Dynsys: We are brainy vikings
Start EStart FStart F#Start GStart G#Start AStart A#Start BStart CStart C#Start DStart D#
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
What shall we do with dynamical systems?
GG#AA#BCC#DD#EFF#
What shall we do with dynamical systems?
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
What shall we do with dynamical systems?
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Sailing windy waters
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
We are the brainy vikings
GG#AA#BCC#DD#EFF#
We are the brainy vikings
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
We are the brainy vikings
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Gathered from all nations
Am A#m Bm Cm C#m Dm D#m Em Fm F#m Gm G#m
We model every ships dynamics
G G# A A# B C C# D D# E F F#
model every ships dynamics
Am A#m Bm Cm C#m Dm D#m Em Fm F#m Gm G#m
model every ships dynamics
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Tracking every movement
Am A#m Bm Cm C#m Dm D#m Em Fm F#m Gm G#m
Use numbers and equations
G G# A A# B C C# D D# E F F#
numbers and equations
Am A#m Bm Cm C#m Dm D#m Em Fm F#m Gm G#m
numbers and equations
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Gathered from all nations
Am A#m Bm Cm C#m Dm D#m Em Fm F#m Gm G#m
at day we use the white box models
G G# A A# B C C# D D# E F F#
at night we use the black box models
Am A#m Bm Cm C#m Dm D#m Em Fm F#m Gm G#m
at day we use the black box models
Am G Am A#m G# A#m Bm A Bm Cm A# Cm C#m B C#m Dm C Dm D#m C# D#m Em D Em Fm D# Fm F#m E F#m Gm F Gm G#m F# G#m
When foggy we use the grey ones
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
We are the nerdy vikings
GG#AA#BCC#DD#EFF#
We are the nerdy vikings
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
We are the nerdy vikings
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Gathered from all nations
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
we build ships for the sea of chaos
GG#AA#BCC#DD#EFF#
we build ships for the sea of chaos
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
we build ships for the sea of chaos
Am G Am A#m G# A#m Bm A Bm Cm A# Cm C#m B C#m Dm C Dm D#m C# D#m Em D Em Fm D# Fm F#m E F#m Gm F Gm G#m F# G#m
of numbers and equations
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
hey ho mathematical models
GG#AA#BCC#DD#EFF#
hey ho mathematical models
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
hey ho mathematical models
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Gathered from all nations
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
What shall we do with an O-D-E?
GG#AA#BCC#DD#EFF#
What shall we do with an O-D-E?
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
What shall we do with an O-D-E?
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Integrate the function
Am A#m Bm Cm C#m Dm D#m Em Fm F#m Gm G#m
you can always use Eulers method
G G# A A# B C C# D D# E F F#
always use Eulers method
Am A#m Bm Cm C#m Dm D#m Em Fm F#m Gm G#m
always use Eulers method
Am G Am A#m G# A#m Bm A Bm Cm A# Cm C#m B C#m Dm C Dm D#m C# D#m Em D Em Fm D# Fm F#m E F#m Gm F Gm G#m F# G#m
or improve with Runge Kutta
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
What shall we do with an S-D-E?
GG#AA#BCC#DD#EFF#
What shall we do with an S-D-E?
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
What shall we do with an S-D-E?
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Use a Kalman filter
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
We drift around in brownian motion
GG#AA#BCC#DD#EFF#
We drift around in brownian motion
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
We drift around in brownian motion
Am G Am A#m G# A#m Bm A Bm Cm A# Cm C#m B C#m Dm C Dm D#m C# D#m Em D Em Fm D# Fm F#m E F#m Gm F Gm G#m F# G#m
diffussed but not confused
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
What are we doin' in the Dynsys section?
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What are we doin' in the Dynsys section?
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
What are we doin' in the Dynsys section?
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
solving math together
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
We are the Dynsys vikings
GG#AA#BCC#DD#EFF#
We are the Dynsys vikings
AmA#mBmCmC#mDmD#mEmFmF#mGmG#m
We are the Dynsys vikings
Am G AmA#m G# A#mBm A BmCm A# CmC#m B C#mDm C DmD#m C# D#mEm D EmFm D# FmF#m E F#mGm F GmG#m F# G#m
Gathered from all nations
## Solo scales## Solo scales## Solo scales## Solo scales## Solo scales## Solo scales## Solo scales## Solo scales## Solo scales## Solo scales## Solo scales## Solo scales
Key: A minor (modal — built on the Am–G vamp)D ey: A# minor (modal — built on the A#m–G# vamp)Dey: B minor (modal — built on the Bm–A vamp)Dey: C minor (modal — built on the Cm–A# vamp)D ey: C# minor (modal — built on the C#m–B vamp)Dey: D minor (modal — built on the Dm–C vamp)D ey: D# minor (modal — built on the D#m–C# vamp)Dey: E minor (modal — built on the Em–D vamp)D ey: F minor (modal — built on the Fm–D# vamp)Dey: F# minor (modal — built on the F#m–E vamp)Dey: G minor (modal — built on the Gm–F vamp)D ey: G# minor (modal — built on the G#m–F# vamp)
