Build a Band
I built a chime instrument with 41 notes:
C C# D D# E F F# G G# A A# B C C# D D# E F F# G G# A A# B C C# D D# E F F# G G# A A# B C C# D D# E
C C# D D# E F F# G G# A A# B C C# D D# E F F# G G# A A# B C C# D D# E F F# G G# A A# B C C# D D# E
Calculation
Raising the note by a half step (like C to C#) multiplies the frequency by 2^(1/12).
To do that, you need to divide the length of the chime by 2^(1/24).
Therefore, the lengths of the chimes were of the form 37.5*2^(n/24) where n is an integer.
(The 37.5 is just a random starting point I chose. It turned out to play a G#.)
To do that, you need to divide the length of the chime by 2^(1/24).
Therefore, the lengths of the chimes were of the form 37.5*2^(n/24) where n is an integer.
(The 37.5 is just a random starting point I chose. It turned out to play a G#.)
Table
NoteC
C# D D# E F F# G G# A A# B C C# D D# E F F# G G# A A# B C C# D D# E F F# G G# A A# B C C# D D# E |
Chime Length (Algebraic Form)37.5*2^(32/24)
37.5*2^(31/24) 37.5*2^(30/24) 37.5*2^(29/24) 37.5*2^(28/24) 37.5*2^(27/24) 37.5*2^(26/24) 37.5*2^(25/24) 37.5*2^(24/24) 37.5*2^(23/24) 37.5*2^(22/24) 37.5*2^(21/24) 37.5*2^(20/24) 37.5*2^(19/24) 37.5*2^(18/24) 37.5*2^(17/24) 37.5*2^(16/24) 37.5*2^(15/24) 37.5*2^(14/24) 37.5*2^(13/24) 37.5*2^(12/24) 37.5*2^(11/24) 37.5*2^(10/24) 37.5*2^(9/24) 37.5*2^(8/24) 37.5*2^(7/24) 37.5*2^(6/24) 37.5*2^(5/24) 37.5*2^(4/24) 37.5*2^(3/24) 37.5*2^(2/24) 37.5*2^(1/24) 37.5*2^(0/24) 37.5*2^(-1/24) 37.5*2^(-2/24) 37.5*2^(-3/24) 37.5*2^(-4/24) 37.5*2^(-5/24) 37.5*2^(-6/24) 37.5*2^(-7/24) 37.5*2^(-8/24) |
Chime Length (Decimal Form)94.49
91.80 89.19 86.65 84.18 81.79 79.46 77.20 75.00 72.86 70.79 68.78 66.82 64.92 63.07 61.27 59.53 57.83 56.19 54.59 53.03 51.52 50.06 48.63 47.25 45.90 44.60 43.33 42.09 40.89 39.73 38.60 37.50 36.43 35.40 34.39 33.41 32.46 31.53 30.64 29.76 |