Level 4 · Accord Construction

Ratio Ladders: Finding an Accord's Balance Point

How to find the right ratio between two materials: build a ladder of mixtures, narrow it in a second round, and allow for materials of very different strength.

In short

A ratio ladder is a series of mixtures of the same two materials at planned ratios, usually stepped geometrically: 1:9, 1:3, 1:1, 3:1, 9:1. You smell them in order, find the best region, then run a narrower ladder inside it. It replaces guessing with a search you can record and repeat.

What you will learn

  • Build a ratio ladder from stock dilutions
  • Narrow a wide search in two rounds
  • Calculate the final ratio in pure material

Before this lesson: Two-Material Accord Studies

Why ratios matter so much

The same two materials can give several quite different results. At one ratio a pair may read as a fused new smell, at another as one material with a slight accent, and at a third as two things arguing. Your pair studies showed that an effect exists. A ladder finds where it is strongest.

Geometric steps are a practical convention. Perception of odor strength does not rise in a straight line with concentration, so equal-sized additions are less informative than equal-ratio ones, especially at low levels.

Round one: find the region

Use two dilutions of similar perceived strength, each in a clean labeled vial. Each mixture below totals 2 g, a small amount that is still weighable on a 0.01 g scale.

A first ladder from two stock dilutions
Ratio A:BWeigh A (g)Weigh B (g)
9:11.800.20
3:11.500.50
1:11.001.00
1:30.501.50
1:90.201.80

Smell in order from one end to the other, then in reverse after a rest. Mark the two neighbors that bracket what you want. If the best is at an end, the range was too narrow, so extend it.

Round two: narrow it

Suppose you prefer the region between 3:1 and 1:1. Weigh 3:1, 2:1, 3:2 and 1:1. Stepping further than this rarely helps a beginner, as differences become smaller than your day-to-day variation. Recheck your choice the next day, because the winner on Monday is not always the winner on Tuesday.

When strengths differ widely

A very strong material needs a lower stock strength, so that the ladder lands in a useful range. Ethyl maltol might go in at 1% against vanillin at 10%. That is sensible, but it means that the ratio of the dilutions is not the ratio of the materials. Always convert at the end.

Worked example. You prefer 2.00 g of A at 10% with 0.50 g of B at 1%.

  • Pure A = 2.00 × 0.10 = 0.200 g.
  • Pure B = 0.50 × 0.01 = 0.005 g.
  • Ratio = 0.200 : 0.005 = 40 : 1.
  • In a 100-part accord: A = 100 × 40 ÷ 41 = 97.6 parts, and B = 2.4 parts.

Here, the dilutions looked like 4:1 on the scale, while the true ratio is 40:1. Record the true one, because it is what you will use when the formula grows. The perfume dilution equation is the same arithmetic in general form.

Comparing fairly

  • Prepare all the strips at the same moment. Older strips have lost their top.
  • Code the bottom of each strip if you can, then judge blind on the second pass.
  • Keep the session short. Five mixtures of the same two materials fatigue the nose quickly.

Practical exercise: Find one balance point in two rounds

About 60 minutes · You will have: a two-round ladder with a chosen ratio stated in pure material

Take the most promising pair from your pair studies.

  1. Write what you want this pair to do, in one sentence, before you smell anything.
  2. Run round one and pick a region. Rest for at least an hour.
  3. Run round two, then choose the best ratio blind if possible.
  4. Retest your choice against its neighbors the next day.
  5. State the final ratio in pure material, and as parts per 100.

You have done this well if your goal was written first, your choice survived the next-day retest (or you recorded that it did not), and your final ratio accounts for both dilutions.

Common mistakes

  • Recording the dilution ratio as the material ratio. The worked example shows how far off that can be.
  • Too many steps. You can only smell so many mixtures reliably, so two short rounds beat one long one.
  • Choosing with no goal. Without a stated aim, you will simply prefer whatever you smelled last.
  • Weighing under the scale's reliable range. Use a weaker stock rather than 0.02 g additions.

Key terms

Ratio ladder
A series of mixtures of two materials at planned ratios, used to find where the balance is best.
Balance point
The ratio at which a pair gives the wanted effect, with neither partner standing out in a way you did not intend.

Knowledge check

1. Why step ratios geometrically (1:9, 1:3, 1:1, 3:1, 9:1) rather than evenly?
Show the answer

Because perception of strength is closer to a ratio scale than a straight line. Doubling or tripling a dose tends to be a more noticeable step than adding the same fixed amount at a high level, so ratio steps search the range more efficiently.

2. You mix 3 g of a 1% dilution of A with 1 g of a 10% dilution of B. What is the ratio of pure A to pure B?
Show the answer

3:10. Pure A = 0.03 g and pure B = 0.1 g, so 0.03:0.1 = 3:10. The weights of the dilutions are not the ratio of the materials.

3. What should round two of a ladder do?
Show the answer

Narrow the search around the best region of round one. Round one finds the region and round two finds the point, with one variable throughout.

Written and reviewed by the RUŌOD Lab team. This is general education, not legal, regulatory, medical or safety advice. Example dilutions and exercises are for learning, are not validated products, and have not been safety-assessed. Completing a lesson confers no qualification. How we check these lessons.