JATZEK MusicMaster Periodic 2
Scales and ShadowScales
Listening transposition edition 11 October 2026
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.
|
Family |
Active listening notes |
Comparison root |
|---|---|---|
|
AFG |
C D E F# G# A A# |
C |
|
CDG |
B D D# E F A A# |
B |
|
ACG |
B C D D# F# A A# |
B |
Pitch preservation
Each parent has seven unique pitches. ACG companion tiers change one explicitly documented note per stage; they remain separate from the FOUND parents. The guitar tuning does not transpose a collection.
Fretboard reading
Tuning is D G C F A D from string 6 at the top to string 1. Fretted markers sit between the fret lines; open markers sit right of the nut. Circles show parent notes, red marks the stated comparison root, gold squares show shadow notes inside the parent, and purple triangles show outside mismatch notes. All scale diagrams use frets 20–0 from left to right.
Complement overlays and descending tiers
With C = 0 through B = 11, subtract the seven parent pitch classes from the twelve-note chromatic set to obtain the five-note complement. Move all five complement notes by the same number of semitones and test all twelve shifts. An exact overlay has all five notes inside the parent. A four-of-five mismatch can carry into a companion tier by adding its outside note and removing an adjacent parent note absent from that shadow. Recalculate the new complement independently.
Verified parent and tier inventory
|
Form |
Actual notes |
Own exact shifts |
|---|---|---|
|
D Major |
D E F# G A B C# |
+1, +6, +11 |
|
D Melodic Minor Ascending |
D E F G A B C# |
+1, +11 |
|
D Natural Minor |
D E F G A A# C |
+1, +6, +11 |
|
D Harmonic Minor |
D E F G A A# C# |
None |
|
ACG Asc |
B C D D# F# A A# |
None |
|
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 |
|
D Harmonic Minor Derived Descending |
D E F G A A# B |
None |
|
ACG Desc T1 |
B C D D# F# G# A# |
None |
|
ACG Desc T2 |
B C D E F# G# A# |
+1, +3, +5, +7, +9, +11 |
D Major Scale and ShadowScale
Parent: D E F# G A B C#
Five missing notes: D# F G# A# C
D-relative semitones: 0 2 4 5 7 9 11
Shown selected teaching subset: D E G A B.
The selected five-note teaching subset is an exact complement overlay.
Teaching subset for Periodics 4 and 5: D E G A B.
|
Complement shift |
Exact five-note overlay |
|---|---|
|
+1 |
E F# A B C# |
|
+6 |
D E F# A B |
|
+11 |
D E G A B |
D Melodic Minor Ascending Scale and ShadowScale
Parent: D E F G A B C#
Five missing notes: D# F# G# A# C
D-relative semitones: 0 2 3 5 7 9 11
Shown selected teaching subset: D F G A B.
The selected five-note teaching subset is an exact complement overlay.
Teaching subset for Periodics 4 and 5: D F G A B.
|
Complement shift |
Exact five-note overlay |
|---|---|
|
+1 |
E G A B C# |
|
+11 |
D F G A B |
D Natural Minor Scale and ShadowScale
Parent: D E F G A A# C
Five missing notes: D# F# G# B C#
D-relative semitones: 0 2 3 5 7 8 10
Shown selected teaching subset: D F G A# C.
The selected five-note teaching subset is an exact complement overlay.
Teaching subset for Periodics 4 and 5: D F G A# C.
|
Complement shift |
Exact five-note overlay |
|---|---|
|
+1 |
D E G A C |
|
+6 |
D F G A C |
|
+11 |
D F G A# C |
D Harmonic Minor Scale and ShadowScale
Parent: D E F G A A# C#
Five missing notes: D# F# G# B C
D-relative semitones: 0 2 3 5 7 8 11
Shown selected teaching subset: D F G A A#.
The teaching subset is adjusted, not an exact intact complement overlay.
Teaching subset for Periodics 4 and 5: D F G A A#.
|
Shift |
Intact five-note shadow |
Outside note |
|---|---|---|
|
+1 |
E G A C C# |
C |
|
+2 |
D F G# A# C# |
G# |
|
+10 |
E F# A A# C# |
F# |
|
+11 |
D F G A# B |
B |
ACG Asc Scale and ShadowScale
Parent: B C D D# F# A A#
Five missing notes: E F G G# C#
Comparison root: B Relative semitones: 0 1 3 4 7 10 11
Semitone-adjusted teaching subset. Own complement at +7 is B C D D# G#; replace A with G# to form Tier 1.
