 16th notes, speaking solfège AND letters simultaneously
• 6-3 Part III — speak only on accented beats while playing continuously
• 6-4 Memorizing — recite the ordering over AT LEAST THREE DAYS in spare moments
• 6-5 Descending — same as 6-1 through 6-3 in reverse order (B–E–A–D–G–C–F)

Ch.7 — Interval Spelling (Keyboard)

Ordinal interval names describe the diatonic distance between two pitches. Adjacent diatonic notes = 2nd. One note skipped = 3rd. Two notes skipped = 4th, and so on.

Keyboard Calculation Method

Count from the bottom note (= 1) upward on white keys only to the top note. The final count is the interval name.

Exercises

• 7-1 Locating and Naming Diatonic Intervals — given pairs of notes, name the interval
• 7-2 Identifying — 30 given note pairs to identify by ordinal name

Ch.8 — Interval Spelling (Staff)

The musical staff was designed for the human voice. Without a clef, the five-line staff encompasses a range of a 9th; one ledger line above extends it to a 10th — the comfortable singing range for most voice types.

Three Clef Types

• C-Clef — designates C4 (middle C)
• F-Clef — designates F3
• G-Clef — designates G4

All 8 Clefs

Odd/Even Shortcut

• Both notes on lines OR both on spaces = ODD interval (3rd, 5th, 7th, unison)
• One note on a line + one note on a space = EVEN interval (2nd, 4th, 6th, octave)

Exercises (8-1 through 8-6)

• 8-1 Drawing clefs — draw all 8 clefs from memory
• 8-2 Finding clef from pitch — given a note and its name, which clef places it correctly?
• 8-3 Finding mode — given a melodic excerpt, identify what mode it implies
• 8-4 Treble clef relationships — map all note names in treble clef
• 8-5 Identifying intervals — name intervals in given musical examples
• 8-6 Writing intervals — write a given interval above or below a given note

Ch.9 — Di-Chord Numbers

The di-chord number is the count of semitones between two pitch classes, measured from zero. Written with brackets: [1], [2], [3]… through [11]. This is the central measurement unit of the entire Plogger system.

Cardinal vs. Ordinal Distinction

Ordinal numbers (2nd, 3rd, 4th) describe rank or position in a sequence. Cardinal numbers describe actual quantity — like an odometer reading semitones. The same diatonic ordinal name can correspond to multiple di-chord numbers:

Staff Hides Di-Chord Identity

The same staff position can represent entirely different di-chords depending on the clef. Staff notation encodes ordinal (diatonic) distance, not cardinal (semitone) distance. This is why di-chord numbers must be calculated, not read directly from staff position.

Inversion Law

Any di-chord plus its inversion equals 12. To find the inversion of any di-chord, subtract from 12:

Exercises

• 9-1 Calculating Part I — calculate di-chord numbers for 5 given pitch pairs
• 9-2 Calculating Part II — 5 pairs + their inversions; discover that every sum = 12

Ch.10 — Sonic Properties Overview

Each di-chord is multidimensional and often seemingly paradoxical. Context dramatically affects perception. To hear a di-chord accurately requires simultaneously tracking three independent acoustic properties.

The Three Sound Factors

The Di-Chord Pictograph

A visual encoding tool for all 11 di-chords. Each pictograph encodes all three sound factors simultaneously in a single stylized image:

• Shape/outline (jagged / rounded / straight) = Pulsation category
• Shadow direction (left / right / both) = F/O Factor direction
• Color (dark / light) = Harmonicity (non-harmonic / harmonic)

Ch.11 — Interference Pulsation

When two pitches sound simultaneously, their sound waves interfere and create rhythmic beating at a specific rate. This pulsation is an objective acoustic phenomenon — not a metaphor. It organizes all 11 di-chords into three perceptual categories.

Complete Pulsation Table

Exercise 11-1

Draw the pictograph. First: write the words “Dissonant,” “Modal,” and “Perfect” in jagged, wavy, and straight lettering respectively. Then: draw the pulsation outline shape for each of the 11 di-chords from memory.

