_JATZEK

JATZEK MUSICMASTER

7/14 SCALE-SHADOWSCALE SYSTEM

PERIODICAL #2 - RELEASE EDITION

Seven base scales, raw missing-note Shadows, overlay shifts, and directional performance forms

Philip John Jatzek (Max) & STORM (ChatGPT)
1 September 2026

RELEASE STATUS: This release records the audited theory and separates confirmed, performance-confirmed, provisional, and rejected results so that experimental conclusions remain clearly identified.

 

JATZEK TRIPLE-SHARP SCALES - COPYRIGHT DECEMBER 21, 1988 BY PHILIP JOHN JATZEK. ALL RIGHTS RESERVED.

PERIODICAL #2 - COPYRIGHT AUGUST 29, 2026 BY PHILIP JOHN JATZEK AND STORM (ChatGPT). ALL RIGHTS RESERVED.

Periodical at a glance

This periodical organizes seven main groups of notes around D as the performance root. For each seven-note scale, the five unused chromatic notes form a raw ShadowScale. The ShadowScale is then moved as one complete shape to test whether it fits inside the parent scale. The archive has eight root-D charts because melodic minor descending and natural minor use the same notes but serve different musical roles. Three scales that do not accept an exact overlay also have experimental descending partners.

Working count	Meaning	Status
7 base collections	Four known collections plus JATZEK 1-3	Inventory supplied and reconciled
8 root-D charts	Natural minor also serves as melodic-minor descent	Organized in supplied archive
7 raw Shadows	Five missing pitch classes for each seven-note base	Method defined
3 nonmatching overlays	D harmonic minor, JATZEK 1, JATZEK 3	Confirmed mathematically
3 descending partners	Derived from nonmatching Shadow notes	All three pairs play-tested and accepted, 28-30 August 2026
10 distinct collections	Seven base collections plus three directional companions	Working theoretical total
11 labeled forms	Eight charts plus three directional companions	When performance direction is counted

 

Evidence labels

Label	Meaning
Confirmed	Notes, missing set, shift, chart and performance checks completed.
Performance-confirmed	Played successfully; one or more final documentation checks remain.
Provisional	Mathematically derived but still awaiting performance or chart verification.
Rejected	A proposed overlay or voicing failed calculation or listening tests.

 

ACCURACY RULE: Every final scale must pass note, mathematical, fretboard and performance checks. A single misplaced semitone changes the scale identity and every derived result.

 

Scope of this periodical

• Define raw ShadowScales as the chromatic pitch classes absent from a seven-note parent scale.

• Separate perfect uniform overlays from nonmatching and semitone-adjusted overlays.

• Document JATZEK 2's selected overlay and its additional valid ShadowScale positions.

• Document the three directional descending constructions without claiming historically unknown pitch collections.

• Preserve the unresolved MusicMaster question: why did the program retain four known patterns and three unmatched JATZEK patterns?

1. Historical background

Philip John Jatzek wrote and used the MusicMaster music-theory sequencer on an Amiga 500 in 1987-1988. The program moved scale notes through possible positions and compared each pattern with the scales stored in its own reference data. When it found a match, it stopped following that search path. Three patterns did not match the stored data and were kept as the JATZEK scales.

Later checks against larger world-scale catalogues found historical names for these note collections, especially in Carnatic music theory. The claim is therefore not that the notes had never existed before. The important result is that MusicMaster found them independently and that the present project organizes them through the ShadowScale method.

CENTRAL RESEARCH QUESTION: Do the four reference scales and three JATZEK scales form a connected seven-scale set under MusicMaster’s single-note movement and cancellation rules?

 

Search-space context

Counting rule	Number
Seven-note collections with a fixed root	462
Scale families with transpositions/modes grouped	66
Forte classes with inversion also grouped	38

 

If MusicMaster had listed every possible seven-note pattern that was missing from its database, seven results would be far too few. The best current explanation is search-tree pruning. In plain language, when the program found a known scale, it stopped exploring every later pattern that would have grown from that branch. This may explain why only four known patterns and three unmatched JATZEK patterns survived.

2. Definitions and conventions

The terms below separate a scale's fixed notes from the movable fretboard shape used to test its ShadowScale. A pitch class means one note name in any octave, such as every D on the instrument. A semitone is one chromatic step, such as D to D#. A transposition moves every note by the same number of semitones. A parent scale is the seven-note scale being tested.

Term	Working definition
Base scale / scale template	A seven-note group used as the main or ascending form. It is the parent scale for the ShadowScale test.
Raw ShadowScale	The five chromatic note names that are missing from the seven-note parent scale.
ShadowScale template	The fixed spacing and fingering pattern formed by the five raw ShadowScale notes. It moves as one complete shape.
Perfect overlay	A fit in which one equal shift places all five notes of the unchanged ShadowScale inside the parent scale.
Multiple overlay	Another complete position of the same unchanged ShadowScale inside the same parent scale.
Nonmatching overlay	A test in which one or more notes of the shifted ShadowScale still fall outside the parent scale.
Semitone-adjusted ShadowScale	A playable repair made by removing an adjacent-semitone conflict from a nonmatching result. It is labeled SEMITONE, not OVERLAY.
Directional companion	A related ascending or descending scale used for one direction of performance. Its notes may differ from the partner used in the other direction.
Performance root	The note heard as the musical centre during playing and listening tests. D is the common performance root in this project.

 

Guitar chart convention

Tuning is D-G-C-F-A-D. Fretboards are displayed from top to bottom as String 6 D, String 5 G, String 4 C, String 3 F, String 2 A and String 1 D. Charts cover frets 0-16. Scale and ShadowScale notes use separate symbols, with D identified as the performance root.

