#microtonal #midi #scales #synthesizer #tuning

bin+lib tune-cli

Explore musical tunings and create synthesizer tuning files for microtonal scales

8 releases (breaking)

0.14.0 Oct 9, 2020
0.13.0 Sep 27, 2020
0.12.0 Sep 20, 2020
0.11.0 Aug 28, 2020
0.7.0 May 17, 2020

#38 in Audio

Download history 4/week @ 2020-06-30 3/week @ 2020-07-07 6/week @ 2020-07-14 7/week @ 2020-07-21 17/week @ 2020-07-28 9/week @ 2020-08-04 20/week @ 2020-08-11 7/week @ 2020-08-18 20/week @ 2020-08-25 16/week @ 2020-09-01 13/week @ 2020-09-08 14/week @ 2020-09-15 19/week @ 2020-09-22 25/week @ 2020-09-29 24/week @ 2020-10-06 8/week @ 2020-10-13

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MIT license

225KB
4.5K SLoC

Explore musical tunings and create synthesizer tuning files for microtonal scales.

Resources

Overview

tune-cli is the command line tool for the microtonal tune library.

Installation

cargo install -f tune-cli

Usage

Introduction

You want to know how to tune your piano in 7-EDO? Just use the following command:

tune scale 62 steps 1:7:2 | tune dump

This instructs tune to print the frequencies and approximate notes of a 7-EDO scale starting at D4 (MIDI number 62).

  ----------Source Scale---------------Pitch-------------Target Scale--------
..
>  62 | IDX    0 |  1/1    +0¢  +0o ‖     293.665 Hz ‖   62 |       D 4 |   +0.000¢
   63 | IDX    1 | 11/10   +6¢  +0o ‖     324.232 Hz ‖   64 |       E 4 |  -28.571¢
   64 | IDX    2 | 11/9    -5¢  +0o ‖     357.981 Hz ‖   65 |       F 4 |  +42.857¢
   65 | IDX    3 |  4/3   +16¢  +0o ‖     395.243 Hz ‖   67 |       G 4 |  +14.286¢
   66 | IDX    4 |  3/2   -16¢  +0o ‖     436.384 Hz ‖   69 |       A 4 |  -14.286¢
   67 | IDX    5 | 18/11   +5¢  +0o ‖     481.807 Hz ‖   71 |       B 4 |  -42.857¢
   68 | IDX    6 | 20/11   -6¢  +0o ‖     531.958 Hz ‖   72 |       C 5 |  +28.571¢
   69 | IDX    7 |  2/1    -0¢  +0o ‖     587.330 Hz ‖   74 |       D 5 |   -0.000¢
..

The table tells us that the first step of the 7-EDO scale (IDX 0) has a frequency of 293.655 Hz and matches D4 exactly. This is obvious since we chose D4 be the origin of the 7-EDO scale. IDX 1, the second step of the scale, is reported to be close to E4 but with an offset of -28.571¢.

You can now detune every note D on your piano by -28.571¢. On an electric piano with octave-based tuning support, this is a very easy task. It is also possible to retune a real piano using a tuning device.

Retune every note of the 7-EDO scale according to the table and the 7-EDO scale will be playable on the white keys!

MIDI Tuning Standard

If you do not want to retune your keyboard manually you can instruct tune-cli to send MIDI Tuning Standard messages to your synthesizer. To do so, locate your target MIDI device first:

tune devices

This will list all available MIDI devices:

Readable MIDI devices:
(0) Midi Through:Midi Through Port-0 14:0
Writable MIDI devices:
(0) Midi Through:Midi Through Port-0 14:0
(1) FLUID Synth (23673):Synth input port (23673:0) 128:0

Now, send a 7-EDO Scale/Octave Tuning message to FLUID Synth:

tune mts --send-to 1 octave 62 steps 1:7:2

Full Keyboard Tuning

The most generic type of tuning message is the Single Note Tuning message providing control over the pitch of each note. Note, however, that many synthesizers do not support this tuning message. The correspondig command is:

tune scale 62 steps 1:7:2 | tune mts from-json

This will print:

== SysEx start ==
0xf0
0x7f
0x7f
0x08
..
0x7f
0x12
0x25
0xf7
Number of retuned notes: 75
Number of out-of-range notes: 52
== SysEx end ==

Some notes are reported to be out of range. This is because 7-EDO has a stronger per-step increase in frequency than 12-EDO, s.t. some frequencies become unmappable.

