Ploidacot/Diploid monocot: Difference between revisions
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{{Breadcrumb}}{{Infobox ploidacot|Ploids=2|Shears=0|Cots=1|Pergen=[P8/2, P5]|Forms=10, 12|Title=Diploid monocot|Wedgie=2}} | {{Breadcrumb}}{{Infobox ploidacot|Ploids=2|Shears=0|Cots=1|Pergen=[P8/2, P5]|Forms=8, 10, 12|Title=Diploid monocot|Wedgie=2}} | ||
'''Diploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is half a [[2/1]] octave, or 600{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{3}{2\sqrt{2}}</math>. Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children. | '''Diploid monocot''' is a temperament archetype where the generator is a [[3/2]] perfect fifth and the period is half a [[2/1]] octave, or 600{{c}}. The generator can also be characterized as a perfect fourth [[4/3]], or as a "perfect semitone" <math>\frac{3}{2\sqrt{2}}</math>. Diploid monocot temperaments usually generate the [[2L 8s]] MOS structure and either [[2L 10s]] (and thus [[12L 2s]]) or [[10L 2s]] as children. | ||
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|+ style="font-size: 105%;" | Diploid monocot intervals (assuming pure fifth and octave) | |+ style="font-size: 105%;" | Diploid monocot intervals (assuming pure fifth and octave) | ||
|- | |- | ||
! colspan=" | ! rowspan="2" | # | ||
! colspan=" | ! colspan="3" | Ploid 1 | ||
! colspan="3" | Ploid 2 | |||
|- | |- | ||
! Cents | ! Cents | ||
! Notation | |||
! Name | ! Name | ||
! Cents | |||
! Notation | ! Notation | ||
! Name | ! Name | ||
|- | |- | ||
| −5 | | −5 | ||
| 90. | | 90.22 | ||
| Db | |||
| minor second | | minor second | ||
| 690.22 | |||
| 690. | |||
| — | | — | ||
| — | | — | ||
| Line 33: | Line 31: | ||
| — | | — | ||
| — | | — | ||
| 792.18 | | 792.18 | ||
| Ab | |||
| minor sixth | | minor sixth | ||
|- | |- | ||
| −3 | | −3 | ||
| 294. | | 294.13 | ||
| Eb | |||
| minor third | | minor third | ||
| 894.13 | |||
| 894. | |||
| — | | — | ||
| — | | — | ||
|- | |- | ||
| −2 | | −2 | ||
|396.09 | | 396.09 | ||
| — | | — | ||
| — | | — | ||
| 996.09 | | 996.09 | ||
| Bb | |||
| minor seventh | | minor seventh | ||
|- | |- | ||
| −1 | | −1 | ||
| 498. | | 498.04 | ||
| F | |||
| perfect fourth | | perfect fourth | ||
| | | 1098.04 | ||
| — | | — | ||
| — | | — | ||
| Line 67: | Line 61: | ||
| 0 | | 0 | ||
| 0 | | 0 | ||
| C | |||
| unison | | unison | ||
| 600 | | 600 | ||
| — | | — | ||
| Line 78: | Line 71: | ||
| — | | — | ||
| — | | — | ||
| 701.96 | | 701.96 | ||
| G | |||
| perfect fifth | | perfect fifth | ||
|- | |- | ||
| 2 | | 2 | ||
| 203.91 | | 203.91 | ||
| D | |||
| major second | | major second | ||
| 803.91 | | 803.91 | ||
| — | | — | ||
| Line 96: | Line 87: | ||
| — | | — | ||
| — | | — | ||
| 905.87 | | 905.87 | ||
| A | |||
| major sixth | | major sixth | ||
|- | |- | ||
| 4 | | 4 | ||
| 407.82 | | 407.82 | ||
| E | |||
| major third | | major third | ||
| | | 1007.82 | ||
| — | | — | ||
| — | | — | ||
| Line 114: | Line 103: | ||
| — | | — | ||
| — | | — | ||
| | | 1109.78 | ||
| | | B | ||
| major seventh | | major seventh | ||
|} | |} | ||
| Line 131: | Line 119: | ||
Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7. | Injera extends [[meantone]] by setting 7/5 equal to 10/7, so that both [[5/4]] and [[7/4]] are found at 4 generators up, offset by a 600{{c}} tritone representing both 7/5 and 10/7. | ||
[[Category:Ploidacot]] | [[Category:Ploidacot|Diploid monocot]] | ||
Revision as of 22:15, 5 January 2026
| Pergen | [P8/2, P5] |
| Numeral form | 2-ploid 1-cot |
| Pure generator size | 101.96 ¢ |
| Pure period size | 600 ¢ |
| Forms | 8, 10, 12 |
| Characteristic multival entry | 2 |
Diploid monocot is a temperament archetype where the generator is a 3/2 perfect fifth and the period is half a 2/1 octave, or 600 ¢. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" [math]\displaystyle{ \frac{3}{2\sqrt{2}} }[/math]. Diploid monocot temperaments usually generate the 2L 8s MOS structure and either 2L 10s (and thus 12L 2s) or 10L 2s as children.
Notation
Diploid monocot notation is complicated as it conventionally requires either the introduction of new "hemipythagorean" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. Note and interval names are provided where diploid monocot intervals align with standard monocot intervals.
| # | Ploid 1 | Ploid 2 | ||||
|---|---|---|---|---|---|---|
| Cents | Notation | Name | Cents | Notation | Name | |
| −5 | 90.22 | Db | minor second | 690.22 | — | — |
| −4 | 192.18 | — | — | 792.18 | Ab | minor sixth |
| −3 | 294.13 | Eb | minor third | 894.13 | — | — |
| −2 | 396.09 | — | — | 996.09 | Bb | minor seventh |
| −1 | 498.04 | F | perfect fourth | 1098.04 | — | — |
| 0 | 0 | C | unison | 600 | — | — |
| 1 | 101.96 | — | — | 701.96 | G | perfect fifth |
| 2 | 203.91 | D | major second | 803.91 | — | — |
| 3 | 305.87 | — | — | 905.87 | A | major sixth |
| 4 | 407.82 | E | major third | 1007.82 | — | — |
| 5 | 509.78 | — | — | 1109.78 | B | major seventh |
Temperament interpretations
By definition, diploid monocot temperaments equate some interval to its octave complement.
Diaschismic
Diaschismic sets 3/2 equal to 16/15 plus a semioctave, setting the semioctave equal to 45/32~64/45, and mapping 5/4 to 2 generators down. Diaschismic naturally extends to prime 17 by setting the flat 16/15 generator also equal to 17/16. Diaschismic is tuned best with fifths slightly sharp of just.
To extend to the 7-limit, a simple mapping (pajara) sets 7/5 equal to the semioctave, meaning 7/4 is a semioctave above 5/4. This suggests tuning the generator to about 709 ¢ (or equivalently 109 ¢). With a slightly less sharp fifth, septimal diaschismic maps 7/4 to 8 generators down.
Injera
Injera extends meantone by setting 7/5 equal to 10/7, so that both 5/4 and 7/4 are found at 4 generators up, offset by a 600 ¢ tritone representing both 7/5 and 10/7.