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

Resources

• Changelog
• Web App

Overview

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

Demo

• The Bedoginning (17-EDO)
• Don't Take Five (16-EDO)

Download / Installation

You can download a precompiled version of tune-cli from the Releases section or you can build a fresh binary from scratch using Cargo:

bash cargo install -f tune-cli

Before installing anything on your computer you can try out the web app first.

Usage

Introduction

Why does western music use 7 white and 5 black keys?

Those two numbers seem arbitrary but, in fact, they can be shown to be a reasonable choice by applying first principles. To cook western tuning soup we only need a few ingredients:

• The number 2 as a periodic interval: Pitches with a frequency ratio of 2 are perceived by humans as equivalent to each other. Therefore, it makes sense to only name the keys within a pitch spectrum of [1f, 2f).
• The number 3 as a generator: Any factor could be used as a generator. However, in the frequency spectrum of most instruments the strongest non-trivial peak is at a factor of 3 above the fundamental frequency. By including that factor in the tuning we make sure that the spectral peaks of multiple keys in a chord match up nicely – a condition which can be a measure of consonance.
• Two step sizes: Applying the generator repeatedly (and reducing by factors of the period) we get a scale that has either two or three step ratios. To make things easier we only accept scales with 2 step ratios i.e. the Moment of Symmetry (MOS) property.

tune-cli can find valid step numbers and sizes based on the above requirements:

bash tune mos find --per 2 3

This will print all xLys (x large steps, y small steps) configurations up to some cutoff limit:

* num_notes = 2, 1L1s, L = +702c, s = +498c num_notes = 3, 2L1s, L = +498c, s = +204c * num_notes = 5, 2L3s, L = +294c, s = +204c num_notes = 7, 5L2s, L = +204c, s = +90c * num_notes = 12, 5L7s, L = +114c, s = +90c num_notes = 17, 12L5s, L = +90c, s = +23c num_notes = 29, 12L17s, L = +67c, s = +23c * num_notes = 41, 12L29s, L = +43c, s = +23c * num_notes = 53, 41L12s, L = +23c, s = +20c num_notes = 94, 53L41s, L = +20c, s = +4c num_notes = 147, 53L94s, L = +16c, s = +4c num_notes = 200, 53L147s, L = +13c, s = +4c num_notes = 253, 53L200s, L = +9c, s = +4c * num_notes = 306, 53L253s, L = +5c, s = +4c num_notes = 359, 306L53s, L = +4c, s = +2c * num_notes = 665, L = s = +2c (*) means convergent i.e. the best EDO configuration so far

We can see that there is a preference for certain reasonable numbers of scale steps:

• 2, 3: Not really scales
• 5: Pentatonic, ubiquitous in music but lacks spice/dissonance
• 7: Diatonic scale, spicy enough but lacks modulation
• 12: Can be considered as modal extensions of 5L2s
• 17, 29, 41, etc.: Even more modal extensions

In western tuning, the 12-tone 5L7s configuration has been chosen to be the sweet spot between expressiveness and complexity. It contains the diatonic 7-tone (5L2s) white-key configuration but leaves enough room for 5 black-key modulations. In order to arrive at an unbounded modulation circle, 5L7s has been equalized (L = s). The result is what we call 12 equal divisions of the octave (12-EDO) or just Modern Western Tuning.

Explore a Xen Tuning

A straight-forward xen tuning to explore is 7-EDO since its diatonic MOS (5L2s) is a subset of the 12-EDO MOS (5L7s). It can be treated as an equalized diatonic scale without any modes i.e. major, minor, dorian, etc. sound the same.

tune-cli can assist you in tuning your piano to 7-EDO. Just use the following command:

