Text2Music is a machine-readable notation system for writing music in (tempered) just intonation.
It supports bare ratios, edo steps, Color notation, Ups-and-Downs notation, pergen notation and HEWMP notation. (The last acronym stands for Helmholtz / Ellis / Wolf / Monzo / Pakkanen).
You can use Text2Music with minimal knowledge of music theory by writing melodies using fractional numbers.
1/1 5/4 3/2 2/1Note frequency is initialized to 440Hz and each ratio multiplies it. Here's the same melody spelled using frequencies.
BF:0
440Hz 550Hz 660Hz 880HzOr as moving ratios that multiply together as we go along.
~1/1 ~5/4 ~6/5 ~4/3Plain ratios use the last moved ratio as the base so use absolute ratios if you want to use the initial base frequency. (Denominators of one can be dropped 2 simply means 2/1).
@1 @5/4 @3/2 @2The project is still in beta so you will have to clone this repository and install manually. I recommend setting up a virtualenv and installing the package as editable.
pip install -e .python -m hewmp.parser examples/giant_steps.hewmp /tmp/giant_steps.midThe Giant Steps example is mostly written in relative intervals. If you wish to read it in absolute pitches use the --absolute command line argument.
python -m hewmp.parser examples/giant_steps.hewmp --absoluteThe Minuet example is written in 3-limit intervals. If you wish to read it in fractional numbers use the --fractional command line argument.
python -m hewmp.parser examples/minuet.hewmp --fractionalTo verify that the diaschismic comma pump example indeed works as intended you can display the cent values with the --cents command line argument.
python -m hewmp.parser examples/diaschismic_comma_pump.hewmp --centsYou should see 0.0c or something very close to zero like 6.15e-12c even towards the end of the piece.
If you're wondering about the composition of the fractions you can use the --monzo command line argument.
echo "P1U M6% va4" | python -m hewmp.parser --monzoBy default the HEWMP parser outputs JSON to the standard output. The format is still under development for easy integration with custom software synths.
To cause the pitch to fall use fractions smaller than one.
1 ~3/4 ~4/5 ~5/6or place a minus sign before the interval (this makes more sense if you think in terms of cents).
1 ~-4/3 ~-5/4 ~-6/5Note duration is specified using square brackets [, ] after a note. The default duration is [1] (one beat).
1/1[2] 6/5 3/2 9/5 2/1[2]Anything after a $ sign is ignored until a newline is reached.
$ This is a comment
1 3/2 $ This another comment after two notes that playTo advance time without playing a note use the rest symbol ..
1 . 5/4 3/2Rests can be chained so .. lasts twice as long as a single rest.
To extend the duration of the last played note (or rest) by one use the pedal symbol !. You can think of it as a loud rest that doesn't cut off the sound. To specify how much to extend the duration use ! followed by a number inside square brackets.
1 ! 6/5 3/2 $ The root note lasts twice as long as the other two
1[!1] 6/5 3/2 $ The samePedals chain so !! extends duration by two. Pedals also chain with rests so 1 !... is a note of duration two followed by a rest of duration three.
Pedal has a special property that allows it to cross tuplet boundaries.
1 (! 3/2) $ A dotted quarter note followed by an eight noteWarning: When inserted after a tuplet the pedal applies to every note inside the tuplet. This makes it easier to work with chords. (1 3/2) ! is a kind of arpeggiate and hold instead of an eight note followed by a quarter note.
Use T! if you want a tie that only affects the last note of the tuplet.
(1 3/2) T! $ An eight note followed by a quarter noteTo only extend the playing duration of the last played note use the soft pedal symbol ?.
1 ?? 5/4 3/2 $ The root note rings throughout the whole arpeggio
1[?2] 5/4 3/2 $ The sameSoft pedal chains with plain pedals so 1 !? is a note of duration three that takes up two units of time.
Soft pedals can leak out of tuplets.
(1 3/2 ??) . $ An eight note followed by a dotted quarter noteTo repeat the last note or tuplet (useful with chords) use %. The pitch(es) will be the same but duration is reset to one.
$ Repeats are not literal so these are the same note
~3/2[2] %Repeats chain with ! so %! is the last note but of duration 2.
Repeats skip over rests.
77/62 $ Something complicated
.%..%!!.%%.% $ Cool rhythm without having to spell it out every timeBarlines | can be used to visually organize your music. They have no effect on the sound.
1[4] | 5/4[2] 3/2[2] | 15/8 2/1[3] ||A section can be repeated by placing it between |: and :|. An optional x can be attached onto :| to specify the number of repeats other than the default two. This means that x1 has no effect and x0 effectively removes the section.
$ Section repeats are literal so the following is an ascending sequence of seven notes
|: ~9/8 :|x7You can place a playhead symbol |> to skip all music written before it. Use a playstop symbol >| to ignore everything after it.
$ This is skipped but the effect of going up an octave is preserved
1 ~2
$ This section is played
|> 2/3 3/4 >|
$ This section is ignored
~2 1To play a note across a barline use pedal extension.
1/1[2] 5/4[2]|[!4] | 3/2 2/1 1/1[2] ||To play a note relative to the previous one and remember it use ~. This can be used to play local scales by using moving intervals for root motion.
$ ii arpeggio
~9/8 6/5 3/2 |
$ V arpeggio
~4/3 5/4 3/2 |
$ I arpeggio
~2/3 5/4 3/2 |
2[3] ||Using @ before an interval measures the pitch from the base frequency.
$ Go up
~9/8 ~9/8 ~9/8
$ Reset back to 440Hz and go to 660Hz
@1 @3/2
$ Go up from there
~9/8 ~9/8 ~9/8You can add an octave to an interval by prefixing it with c.
