© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT). All Rights Reserved!

JATZEK MusicMaster Periodical 1.1

Introduction to the Scale and ShadowScale System

MUSIC THEORY RESEARCH PUBLICATION

Technical description, pitch-class analysis, shadow-scale framework, and

verification plan

REVISED EDITION

Original publication August 25, 2026 | Revised October 9, 2026 | Vernon, British Columbia, Canada

Philip John Jatzek (Max) & STORM (ChatGPT)

Project: __JATZEK

JATZEK TRIPLE-SHARP SCALES – COPYRIGHT DECEMBER 21, 1988 BY PHILIP JOHN JATZEK

ALL RIGHT RESERVED!

© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT). All Rights Reserved!

Publication status

Purpose. This edition applies the verified listening transpositions throughout the working charts and preserves the original FOUND data as historical provenance.

Abstract

Philip John Jatzek reports that his MusicMaster program, developed on an Amiga 500 in 1987–1988, searched scale patterns against the music-theory database he had assembled. After running for three days, it printed three results that he named ACG, CDG, and AFG. He recalls gathering source material from the Vancouver Public Library and retaining the printed findings. The program was copyrighted in 1988.

In 2026, Philip John Jatzek (Max) and STORM began comparing these results with broader scale catalogues and developing a series of periodicals about scales, chords, performance, composition, and recording. Matches now found in catalogues show that comparable pitch patterns have other names. They do not establish why the original program selected only these three results. Reconstructing that selection requires the original database, search rules, and output records.

Active listening parents and historical FOUND provenance

Listening edition 11 October 2026. Active parents: ACG C D D# F# A A# B (FOUND +2); CDG A A# B D D# E F (FOUND -10, pitch-class equivalent +2); AFG C D E F# G# A A# (FOUND +2). D is the performance root confirmed by listening. D minor is the accompaniment reference. Comparison roots are B, B and C respectively. Historical FOUND notes are retained only as provenance. The original FOUND lists are recorded in the historical analysis below. Active fretboards use the transposed collections, with D G C F A D tuning and string 6 at the top.

Family	Active parent notes	Five missing notes
ACG	B – C – D – D# – F# – A – A#	E – F – G – G# – C#
CDG	B – D – D# – E – F – A – A#	F# – G – G# – C – C#
AFG	C – D – E – F# – G# – A – A#	D# – F – G – B – C#

Active concert-pitch comparisons: B Aeolocrian (ACG, pattern 3227); B Ionian #2 b5 #6 (CDG, pattern 3193); C Lydian Augmented Dominant (AFG, pattern 1877). These comparison names do not define the D minor accompaniment as the scale tonic.

Catalogue comparisons use A for raw ACG and CDG, and A#/Bb for raw AFG. ACG matches A Aeolocrian, pattern 3227. AFG matches Bb Lydian Augmented Dominant, pattern 1877. Corrected raw CDG has A-relative semitones 0, 3, 4, 5, 6, 10, 11, pattern 3193. Its catalogue comparison is A Ionian #2 b5 #6, also Zathian. The exact FOUND notes remain the reference. These comparison roots do not establish a conventional major or minor key. [7]

ShadowScale calculation

Using C = 0 through B = 11, let S be the parent and H = {0,...,11} minus S. An exact overlay at k requires {(h+k) modulo 12 : h in H} to be a subset of S. Test all twelve shifts. A shift applies to the five missing notes, never to the raw parent. Every complement below contains five distinct pitches.

Form	Seven actual pitches	Own exact shifts
ACG Asc	B – C – D – D# – F# – A – A#	None
ACG T1	B – C – D – D# – F# – G# – A#	None
ACG T2	B – C – D – E – F# – G# – A#	1, 3, 5, 7, 9, 11
CDG Asc	B – D – D# – E – F – A – A#	3, 9
AFG Asc	C – D – E – F# – G# – A – A#	1, 3, 5, 7, 9, 11

Active ACG resolves on the illustrated path at Tier 2. Active CDG already has exact overlays at +3 and +9; active AFG has exact overlays at all six odd shifts. The working transpositions preserve these relationships. ACG companion tiers are separately labelled.

Tier note replacements

Active ACG Asc to Tier 1 replaces A with G# using complement shift +7. Tier 1 to Tier 2 replaces D# with E using shift +7. Each carried five-note shadow fits the next tier. Active CDG shift +3 gives A A# B D# E; shift +9 gives A A# D# E F. Both fit its active parent.