Organized root-D inventory supplied 1 September 2026

Chart	Parent sequence	Shadow sequence
D major	D-E-F#-G-A-B-C#-D	D-E-G-A-B-D
Melodic minor ascending	D-E-F-G-A-B-C#-D	D-F-G-A-B-D
Melodic minor descending	D-C-Bb-A-G-F-E-D	D-C-Bb-G-F-D
D natural minor	D-E-F-G-A-Bb-C-D	D-F-G-Bb-C-D
D harmonic minor	D-E-F-G-A-Bb-C#-D	D-F-G-A-Bb-D (repaired)
JATZEK 1	D-E-F#-G#-A-Bb-C#-D	D-E-F#-G#-Bb-D
JATZEK 2	D-E-F#-G#-A-Bb-C-D	D-E-F#-G#-C-D
JATZEK 3	D-F-F#-G#-A-Bb-C-D	D-F#-G#-Bb-C-D

 

COUNTING NOTE: Natural minor and melodic minor descending contain the same seven pitch classes. They count once among the seven distinct base collections, but remain separate charts because their performance roles differ.

 

The seven-note scale and the five-note ShadowScale are treated as complete shapes. During a test, the spacing between the ShadowScale notes does not change. The whole five-note shape moves together to a new fretboard position. The test then asks whether all five moved notes land inside the parent scale.

The scale template and ShadowScale template are treated as complete shapes. During an overlay test, the relative finger spacing is never redrawn note by note. The entire five-note ShadowScale footprint is shifted to a new fretboard position and tested against the seven-note scale.

3. Perfect-overlay results

A perfect overlay occurs when all five raw ShadowScale notes move by the same number of semitones and every moved note lands inside the seven-note parent scale. No note is added, removed or moved by itself.

The five-note pattern is therefore a movable ShadowScale template. Its internal finger spacing stays the same wherever it is placed on the fretboard. This is what makes an overlay a controlled test instead of a newly invented five-note scale.

Scale	Raw missing-note shift	Overlay status
D major	Down 1 semitone	Perfect - selected chart overlay
D Dorian	Down 1 semitone	Perfect
D natural minor	Down 1 semitone	Perfect
D melodic minor ascending	Down 1 semitone	Perfect
JATZEK 2 / D Rishabhapriya	Up 1 semitone	Perfect - selected Overlay 1

 

JATZEK 2 - selected overlay

Item	Notes
Base scale	D-E-F#-G#-A-Bb-C-D
Raw missing notes	D#-F-G-B-C#
Selected Shadow	D-E-F#-G#-C-D
Operation	Raise every raw missing note by one semitone

 

Six valid placements of the same five-note ShadowScale template were identified for JATZEK 2. The displayed position is Overlay 1; the five further placements are complete positions of the same unchanged fingering footprint.

Complete overlay inventory

One parent scale may contain several valid positions of the same ShadowScale template. Each complete position is a separate overlay candidate. The candidates may begin on different notes, but they all preserve the same five-note design.

System scale	Concert/catalogue name	Count	Result
D major	D major	3	Perfect template; 2 additional
Melodic minor ascending	D melodic minor ascending	2	Perfect template; 1 additional
Natural minor	D natural minor	3	Also melodic-minor descent
Harmonic minor	D harmonic minor	1	SEMITONE base only
JATZEK 1	D Latangi / Lydian Harmonic Major	1	SEMITONE base only
JATZEK 2	D Rishabhapriya	6	Perfect template; 5 additional
JATZEK 3	D Jyoti Swarupini	1	SEMITONE base only

 

Counting rule: the displayed ShadowScale is Overlay 1. An additional transposition counts only when every note of the unchanged template remains inside the parent scale. Additional placements are performance variations, not newly invented templates.

PERFORMANCE TEST: Cadence, drone response and tonal resolution determine which valid position functions as the primary ShadowScale.

 

4. The three nonmatching overlays

Base scale	Raw overlay result	Working consequence
D harmonic minor	Closest shifts match only four of five notes	Experimental descending companion
JATZEK 1 / D Latangi	No complete uniform overlay	Derived directional companion
JATZEK 3 / D Jyoti Swarupini	No complete uniform overlay	Derived directional companion

 

WORKING INTERPRETATION: A failed overlay identifies the exact ShadowScale notes that cannot enter the ascending scale while the original template remains intact.

 

Constructing a descending scale

MISMATCH NOTICE: When the raw five-note ShadowScale maps only four or fewer notes onto the ascending scale, the mismatch signals that a descending companion scale must be constructed. The mismatch is therefore not only a failed ascending overlay; it identifies where the directional descending form begins.

TO MAKE A DESCENDING SCALE FROM A MISMATCH SHADOWSCALE: On the ascending form, adjust the ShadowScale so that all five notes overlay the parent scale. This produces one adjusted ShadowScale overlay on the ascending scale. For the descending form, keep that mismatch ShadowScale and adjust the parent scale notes to match it. The resulting descending scale then supports two ShadowScale overlays: one mismatch ShadowScale carried over from the ascending scale, and one ShadowScale made from the notes missing from the descending scale.

1. Shift the raw missing-note template toward its closest overlay.

2. Identify the ShadowScale notes remaining outside the base scale.

3. Add those notes to the proposed descending form.

4. Remove the corresponding replaced or conflicting scale notes.

5. Retain D as the performance root and test ascent, descent and ShadowScale by ear.

OVERLAY and SEMITONE ShadowScales

Type	Rule	Meaning
OVERLAY	All five notes and the original fingering footprint survive one uniform shift.	A perfect placement of the unchanged template.
SEMITONE	An obvious adjacent-semitone conflict is removed from a nonmatching result.	A playable derivative, not a perfect overlay.