1 3/2 c5/4You can subtract an octave from an interval by prefixing it with `.
1 3/2 `5/4The base notation system of HEWMP and Ups-and-Downs is Pythagorean i.e. 3-limit just intonation i.e. fractions built from powers of 2 and 3. The absolute pitches form a chain of fifths.
$ A chain of fifths (3/2) around the base note A4
F2 C3 G3 D4 A4 E5 B5
...
$ The same spelled using fractions
@16/81 @8/27 @4/9 @2/3 @1 @3/2 @9/4Adding one to the number after an absolute pitch raises it by an octave.
$ Three A notes in octaves
A4 A5 A6
$ The same
@1 @2 @4From the basic pitches we can derive the basic set of intervals P1, m2, M2, m3, M3, P4, d5, a4, P5, m6, M6, m7 and M7.
$ Perfect unison
C4 C4
C4 P1
$ Major second
C4 D4
C4 M2
$ Major third
C4 E4
C4 M3
$ Perfect fourth
C4 F4
C4 P4
$ Perfect fifth
C4 G4
C4 P5
$ Major sixth
C4 A4
C4 M6
$ Major seventh
C4 B4
C4 M7
$ Perfect octave (same as cP1)
C4 C5
C4 P8
$ Minor seventh
D4 C5
D4 m7
$ Minor sixth
E4 C5
E4 m6
$ Minor third
A4 C5
A4 m3
$ Minor second
B4 C5
B4 m2
$ Augmented fourth
F4 B4
F4 a4
$ Diminished fifth
B3 F4
B3 d5Remember that in just intonation the augmented fourth 729/512 is different from the diminished fifth 1024/729.
An absolute pitch can be raised by a fraction of 2187/2048 (approximately 113.685c) by appending a sharp sign # to either side of the octave (spelled as a hash to remain within ASCII). Unicode ♯ is also supported.
A4 A4# A♯4To raise the pitch by double the amount use a double sharp sign x (spelled as a lowercase 'ex' to remain within ASCII). Unicode 𝄪 is also supported.
A4 A4x A𝄪4To lower the pitch by 2187/2048 append a flat sign b (spelled as a lowercase 'bee'). Unicode ♭ is also supported. The double-flat 𝄫 works as expected.
A4 A4b A♭4 A𝄫4You can stack any number of #, x or b to modify the pitch further.
A4 A4bbIf the base interval is perfect P or major M an augmented version is wider by a fraction of 2187/2048.
P1 a1If the base interval is perfect P or minor m a diminished version is narrower by a fraction of 2187/2048. This can create paradoxical intervals that go down in pitch.
P1 d1Augmented a and diminished d stack.
P1 dd1 aaa1An assortment of intervals between minor and major are also supported. N3 is exactly half the cents of P5.
N2 N3 N6 N7Warning: Not all edos support dividing the fifth in half and this can result in half-edosteps.
Stacking neutral intervals eventually produces half-diminished and half-augmented intervals.
ha1 hd4 ha4 hd5 ha5 hd8The accidentals t and d act as quarter-tone sharp and flat respectively. The associated semi-fraction is 27/32·√1½ the square root of a sharp.
C4 E4d G4 B4d $ Neutral 7th arpeggioMelodic information can be conveyed in a higher-prime agnostic manner by splitting the octave and/or some three limit interval. As we have already seen the split fifth P5/2 is N3. The split octave P8/2 is va4 or ^d5. The split fourth P4/2 is >M2 or <m3. Splitting the fourth can also be achieved by combining neutralish intervals with the ^ arrow as ^hd3 or vha2. The meaning of the arrows ^, v, > and < placed before the interval or pitch is dynamic and often only affects primes 2 and 3. Some temperaments automatically set these arrows for pergen notation. See temperaments for more information.
Equal temperament mode is activated by specifying the number of divisions of the octave with ET:. Using the arrows ^ and v before the interval or pitch raises or lowers the pitch by one edo step.
ET:31
D4 vF4 G4 B4
C4 M3 P5 ^m7 P8See equal temperaments for more information.
To spell intervals beyond the 3-limit HEWMP uses small adjustements defined by prime factors and their exponents. For example 5/4 is spelled M3- (a flat major third), 7/4 is spelled m7< (a flat minor seventh) and 11/8 is spelled P4^ (a sharp perfect fourth). There's a pair of arrows corresponding to every prime up to 31 (ordered by size in cents bellow).
| lower | raise | prime | 2,3,5,7,11,13,17,19,23,29,31-monzo | ratio | cents |
|---|---|---|---|---|---|
| V | A | 19 | [-9 3 0 0 0 0 0 1 0 0 0> | 513/512 | 3.37802 |
| % | * | 17 | [-12 5 0 0 0 0 1 0 0 0 0> | 4131/4096 | 14.73041 |
| n | u | 23 | [5 -6 0 0 0 0 0 0 1 0 0> | 736/729 | 16.54434 |
| - | + | 5 | [-4 4 -1 0 0 0 0 0 0 0 0> | 81/80 | 21.50629 |
| ! | i | 13 | [9 -8 0 0 0 1 0 0 0 0 0> | 6656/6561 | 24.88765 |
| < | > | 7 | [6 -2 0 -1 0 0 0 0 0 0 0> | 64/63 | 27.26409 |
| D | U | 29 | [-8 2 0 0 0 0 0 0 0 1 0> | 261/256 | 33.48720 |
| v | ^ | 11 | [-5 1 0 0 1 0 0 0 0 0 0> | 33/32 | 53.27294 |
| W | M | 31 | [5 0 0 0 0 0 0 0 0 0 -1> | 32/31 | 54.96443 |
The vectors associated with the primes 5, 7 and 11 follow Joe Monzo's original proposition.