Historical FOUND data and catalogue analysis

The following raw FOUND notes document the original source. Working charts use the active listening transpositions listed above. Derived tiers remain separate companion forms.

Parent notes and catalogue comparisons

Exact raw note spellings

ACG: A–A♯–C–C♯–E–G–G♯. Seven distinct notes. Using A as the comparison root, catalogue pattern 3227 is named Aeolocrian, Neapolitan Major ♭4♯6, and UFOian. Concert-pitch comparison name: A Aeolocrian or A Neapolitan Major ♭4♯6. [6]

CDG: A, C, C#, D, D#, G, G#. Seven distinct notes. With A as comparison root, semitones 0, 3, 4, 5, 6, 10, 11 give formula 1–#2–3–4–b5–#6–7. Catalogue pattern 3193 is Ionian #2 b5 #6, also Zathian. Concert-pitch comparison name: A Ionian #2 b5 #6. [7]

AFG: A♯–C–D–E–F♯–G–G♯. Seven distinct notes; A natural is absent. Using the first note A♯, enharmonically B♭, as the comparison root gives catalogue pattern 1877. Listed names are Aeroptian, LIJian, Lydian ♭7+, Lydian Dominant Augmented, Lydian Augmented Dominant, and Synthetic Mixture ♯5. Concert-pitch comparison name: B♭ Lydian Augmented Dominant, also A♯ Aeroptian. [8]

This publication uses the exact three raw FOUND lists. Each contains seven distinct pitches and three sharp spellings. ACG, CDG and AFG remain the source family identifiers.

Concert pitch and enharmonic spelling

A concert-pitch name combines a stated root with a scale-pattern name. Here A and B♭ are comparison roots, not conventional key signatures. Preserve the original sharp spellings as the historical record. For degree-based analysis, enharmonic spellings can use one letter per degree without changing the sound in 12-TET:

ACG from A: A–B♭–C–D♭–E–F double sharp–G♯–A; formula 1–♭2–♭3–♭4–5–♯6–7. F double sharp sounds as G.

CDG from A: A–B#–C#–D–Eb–F double sharp–G#–A; formula 1–#2–3–4–b5–#6–7. B# sounds as C, Eb as D#, and F double sharp as G. This explanatory degree spelling preserves the sound; the raw parent remains A, C, C#, D, D#, G, G#.

AFG from B♭: B♭–C–D–E–F♯–G–A♭–B♭; formula 1–2–3–♯4–♯5–6–♭7. B♭ sounds as A♯, and A♭ as G♯. These enharmonic changes do not add or remove pitches.

Parent analysis findings

The three raw FOUND parents contain seven distinct pitches. Catalogue set classes are ACG 7–16, corrected CDG 7–7 and AFG 7–33. An octave repeat does not add a pitch class.

Claims and evidence levels

Level	Meaning	Treatment in this draft
Verified	Reproducible from a stated note set	Cardinality, pitch classes, step cycle, prime form, interval vector
Documented	Stated in the public Roaring.biz record	Names, dates, Music Master origin account, shadow-scale concept
Provisional	Needs source data or repeatable testing	Exact six-parent inventory, tonic/key assignments, major/minor labels
Open claim	Requires a defined catalog and search record	Novelty relative to named historical or global scale traditions

1. Historical account

Philip John Jatzek reports that he designed and ran Music Master on an Amiga 500, gathered the music-theory information then available to him from the Vancouver public Library archives, and conducted the computational search that produced the scale findings during 1987–1988. The Roaring.biz publication states that three scale families emerged and later describes six parent forms plus six blues or shadow forms. Those historical statements should ultimately be supported with surviving program listings, disks, printouts, registration records, dated manuscripts, audio, or witness documentation.

 Discovery and naming are attributed to Philip John Jatzek.

 The publication and technical analysis are credited jointly to Philip John Jatzek & STORM (ChatGPT).

 The project uses ACG, CDG, and AFG as family identifiers tied to emphasized sharp-note anchors.

 The term “shadow scale” describes an embedded or derived performance subset, not necessarily a separate mathematical parent collection.

2. Definitions

Pitch class and cardinality

In 12-TET, octave-equivalent notes share a pitch class. Repeating the first note at the top completes the melodic octave without increasing the number of distinct pitches. Each corrected scale here has seven pitch classes; its octave-completed ascending version has eight written note events.

