Now that you've learned about defining scales and using generated scales, it's time to talk about transposition. Please see Language Reference for a list of all the directives and their parameters, or run syntoniq doc from the command line. This section will cover the two directives you will use for transposition.
A side note on syntax: the transposition directives all take optional part parameters that specifies part names. We've been using p1 as the part name, but you can call it anything that uses alphanumeric characters or the underscore, like trumpet_2 or Alto or potato. Syntoniq directives can have repeatable options, so if we wanted to change the base pitch of the tuning for parts p1 and p2, we could call set_base_pitch(... part=p1 part=p2). If no part parameters are specified, the directives apply to all parts.
The two directives we will cover here are
set_base_pitch — changes the base pitch of a scale to either an absolute frequency or to a multiple of the current base pitchtranspose — transpose the whole scale so that the note name given as the argument to written takes its pitch from the note name given as pitch_from. Both written and pitch_from may include optional cycle (octave) markers.Let's dive into some examples. The first example takes us on a bit of a wild ride through some strange pivots and modulations. I'm not going to claim that it is a great work of art, but it should demonstrate the basics of Syntoniq transposition. Editorial note: the comments in the score below refer to material in the text after the audio. This is in the hope of making this easier to consume on various screen sizes!
; See Transposition section of manual for the "note x" parts.
syntoniq(version=1)
define_generated_scale(scale="gen-53" divisions=53)
tempo(bpm=40)
use_scale(scale="gen-53")
set_base_pitch(absolute=220*6/5) ; note 1
; Play some chords with some pivots: note 2
[p1.0] 1:A A
[p1.1] 1:E E
[p1.2] 1:C C
[p1.3] 1:A' h':~ ; sustain pivot
; After transpose, `A` will sound like `h` did before: note 3
transpose(written=A pitch_from=h)
; Do it again
[p1.0] 1:A A
[p1.1] 1:E E
[p1.2] 1:C C
[p1.3] 1:A' h':~
; Pivot 7/8 to 11/8: note 4
transpose(written=Cl' pitch_from=h')
; Pivot, then move to a major triad
[p1.0] 1:A A
[p1.1] 1:C C
[p1.2] 1:I' E'
[p1.3] 1:Cl' C'
; Change keys: note 5
transpose(written=A pitch_from=D++)
[p1.0] 2:A
[p1.1] 2:C
[p1.2] 2:A'
[p1.3] 2:E'
; Transpose up by two more steps: note 6, then override: note 7
set_base_pitch(relative=^2|53)
[p1.0] 1:A A A 2:A,
[p1.1] 1:C C! C!19 2:C
[p1.2] 1:A' A' A' 2:E'
[p1.3] 1:E' E!' E!19' 2:A'2Notes from above:
220*6/5 to clearly indicate a 6/5 minor third above 220 Hz. We could have written 264. This is just to show we can set the base pitch to any frequency.h' note, which is the septimal minor seventh. The :~ after the note indicates a sustain. The sustain goes to the next note with the same note number, which comes from the line prefix. In this case, this is [p1.3] (note 3 of part p1), so the note is tied to the next note in [p1.3].transpose(written=A pitch_from=h), we are saying that, after transposition, the "written note A" will get its pitch from the pitch currently belonging to note h. This shifts the pitch down by a ratio of 7/8. It's tricky to indicate the transposition direction clearly, so think of this as describing the "state change". When we transpose, we are saying that a given written note gets its pitch from something else, and in our case, the something else can only be the tuning before transposition. Clear? Hopefully it will become clear!h' and give it to Cl'. The octave marks were superfluous here, but they were used to show that they are valid. Since h is below the root by a little more than a whole step (7/8) and Cl is above the root by a little more than a fourth (11/8), this will move the pitch down by more than a fifth. But you don't really have to worry about that too much. We're saying the new Cl sounds like the old h. That means the new Cl' sounds like the old h'. As we sustain the note in [p1.3] again, the transposition clearly tells us what the new note has to be to keep the same sound.A (the root) should get its pitch from what is currently a fourth up, which would be D. But as a little microtonal twist, let's worm-hole to a new key two 53-EDO steps above the fourth by taking the pitch from D++. We could have also written this as DA2, since A2 means two steps of the current interval division.set_base_pitch(relative=^2|53), meaning to multiply ^2|53 to the pitch. This is the same as going up two steps. We could have used A and A2 in a transpose statement, but the intent is easier to read here. The transposition amount doesn't have to be related to the scale in any way.! to override the divisions and play the pure JI intervals. 53-EDO is tight, so there's not much difference, but there's a little. Then use !19 to find the closest note in 19-EDO. Here, the major third is a bit flat, so this sounds noticeably different. Finally, change the chord's voicing and return to 53-EDO. We could have done all this by defining more scales repeatedly calling use_scale, but to just "borrow" a note from another scale, using the overrides is easier.For a second example, let's take a little melody in one EDO, and then use some steps in a second EDO to change to a new, unrelated key. This melody will start in 17-EDO, one of my personal favorites. The single step in 17-EDO is almost exactly the ratio 25/24 (off by less than 0.1¢), which is what you get if you go up a major third and down a minor third in just intonation ($\frac{5}{4}\times\frac{5}{6} = \frac{25}{24}$). Two steps is almost exactly 13/12, flat by less than 3¢. That makes the notes Y and M particularly useful in 17-EDO. 17-EDO also has a very good fourth and fifth: 10 steps of 17-EDO is less than 4¢ sharp for 3/2. It lacks an interval close to the major third, but 5 steps is a close neutral third, quite close to 11/9. 11/9 can be written as JK in our system. This is a feature that falls out of normal arithmetic. Each single letter represents a single harmonic sequence step by design. That means each pair of adjacent letters represents two steps: JK = $\frac{10}{9}\times\frac{11}{10} = \frac{11}{9}$.