The monzo for i and ! was particularly chosen so that the barbados third 13/10 is spelled M3i+. This in turn makes it possible to write the barbados terrad 10:13:15 as =Mi+ using the chord system (pronounced "major island" see Pronunciation for details).
The inflections are supposed to resemble arrows pointing in opposite directions while the U and D pair bring to mind the words up and down.
If you're not satisfied with the default choices you can define your own inflections with the config I followed by an arrow.
$ Consistent with hewm-53 up to prime 31
Ii:27/26
I*:18/17
IA:19/18
Iu:24/23
13/8 M6! $ Now a major sixth (default a5i)
17/16 M2% $ Now a major second (default m2*)
19/16 M2A $ Now a major second (default m3A)
23/16 P5n $ Now a perfect fifth (default a4u)Color intervals such as y3 for 5/4 are supported. Absolute intervals are made using color commas.
A4 ryC5 $ Jump from wa A4 to ruyo C5
A4 C5&r1&y1 $ The same, but with explicit commas using transpositions
A4 sry3 $ The same, but using color intervals (r1&y1 is sry1)
A4 sryIII $ The same, but using color intervals with roman numeralsFor more details see Color Notation in the Xenharmonic Wiki.
The functionality of the Color Chord system is mostly implemented, but due to limitations of this beta the spelling has been changed. Root note octave and the chord token = is mandatory. Instead of , use + for added tones. Instead of () use \ for replacements. Color Chords are in root position by default.
C4=y $ C yo chord; Cy in the original system.
D4=w\y5 $ D wa yo-5 chord; Dw(y5) in the original.
E4=r+ry4no5 $ E ru ruyo-4 no 5 chord; Er,ry4no5 in the original.If you want to see how a certain fraction is spelled use the notation module.
$ python -m hewmp.notation 5/3
M6-
$ python -m hewmp.notation 5/3 --absolute
F5#-
$ python -m hewmp.notation 5/3 --color
y6Text2Music has multiple ways of specifying groups of notes that sound together.
Use : to spell out chords as extended ratios. The first number is always at the current pitch.
M2=10:12:15 $ ii
P5=4:3:5 $ V
P1=4:5:6:8 $ I
4:5:6 $ The '=' sign is optional if you don't want the pitch to changeWhere otonal chords are composed of members of the harmonic series, utonal chords by contrast are composed of subharmonics and spelled using ;.
$ A minor chord written using utonal syntax
6;5;4
$ The same but using fractions and otonal syntax
1/6:1/5:1/4
$ The same but common factors expanded
10:12:15HEWMP comes with a chord system that applies inflections and pergen arrows to chord tones
$ Major seventh chord with syntonic inflections on the major third and the major seventh
=M7-
$ Same as
8:10:12:15
$ Semaphoric sus chord (meaning depends on the temperament)
=<m $ Same as P1,P4/2,P5See Chord Documentation for more.
Some chords like =pinkan for 10:13:15:19 only have one version and do not support inflections.
Tones can be added to the chord symbols that support inflections.
$ Major seventh chord with an added perfect fourth
=M7-add4Added tones can also be inflected.
$ Interpreting the harmonic segment 6:7:8:9:10 as a septimal minor chord with added tones
=m<add4add6-The third of a chord can be substituted for chords that support inflections.
$ Major seventh chord with the major third replaced by a major second
=M7-sus2Tones can also be removed.
$ Major ninth chord without the fifth
=M9-no5$ Minor seventh chord with syntonic inflections
P1,m3+,P5,m7+
$ Same as
=m7+
$ or
10:12:15:18Chords spelled in otonal, utonal or symbolic style can be inverted using _. A three note chord has three inversions _0 root position, _1 first inversion and _2 second inversion. Chords with four notes have four inversions and so on.
D4=m7+ $ ii
G4=7-_2 $ V7 in second inversion
C4=M-add8 $ I with an octave on topMore complex voicings are created by specifying the order of the chord tones 1 through 7 come in relation to the root R.
D4=m7+_5R573 $ ii with a fifth bellow the root, another fifth above the root,
$ a seventh above that and a third on the next octave.
G4=dom-_57R3 $ V7 with a pythagorean m7 in second inversion
C4=M-_R351 $ I with an octave on topDuration can be attached to otonal, utonal and symbolic chords. Comma-separated pitches need to be wrapped in parenthesis.
6;5;4[1/2]
=sus4[1/2]
(P1,P5)[2]The comma operator , is actually a time rewind operator that goes back to the start of the last note played so that multiple notes can be specified to play at the same time. Multiple , stack and move back by the same amount of time on each usage.
To rewind time to a specific beat use the @ symbol followed by a number inside square brackets [, ].
You can also use @T followed by a number.
Parenthesis (, ) are actually used to define tuplets. Anything placed inside parenthesis will have total duration of one.
$ Steady pedal tone
@T0 1 1 1 1 | 1 1 1 1 ||
$ Funky second voice
@T0 ~3/2 (. 1) 1 (. 1) | (1 1 1)[2] 1 1 ||A bare soft pedal ? inside square brackets extends the durations of notes inside the tuplets so that they end at the same time.
(1 5/4 3/2 15/8)[?] $ All notes of the tetrad hold until the end.
(1 5/4 3/2 15/8)[? !3] $ Notes arpeggiate within one beat of time and
$ hold together for 3 additional beats.To specify a timestamp use T. To jump to the timestamp use @T. The default behaviour is to jump to the beginning of the song.