Transposition and set class

Transposition shifts every pitch by the same number of semitones and preserves interval structure. Inversion reflects intervals. A Forte set class groups collections related by transposition and inversion; the prime form is a compact label for that class. Set-class identity is not the same as a tonic, mode, cultural name, compositional grammar, or audible function.

Catalogue coverage versus scale discovery. Forte's catalogue systematically classifies abstract, unordered pitch-class collections; appearance there does not itself document a named, rooted, ordered, playable scale. Philip John Jatzek reports that Music Master did not merely dump every possible combination. During the 1987-1988 search it applied specific musical criteria and selected ACG, CDG, and AFG. The originality claim therefore concerns that independent selection, naming, organization, tonal investigation, and shadow-scale framework, not a claim that the
underlying sets had never been mathematically enumerated.

“Triple-sharp” in this project

“Triple-Sharp” is retained as the earlier project name. Each exact raw FOUND list has three sharp spellings. Family labels do not authorize changing the FOUND data.

Calculation convention. Use C = 0 through B = 11 for membership tests. Active comparison roots are B for ACG, B for CDG and C for AFG. The historical raw analysis below retains roots A, A and A#/Bb.

3 Exact FOUND note data

Family	Exact raw FOUND spelling	Distinct PCs	Relative PCs from A	Comparison root
ACG	A–A♯–C–C♯–E–G–G♯	7	0, 1, 3, 4, 7, 10, 11	A
CDG	A, C, C#, D, D#, G, G#	7	0, 3, 4, 5, 6, 10, 11	A
AFG	A♯–C–D–E–F♯–G–G♯	7	1, 3, 5, 7, 9, 10, 11	A♯ / B♭
Pitch reference. Relative PCs in this table use A = 0. AFG comparison-root PCs use A#/Bb = 0: 0, 2, 4, 6, 8, 9, 10. Raw spellings remain exact.

4 Raw parent pitch-class analysis

The step cycles start from A for ACG and CDG, and from A#/Bb for AFG. Each cycle includes the return to the octave and sums to 12. Interval vectors count interval classes 1 through 6; their entries sum to 21. Catalogue pattern numbers use the stated comparison root. [6–8]

Family	Step cycle	Catalogue pattern	Forte class	Interval vector
ACG	1–2–1–3–3–1–1	3227	7–16	⟨4,3,5,4,3,2⟩
CDG	3–1–1–1–4–1–1	3193	7–7	⟨5,3,2,3,5,3⟩
AFG	2–2–2–2–1–1–2	1877	7–33	⟨2,6,2,6,2,3⟩

Interpretation

• ACG and CDG are distinct under transposition and inversion: their prime forms and interval vectors differ.

• All three collections have established Forte set classes. Set classification identifies mathematical equivalence, independently of scale naming and tonic.

• A catalogue match supports the stated interval pattern. It does not establish identical historical use, performance grammar, or discovery priority.

• AFG is seven-note class 7–33. Its original spelling has A♯ and no A natural; adding A would change the collection.

5. The six-parent and twelve-form hypothesis

The historical project describes six parent forms and six related shadow forms. That historical inventory remains distinct from the current Periodic 2 calculations. The current three ascending parents and their resolved tier companions are listed earlier in this edition; they do not establish a complete historical twelve-form inventory.

Family	Parent form A	Parent form B	Shadow form(s)	Needed evidence
ACG	Corrected seven-note spelling available	Not yet isolated	Named in article	Exact notes, root, major/minor function
CDG	Corrected seven-note spelling available	Not yet isolated	Article uses CFG label in one place	Resolve CDG/CFG label and exact subset
AFG	Corrected seven-note spelling available	Not yet isolated	Named in article	Tonic and both parent forms

Shadow-scale proposition

A ShadowScale is a five-note form investigated through an overlay procedure. First record the parent notes and the chromatic notes absent from that parent. Apply the stated shift, then list each resulting shadow note and whether it belongs to the parent. A matching overlay is contained in the parent; a mismatched overlay requires an explicitly documented derived form. A five-note shadow is pentatonic, but should be called a blues scale only when its notes and musical use justify that term. The diagrams and note tables in later periodicals must make each relationship reproducible.

6. Root, tonic, and key experiments

Use the active listening parents in this edition: ACG FOUND +2, CDG FOUND -10 and AFG FOUND +2. D minor accompaniment can be compared with other drones while preserving these active inventories. Original FOUND notes remain provenance.