 

A parent scale may accept the unchanged ShadowScale in several fretboard positions. These positions can create different melodic routes or tonal colours. A modal colour is a change in musical character caused by hearing a different note as the centre. The overlay itself does not change shape.

Discovery within the JATZEK 7/14 system

DISCOVERY OF METHOD: Nonmatching empty-note ShadowScale material made the descending-scale notes possible. Semitone removal and note replacement supplied a controlled way to turn that material into playable directional partners.

 

This is a discovery of construction and organization within the JATZEK MUSICMASTER 7/14 Scale-ShadowScale System. It does not claim that the resulting pitch collections were previously unknown in world music theory.

VARIATION NOTE: A scale can have more than one valid overlay. Each keeps the same ShadowScale template intact and shifts it to another position within the seven-note parent.

 

5. Directional performance forms

This directional method is used when a raw ShadowScale does not fit the ascending parent exactly. Harmonic minor, JATZEK 1 and JATZEK 3 still produce playable repaired forms after one adjacent-semitone conflict is handled. These are labeled SEMITONE forms, not perfect overlays. The method is a JATZEK way of composing and analyzing directional scale pairs; it does not claim that their individual note collections were unknown before. In the ascending form, the mismatch ShadowScale is adjusted so that all five ShadowScale tones overlay the ascending parent. In the descending form, the parent scale notes are adjusted to accept the mismatch ShadowScale. The revised descending scale then carries two distinct ShadowScale overlays: A identifies the repaired mismatch ShadowScale inherited from the ascending scale and moved intact to a valid descending overlay position; D identifies the independent verification ShadowScale calculated from the revised descending scale's own missing notes. MISMATCH-SCALE LEGEND: A = Ascending Scale. D = Descending Scale. MISMATCH means four or fewer notes of the raw five-note ShadowScale map to the ascending seven-note scale. SOFAS = ShadowScale Overlay From Ascending Scale, made into a complete five-tone form by a semitone adjustment to the missing mismatch note. MSOFAS = Mismatch ShadowScale Overlay From Ascending Scale. It exists only for mismatch scales, uses the raw mismatch notes, and helps create the descending scale. SOFDS = ShadowScale Overlay From Descending Scale, generated from all notes missing from the revised descending scale.

Construction procedure

1. Ascending: place the scale notes on the fretboard.

2. Find the notes missing from the ascending scale and use them to form the raw five-tone ShadowScale.

3. Overlay the raw ShadowScale on the ascending scale. If only four or fewer tones map, mark it as a mismatch.

4. Use a semitone adjustment on the nonmatching missing-note/scale-note position to create one complete five-tone adjusted ShadowScale, then overlay it on the ascending form.

5. Descending: keep the mismatch ShadowScale intact and adjust the parent scale notes to accept it. Add the nonmatching Shadow material and remove the corresponding replaced or conflicting original-scale note.

6. Retain D as the performance root and write the adjusted parent as a one-octave descending order.

Pair	Ascending/root form	Descending form	Concert identification	Status
JATZEK 1	D-E-F#-G#-A-Bb-C#-D	D-E-F#-G-G#-Bb-C-D	D Latangi -> D Major Locrian	VERIFIED - play-tested 28-30 August 2026
JATZEK 3	D-F-F#-G#-A-Bb-C-D	D-E-F-G#-A-Bb-C-D	D Jyoti Swarupini -> D Shanmukhapriya	VERIFIED - play-tested 28-30 August 2026
JATZEK Harmonic A&D	D-E-F-G-A-Bb-C#-D	D-E-F-G-A-Bb-B-D	D harmonic minor -> D Jhankaradhwani / Raga Jhankara Bhramavi	VERIFIED - play-tested 28-30 August 2026

1. From all notes missing from the revised descending scale, calculate the independent verification ShadowScale. The revised descending scale now has two ShadowScale overlays: the adjusted ascending mismatch overlay and its own descending verification overlay.

2. Play the ascent, descent and both ShadowScale overlays against D before accepting the directional pair.

 

JATZEK 3 performance observation

The JATZEK 3 ascending and descending forms were both played successfully. When their notes are combined, they contain two groups of three neighbouring chromatic notes: E-F-F# and G#-A-Bb. Playing either complete group over D sounded unacceptable in the test. For that reason, the groups are treated as melodic movements used in one direction, not as chord-like blocks that can be placed anywhere.

Harmonic-minor experiment

D harmonic minor has the raw missing set D#-F#-G#-B-C. Shifting down one semitone gives D-F-G-Bb-B: four notes overlay and B remains outside. The experimental descending construction adds B and removes C#, producing D-E-F-G-A-Bb-B-D. This pairing was play-tested and accepted by ear during the experiments of 28-30 August 2026.

6. Concert-name correspondence

These names describe previously catalogued pitch collections. They do not evaluate the JATZEK Shadow method or the proposed directional pairing.

JATZEK/system form	Concert or catalogue correspondence
JATZEK 1 ascending	D Latangi; D Lydian Harmonic Major
JATZEK 1 descending	D Major Locrian
JATZEK 2	D Rishabhapriya equivalent
JATZEK 3 ascending	D Jyoti Swarupini
JATZEK 3 descending	D Shanmukhapriya; D Aeolian #4
Harmonic-minor experimental descending	D Jhankaradhwani; D Aeolian double-flat 7

 

ORIGINALITY CAUTION: The individual note collections are documented. The potentially original contribution is their Shadow-derived organization through raw missing-note Shadows, overlay shifts, perfect/nonmatching classification and unified directional partners.