$ First section soprano voice
(. C5) B4 (. A4) G4 |
$ First section alto voice
@T C4 D4 E4 E4 |
T $ Mark the beginning of the second section
$$$$ Second section soprano voice
(. E5) (. C5) (. F4) C5 |
@T $ Jump to the beginning of the second section
$$$$ Second section alto voice
F4 C4 A4 ! |
$ Final section soprano
T (. G4) (. B4) C5 ! ||
$ Final section alto
@T E4 ! C4 ! ||You can have multiple tracks in your HEWMP score by separating them with --- (three dashes). The first track is used to define the global config and it should be left without any music when using multiple tracks.
$ Global config
ET:19 $ Use 19ed2 as the global tuning
Q:1/4=200 $ Use 200bpm as the global tempo
---
$ Chords
MP:4 $ Reserve four MIDI channels
L:1/1 $ Play full bars
~-P8[0] $ Play in the alto register
~M2=m7+ | ~P4=dom-_2 | ~-P5=M7- | =M- ||
---
$ Melody
MP:1 $ Reserve one MIDI channel
L:1/4 $ Play quarter notes
~M2 m7+ M6- P5 | ~P4 -M2 M3- -P4 | ~-P5 M7- M3- P4 | P5 M3- P1[2] ||
---
$ Drums
N:percussion $ Use percussion notation and MIDI channel 10
MP:0 $ Don't reserve pitched channels
L:1/4 $ Play quarter notes
k h s k,h | k h s k,o | k,h h s k,h | k,c h s . ||Configuration is usually placed near the top of the score and consists of various shorthands in capital letters followed by a colon.
Use the config BF: to define what frequency is used for @P1 and A4. Everything else is calculated in reference to this base pitch. Default is 440Hz.
BF:432 $ Now we're vibingUse the config BN: to change what absolute pitch has the same frequency as @P1. Default is A4.
BN:C4 $ Start from C=440HzUse Q: to define how many beats there are in a minute and what constitutes a beat of tempo. Default is 1/4=120.
Q:1/4=220 $ Quarter notes at 220bpmUse L: to define the duration of one beat on the grid. This is compared to the duration of a beat of tempo to calculate the real duration of a beat. Default is 1/4.
L:1/8 $ Duration of [1] corresponds to an eight noteUse G: to define a non-uniform relative duration for beats on the grid. Default is 1/4=1 1 (straight).
G:1/4=2 1 $ Every span of a quarter note is played in triplet swingUse V: to define the volume of a track. Default is 1.0.
V:0.5 $ Half as loudUse N: to change what notes mean. Used for writing percussion and switching to a non-Pythagorean spine. Default is hewmp.
N:percussionPercussion notation uses shorthands for drums. Here are some basics.
| shorthand | name | notes |
|---|---|---|
| k | Acoustic Bass Drum | "kick" |
| s | Acoustic Snare | |
| h | Closed Hi-hat | |
| o | Open Hi-hat | |
| r | Ride Cymbal 1 | |
| c | Crash Cymbal 1 | |
| t5 | High Tom | |
| t4 | Hi-Mid Tom | |
| t3 | Low-Mid Tom | |
| t2 | Low Tom | |
| t1 | High Floor Tom | |
| t0 | Low Floor Tom |
See percussion for the full list.
Every percussion shorthand has a one letter alternative that chains with rests for concise notation.
N:percussion
L:1/16
$ 3 against 4 against 5 polymeter
T h..h..h..h..h..h..h..h..h..h..h..h..h..h..h..h..h..h..h..h..h
@T s...s...s...s...s...s...s...s...s...s...s...s...s...s...s...s
@T k....k....k....k....k....k....k....k....k....k....k....k....kN:percussion
L:1/1
$ 3 against 4 against 5 polyrhythm
T (k k k)(k k k)(k k k)(k k k)
@T (ss ss)(ss ss)(ss ss)(ss ss)
@T (hhhhh)(hhhhh)(hhhhh)(hhhhh)
$ Same but in a time box to see how everything aligns
T (k...................k...................k...................)
@T (s..............s..............s..............s..............)
@T (h...........h...........h...........h...........h...........)Warning: Some two letter names look like chains. hc is one Hand Clap instead of a Closed Hi-hat followed by Crash Cymbal 1. Only use chaining for patterns longer than three beats to be safe.
To disable two letter names altogether use N:percussion!.
N:percussion!
hc $ Hi-hat followed by a crash cymbalYou can even try "speaking" in percussion as most letters correspond to a sound and most unrecognized letters are skipped. Reserved letters such as T, p or f cannot start a chain.
N:percussion!
You are now speaking in Percussion!Use I: to select an instrument. If the name corresponds to General MIDI the matching program is selected as well.
I:MarimbaSee instruments for the full list.
Text2Music uses per-channel pitch-bends to achieve microtones. Use MP: to reserve some of the available 15 channels for the current track.
MP:2The main reason HEWMP notation is based on relative intervals is to be able to write comma pumps of arbitrary length in just intonation with a finite number of symbols.
$ I-vi-ii-V chord progression that pumps the syntonic comma downwards.
$ (The product of the fractions is 80/81)
|: ~2/3=M- ~5/6=m+ ~4/3=m+ ~4/3=M-_2 :|x12Using a comma-list CL: you can temper out a set of commas so that the pitch doesn't change when pumping said commas. Text2Music accomplishes this by slightly altering the pitch mapping of the primes in the subgroup given by SG:.