You can also save a binary version of the tuning message using the --bin option.

tune scale 62 steps 1:7:2 | tune mts --bin tuning_message.syx from-json

Limitations

The current implementation doesn't allow for gaps in a scale. This means the Single Note Tuning version of the 7-EDO scale has to be played on all piano keys with black and white keys mixed. Hopefully, this is going to be fixed soon.

Live Retuning

If your synthesizer has no support for full-keyboard tuning messages but for octave-based tuning messages, there still is a way to play almost every scale on that device.

To do so, try using tune-cli's live retuning feature which can be activated via the tune live subcommand:

tune live --midi-in 1 --midi-out 1 aot 62 steps 1:22:2

The given command will enable ahead-of-time live retuning for 22-EDO on device 1. The term "ahead-of-time" reflects the fact that several channels will be retuned on startup. After that, each incoming message is mapped to an outgoing message on the channel that has the appropriate tuning applied.

Scala File Format

An alternative tuning method is to upload scl and kbm files to your synthesizer. See the scl and kbm sections below for more information.

Approximate Ratios

The dump command provides information about the qualities of a scale. Let's have a look at the 19-EDO scale:

tune scale 62 steps 1:19:2 | tune dump

The output reveals that some rational intervals are well approximated. Especially the just minor third (6/5) which is approximated by less than than 1¢ and, therefore, displayed as 0¢:

  ----------Source Scale---------------Pitch-------------Target Scale--------
..
   67 | IDX    5 |  6/5    +0¢  +0o ‖     352.428 Hz ‖   65 |       F 4 |  +15.789¢
..

The ratio approximation algorithm is not very advanced yet and does not use prime numbers.

Compare Scales

Imagine, you want to know how well quarter-comma meantone is represented in 31-EDO. All you need to do is create the quarter-comma meantone scale (tune scale) and tune diff it against the 31-EDO scale.

In quarter-comma meantone the fifths are tempered in such a way that four of them match up a frequency ratio of 5. This makes the genator of the scale equal to 5^(1/4) or 1:4:5 in tune expression notation. To obtain a full scale, let's say ionian/major, you need to walk 5 generators/fifths upwards and one downwards which translates to the scale expression rank2 1:4:5 5 1.

The scale expression for the 31-EDO scale is steps 1:31:2, s.t. the full scale comparison command becomes:

tune scale 62 rank2 1:4:5 5 1 | tune diff 62 steps 1:31:2

This will print:

  ----------Source Scale---------------Pitch-------------Target Scale--------
..
>  62 | IDX    0 |  1/1    +0¢  +0o ‖     293.665 Hz ‖   62 | IDX     0 |   +0.000¢
   63 | IDX    1 |  9/8   -11¢  +0o ‖     328.327 Hz ‖   67 | IDX     5 |   -0.392¢
   64 | IDX    2 |  5/4    +0¢  +0o ‖     367.081 Hz ‖   72 | IDX    10 |   -0.783¢
   65 | IDX    3 |  4/3    +5¢  +0o ‖     392.771 Hz ‖   75 | IDX    13 |   +0.196¢
   66 | IDX    4 |  3/2    -5¢  +0o ‖     439.131 Hz ‖   80 | IDX    18 |   -0.196¢
   67 | IDX    5 |  5/3    +5¢  +0o ‖     490.964 Hz ‖   85 | IDX    23 |   -0.587¢
   68 | IDX    6 | 11/6   +34¢  +0o ‖     548.914 Hz ‖   90 | IDX    28 |   -0.979¢
   69 | IDX    7 |  1/1    +0¢  +1o ‖     587.330 Hz ‖   93 | IDX    31 |   +0.000¢
..

You can see that 31-EDO is a very good approximation of quarter-comma meantone with a maximum deviation of -0.979¢. You can also see that the step sizes of the corresponding 31-EDO scale are 5, 5, 3, 5, 5, 5 and 3.

