mbarbin / fingerboard / 116

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Build # 116

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Use Code_error.raise

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/test/test__system.ml

(**********************************************************************************)
(*  Fingerboard - a microtonal geography of the cello fingerboard                 *)
(*  Copyright (C) 2022-2024 Mathieu Barbin <mathieu.barbin@gmail.com>             *)
(*                                                                                *)
(*  This file is part of Fingerboard.                                             *)
(*                                                                                *)
(*  Fingerboard is free software: you can redistribute it and/or modify it under  *)
(*  the terms of the GNU Affero General Public License as published by the Free   *)
(*  Software Foundation, either version 3 of the License, or any later version.   *)
(*                                                                                *)
(*  Fingerboard is distributed in the hope that it will be useful, but WITHOUT    *)
(*  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or         *)
(*  FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License   *)
(*  for more details.                                                             *)
(*                                                                                *)
(*  You should have received a copy of the GNU Affero General Public License      *)
(*  along with Fingerboard. If not, see <https://www.gnu.org/licenses/>.          *)
(**********************************************************************************)

let test_pitch_exn ~system ~(intervals_going_down : Characterized_interval.t array) =
  (* We test that the pitch is the same for the open string and the position on
     the next vibrating string at the position of the interval between the two
     vibrating strings. *)
  for i = 1 to Array.length intervals_going_down do
    let high = Roman_numeral.of_int_exn i in
    let low = Roman_numeral.succ_exn high in
    let open_string =
      System.pitch
        system
        { fingerboard_position = Fingerboard_position.open_string; string_number = high }
    in
    let unison =
      System.pitch
        system
        { fingerboard_position =
            Fingerboard_position.create_exn
              ~name:"unison"
              ~acoustic_interval_to_the_open_string:
                intervals_going_down.(i - 1).acoustic_interval
        ; string_number = low
        }
    in
    if not (Frequency.equal open_string unison)
    then
      Code_error.raise
        "Unexpected pitch calculation."
        [ "high", high |> Roman_numeral.to_dyn
        ; "low", low |> Roman_numeral.to_dyn
        ; "open_string", open_string |> Frequency.to_dyn
        ; "unison", unison |> Frequency.to_dyn
        ]
  done
;;

let%expect_test "4-strings cello" =
  let a = { Note.letter_name = A; symbol = Natural; octave_designation = 3 } in
  let pitch = Frequency.a4_440 |> Acoustic_interval.shift_down Acoustic_interval.octave in
  let intervals_going_down =
    let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
    Array.create
      ~len:3
      (Characterized_interval.create_exn
         ~interval:fifth
         ~acoustic_interval:(Acoustic_interval.pythagorean fifth))
  in
  let system = System.create ~high_vibrating_string:a ~pitch ~intervals_going_down in
  test_pitch_exn ~system ~intervals_going_down;
  print_dyn (system |> System.to_dyn);
  [%expect
    {|
    { vibrating_strings =
        [| { open_string =
               { letter_name = A; symbol = Natural; octave_designation = 3 }
           ; pitch = 220.
           ; roman_numeral = I
           }
        ;  { open_string =
               { letter_name = D; symbol = Natural; octave_designation = 3 }
           ; pitch = 146.666666667
           ; roman_numeral = II
           }
        ;  { open_string =
               { letter_name = G; symbol = Natural; octave_designation = 2 }
           ; pitch = 97.7777777778
           ; roman_numeral = III
           }
        ;  { open_string =