 

A&D pairing search result

Music traditions already use scales whose ascending and descending notes differ. Examples include Western melodic minor and the arohana and avarohana forms of Indian ragas. During the present review, no earlier source was found that documented these three exact directional pairings. The possible original contribution is therefore the Shadow-derived way of joining known note collections into directional pairs, not the invention of the notes themselves.

7. Current 7/10 structure

The supplied root-D archive resolves the base inventory as four known pitch collections plus three JATZEK collections. D melodic minor descending is retained as a separate performance chart but shares its pitch collection with D natural minor. Adding the three derived companions gives ten distinct pitch collections and eleven separately labeled performance forms.

Category	Count	Publication treatment
Known/reference collections	4	Major; melodic minor ascending; natural minor; harmonic minor
Additional directional reference chart	1	Melodic minor descending = natural-minor collection
JATZEK base forms	3	JATZEK 1, 2 and 3
Derived descending partners	3	Harmonic minor, JATZEK 1 and JATZEK 3
Distinct pitch collections	10	Seven base plus three derived
Labeled performance forms	11	Eight supplied charts plus three derived

 

8. Verification protocol

A scale is not accepted as final only because it matches a catalogue name or sounds good in one test. Its notes, missing-note set, overlay movement, fretboard markers and musical result must all be checked.

Check	Requirement
1. Note check	Verify all seven pitches against the original working chart.
2. Missing-set check	Confirm that the five absent chromatic pitches are complete and contain no scale pitch.
3. Shift check	Apply one uniform semitone shift and verify every resulting pitch.
4. Fretboard check	Confirm every marker against D-G-C-F-A-D tuning and frets 0-16.
5. Performance check	Play ascent, descent, Shadow, cadence and D-root resolution.
6. Catalogue check	Identify existing names without treating a name match as proof of the JATZEK method.

 

Performance test sheet

• Play the ascending form slowly from D to D.

• Play the descending form from D to D without borrowing notes from the ascent.

• Play the Shadow alone, then over a sustained D drone.

• Test melodic resolution, bass resolution and tonic harmony.

• Repeat in a later session while rested; record pass, revise or reject.

9. Completed verification work

• DONE - Played and accepted the harmonic-minor / Jhankaradhwani descending pair.

• DONE - Rechecked JATZEK 1 ascending, descending and Shadow notes while rested.

• DONE - Reconfirmed the four reference collections and melodic-descending duplicate relationship.

• DONE - Recalculated every raw missing-note set and overlay shift independently.

• DONE - Audited every fretboard marker against D-G-C-F-A-D tuning.

• OMITTED BY DESIGN - A forced D-root overlay shift can change the scale identity.

• DONE - Added experiment dates (28-30 August 2026) and final evidence labels.

10. Conclusion

The present results divide the seven-scale group into exact and non-exact ShadowScale classes. In an exact case, the complete five-note missing-note set can be moved into the parent scale without changing its shape. In the three non-exact cases - D harmonic minor, JATZEK 1 and JATZEK 3 - some material remains outside. That unmatched material is used to build the experimental descending partners.

The individual note collections already have historical catalogue names. The research value is in the method that connects them: find the five missing chromatic notes, move them as one template, test the fit, identify the failure, and use the unmatched notes to form a descending partner. All three pairs passed the final audit. The system therefore contains seven base collections and ten distinct performance collections. Eleven charts are shown because melodic minor descending has its own performance role even though it shares its notes with natural minor.

RELEASE CONCLUSION: The published results passed the documented note, missing-set, shift, fretboard, catalogue, and performance checks. Primary-candidate ear testing remains an open performance choice where the appendix explicitly provides a test record.

 

Credits and rights

Original MusicMaster program, scale discovery history and JATZEK naming: Philip John Jatzek.

ShadowScale analysis, comparison, drafting and publication development: Philip John Jatzek & STORM (ChatGPT).

JATZEK TRIPLE-SHARP SCALES - COPYRIGHT DECEMBER 21, 1988 BY PHILIP JOHN JATZEK. ALL RIGHTS RESERVED.

PERIODICAL #2 - COPYRIGHT AUGUST 29, 2026 BY PHILIP JOHN JATZEK AND STORM (ChatGPT). ALL RIGHTS RESERVED.

References

• JATZEK Triple-Sharp Scales - Final Publication, 25 August 2026.

• JATZEK scale and ShadowScale fretboard experiments, tuning D-G-C-F-A-D, frets 0-16.

• Ian Ring, A Study of Scales / scale database entries used for pitch-class and common-name comparison.

• MusicMaster recollections and continuing performance tests by Philip John Jatzek.

• Open Music Theory, Scales and Scale Degrees - Western melodic minor ascending/descending convention.

• Narasinh et al., Sequential Pitch Distributions for Raga Detection (2023) - raga identity and differing ascending/descending patterns.

APPENDIX A - PLAYABLE FRETBOARD SCALE DATA

Reference charts | Teaching order top-to-bottom D-G-C-F-A-D | Frets 0-16 | Performance root D

Directional scales are paired on one sheet. All notes, Shadow markers and concert identifications were audited during the experiments of 28-30 August 2026.

APPENDIX B - SHADOWSCALE OVERLAY TEST CHART

This chart lists every ascending and descending overlay candidate. The displayed number records its original fretboard position; Overlay 1 is not automatically the Primary choice. A Primary ShadowScale is the candidate that gives the strongest musical result in performance tests. D always remains BASE 0 for interval measurement, even when the selected Primary begins on another note.