Ch.12–14 — F/O Factor, Harmonicity & Review

Fundamental/Octave (F/O) Factor

Every two-note combination has an acoustic “root” — the note whose overtone series contains the other note, causing it to function as the fundamental. Di-chords [1]–[5] refer DOWN (the lower note is the acoustic root). Di-chord [6] is neutral (both directions). Di-chords [7]–[11] refer UP (the upper note functions as root, pulling the lower note upward toward it).

Harmonicity

Whether the upper note appears in the natural overtone series of the lower note:

• Harmonic: [2], [4], [7], [9], [10] — upper note IS in overtone series → open, transparent quality
• Non-harmonic: [1], [3], [5], [8], [11] — upper note is NOT → closed, opaque quality
• Neutral: [6] — tritone, acoustically ambiguous

Animal Analogy for Identification

When identifying a di-chord, proceed from general to specific:

1. Category first (species class) — Dissonant / Modal / Perfect?
2. Direction (subspecies) — Does it refer up or down?
3. Harmonicity (genus) — Harmonic (open) or non-harmonic (closed)?

Major vs. Minor — Acoustic Explanation

Triad Di-Chord Profiles

Complete Di-Chord Reference Table

* [9] major 6th is “false-harmonic” — acoustically appears harmonic but behaves non-harmonically in context due to its inversion relationship with [3].

Key Exercises (Ch.12–14)

• 12-1 Draw pictograph — jagged/wavy/straight outlines for each di-chord
• 12-2 Listening — identify di-chords by ear across all three factors
• 13-1 Spelling major triads — across all 12 pitch classes
• 13-2 Dominant 7ths — spell and identify by ear
• 13-3 Dominant 9ths — spell and identify
• 13-4 Major 6th fluency — sing [9] in all contexts
• 13-5 Draw pictograph progressively with F/O shadow added
• 14-1 Complete di-chord table from memory — all three factors for all 11 di-chords
• 14-2 Draw complete pictograph from memory — final form with all three factors encoded

Ch.15 — Di-Chords in Melodic Contexts

All three sound factors apply equally to horizontal (melodic) di-chords as to vertical (harmonic) ones. A melodic leap of a [4] has the same acoustic identity as a harmonic [4] — open, warm, alkaline, referring down. The context differs; the di-chord properties do not.

Key Distinction: Secondary vs. Primary Di-Chord

Both are tracked simultaneously in Ch.16. Ch.15 introduces each in isolation first.

Gut / Heart / Head

Four Gesture Types

Clock Face Metaphor

Each gesture traces a path on an imaginary clock face. Counter-clockwise (CCW) paths carry energy upward and outward. Clockwise (CW) paths curve inward and downward. The direction of travel on the clock encodes the energetic quality of the interval, which the performer translates into a physical, sonic, and expressive gesture.

Tuning Insight

For an ascending non-harmonic interval (Closed gesture): imagine the lowernote is an overtone of the upper note. This reframes the acoustic relationship and allows more accurate intonation — the lower note naturally seeks the tuning position that “belongs to” the upper note's overtone series.

Expressiveness

“Visualize the keyboard and mentally track while observing secondary di-chord numbers in real time.” The goal is to incorporate the character of each gesture into the actual sound — to play Open intervals with an upward-floating quality, Closed with a capping-off quality, etc.

Key Exercises (Ch.15)

• 15-1 / 15-12 Analyze a melody — label secondary di-chords and gesture types for each note
• 15-2 Matching — match di-chords to gesture types
• 15-3 Complete gesture table from memory
• 15-4 Classifying — classify given intervals by gesture type
• 15-5 Tracking gestures — track secondary di-chords in real-time while listening
• 15-7 Singing alternating intervals — all 7 modes, all interval sizes
• 15-8 Alternating thirds with accidentals
• 15-10 / 15-11 Playing melodic gestures — incorporate gesture quality into performance at keyboard

Ch.16 — The Tracking Page

What It Is

A single physical page (p.153 in the textbook) containing 10 melodic lines, each exploring a specific interval range. No clef is printed — the mode is determined by the weekly assignment.