SG:2.3.5
CL:81/80,128/125
$ I-vi-ii-V chord progression that pumps the syntonic comma,
$ but the overall pitch doesn't change.
|: ~2/3=M- ~5/6=m+ ~4/3=m+ ~4/3=M-_2 :|x4
$ Chord progression that pumps the diesis without changing the overall pitch.
|: ~1/2=M- ~5/4=M- ~5/4=M-_2 ~5/4=7-_3 :|x4When using a comma list a prime subgroup is automatically selected, but to make full use of Text2Music's tuning capabilities you need to tell it which mappings of primes should be affected by using fractions like 2.3.13/5 or multiples of primes like 2.15.7.
SG:2.3.13/5By default the correct subgroup is inferred from the comma list.
Text2Music comes with a few named presets so that you don't have to type out specific subgroups and comma lists.
$ Same as SG:2.3.5 and CL:250/243
T:porcupine
$ Chord progression that pumps the porcupine comma
|: ~5/3=6:4:5 ~2/3=3:4:5 ~5/3=6:4:5 ~2/3=6:5:4 ~5/6=3:4:5 :|See additional documentation for a list of temperaments.
Not all possible temperaments support pergen notation out of the box so you need to figure out the correct enharmonics yourself.
E:^^^d2 $ Specify what ^ and v mean using a vanishing enharmonic interval
E:<<<m2 $ Specify what > and < mean
P8/3 vM3 $ The v arrow can now be used to spell the third-octave
P5/3 >M2 $ The > arrow can now be used to spell the third-fifthThe tuning algorithm tries to do the least amount of damage to just intonation when tempering out commas, but sometimes you may wish to preserve certain intervals while allowing others to take more of the damage.
T:meantone
$ Specify quarter-comma meantone by constraining
$ octaves to be pure and major thirds to be just
C:P8,M3-Color Temperament Names are supported.
T:Thotho
$ Pergen notation for a 10 note scale (higher prime agnostic)
P1|^P1 |M2 |vM3 |M3 |vP5 |P5 |vM6 |M6 |^M6 |P8|
$ Same but using fractions (explicit higher primes)
1 |27/26 |9/8|39/32 |81/64|13/9|3/2|13/8 |27/16|52/27 |2 |
$ Pergen notation expanded using an explicit half-octave period
P1|P5&-P8/2|M2 |M6&-P8/2|M3 |P8/2|P5 |M2&P8/2|M6 |M3&P8/2|P8|
$ The same but slightly more obscure
P1|M2/2 |M2 |a4/2 |M3 |P8/2|P5 |M10/2 |M6 |a12/2 |P8|Multiple color commas are separated by &.
T:Trigu & Latrizo
$ The octave is split into three equal parts
P1 ~vM3 ~vM3 ~vM3 ~-P8
...
$ The fifth is also split in three. Remeber that
$ lifts and drops are > and < instead of / and \
P1 ~>M2 ~>M2 ~>M2 ~-P5Use command line tools to convert color temperament commas to fractions
$ python -m hewmp.color Thotho
169/162While it is possible to produce an equal temperament without affecting every prime (e.g. T:compton is 12edo that only affects 2 and 3) there's the option to round every prime to the closest number of steps of an equal temperement with ET:. You can use Wart Notation to specify non-standard rounding. To specify another interval to divide besides the default 2 use ED and a number after the number of divisions and the warts.
ET:13b $ 13edo with a flat fifth to make it compatible with Ups and Downs notationET:13ED3 $ Bohlen-Pierce scaleSome equal temperaments have special names: Wendy Carlos' alpha, beta, gamma, delta and Bohlen-Pierce (BP).
It can be fun to spell melodies and harmonies in just intonation even when using ET: as it allows you to untemper the music afterwards
Warning: Large errors in the ET mapping for the prime numbers tend to compound and produce big surprises in how the music sounds compared to its spelling.
Not all possible Xenharmonic music fits into the heptatonic fifth generated mold of the Pythagorean basis of pergen notation. To make music that falls into the gaps you need to change the whole notation. This is done with the spine S: config. The default notation is technically S:2 3 7 and N:lambda is S:3 7 9 but the octaves don't start from the first letter of the alphabet. S: takes five arguments, the period, the generator, number of nominals, (optional) how many generators up the default scale should go (default is half the number of nominals rounded down) and (optional) reference octave (default 5). As a result pitches such as A6 or H5 change meaning as do intervals like P2 or M4. The period and generator are always the perfect intervals.
Up to 14 unique nominals are available in this order: A, B, C, D, E, F, G, H, J, K, O, Q, R, S. Neutral and half-augmented/diminished intervals are also automatically calculated.
CL:176/175 $ Valinorsma aka. Lorubigu
SG:2.5.11/7 $ No-threes, only 11/7
S:4 5 7 6 $ Period 4/1, generator 5/1, 7 notes, 6 gens up
L:1/8
|: ~-M3 (~P2 ~P2 ~P2) :|x4
A6 (G5 F5) | (E5 D5) (C5 B5 A5) |
G4 A5 | A6[2] ||To display information about a spine use the command line tools.
$ python -m hewmp.spine 4 5 7 --up 6In WebAudio the simplest way to produce sound is using oscillators. To set the oscillator waveform use the WF: config. Available values are sine, triangle, square, sawtooth and an assortment of custom timbres if you're playing on lumipakkanen.com/text2music/ . As of writing this documentation those options are warm1, warm2, warm3, warm4, octaver, brightness, harmonicbell, semisine, template, theta1, theta2, theta3, theta4, theta5, oddtheta1, oddtheta2, oddtheta3, oddtheta4 and oddtheta5.
You can also use space separated numbers to directly set the sine components of the PeriodicWave. If you want to set the cosine components as well use a semicolon ; to separate the two lists. The peak amplitude is normalized to 1. This config has no effect on MIDI output.