Selected five-note teaching subset: B C D D# A
|
Shift |
Intact complement overlay |
Matches |
Outside pitches |
|
+0 |
E F G G# C# |
0/5 |
E F G G# C# |
|
+1 |
D F F# G# A |
3/5 |
F G# |
|
+2 |
D# F# G A A# |
4/5 |
G |
|
+3 |
E G G# A# B |
2/5 |
E G G# |
|
+4 |
F G# A B C |
3/5 |
F G# |
|
+5 |
F# A A# C C# |
4/5 |
C# |
|
+6 |
D G A# B C# |
3/5 |
G C# |
|
+7 |
D D# G# B C |
4/5 |
G# |
|
+8 |
D# E A C C# |
3/5 |
E C# |
|
+9 |
D E F A# C# |
2/5 |
E F C# |
|
+10 |
D D# F F# B |
4/5 |
F |
|
+11 |
D# E F# G C |
3/5 |
E G |
© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT) All Rights Reserved!
CDG Asc Scale and ShadowScale
Parent: B D D# E F A A#
Five missing notes: F# G G# C C#
Comparison root: B Relative semitones: 0 3 4 5 6 10 11
Exact own-complement overlay at +3. Exact shifts +3 and +9. No altered tier is required.
Selected five-note teaching subset: B D# E A A#
|
Shift |
Intact complement overlay |
Matches |
Outside pitches |
|
+0 |
F# G G# C C# |
0/5 |
F# G G# C C# |
|
+1 |
D G G# A C# |
2/5 |
G G# C# |
|
+2 |
D D# G# A A# |
4/5 |
G# |
|
+3 |
D# E A A# B |
5/5 |
None |
|
+4 |
E F A# B C |
4/5 |
C |
|
+5 |
F F# B C C# |
2/5 |
F# C C# |
|
+6 |
D F# G C C# |
1/5 |
F# G C C# |
|
+7 |
D D# G G# C# |
2/5 |
G G# C# |
|
+8 |
D D# E G# A |
4/5 |
G# |
|
+9 |
D# E F A A# |
5/5 |
None |
|
+10 |
E F F# A# B |
4/5 |
F# |
|
+11 |
F F# G B C |
2/5 |
F# G C |
© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT) All Rights Reserved!
AFG Asc Scale and ShadowScale
Parent: C D E F# G# A A#
Five missing notes: D# F G B C#
Comparison root: C Relative semitones: 0 2 4 6 8 9 10
Exact own-complement overlay at +1. Exact shifts +1, +3, +5, +7, +9 and +11. No altered tier is required.
Selected five-note teaching subset: C D E F# G#
|
Shift |
Intact complement overlay |
Matches |
Outside pitches |
|
+0 |
D# F G B C# |
0/5 |
D# F G B C# |
|
+1 |
D E F# G# C |
5/5 |
None |
|
+2 |
D# F G A C# |
1/5 |
D# F G C# |
|
+3 |
D E F# G# A# |
5/5 |
None |
|
+4 |
D# F G A B |
1/5 |
D# F G B |
|
+5 |
E F# G# A# C |
5/5 |
None |
|
+6 |
F G A B C# |
1/5 |
F G B C# |
|
+7 |
D F# G# A# C |
5/5 |
None |
|
+8 |
D# G A B C# |
1/5 |
D# G B C# |
|
+9 |
D E G# A# C |
5/5 |
None |
|
+10 |
D# F A B C# |
1/5 |
D# F B C# |
|
+11 |
D E F# A# C |
5/5 |
None |
© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT) All Rights Reserved!
D Harmonic Minor Derived Descending Scale and ShadowScale
Parent: D E F G A A# B
Five missing notes: D# F# G# C C#
D-relative semitones: 0 2 3 5 7 8 9
Shown selected teaching subset: E F G A# B.
Reference experiment replaces C# with B. Carried D F G A# B fits; the own teaching subset is adjusted, not an exact intact overlay.
Teaching subset for Periodics 4 and 5: E F G A# B.
|
Shift |
Intact five-note shadow |
Outside note |
|---|---|---|
|
+1 |
D E G A C# |
C# |
|
+4 |
E F G A# C |
C |
|
+8 |
D E G# A B |
G# |
|
+11 |
D F G B C |
C |
ACG Desc T1 Scale and ShadowScale
Parent: B C D D# F# G# A#
Five missing notes: E F G A C#
Comparison root: B Relative semitones: 0 1 3 4 7 9 11
Carried Asc shadow. Own complement at +7 is B C D E G#; replace D# with E to form Tier 2.