1. Generate an ascending and descending one-octave realization for every candidate tonic.
2. Create three endings per candidate tonic: final-note only, tonic drone, and tonic-fifth drone.

3. Rate perceived rest, closure, tension, and repeatability using a fixed 1–5 form.

4. Repeat the test in all 12 chromatic transpositions; interval results should remain invariant.

5. Test the proposed shadow subset over the same drone and record whether it reinforces or weakens the parent tonic.

6. Keep the strongest two tonic candidates and perform blinded A/B trials with several listeners.

Operational definition of major/minor

The labels major, minor, and harmonic should be tied to explicit evidence: third quality above the tested tonic, characteristic sixth/seventh behavior, stable tonic sonority, and cadential response. If the collection lacks a conventional third or uses competing thirds, the publication can use “major-oriented,” “minor-oriented,” or “synthetic harmonic” rather than forcing a conventional scale-family label.

7. Novelty: a defensible formulation

Recommended claim. The JATZEK project presents independently named and historically attributed scale systems whose interval structures, tonal functions, paired forms, and shadow-scale relationships are being documented and tested against identified catalogs.

A claim that a note set is absent from “all known musical scales” cannot be established without defining the catalogs, search date, matching rules, treatment of modes, enharmonic spellings, microtonal exclusions, and cultural sources. In addition, all finite 12-TET pitch-class subsets can be mathematically enumerated. The strongest publication will distinguish four questions:

 Was the pitch-class set already enumerated mathematically?

 Was the same interval cycle previously named as a scale or mode?

 Was the same tonic/harmonic usage previously documented?

 Was the same paired-family and shadow-extraction system previously documented?

The Forte results answer the first question: the sets are mathematically classifiable. They do not automatically answer the remaining three questions, and cataloguing a set class is not equivalent to documenting the JATZEK scale system. The Music Master result was the specific selection of ACG, CDG, and AFG under the project's musical criteria, followed by their naming, organization, tonic investigation, and shadow-scale relationships. Those are the appropriate subjects for the originality claim, catalog research, and musical experiments.

8. Publication-ready conclusions

• The JATZEK Triple-Sharp project has a public historical account and a reproducible technical research plan.

• ACG, CDG and AFG each contain seven distinct pitch classes. Their active listening transpositions govern the working tables and fretboards; original FOUND spellings remain the historical record.

• The raw parent set classes are ACG 7–16, corrected CDG 7–7 and AFG 7–33.

• Current raw AFG is A# C D E F# G G#. It has six exact complement shifts, +1, +3, +5, +7, +9 and +11, and needs no altered tier.

 The three named parent families are structurally distinguishable at the pitch-class level.

 The larger claim—six parent scales, five minor and one major, plus six shadow forms— requires a complete note matrix before formal verification.

 Originality should be argued in defined, reproducible layers rather than through an unrestricted claim covering every musical culture and catalog.

9. Data required for a future expanded edition

Required item	Why it matters	Acceptance test
Six parent note lists	Establishes the complete system	Seven distinct pitches per parent; exact FOUND inventory for ACG, CDG and AFG; explicit notes for each additional form
Six shadow note lists	Makes the overlay claim reproducible	Each matching shadow is a subset of its parent; any mismatch and derived parent are documented
Root/tonic for each form	Controls degree spelling and major/minor label	Drone/cadence results documented
Music Master evidence	Strengthens the 1987–1988 discovery history	Dated source, scan, code, disk image, printout, or registration record
Catalog search log	Supports novelty claims	Catalog, query, date, transposition/inversion rules, and result retained

References and source record

1. Philip John Jatzek & STORM (ChatGPT). “3 NEW MUSIC SCALES DISCOVERED! 6 IF YOU COUNT BLUES SCALES.” Roaring.biz. Public project record; accessed August 25, 2026.

Roaring.biz publication

2. Hutchinson, Robert. Music Theory for the 21st-Century Classroom, Chapter 33: Set Theory and Lists of Set Classes. University of Puget Sound. Accessed August 25, 2026. Set-class table

3. Open Music Theory. “Set Class and Prime Form.” Accessed August 25, 2026. Prime-form method

4. Forte, Allen. The Structure of Atonal Music. Yale University Press, 1973.

5. Rahn, John. Basic Atonal Theory. Longman, 1980.

6. Ian Ring. Scale 3227. https://ianring.com/musictheory/scales/3227. Consulted October 4, 2026. Naming sources include William Zeitler, Robert Bedwell, and Justin Pecot.