WF:0 100 50 0 10 0 0 30 5 0 0 20 0 0 10 0 2
MP:4
L:1/1
7:11:14:16
4:7:8:11
11:14:16To set the Attack-Decay-Sustain-Release envelope of the WebAudio oscillator use the ADSR: config. Attack time, decay time and release duration are in milliseconds while the sustain level is a percentage.
$ Attack 300ms, decay 200ms, sustain 80%, release 500ms
ADSR:300 200 80 500
WF:theta1
4/4 ?????
5/4 ????
6/4 ???
7/4 ??
8/4 ?
9/4To enter raw monzos use Mzo:, @Mzo: or ~Mzo: syntax. Not real configs, but this keeps raw monzos from messing with the rest of the syntax.
Mzo:0 $ 1/1
Mzo:-1 1 $ 3/2
Mzo:-2 0 1 $ 5/4
Mzo:-2 0 0 1 $ 7/4
Mzo:-3 0 0 0 1 $ 11/8Various configs that don't take parameters go under flags F:.
T:porcupine
F:CR $ Use comma-reduction to simplify outputSometimes the algorithm fails to find the simplest representation. You can increase CRD: from the default 5 to give the search more resources.
CRD:6To change the velocity of notes played use dynamics pppp, ppp, pp, p, mp, mf, f, ff, fff or ffff.
pp P1 P5 $ Two notes played at 25% of maximum velocityYou can manually specify the fraction of maximum velocity after the dynamic, but here are the defaults.
pppp1/16
ppp1/8
pp.25
p1/3
mp.5
mf2/3
f.75
ff7/8
fff.9
ffff1To change the gate length of notes played use articulations ' (staccato), ; (normale) or _ (tenuto).
' P1 P5 $ Two notes played for 50% of their nominal durationYou can manually specify the gate ratio after the articulation, but here are the defaults.
'.5
;.9
_1Warning: ; and _ can look like utonal chords or chord inversions so the best practice is to only use ' with literal gate ratios.
You can add custom messages to the JSON output by using double quotes ".
P1 "gently" M2The $ character acts as as escape inside double quotes. To enter a double quote use $". To enter a dollar sign use $$.
If you want to specify intervals not affected by tuning use cents.
$ 12ed2 A major scale
0c 200c 400c 500c 700c 900c 1100c 1200cWarning: Not even ET: will affect something specified in raw cents.
If a fraction contains primes larger than the supported 31 it will be converted to cents in the output.
1 37/31Warning: This can cause some surprises when tempering.
Beating of similarly tuned notes is a musical phenomenon that is often perceived as a rhythm instead of a pitch difference. Use Hz to specify a frequency offset. See also Phase Offset.
1,1 . 1,1Hz . 1,2Hz $ Three unisons with different amounts of beatingTo combine two intervals use the & symbol. This is mainly useful for specifying Hz offset alongside a pitch.
1/1 3/2&1HzTransposing also allows you to enter absolute frequencies.
0&123HzThe shorthand to enter cents equal to the current ET: step size is 1\. To specify the number of divisions of 2 add a second number after \. To specify another interval to divide besides 2 append it after a second backslash.
0\ 2\ 7\ 12\ $ Steps 0, 2, 7 and 12 in the current ET
0\19 5\19 10\19 19\19 $ Steps 0, 5, 10 and 19 in 19ed2
0\10\3 5\10\3 $ Steps 0 and 5 in 10ed3To specify fractional pitch monzos append a slash / and the desired root degree.
$ Arpeggiated neutral chord
P1 P5/2 P5 $ Same as P1 N3 P5Warning: Interval roots may produce fractional steps if the relevant components of the ET: mapping are not divisible by the root degree.
To further multiply the fractional pitch monzo append an asterisk * and the desired exponent.
$ Step through equal divisions of the pure fourth
P1 P4/3 P4/3*2 P4Text2Music offers many ways to turn notes and tuplets into more complex rhythmic patterns.
Use a to turn a simultaneous chord into a tuplet.
=m7+[a] $ Minor seventh as a quadruplet arpeggioUse r to reverse the order of the notes.
=m7+[r a] $ Minor seventh arpeggiated downUse R to reverse the temporal information within a pattern
=m7+[a R] $ Minor seventh arpeggiated downYou can build complex patterns for further modeling by concatenating them with + (adds durations) or = (preserves the duration of the first tuplet).
=M- + =m+[a] $ Major followed by minor arpeggiated
=M- = =m+[a] $ Major followed by minor arpeggiated, but twice as fastA pattern can be repeated using x followed by a number inside square brackets. By default this doesn't affect the duration of the tuplet. Use a capital X to stretch the duration accordingly.
=M-[a X4] $ Major chord arpeggiated four times over four beats
P8[x5] $ followed by the root note repeated five times over one beat an octave above.Patterns keep internal time separate from song time. You can equalize those using a ~.
=dom-[a x3 ~] $ Dominant arpeggio that takes up 12 beats because of internal reasonsArrows in different directions shuffle around the logic and rhythm in various ways.
(P1 !! P4 ! P5 P8) ... R[^] ... R[<] ... R[v] ... R[>]TODO: Actually explain what these do.
Text2Music has a few rhythm families that do different things based on how many notes there are in the manipulated pattern.
Some natural rhythms such as bouncing balls can be hard to notate using integer multiples and tuplets alone. This is where the Geometric rhythm family comes in. As the name implies the durations are in a geometric progression. You could also call this the Exponential rhythm family due to the way it sounds, but G is more precise in meaning.