               { letter_name = C; symbol = Natural; octave_designation = 2 }
           ; pitch = 65.1851851852
           ; roman_numeral = IV
           }
        |]
    ; intervals_going_down =
        [| { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        ;  { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        ;  { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        |]
    }
    |}];
  (* Creating a few positions and check the intervals between them. *)
  let fourth =
    Fingerboard_position.create_exn
      ~name:"4th"
      ~acoustic_interval_to_the_open_string:
        (Acoustic_interval.pythagorean
           { number = Fourth; quality = Perfect; additional_octaves = 0 })
  in
  let just_minor_ton =
    Fingerboard_position.create_exn
      ~name:"2MZ"
      ~acoustic_interval_to_the_open_string:Acoustic_interval.just_minor_ton
  in
  let pythagorean_minor_third =
    Fingerboard_position.create_exn
      ~name:"2mP"
      ~acoustic_interval_to_the_open_string:
        (Acoustic_interval.pythagorean
           { number = Third; quality = Minor; additional_octaves = 0 })
  in
  let i =
    System.acoustic_interval
      system
      ~from:{ fingerboard_position = fourth; string_number = III }
      ~to_:{ fingerboard_position = pythagorean_minor_third; string_number = I }
    |> Option.value_exn ~here:[%here]
  in
  assert (Acoustic_interval.equal i Acoustic_interval.octave);
  print_string (Acoustic_interval.to_string i);
  [%expect {| 2 |}];
  let i =
    System.acoustic_interval
      system
      ~from:{ fingerboard_position = fourth; string_number = III }
      ~to_:{ fingerboard_position = just_minor_ton; string_number = II }
    |> Option.value_exn ~here:[%here]
  in
  assert (Acoustic_interval.equal i Acoustic_interval.just_major_third);
  print_string (Acoustic_interval.to_string i);
  [%expect {| 5 / 2^2 |}];
  let i =
    System.acoustic_interval
      system
      ~from:{ fingerboard_position = fourth; string_number = III }
      ~to_:{ fingerboard_position = pythagorean_minor_third; string_number = II }
    |> Option.value_exn ~here:[%here]
  in
  assert (
    Acoustic_interval.equal
      i
      (Acoustic_interval.pythagorean
         { number = Fourth; quality = Perfect; additional_octaves = 0 }));
  print_string (Acoustic_interval.to_string i);
  [%expect {| 2^2 / 3 |}];
  let i =
    System.acoustic_interval
      system
      ~from:
        { fingerboard_position = Fingerboard_position.open_string; string_number = II }
      ~to_:{ fingerboard_position = just_minor_ton; string_number = I }
    |> Option.value_exn ~here:[%here]
  in
  assert (Acoustic_interval.equal i Acoustic_interval.just_major_sixth);
  print_string (Acoustic_interval.to_string i);
  [%expect {| 5 / 3 |}];
  let i =
    System.acoustic_interval
      system
      ~from:{ fingerboard_position = just_minor_ton; string_number = I }
      ~to_:{ fingerboard_position = pythagorean_minor_third; string_number = I }
    |> Option.value_exn ~here:[%here]
  in
  assert (Acoustic_interval.equal i Acoustic_interval.just_diatonic_semiton);
  print_string (Acoustic_interval.to_string i);
  [%expect {| 2^4 / (3 * 5) |}];
  ()
;;

let%expect_test "piccolo cello" =
  let e = { Note.letter_name = E; symbol = Natural; octave_designation = 4 } in
  let pitch =
    Frequency.a4_440
    |> Acoustic_interval.shift_down
         (Acoustic_interval.pythagorean
            { number = Fourth; quality = Perfect; additional_octaves = 0 })
  in
  let intervals_going_down =
    let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
    Array.create
      ~len:4
      (Characterized_interval.create_exn
         ~interval:fifth
         ~acoustic_interval:(Acoustic_interval.pythagorean fifth))
  in
  let system = System.create ~high_vibrating_string:e ~pitch ~intervals_going_down in
  test_pitch_exn ~system ~intervals_going_down;
  print_dyn (system |> System.to_dyn);
  [%expect
    {|
    { vibrating_strings =
        [| { open_string =
               { letter_name = E; symbol = Natural; octave_designation = 4 }
           ; pitch = 330.
           ; roman_numeral = I
           }
        ;  { open_string =
               { letter_name = A; symbol = Natural; octave_designation = 3 }
           ; pitch = 220.