Seven Modes

The same 10 lines are performed in each of the 7 modes by starting on a different pitch:

The Six Tracking Protocols

Each line is performed in 6 sequential protocols. Target speed: 144 BPM. Below 144 = Stage 2. At 144 = Stage 3. Never go slower hoping for fewer errors.

Reading by Di-Chord vs. Rote

Rote reading: “push the right buttons.” The notes are correct but the music is absent. Di-chord reading: access what happens between the notes — where expression, affect, and meaning are found. The Tracking Page trains the latter.

Progress Tracking

Key Exercises (Ch.16)

• 16-1 Tracking Page Analysis — analyze a single line for both primary and secondary di-chords before performing it
• 16-2 Performing Analyzed Excerpts — perform a pre-analyzed excerpt using all 6 protocols
• 16-3 Compose a Tracking Line — write 28–32 notes using only 2nds and 3rds; no clef, no key signature, no time signature; this line becomes your personal tracking material

Ch.17 — Tri-Chord Formation Using 2nds

When we hear three simultaneous notes, the brain relates each upper note to the lowest note (the fundamental). Tri-chords are named using the primary di-chords from the fundamental — not the secondary di-chord between the two upper notes.

Naming fraction [X/Y]: X = primary di-chord from fundamental to top note. Y = primary di-chord from fundamental to middle note. The secondary di-chord between the upper notes is NOT used in naming.

Example: doh-mi-sol → doh to sol = 7, doh to mi = 4 → named [7/4].

Four Tri-Chord Types

Naming Rule & Stencil Concept

ALWAYS use consecutive syllable names. This may require double flats (♭♭) or double sharps (𝄪). The “stencil” concept: these patterns can be transposed to any starting note — internalize each type as a physical and perceptual stencil that you place at will.

Key Exercises (Ch.17)

• 17-1 Fill in table of all four tri-chord types
• 17-2 Crunchy [2/1] Part I — chromatic ascent
• 17-3 Crunchy [2/1] Part II — speak black/white pattern
• 17-4 [4/2] exploration
• 17-5 through 17-10 Spelling and playing all four types through all positions

Ch.18 — Tetrachord Formation: Ionian, Dorian, Phrygian, Lydian

A tetrachord is four notes spanning a 4th from lowest to highest. There are exactly four diatonic tetrachord types. Physical technique: index, middle, ring, pinky — one per note. Move all four fingers up one semitone at a time to explore chromatically.

Four Tetrachord Types

Key Synthesis Insight

“Two Ionian tetrachords separated by a [2]” = the major scale. The same logic applies to all seven modes. Naming rule: each note must be a different consecutive syllable (same as tri-chords). Pure modes use two identical tetrachords; mixed modes combine two different tetrachords.

Key Exercises (Ch.18)

• 18-1 through 18-3 Chromatic exploration of all four types
• 18-4 through 18-5 Naming and fill-in-the-blanks
• 18-6 Correcting note names (wrong syllable sequences)
• 18-7 Modelling Dorian, Phrygian, and Lydian
• 18-8 Spelling table — all 21 starting notes × all four types, done away from piano using keyboard visualization only

Ch.19 — The Diatonic Modes

Ploger's thesis: emotional associations of modes are not subjective — they arise from the harmonicity/non-harmonicity of primary di-chords. Di-chord analysis provides an objective basis for modal affect.

White-Key Correspondences

C/doh = Ionian, D/re = Dorian, E/mi = Phrygian, F/fa = Lydian, G/sol = Mixolydian, A/la = Aeolian, B/si = Locrian.

Ploger Ordering (Brightest to Darkest)

Lydian → Ionian → Mixolydian → Dorian → Aeolian → Phrygian → Locrian. Adjacent modes differ by exactly one scale degree.