EDO analysis

The tune est command prints basic information about any equal-step tuning. The step sizes and sharp values are derived based on the arithmetics of meantone tuning.

Example output of tune est 1:17:2:

---- Properties of 17-EDO (Meantone) ----

Number of cycles: 1
1 fifth = 10 EDO steps = +705.9c (pythagorean +3.9c)
1 primary step = 3 EDO steps
1 secondary step = 1 EDO steps
1 sharp = 2 EDO steps

-- Val (13-limit) --
[17, 27, 39, 48, 59, 63]

-- Keyboard layout --
 13  16  2   5   8   11  14  0   3   6
 14  0   3   6   9   12  15  1   4   7
 15  1   4   7   10  13  16  2   5   8
 16  2   5   8   11  14  0   3   6   9
 0   3   6   9   12  15  1   4   7   10
 1   4   7   10  13  16  2   5   8   11
 2   5   8   11  14  0   3   6   9   12
 3   6   9   12  15  1   4   7   10  13
 4   7   10  13  16  2   5   8   11  14
 5   8   11  14  0   3   6   9   12  15

-- Scale steps --
  0. D
  1. Eb
  2. D# / Fb
  3. E
  4. F **JI m3rd**
  5. E# / Gb **JI M3rd**
  6. F#
  7. G **JI P4th**
  8. Ab
  9. G#
 10. A **JI P5th**
 11. Bb
 12. A# / Cb
 13. B
 14. C
 15. B# / Db
 16. C#

Create scl Files / Scale Expressions

  • Equal temperament

    tune scl steps 1:12:2      # 12-EDO
    tune scl steps 100c        # 12-EDO
    tune scl steps 1:36:2      # Sixth-tone
    tune scl steps '(100/3)c'  # Sixth-tone
    tune scl steps 1:13:3      # Bohlen-Pierce
    
  • Meantone temperament

    tune scl rank2 3/2 6       # Pythagorean (lydian)
    tune scl rank2 1.5 6 6     # Pythagorean (12-note)
    tune scl rank2 1:4:5 5 1   # quarter-comma meantone (major)
    tune scl rank2 18:31:2 3 3 # 31-EDO meantone (dorian)
    
  • Harmonic series

    tune scl harm 8            # 8:9:10:11:12:13:14:15:16 scale
    tune scl harm -s 8         # ¹/₁₆:¹/₁₅:¹/₁₄:¹/₁₃:¹/₁₂:¹/₁₁:¹/₁₀:¹/₉:¹/₈ scale
    
  • Custom scale

    tune scl -n "Just intonation" steps 9/8 5/4 4/3 3/2 5/3 15/8 2
    
  • Imported scale

    tune scl import my_scale.scl
    

Create kbm Files / Keyboad Mapping Expressions

  • Start scale at C4 at its usual frequency

    tune kbm 60
    
  • Start scale at C4, 20 cents higher than usual

    tune kbm 60+20c
    
  • Start scale at A4 at 450 Hz

    tune kbm 69@450Hz
    
  • Start scale at C4, A4 should sound at 450 Hz

    tune kbm -r 60 69@450Hz
    

JSON Output

tune uses JSON as an exchange format between pipelined calls. You can use tune's output as an input for an external application (or the other way around) or inspect/modify the output manually before further processing.

Example Usage

tune scale 62 steps 1:7:2

Output (shortened):

{
  "Scale": {
    "root_key_midi_number": 62,
    "root_pitch_in_hz": 293.6647679174076,
    "items": [
      {
        "key_midi_number": 62,
        "pitch_in_hz": 293.6647679174076
      },
      {
        "key_midi_number": 63,
        "pitch_in_hz": 324.23219079306347
      },
    ]
  }
}

Expressions

Ordered by precedence:

  1. <num>:<denom>:<int> evaluates to int^(num/denom)
  2. <num>/<denom> evaluates to num/denom
  3. <cents>c evaluates to 2^(cents/1200)
  4. (<expr>) evaluates to expr

Dependencies

~2.2–4.5MB
~86K SLoC