           ; roman_numeral = II
           }
        ;  { open_string =
               { letter_name = D; symbol = Natural; octave_designation = 3 }
           ; pitch = 146.666666667
           ; roman_numeral = III
           }
        ;  { open_string =
               { letter_name = G; symbol = Natural; octave_designation = 2 }
           ; pitch = 97.7777777778
           ; roman_numeral = IV
           }
        ;  { open_string =
               { letter_name = C; symbol = Natural; octave_designation = 2 }
           ; pitch = 65.1851851852
           ; roman_numeral = V
           }
        |]
    ; intervals_going_down =
        [| { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        ;  { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        ;  { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        ;  { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        |]
    }
    |}];
  ()
;;

let%expect_test "5th Bach's suite for cello" =
  let g = { Note.letter_name = G; symbol = Natural; octave_designation = 3 } in
  let pitch =
    Frequency.a4_440
    |> Acoustic_interval.shift_down
         (Acoustic_interval.pythagorean
            { number = Second; quality = Major; additional_octaves = 1 })
  in
  let intervals_going_down =
    let fourth =
      { Interval.number = Fourth; quality = Perfect; additional_octaves = 0 }
    in
    let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
    Array.concat
      [ [| Characterized_interval.create_exn
             ~interval:fourth
             ~acoustic_interval:(Acoustic_interval.pythagorean fourth)
        |]
      ; Array.create
          ~len:2
          (Characterized_interval.create_exn
             ~interval:fifth
             ~acoustic_interval:(Acoustic_interval.pythagorean fifth))
      ]
  in
  let system = System.create ~high_vibrating_string:g ~pitch ~intervals_going_down in
  test_pitch_exn ~system ~intervals_going_down;
  print_dyn (system |> System.to_dyn);
  [%expect
    {|
    { vibrating_strings =
        [| { open_string =
               { letter_name = G; symbol = Natural; octave_designation = 3 }
           ; pitch = 195.555555556
           ; roman_numeral = I
           }
        ;  { open_string =
               { letter_name = D; symbol = Natural; octave_designation = 3 }
           ; pitch = 146.666666667
           ; roman_numeral = II
           }
        ;  { open_string =
               { letter_name = G; symbol = Natural; octave_designation = 2 }
           ; pitch = 97.7777777778
           ; roman_numeral = III
           }
        ;  { open_string =
               { letter_name = C; symbol = Natural; octave_designation = 2 }
           ; pitch = 65.1851851852
           ; roman_numeral = IV
           }
        |]
    ; intervals_going_down =
        [| { interval =
               { number = Fourth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = 2 }; { prime = 3; exponent = -1 } ]
           }
        ;  { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        ;  { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        |]
    }
    |}];
  ()
;;

let%expect_test "Kodaly sonata for cello solo" =
  let a = { Note.letter_name = A; symbol = Natural; octave_designation = 3 } in
  let pitch = Frequency.a4_440 |> Acoustic_interval.shift_down Acoustic_interval.octave in
  let intervals_going_down =
    let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
    [| Characterized_interval.create_exn
         ~interval:fifth
         ~acoustic_interval:(Acoustic_interval.pythagorean fifth)
     ; Characterized_interval.create_exn
         ~interval:{ Interval.number = Sixth; quality = Minor; additional_octaves = 0 }
         ~acoustic_interval:Acoustic_interval.just_minor_sixth
     ; Characterized_interval.create_exn
         ~interval:fifth
         ~acoustic_interval:(Acoustic_interval.pythagorean fifth)
    |]
  in
  let system = System.create ~high_vibrating_string:a ~pitch ~intervals_going_down in
  test_pitch_exn ~system ~intervals_going_down;
  print_dyn (system |> System.to_dyn);
  [%expect
    {|
    { vibrating_strings =
        [| { open_string =
               { letter_name = A; symbol = Natural; octave_designation = 3 }
           ; pitch = 220.
           ; roman_numeral = I
           }
        ;  { open_string =
               { letter_name = D; symbol = Natural; octave_designation = 3 }
           ; pitch = 146.666666667
           ; roman_numeral = II
           }
        ;  { open_string =
               { letter_name = F; symbol = Sharp; octave_designation = 2 }
           ; pitch = 91.6666666667
           ; roman_numeral = III
           }
        ;  { open_string =
               { letter_name = B; symbol = Natural; octave_designation = 1 }
           ; pitch = 61.1111111111
           ; roman_numeral = IV
           }
        |]
    ; intervals_going_down =
        [| { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        ;  { interval =
               { number = Sixth; quality = Minor; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = 3 }; { prime = 5; exponent = -1 } ]
           }
        ;  { interval =
               { number = Fifth; quality = Perfect; additional_octaves = 0 }
           ; acoustic_interval =
               Reduced_natural_ratio
                 [ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
           }
        |]
    }
    |}];
  ()
;;

let%expect_test "reset-pitch" =
  let a = { Note.letter_name = A; symbol = Natural; octave_designation = 3 } in
  let pitch = Frequency.a4_440 |> Acoustic_interval.shift_down Acoustic_interval.octave in
  let intervals_going_down =
    let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
    Array.create
      ~len:3
      (Characterized_interval.create_exn
         ~interval:fifth
         ~acoustic_interval:(Acoustic_interval.pythagorean fifth))
  in
  let system = System.create ~high_vibrating_string:a ~pitch ~intervals_going_down in
  test_pitch_exn ~system ~intervals_going_down;
  let system1 = Dyn.to_string (system |> System.to_dyn) in
  let change ~f =
    f ();
    let system2 = Dyn.to_string (system |> System.to_dyn) in
    Expect_test_patdiff.print_patdiff system1 system2 ~context:3
  in
  change ~f:(fun () -> System.reset_pitch system (Roman_numeral.of_int_exn 1) ~pitch);
  [%expect {| |}];
  change ~f:(fun () ->
    System.reset_pitch
      system
      (Roman_numeral.of_int_exn 1)
      ~pitch:
        (Frequency.of_float_exn 442.
