The ratio of two numbers or quantities to each other. **Proportion** is in three kinds: (1) multiplex. (2) Superparticularis. (3) Superpartiens. **Proportio multiplex** is when the larger number contains the smaller so many times without a remainder, as 2:1 (dupla), 3:1 (tripla), 4:1 (quadrupla). **Proportio superparticularis** is when the larger number exceeds the smaller by one only as 3:2 (sesquialtera), 4:3 (sesquitertia), 5:4 (sesquiquarta). **Proportio superpartiens** is when the larger number exceeds the smaller by more than one, as 5:3 (superbipartienstertias), 7:4 (supertripartiensquartas), 9:5 (superquadripartiensquintas). [See Ratio]

Thus, it will be understood, that instead of giving simply the ratio between two numbers, early writers on arithmetic and geometry, as well as music, coined a single word to express that ratio; for example, 17:5 was said to be Triplasuperbipartiensquintas, i.e., that the larger number contained the smaller number three times (tripla) with two remainder (bipariens). Again, Triplasupertripartiensquartas proportio, signified that the larger contained the smaller three times and three over, as 15:4, 27:8, etc., the last part of the compound word always pointing out the smaller of the numbers compared, or an exact multiple of it. Lastly, the addition of *sub* showed that the smaller number was compared to the larger, e.g., 4:15 would be called Subtriplasupertripartiensquartas proportio. This system of **proportion** was used not only with reference to intervals but also to the comparative length of notes (time). [Stainer, John; Barrett, W.A.; A Dictionary of Musical Terms; Novello, Ewer and Co., London, pre-1900]

"**Proportion** belongs to geometry and harmony, measurement to the object and to arithmetic; and one necessitates the other. **Proportion** is the comparison of sizes; harmony is the relationship to measures; geometry is the function of numbers." [R. A. Schwaller de Lubicz, The Temple in Man, page 61]

See Also

**Figure 14.10 - Proportionate Tonal Relations dictate Contraction or Expansion**
**Figure 6.17 - Areas and Volumes - Relations and Proportions**
**Figure 6.19 - Sphere to Cube - Relations and Proportions**
**Figure 14.10 - Proportionate Tonal Relations dictate Contraction or Expansion**
**Law of Definite Proportions**
**law of multiple proportions**
**Ratio**
**Reciprocating Proportionality**
**Table 2 - Controlling Modes and Proportions**
**3.13 - Reciprocals and Proportions of Motions and Substance**
**6.8 - Proportionate and Relative Geometries**
**9.12 - Velocity of Sound and its Propagation Rate are Proportional**
**12.00 - Reciprocating Proportionality**
**13.15 - Principle of Proportion**