A musical ratio of 5:4.

**Ramsay**

contrast. In the fifth, the ratio being 2:3, the excess of 3 above 2 is 1; this 1 bears a simple relation to both the notes which awaken it. The grave harmonic in this case gives the octave below the lower of the two sounds; 1 is an octave below 2. This is the simplest relation "a third sound" can have to the two which awaken it, and that is why the fifth has the smallest possible degree of contrast. The octave, the fifth, and the fourth may be reckoned as simple ratios; the **major** and minor thirds and their inversions as moderately complex; the second, which has the ratio of 9:10, and the major fourth F to B and its inversion, are very complex. [Scientific Basis and Build of Music, page 61]

Nine-tenths of a string, if stopped and acted on, gives a tone the ratio of 9:10, but if touched and acted on as a harmonic it gives a note which is three octaves and a **major third** above the whole string. If the remaining tenth of the string be acted on either as a stopped note or a harmonic it will give the same note which is three octaves and a **major third** above the whole string the ratio of 1:10, so that the stopped note of one-tenth and the harmonic of nine-tenths are the same. Indeed the bow acting on stopped note of one-tenth, on harmonic of nine-tenths, or on harmonic of one-tenth, produces the same note, as the note is the production of one-tenth in each case; for in the harmonic, whether you bow on the nine-tenths or the one-tenth, while it is true that the whole string is brought into play, yet by the law of sympathy which permeates the entire string, it vibrates in ten sections of one-tenth each, all vibrating in unison. This is what gives the harmonic note its peculiar brilliancy. [Scientific Basis and Build of Music, page 92]

Whatever interval is sharpened above the tone of the open string, divide the string into the number of parts expressed by the larger number of the ratio of the interval, and operate in that part of the string expressed by the smaller number of it. For example, if we want to get the **major third**, which is in the ratio of 4:5, divide the string into five parts and operate on four. The lengths are inversely proportional to the vibrations. [Scientific Basis and Build of Music, page 100]

See Also

**05 - The Melodic Relations of the sounds of the Common Scale**
**7.12 - Third**
**12.07 - Keelys Thirds Sixths and Ninths**
**14.04 - Thirds as Currents**
**14.05 - Thirds as Differentiations**
**14.07 - Thirds in Magnetic Action**
**14.08 - Thirds as Assimilatives**
**14.10 - Thirds as Ratios within a Whole**
**14.28 - Thirds as Polar and Depolar Parameters**
**16.08 - Polar Link in Thirds**
**Figure 11.01 - Octave composed of Equal Thirds and Triads**
**Interval**
**minor**
**Part 14 - Keelys Mysterious Thirds Sixths and Ninths**
**Table 1 - Relations of Thirds**
**Table 14.01 - All phrases in HyperVibes containing the term thirds**
**Table 14.02 - Neutral Thirds - Energy Radiates from Center - Force Contracts to Center**
**third**
**thirds**