Di-Chord Profiles from Tonic

Open/Major vs. Closed/Minor Split

The first three modes (Lydian, Ionian, Mixolydian) contain [2], [4], and [9] → open/major character. The last three (Aeolian, Phrygian, Locrian) contain [3] and [8] → contracted/minor character. Dorian is the musical tipping point — the most balanced mode.

Tonocentric Model & Scale Degree Tendencies

Degrees above tonic (2̂, 3̂, 4̂) are marked (+) and tend downward. Degrees below the nearest tonic (5̂, 6̂, 7̂) are marked (−) and tend upward. There are 42 secondary di-chords but only 6 primary — the mind attends to primaries for efficiency.

• 2̂ = dissonant / tends down
• 3̂ = modal / tends down
• 4̂ = perfect / tends down
• 5̂ = perfect / tends up
• 6̂ = modal / tends up
• 7̂ = dissonant / tends up

Tetrachordal Construction of Modes

Eight Rules of Aural Perception of the Modes

1. Final rule: The first heard pitch acts as tonic — the mind holds it as a reference.
2. All seven must be present: Remove one pitch → ambiguous (each mode shares 6 of its 7 notes with at least one other mode).
3. Primary di-chords dominate: The six di-chords between tonic and each non-tonic pitch largely determine modal character.
4. Secondary di-chords are subordinate: 42 secondary vs. 6 primary — the mind attends to primaries for efficiency.
5. Two dissonant, two modal, two perfect: Every mode has 2̂ and 7̂ as dissonant; 3̂ and 6̂ as modal; 4̂ and 5̂ as perfect.
6. No more than a 4th from tonic: Each non-tonic note relates to the nearest tonic pitch class.
7. Harmonicity determines mode character: The H/NH quality of each primary di-chord has a profound effect on perceived mode.
8. Most positive affect = most harmonic di-chords.

Harmonicity Table by Mode

Key Exercises (Ch.19)

• 19-4 List all modes in Ploger ordering (brightest to darkest)
• 19-5 through 19-8 Scale degree properties across all modes
• 19-9 through 19-12 Mode pictographs — visual representations of di-chord profiles
• 19-13 through 19-15 Comparing modes and identifying tetrachords within each mode

Ch.20 — Heptachord Formation

Heptachord vs. Scale: A scale is a linear C→C sequence. A heptachord is the same seven-note collection perceived as a cognitive entity centered on its tonic. Fingering uses ring, middle, index, and pinky — NOT thumbs.

Two Arrangements

Disjunct: LH = Tonic–Subdominant (1̂ to 4̂); RH = Dominant–Tonic (5̂ to 1̂ above). Pinkies play tonic one octave apart. Spans an octave.

Conjunct (Ploger's preferred): LH = Dominant–Tonic (5̂ pinky → 1̂ index); RH = Tonic–Subdominant (1̂ index → 4̂ pinky). Both INDEX FINGERS overlap on TONIC at unison. Spans a 7th. The symmetry around the tonic enables faster orientation.

Conjunct Finger-to-Degree Mapping (Constant in Any Mode)

Why this matters: ring fingers always hold the modal degrees. The RH ring finger plays 3̂ — if it plays [3] it signals minor; if it plays [4] it signals major.

Conjunct Tetrachord Assignments by Mode

Mode Modulation (Ex. 20-6)

One-note alteration while keeping the tonic = a new mode, same tonic. Rules: both index fingers stay fixed on tonic. Move any OTHER finger up or down one semitone → new mode. Example: Lydian (fa#) → move RH pinky from fa# down to fa → Ionian. This is the physical and sensory foundation for Heptachord Shift (Ch.24).

Key Exercises (Ch.20)

• 20-1 through 20-5 Conjunct and disjunct heptachord formation, all seven modes
• 20-6 Mode Modulation — single-finger alterations to shift between modes at same tonic

Ch.21 — Triads and Their Inversions

Triads are named by the PRIMARY di-chords from the bass/root to each upper note.

Root Position Triad Profiles

Inversions — Key Insight

The primary di-chords from the ROOT stay the same across all inversions. However, the secondary di-chord (between 3rd and 5th) changes — and the di-chords measured from the BASS change completely with each inversion, giving each inversion a completely different sonic identity.