         |> Acoustic_interval.shift_down Acoustic_interval.octave));
  [%expect
    {|
    -1,22 +1,22
      { vibrating_strings =
          [| { open_string =
                 { letter_name = A; symbol = Natural; octave_designation = 3 }
    -|       ; pitch = 220.
    +|       ; pitch = 221.
             ; roman_numeral = I
             }
          ;  { open_string =
                 { letter_name = D; symbol = Natural; octave_designation = 3 }
    -|       ; pitch = 146.666666667
    +|       ; pitch = 147.333333333
             ; roman_numeral = II
             }
          ;  { open_string =
                 { letter_name = G; symbol = Natural; octave_designation = 2 }
    -|       ; pitch = 97.7777777778
    +|       ; pitch = 98.2222222222
             ; roman_numeral = III
             }
          ;  { open_string =
                 { letter_name = C; symbol = Natural; octave_designation = 2 }
    -|       ; pitch = 65.1851851852
    +|       ; pitch = 65.4814814815
             ; roman_numeral = IV
             }
          |]
    |}];
  change ~f:(fun () ->
    System.reset_pitch
      system
      (Roman_numeral.of_int_exn 2)
      ~pitch:(Frequency.of_float_exn 147.));
  [%expect
    {|
    -1,22 +1,22
      { vibrating_strings =
          [| { open_string =
                 { letter_name = A; symbol = Natural; octave_designation = 3 }
    -|       ; pitch = 220.
    +|       ; pitch = 220.5
             ; roman_numeral = I
             }
          ;  { open_string =
                 { letter_name = D; symbol = Natural; octave_designation = 3 }
    -|       ; pitch = 146.666666667
    +|       ; pitch = 147.
             ; roman_numeral = II
             }
          ;  { open_string =
                 { letter_name = G; symbol = Natural; octave_designation = 2 }
    -|       ; pitch = 97.7777777778
    +|       ; pitch = 98.
             ; roman_numeral = III
             }
          ;  { open_string =
                 { letter_name = C; symbol = Natural; octave_designation = 2 }
    -|       ; pitch = 65.1851851852
    +|       ; pitch = 65.3333333333
             ; roman_numeral = IV
             }
          |]
    |}];
  ()
;;

1	(**********************************************************************************)
2	(* Fingerboard - a microtonal geography of the cello fingerboard *)
3	(* Copyright (C) 2022-2024 Mathieu Barbin <mathieu.barbin@gmail.com> *)
4	(* *)
5	(* This file is part of Fingerboard. *)
6	(* *)
7	(* Fingerboard is free software: you can redistribute it and/or modify it under *)
8	(* the terms of the GNU Affero General Public License as published by the Free *)
9	(* Software Foundation, either version 3 of the License, or any later version. *)
10	(* *)
11	(* Fingerboard is distributed in the hope that it will be useful, but WITHOUT *)
12	(* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or *)
13	(* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Affero General Public License *)
14	(* for more details. *)
15	(* *)
16	(* You should have received a copy of the GNU Affero General Public License *)
17	(* along with Fingerboard. If not, see <https://www.gnu.org/licenses/>. *)
18	(**********************************************************************************)
19
20	let test_pitch_exn ~system ~(intervals_going_down : Characterized_interval.t array) =
21	(* We test that the pitch is the same for the open string and the position on
22	the next vibrating string at the position of the interval between the two
23	vibrating strings. *)
24	for i = 1 to Array.length intervals_going_down do	5✔
25	let high = Roman_numeral.of_int_exn i in	16✔
26	let low = Roman_numeral.succ_exn high in	16✔
27	let open_string =	16✔
28	System.pitch
29	system
30	{ fingerboard_position = Fingerboard_position.open_string; string_number = high }
31	in
32	let unison =	16✔
33	System.pitch
34	system
35	{ fingerboard_position =
36	Fingerboard_position.create_exn
37	~name:"unison"
38	~acoustic_interval_to_the_open_string:
39	intervals_going_down.(i - 1).acoustic_interval
40	; string_number = low
41	}
42	in
43	if not (Frequency.equal open_string unison)	16✔
44	then
45	Code_error.raise	×
46	"Unexpected pitch calculation."
