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.

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)

See Also

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
Reciprocating Proportionality
Table 2 - Controlling Modes and Proportions
Table of Plate Harmonics and Intervals
Universal Ratios
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

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