bash tune dump ref-note 62 --lo-key 61 --up-key 71 steps 1:7:2

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

``` ----------Source Scale----------- ‖ ----Pitch----- ‖ --------Target Scale-------- 61 | IDX -1 | 20/11 -6¢ -1o ‖ 265.979 Hz ‖ 60 | C 4 | +28.571¢

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¢ 70 | IDX 8 | 11/10 +6¢ +1o ‖ 648.464 Hz ‖ 76 | E 5 | -28.571¢ ```

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 electric piano manually you can instruct tune-cli to send a MIDI Tuning Standard (MTS) message to your synthesizer. To do so, locate your target MIDI device first:

bash tune devices

This will list all available MIDI devices:

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

You can now send a 7-EDO Scale/Octave Tuning message to FLUID Synth:

bash tune mts --send-to fluid octave ref-note 62 steps 1:7:2

Moreover, the command will print the tuning message to stdout:

== SysEx start (channel 0) == 0xf0 0x7e 0x7f 0x08 .. 0x32 0x40 0x15 0xf7 Sending MIDI data to FLUID Synth (8506):Synth input port (8506:0) 128:0 == SysEx end ==

Full Keyboard Tuning

The Scale/Octave Tuning message is of very limited use: It can only slightly detune the 12 note letters within an octave which means that it is impossible to squeeze more than 12 notes into an octave or to model a non-octave-based tuning like Bohlen-Pierce or a stretched EDO.

To overcome this limitation, synthesizers can respond to the Single Note Tuning Change message. It provides full control over the pitch of each individual MIDI note s.t. any tuning scenario becomes achievable. Unfortunately, many synthesizers do not respond to this tuning message.

To send a Single Note Tuning Change message to a synthesizer use:

bash tune mts --send-to 1 full ref-note 62 steps 1:7:2

Output:

== SysEx start == 0xf0 0x7f 0x7f 0x08 .. 0x7f 0x12 0x25 0xf7 Sending MIDI data to FLUID Synth (8506):Synth input port (8506:0) 128:0 Number of retuned notes: 75 Number of out-of-range notes: 13 == 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 does s.t. some (inaudible) frequencies become unmappable.

Keyboard Mappings

Unlike the octave-based mapping, the full keyboard mapping by default maps adjacent keys to adjacent degrees of your tuning. For 7-EDO, however, it would be convenient to skip/ignore the black keys in the mapping.

To specify a white-key-only keyboard mapping use the following syntax:

bash tune mts --send-to 1 full ref-note 62 --key-map 0,x,1,2,x,3,x,4,x,5,6,x --octave 7 steps 1:7:2

The --key-map parameter specifies that key D is mapped to degree 0, key D# is unmapped, E is mapped to degree 1, F is mapped to degree 2 and so on. The parameter --octave tells us that the 12th keyboard degree (D plus one octave) should be mapped to scale degree 7 (one octave in 7-EDO).

Live Retuning

The risk is high that you are not satisfied with your synth's tuning capabilities because:

• Your synth supports Single Note Tuning Change messages but it selects the sound sample based on the MIDI note number and not on the desired pitch (Slow-motion or time-lapse effect – sad but true!)
• Your synth has Scale/Octave Tuning support but you need more than 12 notes in an octave and/or your tuning isn't octave-based
• Your synth has no MTS support at all

The Live Retuning feature is where tune-cli shines. tune-cli can apply a couple of workarounds to make even a very basic keyboard with a pitch-bend wheel play Bohlen-Pierce scales.

This, of course comes, at some cost. Your virtual instrument will either consume multiple MIDI channels instead of only one or you have to accept that simultaneously played notes can get in a conflict situation.

To understand what live retuning does, have a look at the CLI help of the live subcommand:

bash tune live --help

Ahead-of-Time Live Retuning

The following command enables 31-EDO ahead-of-time live retuning with Scale/Octave tuning messages:

bash tune live --midi-in 'musescore port-0' --midi-out fluid aot octave ref-note 62 steps 1:31:2

Example Output:

Receiving MIDI data from MuseScore:MuseScore Port-0 129:2 Sending MIDI data to FLUID Synth (40097):Synth input port (40097:0) 128:0 in-channel 0 -> out-channels [0..3)

The term "ahead-of-time" reflects the fact that several channels will be retuned in a first stage where the number of MIDI channels is fixed and depends on the selected tuning and tuning method (tune live aot --help for more info). In our case, 3 channels (0, 1 and 2) are used. Note that tune-cli uses 0-based channels and right-exclusive ranges – a convention which effectively avoids programming errors.

The second stage is the live performance stage. No further tuning message will be sent. Instead, each incoming MIDI message will be transformed into another message or a batch of outgoing MIDI messages on the channels that have the appropriate tuning applied.

Ahead-of-time live retuning always allocates enough channels s.t. any combination of notes can be played simultaneously.

Just-in-Time Live retuning

If you want to allocate fewer channels than aot does (let's say two instead of three) you can apply just-in-time live retuning:

bash tune live --midi-in 'musescore port-0' --midi-out fluid jit --out-chans 2 octave ref-note 62 steps 1:31:2

Example Output:

Receiving MIDI data from MuseScore:MuseScore Port-0 129:2 Sending MIDI data to FLUID Synth (40097):Synth input port (40097:0) 128:0 in-channel 0 -> out-channels [0..2)

On the surface, jit just looks very similar to aot. However, there is a big difference in its implementation: While aot uses a fixed mapping with a fixed number of channels, jit uses a dynamic mapping that gets updated whenever a new note is triggered.

In the given example we decided to use two jit channels instead of three aot channels. This means some combinations of three notes cannot be played simultaneously in the correct tuning. Although this sounds like a hard limitation, in our case it isn't. The reason is that in order for a clash of three notes to occur, all notes must map to the same note letter. This would be the case for the notes 61, 62 and 63, all of which are an 31-EDO-step apart. Usually, the limitation only comes into play when a very dissonant note cluster is pressed.

Whole Channel Live Retuning

If your synthesizer has no support for complex tuning messages at all chances are that your synth understands one of the following message types:

• Channel Fine Tuning message
• Pitch-bend message

The above messages have an effect on all notes in a channel. This means, when your tuning contains m different deviations from 12-EDO, the corresponding aot live retuning command will allocate m channels. 16-EDO has 4 different deviations from 12-EDO s.t. the aot command works reasonably well:

bash tune live --midi-in 'musescore port-0' --midi-out fluid aot channel ref-note 62 steps 1:16:2 tune live --midi-in 'musescore port-0' --midi-out fluid aot pitch-bend ref-note 62 steps 1:16:2

Example Output:

Receiving MIDI data from MuseScore:MuseScore Port-0 129:2 Sending MIDI data to FLUID Synth (40097):Synth input port (40097:0) 128:0 in-channel 0 -> out-channels 0..4

In general, the number of aot channels can grow quite large as is the case for 17-EDO. In that case, use jit.

bash tune live --midi-in 'musescore port-0' --midi-out fluid jit --out-chans 8 channel ref-note 62 steps 1:17:2 tune live --midi-in 'musescore port-0' --midi-out fluid jit --out-chans 8 pitch-bend ref-note 62 steps 1:17:2

In the whole-channel tuning scenario --out-chans can be directly associated with the degree of polyphony.

What Tuning Method Should I Use?

It is completely up to you to set the balance between channel consumption and tuning conflict prevention. The rules of thumb are:

• More advanced tuning features of your synth ⇒ Less channels/conflicts
• Simpler tuning (octave-based, shares some intervals with with 12-EDO) ⇒ Less channels/conflicts