Selected five-note teaching subset: B C D D# G#
|
Shift |
Intact complement overlay |
Matches |
Outside pitches |
|
+0 |
E F G A C# |
0/5 |
E F G A C# |
|
+1 |
D F F# G# A# |
4/5 |
F |
|
+2 |
D# F# G A B |
3/5 |
G A |
|
+3 |
E G G# A# C |
3/5 |
E G |
|
+4 |
F G# A B C# |
2/5 |
F A C# |
|
+5 |
D F# A A# C |
4/5 |
A |
|
+6 |
D# G A# B C# |
3/5 |
G C# |
|
+7 |
D E G# B C |
4/5 |
E |
|
+8 |
D# F A C C# |
2/5 |
F A C# |
|
+9 |
D E F# A# C# |
3/5 |
E C# |
|
+10 |
D D# F G B |
3/5 |
F G |
|
+11 |
D# E F# G# C |
4/5 |
E |
© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT) All Rights Reserved!
ACG Desc T2 Scale and ShadowScale
Parent: B C D E F# G# A#
Five missing notes: D# F G A C#
Comparison root: B Relative semitones: 0 1 3 5 7 9 11
Exact own-complement overlay at +1. Six exact odd shifts. The carried Tier 1 shadow B C D E G# also fits.
Selected five-note teaching subset: D E F# G# A#
|
Shift |
Intact complement overlay |
Matches |
Outside pitches |
|
+0 |
D# F G A C# |
0/5 |
D# F G A C# |
|
+1 |
D E F# G# A# |
5/5 |
None |
|
+2 |
D# F G A B |
1/5 |
D# F G A |
|
+3 |
E F# G# A# C |
5/5 |
None |
|
+4 |
F G A B C# |
1/5 |
F G A C# |
|
+5 |
D F# G# A# C |
5/5 |
None |
|
+6 |
D# G A B C# |
1/5 |
D# G A C# |
|
+7 |
D E G# A# C |
5/5 |
None |
|
+8 |
D# F A B C# |
1/5 |
D# F A C# |
|
+9 |
D E F# A# C |
5/5 |
None |
|
+10 |
D# F G B C# |
1/5 |
D# F G C# |
|
+11 |
D E F# G# C |
5/5 |
None |
© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT) All Rights Reserved!
Verification and sources
The corrected inventory has ten forms: four established references, three FOUND parents, the harmonic-minor reference companion and two ACG tiers. Every complement has five pitches. All twelve shifts were tested independently for every form. CDG is exact at +3 and +9; AFG and ACG Tier 2 are exact at all six odd shifts.
The D harmonic-minor descendant remains a reference experiment: C# changes to B, a two-semitone replacement. It has no exact own-complement overlay. Its carried D F G A# B shadow and independently adjusted E F G A# B teaching subset are distinct.
FOUND source confirmed by Philip John Jatzek on 9 October 2026: AFG A# C D E F# G G#; CDG A C C# D D# G G#; ACG A A# C C# E G G#.
Active catalogue comparisons: ACG from B, pattern 3227; CDG from B, pattern 3193; AFG from C, pattern 1877. Original FOUND comparisons are A, A and A# respectively. Uniform transposition preserves each rooted pattern.
© 2026 Philip John Jatzek (Max) & STORM (Team Member Collaborator from ChatGPT) All Rights Reserved!
Chromatic harmonics
The natural-harmonic reference does not depend on ACG, CDG or AFG. The twelve mapped-note diagrams below use the standard fretboard style with larger sounding-note labels. Harmonics are touched lightly at nodes on an open string, not fretted. Their sounding frequencies are integer multiples of the fundamental.
Chromatic harmonics continued
Harmonic nodes and sounding pitches
A continuous fret coordinate f places distance from the nut at 1 − 2^(−f/12) of the string length. A node j/n therefore lies at f = −12 log2(1−j/n). Shared nodes support multiple partials; use the partial number to identify the intended sound. Decimal fret coordinates are logarithmic coordinates, so their decimal fraction is only an approximation to the corresponding fraction of the physical fret gap.