7. Ian Ring. Scale 3193. https://ianring.com/musictheory/scales/3193. Consulted October 9, 2026. Catalogue comparison: Ionian #2 b5 #6; other listed names include Zathian and USRian.

8. Ian Ring. Scale 1877. https://ianring.com/musictheory/scales/1877. Consulted October 4, 2026. Naming sources include William Zeitler, Justin Pecot, Robert Bedwell, Jeffrey Carl, and the Scale Omnibus.

Names dates and locations. The corrected matches are indexed under Western altered-scale or modern catalogue naming systems. The consulted entries do not identify an original discovery date or discovery location for any of these patterns. Bedwell’s cited book was published in 2023 by Locrian Publishing in Brighton, East Sussex, and Cochrane’s cited encyclopedia is associated with Big Noise Publishing in London, UK. Those are publication locations, not scale origins. The earlier Carnatic rāga associations described different, damaged note inventories and do not apply to these corrected root comparisons. [6–8]

Authorship and rights statement

Project origin, names, historical account, and scale-system development: Philip John Jatzek (Max). Research organization, computation, technical checking, and editorial drafting: Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT).

JATZEK TRIPLE-SHARP SCALES – COPYRIGHT DECEMBER 21, 1988 BY PHILIP JOHN JATZEK ALL RIGHT RESERVED!

© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT). All Rights Reserved!

FURTHER DOCUMENTATION | Testing a proposed scale against existing catalogues

Research addition • 26 September 2026 • Philip John Jatzek & STORM (ChatGPT)

Record each distinct pitch class once, relative to the chosen tonic, before searching a catalogue. Two spellings such as A# and Bb have the same pitch class in twelve-tone equal temperament but can imply different scale degrees in notation. Keep both the actual spelling and the semitone list in the research record.

A catalogue match identifies an equivalent pitch collection or interval pattern; it does not settle who discovered it first or whether the scale has a unique historical name. Repeat the comparison after transposition and document the source and date of the match. This gives the original MusicMaster account a reproducible modern check.

Reference websites consulted

https://ianring.com/musictheory/scales/

https://openmusictheory.github.io/interval(Class).html

The external references explain standard music concepts; MusicMaster-specific scale and ShadowScale results retain the definitions and evidence levels given in this periodical.

NEED TO KNOW | PERIODICAL 1

Scale spelling and pitch class checks

Spell first, then compare sound

Write each note with its intended letter name and accidental before converting it to a pitch class (C = 0 through B = 11). Two different spellings can produce the same sounding pitch in twelve tone equal temperament; preserve both spellings when explaining harmonic function.

Check the interval cycle

Convert the ascending notes to semitone distances, including the return to the octave. Their sum must equal 12 for a complete octave cycle. If a note repeats, distinguish a seven written note collection from seven distinct pitch classes.

Separate transposition from inversion

A transposition adds the same number of semitones to every pitch class modulo 12. Inversion maps each pitch class around an axis. Compare these operations explicitly before calling two collections distinct.

Test musical use

Place a scale over a bass note and a short chord progression. Mark stable chord tones, available passing tones, and pitches that need deliberate resolution; the note inventory alone does not determine musical effect.

Further reading

https://www.musictheory.net/lessons

https://ianring.com/musictheory/book/

MUSIC GLOSSARY

Naming conventions

In this chapter, distinguish a pitch-class set from a rooted scale. “Triple-Sharp” is the historical project name, not a triple-sharp accidental. Scale names, Forte classes, and listening judgments answer different questions.

1

12-tone equal temperament

A tuning system that divides each octave into twelve equal semitone steps; octave-related pitches repeat after twelve steps.

A

Accidental

A sign such as ♯, ♭ or ♮ that changes a written pitch relative to the key signature.

Ascending form

A scale written or played from lower to higher pitch; this project may specify a distinct descending form.

Audible tonic

The pitch heard as home in a listening test, which may need a drone or cadence to establish it.

C

Cadence

A melodic or harmonic arrival that helps listeners judge whether a proposed tonic feels settled.

Cardinality

The number of distinct pitch classes in a collection; the repeated octave does not increase it.

Chromatic scale

All twelve pitch classes within an octave, ordered by semitone.

Collection

A group of pitch classes considered by membership before choosing their order or tonic.