UNCOV 47	[ "high", high \|> Roman_numeral.to_dyn	×
UNCOV 48	; "low", low \|> Roman_numeral.to_dyn	×
UNCOV 49	; "open_string", open_string \|> Frequency.to_dyn	×
UNCOV 50	; "unison", unison \|> Frequency.to_dyn	×
51	]
52	done
53	;;
54
55	let%expect_test "4-strings cello" =
56	let a = { Note.letter_name = A; symbol = Natural; octave_designation = 3 } in	1✔
57	let pitch = Frequency.a4_440 \|> Acoustic_interval.shift_down Acoustic_interval.octave in
58	let intervals_going_down =	1✔
59	let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
60	Array.create	1✔
61	~len:3
62	(Characterized_interval.create_exn
63	~interval:fifth
64	~acoustic_interval:(Acoustic_interval.pythagorean fifth))	1✔
65	in
66	let system = System.create ~high_vibrating_string:a ~pitch ~intervals_going_down in
67	test_pitch_exn ~system ~intervals_going_down;
68	print_dyn (system \|> System.to_dyn);	1✔
69	[%expect	1✔
70	{\|
71	{ vibrating_strings =
72	[\| { open_string =
73	{ letter_name = A; symbol = Natural; octave_designation = 3 }
74	; pitch = 220.
75	; roman_numeral = I
76	}
77	; { open_string =
78	{ letter_name = D; symbol = Natural; octave_designation = 3 }
79	; pitch = 146.666666667
80	; roman_numeral = II
81	}
82	; { open_string =
83	{ letter_name = G; symbol = Natural; octave_designation = 2 }
84	; pitch = 97.7777777778
85	; roman_numeral = III
86	}
87	; { open_string =
88	{ letter_name = C; symbol = Natural; octave_designation = 2 }
89	; pitch = 65.1851851852
90	; roman_numeral = IV
91	}
92	\|]
93	; intervals_going_down =
94	[\| { interval =
95	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
96	; acoustic_interval =
97	Reduced_natural_ratio
98	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
99	}
100	; { interval =
101	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
102	; acoustic_interval =
103	Reduced_natural_ratio
104	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
105	}
106	; { interval =
107	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
108	; acoustic_interval =
109	Reduced_natural_ratio
110	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
111	}
112	\|]
113	}
114	\|}];	1✔
115	(* Creating a few positions and check the intervals between them. *)
116	let fourth =
117	Fingerboard_position.create_exn
118	~name:"4th"
119	~acoustic_interval_to_the_open_string:
120	(Acoustic_interval.pythagorean	1✔
121	{ number = Fourth; quality = Perfect; additional_octaves = 0 })
122	in
123	let just_minor_ton =
124	Fingerboard_position.create_exn
125	~name:"2MZ"
126	~acoustic_interval_to_the_open_string:Acoustic_interval.just_minor_ton
127	in
128	let pythagorean_minor_third =
129	Fingerboard_position.create_exn
130	~name:"2mP"
131	~acoustic_interval_to_the_open_string:
132	(Acoustic_interval.pythagorean	1✔
133	{ number = Third; quality = Minor; additional_octaves = 0 })
134	in
135	let i =
136	System.acoustic_interval
137	system
138	~from:{ fingerboard_position = fourth; string_number = III }
139	~to_:{ fingerboard_position = pythagorean_minor_third; string_number = I }
140	\|> Option.value_exn ~here:[%here]	1✔
141	in
142	assert (Acoustic_interval.equal i Acoustic_interval.octave);	1✔
143	print_string (Acoustic_interval.to_string i);	1✔
144	[%expect {\| 2 \|}];	1✔
145	let i =
146	System.acoustic_interval
147	system
148	~from:{ fingerboard_position = fourth; string_number = III }
149	~to_:{ fingerboard_position = just_minor_ton; string_number = II }
150	\|> Option.value_exn ~here:[%here]	1✔
151	in
152	assert (Acoustic_interval.equal i Acoustic_interval.just_major_third);	1✔
153	print_string (Acoustic_interval.to_string i);	1✔
154	[%expect {\| 5 / 2^2 \|}];	1✔