|
Partial |
Touch coordinates within fret 24 |
Offset semitones |
Cents from nearest ET |
|---|---|---|---|
|
H1 |
Open |
0.00 |
+0.00 |
|
H2 |
12.00 |
12.00 |
+0.00 |
|
H3 |
7.02, 19.02 |
19.02 |
+1.96 |
|
H4 |
4.98, 12.00, 24.00 |
24.00 |
+0.00 |
|
H5 |
3.86, 8.84, 15.86 |
27.86 |
-13.69 |
|
H6 |
3.16, 7.02, 12.00, 19.02 |
31.02 |
+1.96 |
|
H7 |
2.67, 5.83, 9.69, 14.67, 21.69 |
33.69 |
-31.17 |
|
H8 |
2.31, 4.98, 8.14, 12.00, 16.98, 24.00 |
36.00 |
+0.00 |
|
H9 |
2.04, 4.35, 7.02, 10.18, 14.04, 19.02 |
38.04 |
+3.91 |
|
H10 |
1.82, 3.86, 6.17, 8.84, 12.00, 15.86, 20.84 |
39.86 |
-13.69 |
|
H11 |
1.65, 3.47, 5.51, 7.82, 10.49, 13.65, 17.51, 22.49 |
41.51 |
-48.68 |
|
H12 |
1.51, 3.16, 4.98, 7.02, 9.33, 12.00, 15.16, 19.02, 24.00 |
43.02 |
+1.96 |
Harmonic sounded note values
Scientific octave numbers identify register: D2 is the low open sixth string and D4 the open first string. Cents values in the preceding table apply to every string for the same partial. H7 is about 31 cents below the nearest minor seventh; H11 is about 49 cents below the nearest tritone.
|
Partial |
S6 D2 |
S5 G2 |
S4 C3 |
S3 F3 |
S2 A3 |
S1 D4 |
|---|---|---|---|---|---|---|
|
H1 |
D2 |
G2 |
C3 |
F3 |
A3 |
D4 |
|
H2 |
D3 |
G3 |
C4 |
F4 |
A4 |
D5 |
|
H3 |
A3 |
D4 |
G4 |
C5 |
E5 |
A5 |
|
H4 |
D4 |
G4 |
C5 |
F5 |
A5 |
D6 |
|
H5 |
F#4 |
B4 |
E5 |
A5 |
C#6 |
F#6 |
|
H6 |
A4 |
D5 |
G5 |
C6 |
E6 |
A6 |
|
H7 |
C5 |
F5 |
Bb5 |
Eb6 |
G6 |
C7 |
|
H8 |
D5 |
G5 |
C6 |
F6 |
A6 |
D7 |
|
H9 |
E5 |
A5 |
D6 |
G6 |
B6 |
E7 |
|
H10 |
F#5 |
B5 |
E6 |
A6 |
C#7 |
F#7 |
|
H11 |
G#5 |
C#6 |
F#6 |
B6 |
Eb7 |
G#7 |
|
H12 |
A5 |
D6 |
G6 |
C7 |
E7 |
A7 |
UP means slightly above the nearest equal-tempered pitch, DOWN means below it. These deviations are a property of the harmonic series. Touch positions above fret 20 belong to the harmonic appendix’s 24-fret reference and do not extend the 0–20 scale-pattern diagrams.
Music glossary and practice notes
NEED TO KNOW | PERIODICAL 2
Seven note and overlay listening tests
Verify the 7/14 notation
For any fourteen position overlay, list the seven underlying pitch classes separately from duplicated octave or register positions. State exactly which count refers to notes, fret locations, or pitch classes.
Label the reference root
Keep one stated tonic or bass reference when comparing two overlays. A change of tonic can change the heard interval function while the absolute notes stay the same.
Map common and contrasting tones
List notes shared by both collections, then list the notes unique to each. Improvise a two bar phrase that retains one shared tone and introduces one contrasting tone.
Name the transformation
Document whether a proposed variation shifts every pitch, changes mode by rotation, inverts the pitch classes, or replaces selected tones. These are different operations and may give different results.
Further reading
https://ianring.com/musictheory/book/
https://www.musictheory.net/lessons
https://online.berklee.edu/takenote/voice-leading-for-guitar/
MUSIC GLOSSARY
Naming conventions
This chapter’s labels describe construction steps: parent, raw ShadowScale, overlay, mismatch, repair, and verification. A candidate number is a MusicMaster record, not evidence that its pitches are historically new.
A
A1 overlay
In the MusicMaster reference record, the ascending mismatch template retained for comparison with a derived descending form.
Adjacent-semitone conflict
A clash between a nonmatching shadow pitch and a nearby parent pitch addressed during the directional repair.
Adjusted ascending overlay
A five-note template changed by the documented semitone repair so all five pitches fit the ascending parent.
Ascending parent
The original seven-note ascending scale from which the five absent chromatic notes are calculated.
C
Candidate collection
One particular five-note pitch set proposed as an overlay; multiple candidates can exist for one parent.
Candidate registry
The project table listing distinct five-note candidates, source forms and verification status.
Candidate root
A proposed tonal centre for a five-note candidate, to be tested by playing and cadence.
