Relation or proportion of one measure to another which can be linear, geometric or volumetric. It can be one sound to another or one volume to another or just about any one class of things, forces or vibrations. Can also be expressed in parts. [See Proportion, Reciprocating Proportionality]
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.
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.
1:2 (1 is to 2)
Ratio of two ratios
1:2::2:4 (1 is to 2 as 2 is to 4)
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
Table 2 - Controlling Modes and Proportions
Table of Plate Harmonics and Intervals
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