; See Transposition section of manual for the "note x" parts.
syntoniq(version=1)
define_generated_scale(scale="gen-17" divisions=17)
define_generated_scale(scale="gen-13" divisions=13)
tempo(bpm=40)
use_scale(scale="gen-17")
; Use a bar check: note 1
[p1.0] 1:A A 2:A | 1:A MA 2:A
[p1.1] 1:JK I 2:JK | 1:JK MJK 2:JK
[p1.2] 1:C D 2:C | 1:C MC 2:C
[p1.3] 1:CJK DJK 2:CJK | 1:CJK MCJK 2:CJK
[p1.4] 1:I' A' 2:I' | 1:I' MI' 2:I'
; Repeat up a step: note 2
transpose(written=A pitch_from=Y)
[p1.0] 1:A A 2:A | 1:A MA 2:A
[p1.1] 1:JK I 2:JK | 1:JK MJK 2:JK
[p1.2] 1:C D 2:C | 1:C MC 2:C
[p1.3] 1:CJK DJK 2:CJK | 1:CJK MCJK 2:CJK:~ ; sustain
[p1.4] 1:I' A' 2:I' | 1:I' MI' 2:I'
; Sustain and pivot: note 3
use_scale(scale="gen-13")
transpose(written=A pitch_from=CJK!17)
[p1.3] 1:a a1 a2 a3
use_scale(scale="gen-17")
transpose(written=CJK pitch_from=a4!13)
; Repeat after stepping in 13-EDO: note 4
[p1.0] 1:A A 2:A | 1:A MA 2:A
[p1.1] 1:JK I 2:JK | 1:JK MJK 2:JK
[p1.2] 1:C D 2:C | 1:C MC 2:C
[p1.3] 1:CJK DJK 2:CJK | 1:CJK MCJK 2:CJK
[p1.4] 1:I' A' 2:I' | 1:I' MI' 2:I'
; Closing sequence: note 5
[p1.0] 6:A,
[p1.1] 6:C,
[p1.2] 1:I IM I Im 2:I
[p1.3] 1:C CM C Cm 2:C
[p1.4] 4:~ 2:CE#Notes:
| character as a "bar check". Syntoniq makes sure that each line in a score block has the same number of bar checks and that each bar check happens at the same beat offset. While Syntoniq doesn't have the concept of time signatures, these can be useful checks. Syntoniq also ensures beats are consistent at the end of each line. This first passage is some native 17-EDO harmonies involving use of the neutral third and the two-step 13/12 interval.Y, which corresponds closely to a single 17-EDO step...but this would be portable to other scales and would sound similar but with the flavor of that tuning system.a notes). 13-EDO doesn't map very well to the diatonic scale, and the intention here is to just demonstrate stepping. Notice that our transposition assigns the pitch to the note A from CJK!17. This prevents us from having to do the transposition in multiple steps. We can be in 13-EDO and still take a pitch from a note in 17-EDO. Then we just step a single note along in 13-EDO.[p1.4] is CE#. 17-EDO doesn't have a major third (E), and the closest note to 5/4 is the 5-step neutral third. By including the # character, we are telling Syntoniq to go to the next higher step instead of the closest step. This gives us a very sharp major third (almost a flat fourth)—an intentional musical choice in this case.In addition to the directives introduced in this section, you can transpose by saving and restoring pitches. This is covered in the next section.