P1[x22 G0.9 10] $ Note played in a bouncing ball rhythm of 22 bounces over 10 beats such that
$ each bounce is 90% of the duration of the last one.An arithmetic progression starts with an initial duration and progressively adds a fixed duration to it. The initial duration is to the left of CA and the fixed duration is to the right. Concatenated arithmetic rhythms align with a grid while geometric rhythms generally do not.
=M-[x2 6CA-1 4] $ Notes of a major chord with relative durations
$ 6, 5, 4, 3, 2 and 1 such that the whole figure takes up 4 beats.Geometric rhythms can get pretty fast pretty quickly to the point that they produce a pitched squeal. Harmonic progressions (1/1, 1/2, 1/3, 1/4, etc.) of durations are more subdued while still producing a good accelerando. In {initial}CH{delta} the durations are calculated as 1/(initial + n*delta) for the nth note in the pattern.
N:percussion
(k h s h)[x8 3CH2 6] $ A drum pattern gettin progressively faster over 6 beats.On the other hand setting the onset times themselves into a harmonic progression produces an extreme ritardando. (The parameters default to 1)
N:percussion
X[x100 H 6] $ Claves in a pattern that resembles a Geiger counter being pulled away from a radioactive sourceThe rhythm families introduced so far produce either accelerating or deccelerating patterns. A sigmoid patterns slows down and speeds up with controls for biasing the onsets towards the beginning or the end and scaling the intensity of the overall effect.
N:percussion
x[x50 10S.1 6] $ Hand claps in a pattern that slows down only to speed up even more towards the endThe Euclidean rhythms are produced in a way analoguous to Euclid's algorithm for finding the greatest common divisor of two numbers and are common in traditional world music. For example two notes in E5 produce a Persian rhythm called Khafif-e-ramal x.x.. while three notes in E8 creates the Cuban tresillo x..x..x.. You can rotate the pattern to the left using numbers on the left side of E. Three notes in 1E8 is x..x.x.. and in 2E8 it is x.x..x...
$ Rhythm section composed of claves, hand claps and wood blocks.
N:percussion
cs[x5 E8 4 X4]
@T hc[x7 E16 4 X4]
@T (W W w w W)[E16 4 X4]See the first few patterns here.
All of the Euclidean rhythms are MOS or Multi-MOS rhythms meaning that they only have gaps of two sizes between onsets. All MOS rhythms can be produced with a period (size of the pattern) and a generator (a fixed distance between two onsets, not necessarily adjacent) that wraps around the period. Multi-MOS patterns are simply repeated MOS patterns. You can specify the period and the generator using PG.
P1[x5 7PG12 4] $ Rhythmic pattern inspired by the layout of the white keys on a pianoThe default period is one and fractional generators are supported.
$ Quartal arpeggio in a rhythm based on the golden ratio
(P1 P4 m7 cm3 cm6)[x11 .618033988749895PG 13]See some patterns with integer parameters here.
| arrow | pronunciation | prime* | notes |
|---|---|---|---|
| + | plus | 1/5 | |
| +2 | plus two | 1/25 | double the effect of a single + |
| - | minus | 5 | |
| -3 | minus three | 125 | triple the effect of a single - |
| > | more | 1/7 | |
| < | less | 7 | |
| ^ | up | 11 | |
| v | down | 1/11 | |
| i | aye | 13 | i+ is pronounced "island", motivated by the various island temperaments |
| ! | lei | 1/13 | !- is pronounced "lake", opposite of an island |
| * | star | 17 | |
| % | holes | 1/17 | think of stars and black holes |
| A | high | 19 | A looks like a big carret ^ with a line across |
| V | low | 1/19 | |
| u | hook | 23 | think "up" |
| n | sinker | 1/23 | looks like an upside down u |
| U | arc | 29 | think "Up" |
| D | bow | 1/29 | think "Down" |
| M | mighty | 1/31 | M looks like two arrows pointing up |
| W | weak | 31 | W looks like two arrows pointing down |
Example cM7-<3A2 "Compound major seventh minus less three high 2" or 987069284145/274877906944.
To control when the beats of two similarly tuned notes occur use a phase offset defined in degrees. You will most likely have to write your own synths to take advantage of this.
(1,1Hz&90deg)[5]Warning: Phase offset is ignored in MIDI output.
Because HEWMP is mainly focused on notating just intonation and temperaments thereof it can produce quite surprising results for edos. First an expression is parsed into a fraction and then the prime components of that fraction are used to decide what scale degree should represent that factor. If a prime component is mapped inaccurately the error will compound. This is especially damaging if the prime in question is 3 as it breaks the whole Pythagorean basis of the notation.
| Consider 11ed2: | Degree | Pythagorean interval | Orgone interval |
|---|---|---|---|
| 0 | P1 | P1 | |
| 1 | M2 | m2 | |
| 2 | M3 | M2 | |
| 3 | m2 | P3 | |
| 4 | m3 | m4 | |
| 5 | P4 | M4 | |
| 6 | P5 | m5 | |
| 7 | M6 | M5 | |
| 8 | M7 | P6 | |
| 9 | m6 | m7 | |
| 10 | m7 | M7 | |
| 11 | P8 | P8 |
The Pythagorean notation is poorly aligned and we end up with m2 being larger in size than M3. Contrast this to the orgone intervals that come in clean numerical order.
Orgone notation is generated by P3 the perfect smithird which is equal to √(16/11) (or equally generated by cP6 the perfect compound smisixth equal to √11). This particular semi-ratio comes from the highly accurate Orgone temperament for the 2.7.11 subgroup where P3 is equal to 77/64 and three of them equal 7/4. By definition a stack of two smithirds is equal to 16/11 so the whole subgroup is covered in mere three steps. Contrast this with Meantone temperament which needs four steps of P5 to cover 2.3.5. In terms of the spine N:orgone is S:2 16/11/2 7.