WORKING THEORY: All overlays use exactly the same ShadowScale template; only the template position within the parent scale changes. The chart may reveal one primary true ShadowScale position plus secondary playable positions.

 

System scale	Notes of scale	Notes of overlays	Interval from D	# overlays
D major	D-E-F#-G-A-B-C#-D	1. D-E-G-A-B-D 2. E-F#-A-B-C#-E 3. A-B-D-E-F#-A	BASE 0 / +2 / +7	3
D melodic minor ascending	D-E-F-G-A-B-C#-D	1. D-F-G-A-B-D 2. E-G-A-B-C#-E	BASE 0 / +2	2
D melodic minor descending	D-C-Bb-A-G-F-E-D	1. D-C-Bb-G-F-D 2. E-D-C-A-G-E 3. A-G-F-D-C-A	BASE 0 / +2 / +7	3
D natural minor	D-E-F-G-A-Bb-C-D	1. D-F-G-Bb-C-D 2. E-G-A-C-D-E 3. A-C-D-F-G-A	BASE 0 / +2 / +7	3
D harmonic minor ascending	D-E-F-G-A-Bb-C#-D	1. D-F-G-A-Bb-D	BASE 0	1
D harmonic minor descending	D-E-F-G-A-Bb-B-D	1. D-F-G-Bb-B-D	BASE 0	1
JATZEK 1 ascending / D Latangi	D-E-F#-G#-A-Bb-C#-D	1. D-E-F#-G#-Bb-D	BASE 0	1
JATZEK 1 descending / D Major Locrian	D-E-F#-G-G#-Bb-C-D	A1: D-E-F#-G#-Bb-D (ascending mismatch template; six positions A1-A6 listed on the scale chart) D1: D-E-F#-Bb-C-D (descending missing-note template; six positions D1-D6 listed on the scale chart)	A: BASE 0 D: BASE 0	12 total (6 A + 6 D)
JATZEK 2 / D Rishabhapriya	D-E-F#-G#-A-Bb-C-D	1. D-E-F#-G#-C-D 2. E-F#-G#-Bb-D-E 3. F#-G#-Bb-C-E-F# 4. G#-Bb-C-D-F#-G# 5. Bb-C-D-E-G#-Bb 6. C-D-E-F#-Bb-C	BASE 0 / +2 / +4 / +6 / +8 / -2	6
JATZEK 3 ascending / D Jyoti Swarupini	D-F-F#-G#-A-Bb-C-D	1. D-F#-G#-Bb-C-D	BASE 0	1
JATZEK 3 descending / D Shanmukhapriya	D-E-F-G#-A-Bb-C-D	A1 (ascending mismatch template): D-E-G#-Bb-C-D D1 (descending missing-note template): D-E-F-A-Bb-D	A: BASE 0 D: BASE 0	2 (1 A + 1 D)

B-2. FULL SHADOWSCALE CANDIDATE NAMING CHART

NAMING RULE: SCALE NAME NOT FOUND IN EXTENSIVE REFERENCE SEARCH

Each complete overlay has two useful identities. The first is the key and catalogue name suggested by the five-note template itself. The second is the way that candidate may sound when D remains the parent and performance root. A candidate without D can still be tested over D, but it cannot complete a five-note cadence to D by itself. A cadence is a short ending that creates a sense of arrival at the tonal centre.

PRIMARY RULE: No displayed candidate is automatically Primary. Test every candidate that contains D by playing it upward, downward, against a sustained D drone, and as a cadence. A drone is one long held note used as a tonal reference. Choosing the strongest Primary does not change the interval numbers; every interval is still measured from D.

D MAJOR - THREE CANDIDATES

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-E-G-A-B-D	D Yo (Ritsu/Scottish) pentatonic	YES - D Yo pentatonic; D-root Primary candidate
2	E-F#-A-B-C#-E	E Yo (Ritsu/Scottish) pentatonic	NO - offset overlay; test over the D parent
3	A-B-D-E-F#-A	A Yo (Ritsu/Scottish) pentatonic	YES - reorder D-E-F#-A-B-D: D major pentatonic; D-root Primary candidate

D MELODIC MINOR ASCENDING - TWO CANDIDATES

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-F-G-A-B-D	D minor-added-sixth pentatonic (Kyemyonjo)	YES - self-contained D-root Primary candidate
2	E-G-A-B-C#-E	E minor-added-sixth pentatonic (Kyemyonjo)	NO - offset overlay; test over the D parent

D MELODIC MINOR DESCENDING - THREE DIRECTIONAL CANDIDATES

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-C-Bb-G-F-D	D Man Gong / minor pentatonic type 3 (descending)	YES - self-contained D-root Primary candidate
2	E-D-C-A-G-E	E Man Gong / minor pentatonic type 3 (descending)	YES - reorder D-E-G-A-C-D: D suspended/Egyptian-type pentatonic; test as D root
3	A-G-F-D-C-A	A Man Gong / minor pentatonic type 3 (descending)	YES - reorder D-F-G-A-C-D: D minor pentatonic; D-root Primary candidate

D NATURAL MINOR - THREE CANDIDATES

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-F-G-Bb-C-D	D Man Gong / minor pentatonic type 3	YES - self-contained D-root Primary candidate
2	E-G-A-C-D-E	E Man Gong / minor pentatonic type 3	YES - reorder D-E-G-A-C-D: D suspended/Egyptian-type pentatonic; test as D root
3	A-C-D-F-G-A	A Man Gong / minor pentatonic type 3	YES - reorder D-F-G-A-C-D: D minor pentatonic; D-root Primary candidate

