Ploidacot/Monocot
Monocot is a temperament archetype where the generator is a 3/2 perfect fifth, and the period is a 2/1 octave. In other words, it is the standard chain of fifths, repeating every octave. Monocot temperaments usually generate the (mos)diatonic scale (5L 2s) and one of its chromatic children (5L 7s or 7L 5s) (though there are exotempered exceptions such as mavila (2L 5s) and trienstonian (5L 3s)) and as such they are very commonly used and are a well-explored category of temperaments.
Intervals and notation
Monocot is the only ploidacot to have an agreed-upon, fully unambiguous scheme for interval and note names, which can be found at Chain-of-fifths notation.
| # | Steps | Notation | Name |
|---|---|---|---|
| -7 | 113.69 | C# | Augmented unison |
| -6 | 611.73 | F# | Augmented fourth |
| -5 | 1,109.78 | B | Major seventh |
| -4 | 407.82 | E | Major third |
| -3 | 905.87 | A | Major sixth |
| -2 | 203.91 | D | Major second |
| -1 | 701.96 | G | Perfect fifth |
| 0 | 0 | C | Perfect unison / Perfect octave |
| 1 | 498.05 | F | Perfect fourth |
| 2 | 996.09 | Bb | Minor seventh |
| 3 | 294.14 | Eb | Minor third |
| 4 | 792.18 | Ab | Minor sixth |
| 5 | 90.22 | Db | Minor second |
| 6 | 588.27 | Gb | Diminished fifth |
| 7 | 1,086.32 | Cb | Diminished octave |
Temperament interpretations
Monocot temperaments involve equating a number of stacked fifths to some other just interval of the 5-limit or greater.
Mavila
Mavila is an exotemperament that flattens the fifth beyond the diatonic range (to around 670-680 cents) so that the "major third" is flatter than the "minor third", meaning that the "minor third" can be assigned to 5/4 and the "major third" can be assigned to 6/5. This has the effect of "swapping" major and minor intervals from what they are in meantone. This means that the normal chain-of-fifths interval names stop making much sense (but see in Mavila#Notation).
Deeptone
Deeptone flattens the fifth to around 690 cents, so the major third is a 16/13 and the augmented third is 5/4.
Meantone
Meantone can be seen as the most "basic" monocot temperament, which flattens the fifth slightly to around 696 cents so that the major third is 5/4. Consequently, the minor third becomes 6/5, and the major sixth becomes 5/3.
In the 7-limit, the augmented sixth becomes 7/4, resulting in septimal meantone. Alternately, the fifth can be flattened further (to around 693 cents) so that the diminished seventh is sharper than the augmented sixth. Then, it makes sense to interpret the diminished seventh as 7/4, resulting in flattone temperament.
Schismic
Schismic interprets the diminished fourth, an interval of about 384 cents when justly tuned, as 5/4. This makes it a very accurate microtemperament, and it naturally extends to prime 19 by finding 19/16 at the minor third (called nestoria).
In the 7-limit, the doubly-diminished octave, an interval of about 973 cents when justly tuned, can be interpreted as 7/4 with a small loss of accuracy compared to 5-limit schismic; this is called garibaldi.
Superpyth
Superpyth interprets the minor seventh as 7/4, which suggests a tuning of the perfect fifth at around 710 cents. 5/4 can then be seen as the augmented second (for standard superpyth) or the double-augmented unison (for ultrapyth, which also extends to prime 13 by setting the major third equal to 13/10).
Trienstonian
Trienstonian is an exotemperament where the fifth is sharpened so that the major sixth is 7/4. This is thus tuned best with tunings around or sharp of 5edo, which do not generate a (usable) diatonic scale.