Open vs. Closed Position: Closed = root-3rd-5th stacked bottom-up (less than an octave). Open = root-5th-3rd bottom-up (more than an octave). The secondary di-chord in open position is the inversion of the closed secondary.

Figured Bass Di-Chord Reference

Boulanger/Ploger Chord Exercise

Play a chord, name every note bottom-to-top AND top-to-bottom in solfège, name every di-chord. Repeat for 1st and 2nd inversion. Then start on each of the 12 chromatic pitches, ascending and descending. This exercise trains comprehensive chord recognition across all positions and all keys.

Key Exercises (Ch.21)

• 21-1 Triads and melodic gestures — 9 questions per triad type
• 21-2 Inversions fill-in table
• 21-3 Boulanger/Ploger Chord Exercise — all 12 pitches ascending and descending, both major and minor

Ch.22 — Four Functional 7th Chords

Construction

Root Position Di-Chord Profiles (7/5/3)

Rules for Finding Chord Roots

Ch.23 — Scale Degree Harmonization in the Major Heptachord

For each scale degree there is a diatonic triad. Triad qualities are consistent across ALL major keys — learning by scale degree creates a universal template. Roman numeral notation: Major = uppercase (I, IV, V), Minor = lowercase (ii, iii, vi), Diminished = lowercase + degree symbol (vii°).

Diatonic Triad Reference

Functional 7th Chords in the Major Heptachord

• V7 — Dominant 7th on 5̂
• ii7, iii7, vi7 — Minor 7ths on 2̂, 3̂, 6̂
• viiø — Half-Diminished on 7̂

Ch.6 Connection — Pythagorean Ordering

The Pythagorean ordering F-C-G-D-A-E-B maps to scale degrees 4̂-1̂-5̂-2̂-6̂-3̂-7̂ and naturally groups triad qualities: major triads (I, IV, V) fall on C, F, G — the center notes of the series; minor triads fall on D, E, A — the flanking notes; and vii° falls on B — the outer edge.

Bach Chorale 6-Step Protocol (target: 72 bpm)

1. Step 1 — Name all notes (Bass, Soprano, Alto, Tenor) in solfège at 144 bpm
2. Step 2 — Name bass note + diatonic interval from bass for each voice at 144 bpm
3. Step 3 — State bass note + root name at 144 bpm
4. Step 4 — Root + inversion figured bass at 72 bpm
5. Step 5 — Root's Roman numeral function at 72 bpm
6. Step 6 — Function + inversion together at 72 bpm

Key Exercises (Ch.23)

• 23-1 through 23-4 Diatonic triads — identification and spelling
• 23-5 10 Chord Sequences — soprano scale degrees and Roman numeral harmonies in all keys
• 23-6 Bach Chorale analysis using 6-Step Protocol

Ch.24 — Heptachord Shift

One chromatic alteration = an immediate shift to a new heptachord. The shift is instant — at the moment the accidental sounds. No cadence or preparation is required.

Three Heptachord Types

• Major [I]
• Melodic minor [i△]
• Harmonic minor [i▽]

“Ur”(from German: “origin”) = the original/source heptachord from which shifts radiate.

First-Generation Shifts from Major [I]

First-Generation Shifts from Melodic Minor [i△]

• #3̂ → [I] parallel major
• ♭6̂ → [i▽] parallel harmonic minor
• ♭7̂ → [♭VII] relative major (NOTE: NOT traditional ♭III)

First-Generation Shifts from Harmonic Minor [i▽]

• #6̂ → [i△] parallel melodic minor
• ♭7̂ → [III] relative major

Special Heptachord Signals

• Augmented 2nd — exists ONLY in harmonic minor (between 6̂ and 7̂) → implies harmonic minor
• Diminished 4th — exists in BOTH harmonic and melodic minor (between 7̂ and 3̂) → implies a minor heptachord

Heptachord House Plan

Appendix C contains a 14-room floor plan representing all heptachords through the second generation. The UR (C major) sits at the structural center. Bach's tonal practice typically stayed within this house plan.