155	let i =
156	System.acoustic_interval
157	system
158	~from:{ fingerboard_position = fourth; string_number = III }
159	~to_:{ fingerboard_position = pythagorean_minor_third; string_number = II }
160	\|> Option.value_exn ~here:[%here]	1✔
161	in
162	assert (	1✔
163	Acoustic_interval.equal	1✔
164	i
165	(Acoustic_interval.pythagorean	1✔
166	{ number = Fourth; quality = Perfect; additional_octaves = 0 }));
167	print_string (Acoustic_interval.to_string i);	1✔
168	[%expect {\| 2^2 / 3 \|}];	1✔
169	let i =
170	System.acoustic_interval
171	system
172	~from:
173	{ fingerboard_position = Fingerboard_position.open_string; string_number = II }
174	~to_:{ fingerboard_position = just_minor_ton; string_number = I }
175	\|> Option.value_exn ~here:[%here]	1✔
176	in
177	assert (Acoustic_interval.equal i Acoustic_interval.just_major_sixth);	1✔
178	print_string (Acoustic_interval.to_string i);	1✔
179	[%expect {\| 5 / 3 \|}];	1✔
180	let i =
181	System.acoustic_interval
182	system
183	~from:{ fingerboard_position = just_minor_ton; string_number = I }
184	~to_:{ fingerboard_position = pythagorean_minor_third; string_number = I }
185	\|> Option.value_exn ~here:[%here]	1✔
186	in
187	assert (Acoustic_interval.equal i Acoustic_interval.just_diatonic_semiton);	1✔
188	print_string (Acoustic_interval.to_string i);	1✔
189	[%expect {\| 2^4 / (3 * 5) \|}];	1✔
190	()
191	;;
192
193	let%expect_test "piccolo cello" =
194	let e = { Note.letter_name = E; symbol = Natural; octave_designation = 4 } in	1✔
195	let pitch =
196	Frequency.a4_440
197	\|> Acoustic_interval.shift_down
198	(Acoustic_interval.pythagorean	1✔
199	{ number = Fourth; quality = Perfect; additional_octaves = 0 })
200	in
201	let intervals_going_down =	1✔
202	let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
203	Array.create	1✔
204	~len:4
205	(Characterized_interval.create_exn
206	~interval:fifth
207	~acoustic_interval:(Acoustic_interval.pythagorean fifth))	1✔
208	in
209	let system = System.create ~high_vibrating_string:e ~pitch ~intervals_going_down in
210	test_pitch_exn ~system ~intervals_going_down;
211	print_dyn (system \|> System.to_dyn);	1✔
212	[%expect	1✔
213	{\|
214	{ vibrating_strings =
215	[\| { open_string =
216	{ letter_name = E; symbol = Natural; octave_designation = 4 }
217	; pitch = 330.
218	; roman_numeral = I
219	}
220	; { open_string =
221	{ letter_name = A; symbol = Natural; octave_designation = 3 }
222	; pitch = 220.
223	; roman_numeral = II
224	}
225	; { open_string =
226	{ letter_name = D; symbol = Natural; octave_designation = 3 }
227	; pitch = 146.666666667
228	; roman_numeral = III
229	}
230	; { open_string =
231	{ letter_name = G; symbol = Natural; octave_designation = 2 }
232	; pitch = 97.7777777778
233	; roman_numeral = IV
234	}
235	; { open_string =
236	{ letter_name = C; symbol = Natural; octave_designation = 2 }
237	; pitch = 65.1851851852
238	; roman_numeral = V
239	}
240	\|]
241	; intervals_going_down =
242	[\| { interval =
243	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
244	; acoustic_interval =
245	Reduced_natural_ratio
246	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
247	}
248	; { interval =
249	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
250	; acoustic_interval =
251	Reduced_natural_ratio
252	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
253	}
254	; { interval =
255	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
256	; acoustic_interval =
257	Reduced_natural_ratio
258	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
259	}
260	; { interval =
261	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
262	; acoustic_interval =