- A natural minor / Aeolian (A B C D E F G) — safe default, dark shanty feel- A# natural minor / A#eolian (A# C C# D# F F# G#) — safe default, dark shanty feel- B natural minor / Beolian (B C# D E F# G A) — safe default, dark shanty feel- C natural minor / Ceolian (C D D# F G G# A#) — safe default, dark shanty feel- C# natural minor / C#eolian (C# D# E F# G# A B) — safe default, dark shanty feel- D natural minor / Deolian (D E F G A A# C) — safe default, dark shanty feel- D# natural minor / D#eolian (D# F F# G# A# B C#) — safe default, dark shanty feel- E natural minor / Eeolian (E F# G A B C D) — safe default, dark shanty feel- F natural minor / Feolian (F G G# A# C C# D#) — safe default, dark shanty feel- F# natural minor / F#eolian (F# G# A B C# D E) — safe default, dark shanty feel- G natural minor / Geolian (G A A# C D D# F) — safe default, dark shanty feel- G# natural minor / G#eolian (G# A# B C# D# E F#) — safe default, dark shanty feel
- A minor pentatonic (A C D E G) — simplest default, can't miss over the riff- A# minor pentatonic (A# C# D# F G#) — simplest default, can't miss over the riff- B minor pentatonic (B D E F# A) — simplest default, can't miss over the riff- C minor pentatonic (C D# F G A#) — simplest default, can't miss over the riff- C# minor pentatonic (C# E F# G# B) — simplest default, can't miss over the riff- D minor pentatonic (D F G A C) — simplest default, can't miss over the riff- D# minor pentatonic (D# F# G# A# C#) — simplest default, can't miss over the riff- E minor pentatonic (E G A B D) — simplest default, can't miss over the riff- F minor pentatonic (F G# A# C D#) — simplest default, can't miss over the riff- F# minor pentatonic (F# A B C# E) — simplest default, can't miss over the riff- G minor pentatonic (G A# C D F) — simplest default, can't miss over the riff- G# minor pentatonic (G# B C# D# F#) — simplest default, can't miss over the riff
- C major pentatonic (C D E G A) — relative major, brighter lift for a contrasting pass- C# major pentatonic (C# D# F G# A#) — relative major, brighter lift for a contrasting pass- D major pentatonic (D E F# A B) — relative major, brighter lift for a contrasting pass- D# major pentatonic (D# F G A# C) — relative major, brighter lift for a contrasting pass- E major pentatonic (E F# G# B C#) — relative major, brighter lift for a contrasting pass- F major pentatonic (F G A C D) — relative major, brighter lift for a contrasting pass- F# major pentatonic (F# G# A# C# D#) — relative major, brighter lift for a contrasting pass- G major pentatonic (G A B D E) — relative major, brighter lift for a contrasting pass- G# major pentatonic (G# A# C D# F) — relative major, brighter lift for a contrasting pass- A major pentatonic (A B C# E F#) — relative major, brighter lift for a contrasting pass- A# major pentatonic (A# C D F G) — relative major, brighter lift for a contrasting pass- B major pentatonic (B C# D# F# G#) — relative major, brighter lift for a contrasting pass
- A Dorian (A B C D E F# G) — modal option; the raised F# over the G is the classic "Drunken Sailor" colour- A# D#orian (A# C C# D# F G G#) — modal optionB the raised G over the G# is the classic "D#runken Sailor" colour- B Eorian (B C# D E F# G# A) — modal optionB the raised G# over the A is the classic "Erunken Sailor" colour- C Forian (C D D# F G A A#) — modal optionB the raised A over the A# is the classic "Frunken Sailor" colour- C# F#orian (C# D# E F# G# A# B) — modal optionB the raised A# over the B is the classic "F#runken Sailor" colour- D Gorian (D E F G A B C) — modal optionB the raised B over the C is the classic "Grunken Sailor" colour- D# G#orian (D# F F# G# A# C C#) — modal optionB the raised C over the C# is the classic "G#runken Sailor" colour- E Aorian (E F# G A B C# D) — modal optionB the raised C# over the D is the classic "Arunken Sailor" colour- F A#orian (F G G# A# C D D#) — modal optionB the raised D over the D# is the classic "A#runken Sailor" colour- F# Borian (F# G# A B C# D# E) — modal optionB the raised D# over the E is the classic "Brunken Sailor" colour- G Corian (G A A# C D E F) — modal optionB the raised E over the F is the classic "Crunken Sailor" colour- G# C#orian (G# A# B C# D# F F#) — modal optionB the raised F over the F# is the classic "C#runken Sailor" colour
- Fiddle / tin whistle: stay in A Dorian and lean on the F# against the G for the sea-shanty bounce- F#iddle / tin whistle: stay in A# D#orian and lean on the G against the G# for the sea-shanty bounce- Giddle / tin whistle: stay in B Eorian and lean on the G# against the A for the sea-shanty bounce- G#iddle / tin whistle: stay in C Forian and lean on the A against the A# for the sea-shanty bounce- Aiddle / tin whistle: stay in C# F#orian and lean on the A# against the B for the sea-shanty bounce- A#iddle / tin whistle: stay in D Gorian and lean on the B against the C for the sea-shanty bounce- Biddle / tin whistle: stay in D# G#orian and lean on the C against the C# for the sea-shanty bounce- Ciddle / tin whistle: stay in E Aorian and lean on the C# against the D for the sea-shanty bounce- C#iddle / tin whistle: stay in F A#orian and lean on the D against the D# for the sea-shanty bounce- Diddle / tin whistle: stay in F# Borian and lean on the D# against the E for the sea-shanty bounce- D#iddle / tin whistle: stay in G Corian and lean on the E against the F for the sea-shanty bounce- Eiddle / tin whistle: stay in G# C#orian and lean on the F against the F# for the sea-shanty bounce