 # Ratio

Relation or proportion.

a relationship, or interval, expressing the vibrations per second, or cycles, of the two tones concerned, generally in the lowest possible (integer?) terms; simultaneously a representative of a tone and an implicit relationship to a "keynote" - or unity.

Euclid?'s definition: a mutual relation of two magnitudes of the same kind to one another in respect of quantity. (from Partch 1974, Genesis of a Music, 2nd ed., Da Capo Press, New York, p. 73)

The ratio expressed as 1:2 says the first quantity is half the second quantity which is twice the first quantity. Music intervals are generally expressed as ratios.

Simple ratio
1:2 (1 is to 2)

Ratio of two ratios
1:2::2:4 (1 is to 2 as 2 is to 4)

6.8 - Proportionate and Relative Geometries
9.12 - Velocity of Sound and its Propagation Rate are Proportional
12.00 - Reciprocating Proportionality
3.13 - Reciprocals and Proportions of Motions and Substance
13.15 - Principle of Proportion
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
Fundamental
Interval
Keynote
Reciprocating Proportionality
Table 2 - Controlling Modes and Proportions
Table of Plate Harmonics and Intervals
Universal Ratios