Publication status
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Purpose. This revision continues the first Roaring.biz publication while separating verified pitch-class facts from historical claims and from items that still require confirmation.
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Abstract
The JATZEK Triple-Sharp project records a family of scale constructions attributed to Philip John Jatzek's Music Master experiments and scale-discovery work of 1987–1988. The public material names three parent systems—ACG, CDG, and AFG—and related blues or “shadow” forms. This publication formalizes the currently published note collections in twelve-tone equal temperament (12-TET), introduces reproducible pitch-class-set measurements, and defines listening and tonic-identification experiments for the next stage. It does not treat catalog presence as proof that a scale system lacks musical originality: a pitch-class set, its tonal interpretation, its naming, and its compositional practice are different kinds of claims.
Key finding in this revision
The public ACG and CDG spellings each contain six distinct pitch classes, with the opening A repeated at the octave. They are therefore hexatonic pitch collections as presently written, not heptatonic collections. Both also have ordinary Forte set-class classifications. This corrects two statements in the earlier article without rejecting the broader JATZEK system. The AFG spelling has been confirmed by the author; its intended root remains provisional pending the planned listening and harmonic tests.
Claims and evidence levels
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Level
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Meaning
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Treatment in this draft
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Verified
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Reproducible from a stated note set
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Cardinality, pitch classes, step cycle, prime form, interval vector
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Documented
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Stated in the public Roaring.biz record
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Names, dates, Music Master origin account, shadow-scale concept
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Provisional
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Needs source data or repeatable testing
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Exact six-parent inventory, tonic/key assignments, major/minor labels
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Open claim
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Requires a defined catalog and search record
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Novelty relative to named historical or global scale traditions
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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, 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 A at the top of an A-based scale completes the melodic octave but does not add a seventh pitch class. Cardinality counts distinct pitch classes, not printed 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, unified by the project's three-sharp-anchor condition. 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
Here, “Triple-Sharp” is retained as the project name for a system organized around three sharp-note anchors. It should not be confused with the notation symbol for a single note raised by three semitones. The publication should state this explicitly to prevent readers from misunderstanding the title.
3. Current public note data
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Family
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Published ascending spelling
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Distinct PCs
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Relative PCs from A
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Current status
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ACG
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A–A♯–C♯–D–E–G♯–A
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6
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0, 1, 4, 5, 7, 11
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Public; internally analyzable
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CDG
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A–B–C♯–D♯–E–G♯–A
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6
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0, 2, 4, 6, 7, 11
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Public; internally analyzable
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AFG
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A–B–C–C♯–D♯–F–G♯
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7
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0, 2, 3, 4, 6, 8, 10
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Author-confirmed public spelling; tonic provisional
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Notation caution. The degree labels in the first article use spellings such as ♯3 and ♯7 that can obscure semitone content. The pitch-class rows above are the controlling data for computation; functional degree names should be assigned only after the tonic is experimentally established.
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4. Reproducible pitch-class analysis
The following results use A = 0 and semitone counting modulo 12. Prime forms and Forte labels follow the common Rahn/Straus ordering used by the University of Puget Sound set-class table. Interval vectors count interval classes 1 through 6.
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Family
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Step cycle
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Prime form
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Forte class
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Interval vector
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ACG
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1–3–1–2–4–1
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(012568)
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6–Z43
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⟨3,2,2,3,3,2⟩
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CDG
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2–2–2–1–4–1
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(013578)
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6–Z26
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⟨2,3,2,3,4,1⟩
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AFG
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2–1–1–2–2–2–2
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(012468T)
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7–33
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⟨2,6,2,6,2,3⟩
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Interpretation
ACG and CDG are not the same pitch-class set under transposition or inversion because they have different prime forms and interval vectors.
Each belongs to a previously enumerated Forte set class. Therefore the earlier phrase “no Forte set-class equivalence found” must be withdrawn.
Forte classification does not settle whether the JATZEK naming, tonic behavior, paired major/minor organization, shadow extraction, or historical discovery is distinctive.
Using the author-confirmed public spelling above, AFG belongs to Forte class 7–33.
5. The six-parent and twelve-form hypothesis
The project currently describes three named families, six parent scales, and six related shadow/blues scales, for twelve forms in total. The proposed tonal balance is five minor-oriented parent forms and one major-oriented parent form. The available public note lists are not yet sufficient to reproduce that full matrix without guessing. The final publication should therefore print all six parent rows and all six shadow rows explicitly.
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Family
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Parent form A
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Parent form B
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Shadow form(s)
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Needed evidence
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ACG
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Public spelling available
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Not yet isolated
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Named in article
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Exact notes, root, major/minor function
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CDG
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Public spelling available
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Not yet isolated
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Article uses CFG label in one place
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Resolve CDG/CFG label and exact subset
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AFG
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Public spelling confirmed
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Not yet isolated
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Named in article
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Tonic and both parent forms
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Shadow-scale proposition
A shadow scale is described as a five-note blues-oriented subset revealed by an overlay procedure: map positions not occupied in one display, shift a pentatonic template, and identify the notes that coincide with the parent system. For publication, this must be demonstrated with a numbered diagram or a complete position table for each family. Until those mappings are printed, “structurally embedded” should be presented as a testable proposition rather than as a proven non-random result.
6. Root, tonic, and key experiments
A pitch collection alone does not guarantee one root. The root/tonic question should be answered by controlled listening and harmonic tests across all transpositions. The same MIDI rhythm, register, tempo, and timbre should be used so that only pitch organization changes.
Generate an ascending and descending one-octave realization for every candidate tonic.
Create three cadential endings per candidate tonic: final-note only, tonic drone, and tonic-fifth drone.
Rate perceived rest, closure, tension, and repeatability using a fixed 1–5 form.
Repeat the test in all 12 chromatic transpositions; interval results should remain invariant.
Test the proposed shadow subset over the same drone and record whether it reinforces or weakens the parent tonic.
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
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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.
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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 documented public history and a clear research program.
As currently printed, ACG and CDG are six-pitch-class collections completed by an octave repetition.
ACG maps to Forte class 6–Z43; CDG maps to 6–Z26.
The author-confirmed AFG spelling maps to Forte class 7–33; its tonic remains subject to the planned listening and harmonic tests.
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
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Required item
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Why it matters
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Acceptance test
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Six parent note lists
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Establishes the complete system
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Seven intended degrees or explicit hexatonic status for every row
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Six shadow note lists
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Makes the overlay claim reproducible
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Every subset maps to its stated parent without foreign pitches
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Root/tonic for each form
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Controls degree spelling and major/minor label
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Drone/cadence results documented
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Music Master evidence
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Strengthens the 1987–1988 discovery history
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Dated source, scan, code, disk image, printout, or registration record
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Catalog search log
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Supports novelty claims
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Catalog, query, date, transposition/inversion rules, and result retained
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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.
Authorship and rights statement
Project origin, names, historical account, and claimed scale system: Philip John Jatzek. Research organization, computation, technical checking, and editorial drafting: Philip John Jatzek & STORM (ChatGPT). The copyright statement in this draft applies to the written and designed publication; the legal protectability of musical scales, methods, names, or underlying pitch collections is a separate jurisdiction-dependent question.
JATZEK TRIPLE-SHARP SCALES – COPYRIGHT DECEMBER 21, 1988 BY PHILIP JOHN JATZEK ALL RIGHT RESERVED!
JATZEK TRIPLE-SHARP SCALES PUBLICATION – COPYRIGHT AUGUST 25, 2026 BY PHILIP JOHN JATZEK AND STORM (ChatGPT) ALL RIGHTS RESERVED!
