Octave Manipulation

The octave is the simplest interval there is: 2/1. Double a frequency and you are an octave up; halve it and you are an octave down. This tutorial covers the one-click way, the by-hand way, and how to read octaves off the screen.

Prerequisites: Note Dependencies.

The ▲/▼ arrows

Every note with a frequency carries a narrow column on its left inner edge, split in half: ▲ in the upper half, ▼ in the lower. Click a half and the note's frequency expression is multiplied by an interval.

The same pair of buttons appears in the note widget, at the right end of the frequency row's Evaluated: line.

Out of the box, ▲ is ×2 and ▼ is ×1/2 — an octave up and an octave down. Hover a widget button and the tooltip tells you exactly what it will do: Transpose up ×2, Transpose down ×1/2.

The arrows are not octave-only

The interval is a setting, not a law. Settings → Arrows (the gear in the top bar) has quick-pick chips for a fifth (3/2), a fourth (4/3), a major third (5/4), a whole tone (9/8) and a syntonic comma (81/80), plus a numerator/denominator pair you can type into. The ratio must be built from whole numbers, must not be 1, and is clamped between 1/16 and 16. The tooltips follow — set the up interval to 3/2 and the button reads Transpose up ×3/2.

The rest of this page assumes the default 2/1, because that is what ships. If your arrows are doing something other than octaves, that is why. See Transposing with Arrows.

You can also switch the arrows off entirely in that tab, in which case the ▲/▼ glyphs and their click zones disappear from every note, and the widget buttons are not rendered at all.

What the arrows do to your expression

Try it. Create a note with frequency base.f, then click ▲.

Expression	You click	It becomes
base.f	▲	2 * base.f
2 * base.f	▲	4 * base.f
4 * base.f	▼	2 * base.f
2 * base.f	▼	base.f

The factor is folded into the expression's coefficient, not stacked in front of it. Up-then-down returns you to exactly base.f — not (1/2) * 2 * base.f. Press ▲ ten times and the expression is 1024 * base.f, not a tower of multiplications.

Power terms are left alone, so a TET note keeps its shape:

Expression	You click	It becomes
base.f * 2^(7/12)	▲	2 * base.f * 2^(7/12)

The 2^(7/12) is untouched, so the note stays a 12-TET fifth — it just moved up an octave.

WARNING

This folding applies to DSL expressions. A note stored in the old method-chain format and containing a .pow( call is instead wrapped on every press, so repeated arrow clicks genuinely nest multipliers in it. That is deliberate — folding would destroy the power term — but it means "up then down restores the expression" holds for DSL notes, not for legacy TET ones. Everything the app writes today is DSL.

Arrows move whole structures

Because dependents follow their parents, an arrow on a root moves everything anchored to it.

1. Build a major triad rooted at Note 1: root base.f, third (5/4) * [1].f, fifth (3/2) * [1].f.
2. Select Note 1 and click ▲.

The whole chord jumps an octave. Notes 2 and 3 were not edited; their expressions still reference [1].f, and they came along. The same trick moves an entire progression if its later roots reference the first one — which is exactly how the shipped Progressions modules are built.

INFO

Arrows act on one note per click. There is no group transposition: selecting several notes and clicking an arrow is not a thing. Transposing a root is how you move many notes at once.

Writing octaves by hand

Sometimes you want the octave inside a larger expression.

[1].f * 2        # one octave up
[1].f / 2        # one octave down
[1].f * 4        # two octaves up
[1].f / 8        # three octaves down

Or with the power operator, which is the same thing spelled differently:

[1].f * 2^2      # × 4  — two octaves up
[1].f * 2^(-1)   # × ½  — one octave down

No variables

The DSL has no variables. [1].f * 2^n is not an expression — it is a parse error, because n is not anything the parser knows. The only things you can write are numbers, fraction literals, note references ([N].f, base.f), the three helpers (beat, tempo, measure), and the operators. If you want three octaves, write 2^3 or 8.