You switch to Orgone mode with N:orgone. Unlike scientific pitch notation the octave boundary is at the first letter of the alphabet A.
N:orgone
$ A chain of smi3rds around the base note A5
B4 D4 F4 A5 C5 E5 G5
...
$ The same spelled using semi-fractions
@1331/4096/2 @11/16 @11/16/2 @1 @16/11/2 @16/11 @4096/1331/2And these in turn define the orgone intervals.
N:orgone
A4 P1 A4 $ Perfect unison
A4 M2 B4 $ Major smi2nd
A4 P3 C4 $ Perfect smi3rd
A4 M4 D4 $ Major smi4th a.k.a. undecimal superfourth 11/8
A4 m5 E4 $ Minor smi5th a.k.a. undecimal subfifth 16/11
A4 P6 F4 $ Perfect smi6th
A4 m7 G4 $ Minor smi7th
A4 P8 A5 $ Perfect octave
B4 m2 C4 $ Minor smi2nd
B4 m4 E4 $ Minor smi4th
B4 d6 G4 $ Diminished smi6th
G4 a3 B5 $ Augmented smi3rd
E4 M5 B5 $ Major smi5th
C4 M7 B5 $ Major smi7thA sharp sign # raises an orgone pitch by 19487171/16777216/2 (approximately 129.613c) the same amount a perfect or major interval differs from its augmented counterpart.
A5 A5#
@P1 @a1
@1 @19487171/16777216/2A flat sign b lowers an orgone pitch by 19487171/16777216/2 the same amount a perfect or minor interval differs from its diminished counterpart.
A5 A5b
@P1 @d1
@1 @16777216/19487171/2| lower | raise | prime | 2,3,5,7,11,13,17,19,23,29,31-monzo | ratio | cents |
|---|---|---|---|---|---|
| < | > | 7 | [-8 0 0 -1 -1.5 0 0 1 0 0 0> | 256/77/√11 | 4.19718 |
| % | * | 17 | [-11 0 0 0 2 0 1 0 0 0 0> | 2057/2048 | 7.59129 |
| n | u | 23 | [8 0 0 0 -1 0 0 0 -1 0 0> | 256/253 | 20.40771 |
| V | A | 19 | [6 0 0 0 -0.5 0 0 -1 0 0 0> | 64/19/√11 | 26.82801 |
| ! | i | 13 | [2 0 0 0 0.5 -1 0 0 0 0 0> | √11·4/13 | 35.13131 |
| v | ^ | 3 | [-5 1 0 0 1 0 0 0 0 0 0> | 33/32 | 53.27294 |
| W | M | 31 | [5 0 0 0 0 0 0 0 0 0 -1> | 32/31 | 54.96443 |
| D | U | 29 | [-10 0 0 0 1.5 0 0 0 0 1 0> | √11·319/1024 | 56.55411 |
| - | + | 5 | [-4 0 1 0 0.5 0 0 0 0 0 0> | √11·5/16 | 61.97269 |
Currently there are two orgone chords that support inflections =O and =u and and an extra augmented chord =oaug.
$ The otonal tetrad
=O<
$ Equal to
8:11:14
$ The utonal tetrad
=u<
$ Equal to
14;11;8
$ The orgone augmented tetrad
=oaug
$ Equal to
64:88:121While not the most accurate edo for the Orgone temperament, 18ed2 does greatly benefit from the notation.
| Degree | Pythagorean interval | Orgone interval |
|---|---|---|
| 0 | P1 | P1 |
| 1 | dd5 | a1,d2 |
| 2 | d4 | m2 |
| 3 | m3 | M2 |
| 4 | M2 | a2,d3 |
| 5 | a1,d6 | P3 |
| 6 | d5 | a3,d4 |
| 7 | P4 | m4 |
| 8 | M3 | M4 |
| 9 | a2,d7 | a4,d5 |
| 10 | m6 | m5 |
| 11 | P5 | M5 |
| 12 | a4 | a5,d6 |
| 13 | a3,d8 | P6 |
| 14 | m7 | a6,d7 |
| 15 | M6 | m7 |
| 16 | a5 | M7 |
| 17 | aa4 | a7,d8 |
| 18 | P8 | P8 |
Please note that 18bED2 can be easily notated using Ups and Downs. The wartless version is here just for show.
Lambda notations is suitable for Bohlen-Pierce. The spine is generated by 7/3 against a period of 3/1.
ET:Bohlen-Pierce
N:lambda
$ A nine note scale
C4 D4 E4 F4 G4 H4 J4 A4 B4 C5
$ The chromatic scale
C4 C#4 D4 E4 F4 F4# G4 H4 H#4 J4 A4 A#4 B4 C5
C4 1\ 2\ 3\ 4\ 5\ 6\ 7\ 8\ 9\ 10\ 11\ 12\ 13\Preed is an experimental notation based on the breedsma 2401/2400. Observe that in the Breed microtemperament M3-/2 and P5/4 are enough to build any 7-limit interval and higher prime limits are represented fairly accurately as well. In Preed the usual 5-limit pitches and intervals are simply halved. P5 now sounds like N3 and N3 is a useful eight-tone building block for something that sounds like 7-limit especially if you use T:breed along with N:preed. The syntonic arrows + and - are halved while the rest of the inflections use eight tones to achieve unhalved primes, but you shouldn't really need them. Everything withing 31-limit can be built from half-sharps, + and - to a high degree of accuracy. T:preed exists to improve that accuracy even further.
N:preed
T:breed
P1 a5-- M9 ha12- M17
4/4 5/4 6/4 7/4 9/4See ASCII semantics in the docs.