• Less keys to map ⇒ Less channels/conflicts
• More channels ⇒ Less conflicts
• Less conflicts ⇒ Better polyphony

Tips:

• Prefer aot/jit full over aot/jit octave.
• Prefer aot/jit octave over aot/jit channel.
• Prefer aot/jit channel over aot/jit pitch-bend.
• When aot full/octave allocates more than 3 channels: Consider using jit with --out-chans=3.
• But before: Check if excluding keys (ref-note --lo-key/--up-key/--key-map / YAML scale) is an option.
• You only benefit from jit if you select less channels than aot would use.
• aot channel/pitch-bend works well for n-EDOs where gcd(n, 12) is large.
• aot channel/pitch-bend can work for ED1900cents (quasi-EDTs) e.g. steps 1:13:1900c.
• jit will always work in some way. Configure your polyphony options with the --out-chans and --clash parameters.

Scala File Format

An alternative tuning method, mostly on software-based synthesizers, is to upload an scl and kbm file to your synthesizer.

Create scl Files / Scale Expressions

The Scala scale file format defines a scale in terms of relative pitches. It does not reveal any information about the root pitch of a scale.

• Equal temperament bash tune scl steps --help # Print help for the `steps` subcommand 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 bash tune scl rank2 --help # Print help for the `rank2` subcommand 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 bash tune scl harm --help # Print help for the `harm` subcommand tune scl harm 8 # 8:9:10:11:12:13:14:15:16 scale tune scl harm --sub 8 # ¹/₁₆:¹/₁₅:¹/₁₄:¹/₁₃:¹/₁₂:¹/₁₁:¹/₁₀:¹/₉:¹/₈ scale

• Imported scale bash tune scl import --help # Print help for the `import` subcommand tune scl import my_scale.scl # Import my_scale.scl

• Name the scale bash tune scl --name "Just intonation" steps 9/8 5/4 4/3 3/2 5/3 15/8 2

• Write the scale to a file bash tune --of edo-22.scl scl steps 1:22:2

Steps Syntax

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

Create kbm Files / Keyboard Mapping Expressions

Keyboard mappings specify the roots and reference pitches of microtonal scales. In addition, the format defines a mapping between (physical) keys and the scale degree to use for the given key. If no such mapping is provided a linear mapping is used as a default.

• Print help for the kbm subcommand bash tune kbm ref-note --help

• Start scale at C4 at its usual frequency bash tune kbm ref-note 60

• Start scale at C4, 20 cents higher than usual bash tune kbm ref-note 60+20c

• Start scale at A4 at 450 Hz bash tune kbm ref-note 69@450Hz

• Start scale at C4, A4 should sound at 450 Hz bash tune kbm ref-note 69@450Hz --root 60

• Start scale at C4, use D4 as a reference note, white keys only bash tune kbm ref-note 62 --root 60 --key-map 0,x,1,x,2,3,x,4,x,5,x,6 --octave 7

• Write the keyboard mapping to a file bash tune --of root-at-d4.kbm kbm ref-note 62

Tuning Analysis

Approximate Ratios

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

bash dump ref-note 62 --lo-key 61 --up-key 71 steps 1:19:2

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-------- 61 | IDX -1 | 2/1 -63¢ -1o ‖ 283.145 Hz ‖ 61 | C#/Db 4 | +36.842¢

62 | IDX 0 | 1/1 +0¢ +0o ‖ 293.665 Hz ‖ 62 | D 4 | +0.000¢ 63 | IDX 1 | 1/1 +63¢ +0o ‖ 304.576 Hz ‖ 63 | D#/Eb 4 | -36.842¢ 64 | IDX 2 | 12/11 -24¢ +0o ‖ 315.892 Hz ‖ 63 | D#/Eb 4 | +26.316¢ 65 | IDX 3 | 10/9 +7¢ +0o ‖ 327.629 Hz ‖ 64 | E 4 | -10.526¢ 66 | IDX 4 | 7/6 -14¢ +0o ‖ 339.803 Hz ‖ 65 | F 4 | -47.368¢ 67 | IDX 5 | 6/5 +0¢ +0o ‖ 352.428 Hz ‖ 65 | F 4 | +15.789¢ 68 | IDX 6 | 5/4 -7¢ +0o ‖ 365.522 Hz ‖ 66 | F#/Gb 4 | -21.053¢ 69 | IDX 7 | 9/7 +7¢ +0o ‖ 379.103 Hz ‖ 66 | F#/Gb 4 | +42.105¢ 70 | IDX 8 | 4/3 +7¢ +0o ‖ 393.189 Hz ‖ 67 | G 4 | +5.263¢ ```

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 generator 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:

bash tune scale ref-note 62 --lo-key 61 --up-key 71 rank2 1:4:5 5 1 | tune diff stdin ref-note 62 steps 1:31:2

This will print:

``` ----------Source Scale----------- ‖ ----Pitch----- ‖ --------Target Scale-------- 61 | IDX -1 | 11/6 +34¢ -1o ‖ 274.457 Hz ‖ 59 | IDX -3 | -0.979¢

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¢ 70 | IDX 8 | 9/8 -11¢ +1o ‖ 656.654 Hz ‖ 98 | IDX 36 | -0.392¢ ```

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.

Equal-Step Tuning Analysis

The tune est command prints basic information about any equal-step tuning.

Example output of tune est 1:19:2:

``` ==== Properties of 19-EDO ====

-- Patent val (13-limit) -- val: <19, 30, 44, 53, 66, 70| errors (absolute): [-0.0c, -7.2c, -7.4c, -21.5c, +17.1c, -19.5c] errors (relative): [-0.0%, -11.4%, -11.7%, -34.0%, +27.1%, -30.8%] TE simple badness: 35.440‰ subgroup: 2.3.5.7.11.13

• supports meantone temperament
• tempers out 3-limit 1162261467/1073741824 (Pythagorean-19 comma)
• tempers out 5-limit 81/80 (syntonic comma, Didymus comma)
• tempers out 5-limit 3125/3072 (small diesis, magic comma)
• tempers out 5-limit 6561/6400 (Mathieu superdiesis)
• tempers out 5-limit 15625/15552 (kleisma, semicomma majeur)
• tempers out 5-limit 16875/16384 (double augmentation diesis, Negri comma)
• tempers out 5-limit 78732/78125 (medium semicomma, Sensi comma)
• tempers out 5-limit 1594323/1562500 (Unicorn comma)
• tempers out 5-limit 48828125/47775744 (Sycamore comma)
• tempers out 5-limit 1224440064/1220703125 (parakleisma)
• tempers out 5-limit 19073486328125/19042491875328 ('19-tone' comma)
• tempers out 7-limit 49/48 (slendro diesis, septimal 1/6-tone)
• tempers out 7-limit 126/125 (septimal semicomma, Starling comma)
• tempers out 7-limit 225/224 (septimal kleisma)
• tempers out 7-limit 245/243 (minor BP diesis, Sensamagic comma)
• tempers out 7-limit 525/512 (Avicenna enharmonic diesis)
• tempers out 7-limit 686/675 (senga)
• tempers out 7-limit 875/864 (keema)
• tempers out 7-limit 1029/1000 (keega)
• tempers out 7-limit 3136/3125 (middle second comma)
• tempers out 7-limit 4375/4374 (ragisma)
• tempers out 7-limit 10976/10935 (hemimage)
• tempers out 7-limit 19683/19600 (cataharry comma)
• tempers out 7-limit 59049/57344 (Harrison's comma)
• tempers out 11-limit 45/44 (1/5-tone)
• tempers out 11-limit 56/55 (undecimal diesis, konbini comma)
• tempers out 11-limit 100/99 (Ptolemy's comma)
• tempers out 11-limit 385/384 (undecimal kleisma, Keemun comma)
• tempers out 11-limit 540/539 (Swets' comma)
• tempers out 11-limit 729/704 (undecimal major diesis)
• tempers out 11-limit 896/891 (undecimal semicomma, pentacircle)
• tempers out 11-limit 26411/26244 (mechanism comma)
• tempers out 11-limit 65536/65219 (orgonisma)
• tempers out 13-limit 65/64 (13th-partial chroma)
• tempers out 13-limit 78/77 (tridecimal minor third comma)
• tempers out 13-limit 91/90 (medium tridecimal comma, superleap)
• tempers out 13-limit 105/104 (small tridecimal comma)
• tempers out 13-limit 144/143 (Grossma)
• tempers out 13-limit 169/168 (Schulter's comma)
• tempers out 13-limit 196/195 (mynucuma)
• tempers out 13-limit 325/324 (marveltwin)
• tempers out 13-limit 351/350 (ratwolf comma)
• tempers out 13-limit 676/675 (island comma)
• tempers out 13-limit 729/728 (squbema)
• tempers out 13-limit 1001/1000 (fairytale comma)
• tempers out 13-limit 1053/1024 (tridecimal major diesis)
• tempers out 13-limit 2080/2079 (ibnsinma)
• tempers out 13-limit 10985/10976 (cantonisma)

Tempered vs. patent location of 7/6: 4 vs. 4 Tempered vs. patent location of 6/5: 5 vs. 5 Tempered vs. patent location of 5/4: 6 vs. 6 Tempered vs. patent location of 4/3: 8 vs. 8 Tempered vs. patent location of 3/2: 11 vs. 11 Tempered vs. patent location of 7/4: 15 vs. 15 Tempered vs. patent location of 2/1: 19 vs. 19

== Meantone notation ==

-- Step sizes -- Number of cycles: 1 1 primary step = 3 EDO steps 1 secondary step = 2 EDO steps 1 sharp (# or -) = 1 EDO steps (diatonic)

-- Scale steps -- 0. D 1. D# 2. Eb 3. E 4. E#/Fb 5. F 6. F# 7. Gb 8. G 9. G# 10. Ab 11. A 12. A# 13. Bb 14. B 15. B#/Cb 16. C 17. C# 18. Db

-- Keyboard layout -- 11 14 17 1 4 7 10 13 16 0 13 16 0 3 6 9 12 15 18 2 15 18 2 5 8 11 14 17 1 4 17 1 4 7 10 13 16 0 3 6 0 3 6 9 12 15 18 2 5 8 2 5 8 11 14 17 1 4 7 10 4 7 10 13 16 0 3 6 9 12 6 9 12 15 18 2 5 8 11 14 8 11 14 17 1 4 7 10 13 16 10 13 16 0 3 6 9 12 15 18 ```

YAML Output

tune uses YAML as an explicit scale format. You can use tune's output as an input for an external application or the other way around. It is possible to export a scale first, then modify it and, finally use it as in input parameter for another tune command.

Example Usage

bash tune scale ref-note 62 --lo-key 61 --up-key 64 steps 1:7:2 Output

```yml

Scale: rootkeymidinumber: 62 rootpitchinhz: 293.6647679174076 items: - keymidinumber: 61 pitchinhz: 265.9791296633641 - keymidinumber: 62 pitchinhz: 293.6647679174076 - keymidinumber: 63 pitchinhz: 324.23219079306349 ```