Neutral third

In addition to the above examples, a square root neutral third can be characterized by a ratio of

Such a definition stems from the two thirds traditionally making a fifth-based triad.

In two separate case studies of the progression and development of these improvisations, neutral thirds were found to arise in infants' songs after major and minor seconds and thirds, but before intervals smaller than a semitone and also before intervals as large as a perfect fourth or larger.

[8] The neutral third has been used by a number of modern composers, including Charles Ives, James Tenney, and Gayle Young.

[9] Claudius Ptolemy describes an "even diatonic" tuning which uses two justly tuned neutral thirds in Harmonikon built off the 12:11 and 11:10 neutral seconds in compound intervals with 9:8 and 10:9 whole tones, forming the intervals: (12/11)*(9/8) = 27/22, (11/10)*(10/9) = 11/9.

All the other tuning systems mentioned above fail to distinguish between these intervals; they temper out the comma 144:143.