D HARMONIC MINOR ASCENDING - SEMITONE CANDIDATE

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-F-G-A-Bb-D	D minor 6/11 pentatonic / Raga Kokil Pancham	YES - SEMITONE-repaired D-root Primary candidate

D HARMONIC MINOR DESCENDING - SEMITONE CANDIDATE

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-F-G-Bb-B-D	D FAMian pentatonic (scale 809; Forte 5-32)	YES - SEMITONE-repaired D-root candidate

JATZEK 1 ASCENDING / D LATANGI - SEMITONE CANDIDATE

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-E-F#-G#-Bb-D	D Augmented Ninth Mode IV pentatonic	YES - SEMITONE-repaired D-root Primary candidate

JATZEK 1 DESCENDING / D MAJOR LOCRIAN - DIRECTIONAL CANDIDATE

Source	Concert notes	Role	Status
A1	D-E-F#-G#-Bb-D	Ascending mismatch ShadowScale on descending parent	BASE 0 - complete overlay
D1	D-E-F#-Bb-C-D	Descending missing-note verification ShadowScale	BASE 0 - complete overlay

JATZEK 2 / D RISHABHAPRIYA - SIX CANDIDATES

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-E-F#-G#-C-D	D Five-Note Prometheus	YES - D Five-Note Prometheus; D-root Primary candidate
2	E-F#-G#-Bb-D-E	E Five-Note Prometheus	YES - reorder D-E-F#-G#-Bb-D: D Augmented Ninth Mode IV; D-root candidate
3	F#-G#-Bb-C-E-F#	F# Five-Note Prometheus	NO - offset overlay; test over the D parent
4	G#-Bb-C-D-F#-G#	G# Five-Note Prometheus	YES - D Augmented Ninth Mode III; test as D root
5	Bb-C-D-E-G#-Bb	Bb Five-Note Prometheus	YES - D Augmented Ninth Mode II; test as D root
6	C-D-E-F#-Bb-C	C Five-Note Prometheus	YES - D Augmented Ninth Mode I; test as D root

JATZEK 3 ASCENDING / D JYOTI SWARUPINI - SEMITONE CANDIDATE

Cand.	Concert notes	Shifted-template key/name	D-root status or interpretation
1	D-F#-G#-Bb-C-D	D Augmented Ninth Mode III pentatonic (scale 1361)	YES - SEMITONE-repaired D-root Primary candidate

JATZEK 3 DESCENDING / D SHANMUKHAPRIYA - VERIFIED SHADOWSCALE OVERLAY

Source	Concert notes	Role	Status
A1	D-E-G#-Bb-C-D	Ascending mismatch ShadowScale shifted +2 on descending parent	BASE 0 - complete overlay; template shifted +2
D1	D-E-F-A-Bb-D	Descending missing-note verification ShadowScale	BASE 0 - SEMITONE repaired

B-3. PRIMARY SHADOWSCALE AND PERFORMANCE-ROOT TEST RECORD

Complete these fields after the guitar tests. Record the Primary candidate selected by ear, its performance root and its final concert name. Interval values always use D as BASE 0. Choosing a Primary candidate never creates a new zero point.

Parent/direction	Primary cand.	Performance root	Final concert name	Intervals from D
D major	________	________	________________	________________
D melodic minor ascending	________	________	________________	________________
D melodic minor descending	________	________	________________	________________
D natural minor	________	________	________________	________________
D harmonic minor ascending	________	________	________________	________________
D harmonic minor descending	________	________	________________	________________
JATZEK 1 ascending / D Latangi	________	________	________________	________________
JATZEK 1 descending / D Major Locrian	________	________	________________	________________
JATZEK 2 / D Rishabhapriya	________	________	________________	________________
JATZEK 3 ascending / D Jyoti Swarupini	________	________	________________	________________
JATZEK 3 descending / D Shanmukhapriya	________	________	________________	________________

D-REFERENCE INTERVAL RULE: D = BASE 0; D#/Eb = +1; E = +2; F = +3; F# = +4; G = +5; G# = +6; A = +7; Bb/A# = +8; B = -3; C = -2; C# = -1. Values above +8 are written as the shorter downward movement from D. Primary selection does not change these values.

B-4. VERIFICATION PENTATONIC REGISTRY

This registry gathers the five-note verification ShadowScales produced by the three derived descending forms. There are three source families: harmonic minor descending, JATZEK 1 descending and JATZEK 3 descending. A repeated octave-closing note is counted once. Every entry below therefore contains five distinct pitch classes.

INTERNAL REGISTRATION RULE: The five distinct candidate pitch collections are registered inside this project as JATZEK Pentatonic Minor 1 through 5. These are JATZEK system names for the verification function and source relationship. They do not replace the established catalogue names and do not claim discovery of previously undocumented pitch sets.

Reference-search method

For each candidate, the octave repeat was removed, the remaining notes were converted to pitch-class intervals from the candidate root, and the exact interval set was compared under transposition. Searches covered Ian Ring's A Study of Scales database, Manuel Op de Coul's List of Musical Modes, the AllScales/Daqarta list, and the scale sources cited by those catalogues. Searches used exact pitch sets, interval patterns, modal rotations, catalogue numbers and alternate spellings.

SEARCH RESULT: The earlier wording 'verification pentatonic' meant that a concert name had not yet been assigned in this document. The expanded reference search found catalogue correspondences for every distinct candidate collection. Therefore none of these entries uses the fallback label SCALE NAME NOT FOUND IN EXTENSIVE REFERENCE SEARCH, and none is presented as a newly discovered pitch collection.