Concert pitch

The pitch that sounds, as distinct from written pitch for a transposing instrument.

Consonance

A relatively stable or settled combination of tones in a musical context.

D

D Dorian

The mode D–E–F–G–A–B–C, heard with D as its tonal centre.

D major

The major scale D–E–F♯–G–A–B–C♯.

D natural minor

The natural minor scale D–E–F–G–A–B♭–C.

Diatonic scale

A seven-note scale organized by a particular pattern of whole and half steps.

Drone

A held or repeated pitch that provides a stable reference while a scale is tested.

E

Enharmonic spelling

Different written note names that sound at the same pitch in equal temperament, such as A♯ and B♭.

Equal-tempered semitone

One of twelve equal pitch steps in an octave; on a guitar it ordinarily equals one fret.

F

Fifth

An interval between scale degrees five letter names apart; a perfect fifth spans seven semitones.

Forte set class

A numbered category for pitch-class collections related by transposition or inversion; it does not by itself name a rooted scale.

Frequency

The repetition rate of a sound wave, measured in hertz; a doubled frequency is one octave higher.

H

Harmonic minor

A minor scale with a raised seventh relative to natural minor; the usual harmonic-minor form uses the same notes ascending and descending.

I

Interval

The measured distance between two pitches, expressed by note name and quality or semitone count.

Interval class

The smaller of an interval and its inversion within the twelve-semitone octave, numbered 1 through 6.

Interval vector

Six counts showing how many unordered pitch-class pairs in a set belong to interval classes 1 through 6.

Inversion of a set

Reflection of every pitch class around an axis modulo twelve; different from placing a chord tone in the bass.

K

Key signature

Sharps or flats printed at the start of a staff to state the default note spellings.

M

Major third

An interval spanning four semitones; its quality above a tested tonic helps identify major character.

Melodic minor

A minor-scale family often taught with raised sixth and seventh ascending and natural-minor descent; specify the form in use.

Minor third

An interval spanning three semitones; its quality above a tested tonic helps identify minor character.

Modal colour

The characteristic sound of a mode created by its scale degrees and emphasis around a centre.

Modulo twelve

Reducing semitone numbers by multiples of twelve so octave-equivalent notes have the same pitch-class number.

N

Note spelling

The written letter name and accidental of a pitch; preserve it when interpreting harmony.

O

Octave

An interval of twelve equal-tempered semitones between two notes of the same letter name.

Octave equivalence

Treating pitches separated by octaves as the same pitch class for set comparison.

P

Parallel key

A major or minor key sharing the same tonic with another mode, such as D major and D minor.

Performance root

The pitch selected as the home reference when a MusicMaster scale is played or tested.

Pitch

The perceived highness or lowness of a sound; the same note name can occur in several octaves.

Pitch class

A pitch identity without octave; every D belongs to pitch class D.

Prime form

A standardized representation of a pitch-class set used to compare transposition and inversion classes.

Proposed scale name

A project label for a candidate collection; a distinct name does not prove the pitch set is historically new.

R

Root

The pitch from which a scale formula is counted, or the note that names a chord.

Rooted scale

A pitch collection interpreted with a specified root and tonal behaviour rather than as an unordered set alone.

S

Scale

A selected set of pitches organized around a root and ordinarily presented in an order for playing.

Scale degree

A numbered pitch position relative to the scale root.

Scale formula

The sequence of intervals or altered degrees that defines a scale from its root.

Scale spelling

The chosen sequence of note names and accidentals that makes the interval structure legible.

Semitone

A half step in the twelve-tone system; successive chromatic guitar frets are a semitone apart.

Set class

A family of pitch-class collections equivalent under specified transformations such as transposition and inversion.

Sharp

An accidental that raises a written pitch one semitone.

Sonic comparison

Listening to candidates under controlled accompaniment instead of relying only on written pitch membership.

T

Tonic

The perceived home pitch established by musical context, which is not guaranteed by a pitch list alone.

Tonic-fifth ending

A cadence test pairing a proposed tonic with its fifth to assess a sense of closure.

Transposition

Moving every pitch in a collection by the same number of semitones while preserving intervals.

Transposition class

A grouping of sets related by uniform pitch shifts; rooted names can still differ.

Triple-sharp project name

The historical name of this MusicMaster scale project, referring here to three sharp-note anchors; it is not a triple-sharp accidental on one note.

W

Whole step

An interval of two equal-tempered semitones.