263	Reduced_natural_ratio
264	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
265	}
266	\|]
267	}
268	\|}];	1✔
269	()
270	;;
271
272	let%expect_test "5th Bach's suite for cello" =
273	let g = { Note.letter_name = G; symbol = Natural; octave_designation = 3 } in	1✔
274	let pitch =
275	Frequency.a4_440
276	\|> Acoustic_interval.shift_down
277	(Acoustic_interval.pythagorean	1✔
278	{ number = Second; quality = Major; additional_octaves = 1 })
279	in
280	let intervals_going_down =	1✔
281	let fourth =
282	{ Interval.number = Fourth; quality = Perfect; additional_octaves = 0 }
283	in
284	let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
285	Array.concat	1✔
286	[ [\| Characterized_interval.create_exn
287	~interval:fourth
288	~acoustic_interval:(Acoustic_interval.pythagorean fourth)	1✔
289	\|]
290	; Array.create	1✔
291	~len:2
292	(Characterized_interval.create_exn
293	~interval:fifth
294	~acoustic_interval:(Acoustic_interval.pythagorean fifth))	1✔
295	]
296	in
297	let system = System.create ~high_vibrating_string:g ~pitch ~intervals_going_down in
298	test_pitch_exn ~system ~intervals_going_down;
299	print_dyn (system \|> System.to_dyn);	1✔
300	[%expect	1✔
301	{\|
302	{ vibrating_strings =
303	[\| { open_string =
304	{ letter_name = G; symbol = Natural; octave_designation = 3 }
305	; pitch = 195.555555556
306	; roman_numeral = I
307	}
308	; { open_string =
309	{ letter_name = D; symbol = Natural; octave_designation = 3 }
310	; pitch = 146.666666667
311	; roman_numeral = II
312	}
313	; { open_string =
314	{ letter_name = G; symbol = Natural; octave_designation = 2 }
315	; pitch = 97.7777777778
316	; roman_numeral = III
317	}
318	; { open_string =
319	{ letter_name = C; symbol = Natural; octave_designation = 2 }
320	; pitch = 65.1851851852
321	; roman_numeral = IV
322	}
323	\|]
324	; intervals_going_down =
325	[\| { interval =
326	{ number = Fourth; quality = Perfect; additional_octaves = 0 }
327	; acoustic_interval =
328	Reduced_natural_ratio
329	[ { prime = 2; exponent = 2 }; { prime = 3; exponent = -1 } ]
330	}
331	; { interval =
332	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
333	; acoustic_interval =
334	Reduced_natural_ratio
335	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
336	}
337	; { interval =
338	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
339	; acoustic_interval =
340	Reduced_natural_ratio
341	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
342	}
343	\|]
344	}
345	\|}];	1✔
346	()
347	;;
348
349	let%expect_test "Kodaly sonata for cello solo" =
350	let a = { Note.letter_name = A; symbol = Natural; octave_designation = 3 } in	1✔
351	let pitch = Frequency.a4_440 \|> Acoustic_interval.shift_down Acoustic_interval.octave in
352	let intervals_going_down =	1✔
353	let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
354	[\| Characterized_interval.create_exn
355	~interval:fifth
356	~acoustic_interval:(Acoustic_interval.pythagorean fifth)	1✔
357	; Characterized_interval.create_exn
358	~interval:{ Interval.number = Sixth; quality = Minor; additional_octaves = 0 }
359	~acoustic_interval:Acoustic_interval.just_minor_sixth
360	; Characterized_interval.create_exn
361	~interval:fifth
362	~acoustic_interval:(Acoustic_interval.pythagorean fifth)	1✔
363	\|]
364	in
365	let system = System.create ~high_vibrating_string:a ~pitch ~intervals_going_down in
366	test_pitch_exn ~system ~intervals_going_down;
367	print_dyn (system \|> System.to_dyn);	1✔
368	[%expect	1✔
369	{\|
370	{ vibrating_strings =
371	[\| { open_string =
372	{ letter_name = A; symbol = Natural; octave_designation = 3 }
373	; pitch = 220.