Three registered verification families

JATZEK registration(s)	Source descending scale	Candidate positions	Catalogue-family result
JATZEK Pentatonic Minor 1-2	D harmonic minor descending / D Jhankaradhwani	2	Japanese Pentachord family; Yo / Scottish pentatonic
JATZEK Pentatonic Minor 3	JATZEK 1 descending / D Major Locrian	6 transpositions	Augmented Ninth Mode I family
JATZEK Pentatonic Minor 4-5	JATZEK 3 descending / D Shanmukhapriya	2 repaired variants	Aeolian pentatonic; Augmented Ninth Mode II

Candidate note and catalogue record

Ref.	Source	Notes	Root	Pitch set	Concert/catalogue correspondence	Gaps
JPM-1	Harmonic minor descending	E-F-G-Bb-B-E	E	0-1-3-6-7	Japanese Pentachord / Minor Add b9/11 Mode I; scale 203; Forte 5-19	1-2-3-1-5
JPM-2	Harmonic minor descending	D-E-G-A-B-D	D	0-2-5-7-9	D Yo / Ritsu / Scottish pentatonic; scale 677	2-3-2-2-3
JPM-3	JATZEK 1 descending	D-E-F#-Bb-C-D	D	0-2-4-8-10	D Augmented Ninth Mode I; scale 1301	2-2-4-2-2
JPM-4	JATZEK 3 descending	D-E-F-A-Bb-D	D	0-2-3-7-8	D Aeolian Pentatonic / Hirajoshi / Kata-kumoi; scale 397	2-1-4-1-4
JPM-5	JATZEK 3 descending	D-E-G#-Bb-C-D	D	0-2-6-8-10	D Augmented Ninth Mode II; scale 1349	2-4-2-2-2

JATZEK PENTATONIC MINOR 3 TRANSPOSITION RECORD: The six JATZEK 1 positions shown in the source table are transpositions of one interval template (0-2-4-8-10); they are not six separate pentatonic types.

PRIMARY-SELECTION STATUS: Registration numbers identify five distinct verification pitch collections. The final Primary member used with each descending source scale must still be chosen by the ShadowScale ear test; catalogue matching alone cannot choose the strongest musical position.

APPENDIX C - CHROMATIC HARMONICS

Natural-harmonic touch positions and sounded concert-note values for D2-G2-C3-F3-A3-D4 tuning

HOW THE CHROMATIC-HARMONIC TABLES WORK

A natural harmonic is made by touching an open string very lightly at a harmonic node without pressing it to the fretboard. Pluck the string at another point, usually closer to the bridge, and lift the touching finger after the clear bell-like note begins to ring.

Each harmonic has a shared partial number: H1, H2, H3 and so on. A partial is one frequency in the natural harmonic series. H1 is the open-string fundamental, meaning the main pitch of the open string. Use the same H-number to move between the position table and the sounded-note table.

Table C-1 identifies the partial, every practical touch position within the 24-fret range, and its interval or octave offset. Table C-2 uses that same partial number to identify the sounded concert note and scientific octave value on each open string.

Example: Find H5 in Table C-1 and touch near 3.86, 8.84 or 15.86. Then find H5 in Table C-2. On the open D2 string it sounds approximately F-sharp 4; on the open G2 string it sounds approximately B4.

READING DECIMAL FRET POSITIONS

Decimal fret numbers describe positions relative to the fret wires. A whole number is directly above that numbered fret wire. Position 3.68 is between fret wires 3 and 4, 68 percent of the distance from fret wire 3 toward fret wire 4. Position 5.50 is halfway between fret wires 5 and 6. The centre between fret wires 4 and 5 is therefore 4.50.

These are light-touch positions, not fretted notes. If a higher harmonic is weak, move the touching finger slightly to either side of the listed point and change the plucking position until the clearest note rings.

TABLE C-0 - CHROMATIC-HARMONIC FRETBOARD NOTE MAP

The fretboards below place every H1-H12 sounded-note value at each corresponding touch position. A node is touched lightly above the listed decimal position; it is not pressed as a fretted note. Where several partials share one position, use the separate H-panels to distinguish the resulting note values.