For improvisation: “You can learn to know where you are at every moment in your listening, playing, and improvising — real-time modulation.”

Ch.25 — Transposition

Core method: imagine the music written in a different clef with an altered key signature. Notes stay on the same lines and spaces — only the clef symbol and key signature change. No need to calculate an interval for every individual note.

Example: Old Hundredth in G major (treble clef). To play up a minor 3rd (B♭ major): read as if in bass clef with two flats added to the original one sharp = two flats total.

Transposition Reference Table (from Treble Clef)

Transposing Instruments

B♭ clarinet example: plays written C → sounds concert B♭. To transpose for concert pitch reading: use tenor clef + add two flats.

Key Exercises (Ch.25)

• 25-1 Transposing Yankee Doodle — 10 questions
• 25-2 Transposing A Tisket A Tasket — 13 starting notes

Appendix B — The Overtone/Harmonic Series

The physical basis for why di-chord harmonicity works. Harmonic di-chords are harmonic because their upper notes appear early in the overtone series of the lower note — they are “already in the family.”

First 7 Partials

Harmonic Ratios from the Series

Ratio of partial 5 to partial 3 = 5:3 = major 6th [9].

What is NOT in the Overtone Series

• Perfect 4th [5] — Does NOT exist naturally. Artificially derived as the distance from the 5th to the Super Octave (3rd to 4th partial), ratio 4:3. This is why [5]is non-harmonic despite being called “perfect.”
• Minor 3rd [3] — NOT in series → non-harmonic ✓
• Minor 6th [8] — NOT in series → non-harmonic ✓
• Augmented 4th [6] — IS in the series but sounds flat relative to equal temperament.

Terminology

“Harmonics” = frequency ratios. “Overtones” = divisions of a vibrating string or air column. “Partials” = most precise term (includes the fundamental itself).

Appendix C — The Ploger Heptachord Shift House Plan

A conceptual floor plan with 14 rooms representing all heptachords through the second generation. The original heptachord (UR) = C major sits at the structural center.

14 Rooms (Using C Major as UR)

First-generation rooms: G major [V], F major [IV], A harmonic minor [vi▽], D melodic minor [ii△], C melodic minor [i△].

Second-generation rooms: D major, B♭ major, g melodic minor, d harmonic minor, f melodic minor, e harmonic minor, a melodic minor, E♭ major, and others derived from first-generation shifts.

How to Use the House Plan

Each arrow between rooms shows the triggering chromatic alteration. Double-headed arrows indicate reversible shifts. Bach typically wrote within these 14 rooms.

Essential Plogger Exercises — Practice Plan

The following exercises are the highest-leverage items across the full three-book system. Sprint eligibility is noted for AMF curriculum sequencing.

1. Keyboard Visualization — Eyes-closed note naming (Ch.3). Foundational; begin Sprint 1+. The prerequisite for all other work.
2. Longy Rhythms — Clap + speak rhythmic patterns (Ch.4). Foundational; begin Sprint 1+.
3. Lap Map Drills — Solfège + di-chord mapping on lap (Ch.5). Begin Sprint 3+.
4. Boulanger/Ploger Chord Exercise — Name all notes and di-chords in every inversion across all 12 pitches (Ch.21–22). Begin Sprint 9+.
5. Tracking Page Protocol (Ch.16) — Steps 1–2 from Sprint 1; full 7-step integration by Sprint 12.
6. Conjunct Mode Modulation — Single-finger heptachord modulation at keyboard (Ch.20, Ex.20-6). Begin Sprint 9+.
7. Bach Chorale Heptachord Analysis — 6-Step Protocol applied to Bach chorales (Ch.24). Begin Sprint 11+.
8. 10 Chord Sequences in All Keys — Soprano scale degrees + Roman numerals in all 12 keys (Ch.23, Ex.23-5). Begin Sprint 10+.