Likewise a bare property name is not an expression: frequency * 2 does not parse. You must say whose frequency — base.f * 2 or [1].f * 2.

The power operator earns its keep in equal temperament, where the exponent is a fraction and no plain ratio will do:

base.f * 2^(7/12)     # a 12-TET fifth
base.f * 2^(1/12)     # one 12-TET semitone

^ binds tighter than *, so [1].f * 2^(1/12) means [1].f * (2^(1/12)), which is what you want. See Microtonal Composition.

The octave guides

Look at the workspace background: faint dotted horizontal lines, each with a label at the left.

They mark octaves. The line labelled BaseNote sits at the BaseNote's frequency; the ones above it are labelled +1, +2, and so on, each one a doubling; below it, -1, -2, each a halving.

They re-anchor to whatever you select. Click a note that has a frequency and the 0 line jumps to that note's pitch and its label changes to Note [N]. The other lines follow — so the guides now show you the octaves of the note you are working on, and you can see at a glance whether two notes are an octave apart.

Octave equivalence and reduction

Any interval wider than an octave can be folded back into one by halving.

Compound interval	Ratio	Reduced	Ratio
Major 9th	9/4	Major 2nd	9/8
Minor 10th	12/5	Minor 3rd	6/5
Perfect 11th	8/3	Perfect 4th	4/3
Perfect 12th	3/1	Perfect 5th	3/2

To reduce, divide by 2 until the ratio lands between 1 and 2:

[1].f * (9/4) / 2

Save that and the app simplifies it for you — it stores [1].f * (9/8). The simplifier folds rational coefficients automatically, so you can write the arithmetic the way you think about it and let the app tidy up.

The reverse is just as easy: to voice a third an octave up, multiply the third by two and write [1].f * (5/2).

Practical: an octave-spanning chord

A wide voicing, all four notes rooted at Note 1 so the whole thing transposes as a unit.

Create the root from the BaseNote, then add each of the other three At Start from Note 1:

Note	Voice	Frequency
1	root, low	base.f / 2
2	fifth	[1].f * (3/2)
3	third, an octave up	[1].f * (5/2)
4	root, two octaves up	[1].f * 4

Play it. Now select Note 1 and press ▲ — the whole voicing lifts an octave and stays a chord.

Exercises

1. Octave doubling

Give a melody note (say Note 4) a bass partner an octave below that follows it everywhere:

Property	Expression
frequency	[4].f / 2
startTime	[4].t
duration	[4].d

Now move, resize or transpose Note 4. The bass tracks all three.

2. Arpeggiated octaves

Four sixteenth notes climbing by octaves and falling back. Set every duration to beat(base) * (1/4).

Note	Frequency	Start time
1	base.f	base.t
2	[1].f * 2	[1].t + [1].d
3	[2].f * 2	[2].t + [2].d
4	[1].f	[3].t + [3].d

3. Turn the arrows into fifths

Open Settings → Arrows and click the Fifth 3/2 quick-pick chip. The cents readout shows 702.0¢. Now select a note and press ▲ repeatedly: base.f, then (3/2) * base.f, then (9/4) * base.f. You are stacking fifths — the raw material of Pythagorean tuning.

Click Octave 2/1 to put it back.

4. Prove the round trip

Select a note and press ▲ five times, then ▼ five times. Read the Raw: field. It should be the expression you started with, character for character.

What you learned

• The ▲/▼ arrows apply an interval that defaults to the octave and is configurable.
• Arrow factors fold into the coefficient, so transposition is reversible.
• The DSL has no variables — write 2^3, never 2^n.
• The octave guides re-anchor to the selected note.
• Transposing a root moves everything anchored to it.

Next

• Working with Measures — structure in time
• Microtonal Composition — where ^ becomes essential
• Transposing with Arrows — every arrow setting, in full