TABLE C-1 - HARMONIC TOUCH POSITIONS

TABLE C-1 - COMPLETE HARMONIC POSITION VALUES

Partial #	Position, interval and tuning data
H1	Touch positions: Open string - no touch node Sounding offset: 0.00 semitones Interval: Fundamental open note Equal-temperament difference: Reference
H2	Touch positions: 12.00 Sounding offset: +12.00 semitones Interval: +1 octave Equal-temperament difference: Exact
H3	Touch positions: 7.02, 19.02 Sounding offset: +19.02 semitones Interval: +1 octave + perfect fifth Equal-temperament difference: +1.96 cents
H4	Touch positions: 4.98, 12.00, 24.00 Sounding offset: +24.00 semitones Interval: +2 octaves Equal-temperament difference: Exact
H5	Touch positions: 3.86, 8.84, 15.86 Sounding offset: +27.86 semitones Interval: +2 octaves + major third Equal-temperament difference: -13.69 cents
H6	Touch positions: 3.16, 7.02, 12.00, 19.02 Sounding offset: +31.02 semitones Interval: +2 octaves + perfect fifth Equal-temperament difference: +1.96 cents
H7	Touch positions: 2.67, 5.83, 9.69, 14.67, 21.69 Sounding offset: +33.69 semitones Interval: +2 octaves + harmonic seventh Equal-temperament difference: -31.17 cents vs minor seventh
H8	Touch positions: 2.31, 4.98, 8.14, 12.00, 16.98, 24.00 Sounding offset: +36.00 semitones Interval: +3 octaves Equal-temperament difference: Exact
H9	Touch positions: 2.04, 4.35, 7.02, 10.18, 14.04, 19.02 Sounding offset: +38.04 semitones Interval: +3 octaves + major second Equal-temperament difference: +3.91 cents
H10	Touch positions: 1.82, 3.86, 6.17, 8.84, 12.00, 15.86, 20.84 Sounding offset: +39.86 semitones Interval: +3 octaves + major third Equal-temperament difference: -13.69 cents
H11	Touch positions: 1.65, 3.47, 5.51, 7.82, 10.49, 13.65, 17.51, 22.49 Sounding offset: +41.51 semitones Interval: +3 octaves + undecimal interval Equal-temperament difference: -48.68 cents vs tritone
H12	Touch positions: 1.51, 3.16, 4.98, 7.02, 9.33, 12.00, 15.16, 19.02, 24.00 Sounding offset: +43.02 semitones Interval: +3 octaves + perfect fifth Equal-temperament difference: +1.96 cents

TABLE C-2 - HARMONIC SOUNDED NOTES

Select the open string being played, then read across from the Partial # found in Table C-1. Arrows identify natural-series tuning differences from an equal-tempered chromatic note.

HOW TO READ THE SOUNDED-NOTE VALUES

The letter gives the note name. The number immediately after it is the scientific octave register; it does not mean that number of octaves upward. G3 therefore means the note G in octave register 3.

UP and DOWN describe fine tuning relative to the nearest equal-tempered note, not a change of octave. A3 UP means a pitch slightly sharper than equal-tempered A3. F-sharp 4 DOWN means a pitch slightly flatter than equal-tempered F-sharp 4.

A change of octave is written separately in the interval column. For example, H2 is +1 octave and H4 is +2 octaves.

TABLE C-2A - HARMONIC INTERVAL VALUES

Partial #	Interval / value
H1	Open fundamental
H2	+1 octave
H3	+1 octave + fifth (slightly sharp)
H4	+2 octaves
H5	+2 octaves + major third (flat)
H6	+2 octaves + fifth (slightly sharp)
H7	Harmonic seventh (31 cents flat)
H8	+3 octaves
H9	+3 octaves + major second (sharp)
H10	+3 octaves + major third (flat)
H11	Undecimal interval (49 cents below tritone)
H12	+3 octaves + fifth (slightly sharp)

TABLE C-2B - STRING 6 SOUNDED NOTES

Partial #	String 6 - D2
H1	D2
H2	D3
H3	A3 up
H4	D4
H5	F-sharp 4 down
H6	A4 up
H7	C5 down
H8	D5
H9	E5 up
H10	F-sharp 5 down
H11	G-sharp 5 down down
H12	A5 up

TABLE C-2C - STRING 5 SOUNDED NOTES

Partial #	String 5 - G2
H1	G2
H2	G3
H3	D4 up
H4	G4
H5	B4 down
H6	D5 up
H7	F5 down
H8	G5
H9	A5 up
H10	B5 down
H11	C-sharp 6 down down
H12	D6 up

TABLE C-2D - STRING 4 SOUNDED NOTES

Partial #	String 4 - C3
H1	C3
H2	C4
H3	G4 up
H4	C5
H5	E5 down
H6	G5 up
H7	B-flat 5 down
H8	C6
H9	D6 up
H10	E6 down
H11	F-sharp 6 down down
H12	G6 up

TABLE C-2E - STRING 3 SOUNDED NOTES

Partial #	String 3 - F3
H1	F3
H2	F4
H3	C5 up
H4	F5
H5	A5 down
H6	C6 up
H7	E-flat 6 down
H8	F6
H9	G6 up
H10	A6 down
H11	B6 down down
H12	C7 up

TABLE C-2F - STRING 2 SOUNDED NOTES

Partial #	String 2 - A3
H1	A3
H2	A4
H3	E5 up
H4	A5
H5	C-sharp 6 down
H6	E6 up
H7	G6 down
H8	A6
H9	B6 up
H10	C-sharp 7 down
H11	D-sharp 7 down down
H12	E7 up

TABLE C-2G - STRING 1 SOUNDED NOTES

Partial #	String 1 - D4
H1	D4
H2	D5
H3	A5 up
H4	D6
H5	F-sharp 6 down
H6	A6 up
H7	C7 down
H8	D7
H9	E7 up
H10	F-sharp 7 down
H11	G-sharp 7 down down
H12	A7 up

REFERENCE NOTES

UP: the natural harmonic is sharper than the nearest equal-tempered note.

DOWN: the natural harmonic is flatter than the nearest equal-tempered note.

DOWN DOWN: the H11 pitch is substantially flatter than the named equal-tempered tritone note and lies between ordinary chromatic pitch positions.

Natural harmonics follow whole-number frequency ratios. Because these ratios do not always match equal-tempered tuning exactly, some harmonics sound slightly sharp or flat. This is a normal property of the harmonic series, not automatically a guitar-tuning error.

The H2-H12 range represents the principal practical reference set for this appendix. Higher partials continue mathematically, but their nodes become increasingly close together and their sounded notes are normally weaker and less dependable for scale testing.

Tables C-1 and C-2 may be compared with the main scales and ShadowScales to identify naturally resonant notes within the JATZEK MUSICMASTER 7/14 SCALE-SHADOWSCALE SYSTEM.