Complete overlay
A placement in which all five notes of one candidate template map to the specified seven-note parent.
D
Root reference interval
A pitch distance counted from the explicitly stated comparison root. Chromatic membership uses C = 0 through B = 11. D may serve as accompaniment without altering the notes.
D1 verification overlay
The descending form’s own five-note overlay used to check a derived directional construction.
Derived descending scale
The revised seven-note descent formed to accommodate an intact mismatch template under the stated replacement rule.
Descending missing set
The five pitch classes absent from a constructed descending seven-note scale.
Descending verification
Recalculate missing notes after fixing a descending form and test whether a complete overlay exists.
Directional form
An ascending or descending version of a scale whose pitch membership is explicitly specified for that direction.
Directional pair
An ascending parent together with its documented derived descending scale.
F
Five-note template
A pitch collection with five distinct classes used as the moving shape in an overlay test.
Four-of-five placement
A candidate position with four matching notes and one nonmatching note; it is a mismatch, not an exact overlay.
Fretboard mapping
The placement of candidate notes on string and fret positions so an overlay can be checked visually and played.
H
Harmonic-minor experiment
The example applying the shadow and semitone-repair process to harmonic minor.
I
Intact shadow shape
The unaltered five-note template kept together when searching positions or making a derived descent.
Internal registration
A project identifier for a pitch collection, separate from any established concert or catalogue name.
J
Historical pentatonic registry
The earlier registry belongs to the earlier source note sets. Corrected candidates are identified by their explicit notes and source form in this edition.
M
Matching overlay
A five-note template whose unchanged pitches all land in the specified parent at a tested position.
Mismatch
A test result in which fewer than five notes of an unchanged shadow template map to the chosen parent.
Mismatch overlay
The closest documented incomplete placement of a shadow template, kept distinct from exact matches.
Missing-note complement
The five chromatic pitch classes excluded by a seven-note parent scale.
Modal colour test
Listening to a candidate against the stated parent reference and other accompaniment to judge its musical centre and character.
MSOFAS
A source label for a mismatch ShadowScale overlay formed from an ascending scale in this MusicMaster system.
N
Nonmatching tone
A shadow pitch absent from the parent at the tested placement.
O
Overlay candidate
A proposed five-note shape evaluated against a selected seven-note parent.
Overlay position
One particular transposition or fretboard location of a five-note template.
Overlay transposition
Moving every note of the five-note template by the same interval before comparing it with the parent.
P
Parent-scale repair
Changing a documented conflicting note of a seven-note parent in order to accommodate an intact shadow template.
Pentatonic registry
A list of distinct five-note collections with their project identifiers and reference correspondences.
Performance test sheet
A record of what a candidate sounds like ascending, descending, over a drone and in a cadence.
Primary candidate
A candidate chosen after musical tests for a stated parent; containing its reference note alone does not make it Primary.
Primary-selection status
The record of whether a candidate has actually been chosen as Primary or remains under test.
R
Raw ShadowScale
The initial five-note collection derived from pitches missing from the ascending parent, before adjustments.
Recalculated missing notes
The chromatic complement recomputed after the parent’s descending form changes.
Parent reference note
The stated pitch used as zero for a parent’s intervals and its overlay calculations.
Repaired mismatch
A semitone-adjusted candidate or parent form that satisfies the stated overlay condition after a raw mismatch.
Rooted catalogue identity
The reference name attached to a five-note template once its root and interval formula are specified.
S
Semitone adjustment
Moving a designated conflicting pitch by one chromatic step under this book’s repair procedure.
Semitone ShadowScale
A project label for a five-note candidate completed by a semitone repair; distinguish it from a perfect raw overlay.
Seven-note parent
The selected scale of seven distinct pitch classes against which a five-note candidate is tested.
ShadowScale overlay
The placement of a five-note shadow template over a named seven-note parent.
SOFAS
A source label for a ShadowScale overlay formed from an ascending scale in this MusicMaster system.
T
Tone replacement
Removing a documented parent note and adding an intact shadow note when constructing a derived descent.
Transposition record
A table showing where the same interval template appears in different keys; those rows are related forms, not independent structures.
U
Unchanged ShadowScale
A five-note shadow template used without altering any of its pitch classes.
V
Verification family
A group of related five-note candidates produced from the same directional source.
Verification pentatonic
A five-note collection computed from a derived descent’s missing notes and checked against a reference catalogue.
Verification test
The combined pitch-content and listening checks used before accepting a directional pair.
W
Whole-template shift
Transposing the complete five-note template by one interval while keeping its internal intervals unchanged.