374	; roman_numeral = I
375	}
376	; { open_string =
377	{ letter_name = D; symbol = Natural; octave_designation = 3 }
378	; pitch = 146.666666667
379	; roman_numeral = II
380	}
381	; { open_string =
382	{ letter_name = F; symbol = Sharp; octave_designation = 2 }
383	; pitch = 91.6666666667
384	; roman_numeral = III
385	}
386	; { open_string =
387	{ letter_name = B; symbol = Natural; octave_designation = 1 }
388	; pitch = 61.1111111111
389	; roman_numeral = IV
390	}
391	\|]
392	; intervals_going_down =
393	[\| { interval =
394	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
395	; acoustic_interval =
396	Reduced_natural_ratio
397	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
398	}
399	; { interval =
400	{ number = Sixth; quality = Minor; additional_octaves = 0 }
401	; acoustic_interval =
402	Reduced_natural_ratio
403	[ { prime = 2; exponent = 3 }; { prime = 5; exponent = -1 } ]
404	}
405	; { interval =
406	{ number = Fifth; quality = Perfect; additional_octaves = 0 }
407	; acoustic_interval =
408	Reduced_natural_ratio
409	[ { prime = 2; exponent = -1 }; { prime = 3; exponent = 1 } ]
410	}
411	\|]
412	}
413	\|}];	1✔
414	()
415	;;
416
417	let%expect_test "reset-pitch" =
418	let a = { Note.letter_name = A; symbol = Natural; octave_designation = 3 } in	1✔
419	let pitch = Frequency.a4_440 \|> Acoustic_interval.shift_down Acoustic_interval.octave in
420	let intervals_going_down =	1✔
421	let fifth = { Interval.number = Fifth; quality = Perfect; additional_octaves = 0 } in
422	Array.create	1✔
423	~len:3
424	(Characterized_interval.create_exn
425	~interval:fifth
426	~acoustic_interval:(Acoustic_interval.pythagorean fifth))	1✔
427	in
428	let system = System.create ~high_vibrating_string:a ~pitch ~intervals_going_down in
429	test_pitch_exn ~system ~intervals_going_down;
430	let system1 = Dyn.to_string (system \|> System.to_dyn) in	1✔
431	let change ~f =	1✔
432	f ();	3✔
433	let system2 = Dyn.to_string (system \|> System.to_dyn) in	3✔
434	Expect_test_patdiff.print_patdiff system1 system2 ~context:3	3✔
435	in
436	change ~f:(fun () -> System.reset_pitch system (Roman_numeral.of_int_exn 1) ~pitch);	1✔
437	[%expect {\| \|}];	1✔
438	change ~f:(fun () ->
439	System.reset_pitch	1✔
440	system
441	(Roman_numeral.of_int_exn 1)	1✔
442	~pitch:
443	(Frequency.of_float_exn 442.
444	\|> Acoustic_interval.shift_down Acoustic_interval.octave));	1✔
445	[%expect
446	{\|
447	-1,22 +1,22
448	{ vibrating_strings =
449	[\| { open_string =
450	{ letter_name = A; symbol = Natural; octave_designation = 3 }
451	-\| ; pitch = 220.
452	+\| ; pitch = 221.
453	; roman_numeral = I
454	}
455	; { open_string =
456	{ letter_name = D; symbol = Natural; octave_designation = 3 }
457	-\| ; pitch = 146.666666667
458	+\| ; pitch = 147.333333333
459	; roman_numeral = II
460	}
461	; { open_string =
462	{ letter_name = G; symbol = Natural; octave_designation = 2 }
463	-\| ; pitch = 97.7777777778
464	+\| ; pitch = 98.2222222222
465	; roman_numeral = III
466	}
467	; { open_string =
468	{ letter_name = C; symbol = Natural; octave_designation = 2 }
469	-\| ; pitch = 65.1851851852
470	+\| ; pitch = 65.4814814815
471	; roman_numeral = IV
472	}
473	\|]
474	\|}];	1✔
475	change ~f:(fun () ->
476	System.reset_pitch	1✔
477	system
478	(Roman_numeral.of_int_exn 2)	1✔
479	~pitch:(Frequency.of_float_exn 147.));	1✔
480	[%expect
481	{\|
482	-1,22 +1,22
483	{ vibrating_strings =
484	[\| { open_string =
485	{ letter_name = A; symbol = Natural; octave_designation = 3 }
486	-\| ; pitch = 220.
487	+\| ; pitch = 220.5
488	; roman_numeral = I
489	}
490	; { open_string =
491	{ letter_name = D; symbol = Natural; octave_designation = 3 }
492	-\| ; pitch = 146.666666667
493	+\| ; pitch = 147.
494	; roman_numeral = II
495	}
496	; { open_string =
497	{ letter_name = G; symbol = Natural; octave_designation = 2 }
498	-\| ; pitch = 97.7777777778
499	+\| ; pitch = 98.
500	; roman_numeral = III
501	}
502	; { open_string =
503	{ letter_name = C; symbol = Natural; octave_designation = 2 }
504	-\| ; pitch = 65.1851851852
505	+\| ; pitch = 65.3333333333
506	; roman_numeral = IV
507	}
508	\|]
509	\|}];	1✔
510	()
511	;;

mbarbin / fingerboard / 116

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