Ploidacot/Diploid dicot: Difference between revisions
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{{Breadcrumb}}{{Infobox ploidacot|Ploids=2|Shears=0|Cots=2|Pergen=[P8/2, P4/2]|Forms=6, 10, 14|Title=Diploid dicot|Wedgie=4}}'''Diploid dicot''' is a temperament archetype where the generator is a neutral third, two of which stack to a [[3/2]] perfect fifth, and the period is half a [[2/1]] octave, or 600{{cent}}. In other words, this is the same as the [[hemipythagorean]] structure. The generator can also be characterized as an inframinor third or ultramajor second, two of which reach a perfect fourth. Diploid dicot temperaments usually generate the decatonic scale [[4L 6s]] and the 14-note scale [[10L 4s]]. | {{Breadcrumb}}{{Infobox ploidacot|Ploids=2|Shears=0|Cots=2|Pergen=[P8/2, P4/2]|Forms=6, 10, 14, 24|Title=Diploid dicot|Wedgie=4}}'''Diploid dicot''' is a temperament archetype where the generator is a neutral third, two of which stack to a [[3/2]] perfect fifth, and the period is half a [[2/1]] octave, or 600{{cent}}. In other words, this is the same as the [[hemipythagorean]] structure. The generator can also be characterized as an inframinor third or ultramajor second, two of which reach a perfect fourth. Diploid dicot temperaments usually generate the decatonic scale [[4L 6s]] and the 14-note scale [[10L 4s]]. | ||
== | == Intervals and notation == | ||
Diploid dicot 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 dicot intervals align with standard dicot intervals (which use [[neutral chain-of-fifths notation]]). | Diploid dicot 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 dicot intervals align with standard dicot intervals (which use [[neutral chain-of-fifths notation]]). | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Diploid dicot intervals (assuming pure fifth and octave) | |||
|- | |- | ||
! rowspan="2" | # | ! rowspan="2" | # | ||
| Line 20: | Line 21: | ||
| 543.157 | | 543.157 | ||
| | | | ||
| | | – | ||
| 1143.157 | | 1143.157 | ||
| Cd | | Cd | ||
| Line 31: | Line 32: | ||
| 894.135 | | 894.135 | ||
| | | | ||
| | | – | ||
|- | |- | ||
| −5 | | −5 | ||
| 45.112 | | 45.112 | ||
| | | | ||
| | | – | ||
| 645.112 | | 645.112 | ||
| Gd | | Gd | ||
| Line 44: | Line 45: | ||
| 396.090 | | 396.090 | ||
| | | | ||
| | | – | ||
| 996.090 | | 996.090 | ||
| Bb | | Bb | ||
| Line 55: | Line 56: | ||
| 747.067 | | 747.067 | ||
| | | | ||
| | | – | ||
|- | |- | ||
| −2 | | −2 | ||
| Line 63: | Line 64: | ||
| 1098.045 | | 1098.045 | ||
| | | | ||
| | | – | ||
|- | |- | ||
| −1 | | −1 | ||
| 249.022 | | 249.022 | ||
| | | | ||
| | | – | ||
| 849.022 | | 849.022 | ||
| Ad | | Ad | ||
| Line 79: | Line 80: | ||
| 600 | | 600 | ||
| | | | ||
| | | – | ||
|- | |- | ||
| 1 | | 1 | ||
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| 950.978 | | 950.978 | ||
| | | | ||
| | | – | ||
|- | |- | ||
| 2 | | 2 | ||
| 101.955 | | 101.955 | ||
| | | | ||
| | | – | ||
| 701.955 | | 701.955 | ||
| G | | G | ||
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| 452.933 | | 452.933 | ||
| | | | ||
| | | – | ||
| 1052.933 | | 1052.933 | ||
| Bd | | Bd | ||
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| 803.910 | | 803.910 | ||
| | | | ||
| | | – | ||
|- | |- | ||
| 5 | | 5 | ||
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| 1154.888 | | 1154.888 | ||
| | | | ||
| | | – | ||
|- | |- | ||
| 6 | | 6 | ||
| 305.865 | | 305.865 | ||
| | | | ||
| | | – | ||
| 905.865 | | 905.865 | ||
| A | | A | ||
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| 656.843 | | 656.843 | ||
| | | | ||
| | | – | ||
|} | |} | ||
== Temperament interpretations == | == Temperament interpretations == | ||
A diploid dicot temperament must temper out at least two commas: one to equate | A diploid dicot temperament must temper out at least two commas: one to equate a pair of intervals to the semioctave, and one to equate another pair of intervals to the hemififth. As a result, diploid dicot temperaments must have at least 4 primes. | ||
There are few temperaments that follow specifically the diploid dicot archetype, and those that do are often the lucky intersection of a diploid and an (alpha-)dicot temperament; lucky, because it's possible that the intersection of such a pair of temperaments produces a new one that cannot be expressed through diploid dicot, or any kind of chain of fifths. | |||
=== Sruti === | |||
The intersection of septimal [[diaschismic]] and [[namo]], which equates all of 16/13, 27/22, 11/9 and 39/32 to the neutral third, 45/32 and 64/45 with the semioctave. It is not very good for a diaschismic extension. | |||
[[ | === Semihemi === | ||
The intersection of [[hemififths]] and [[kalismic]] and [[barbados]], which maps 15/13 to the hemifourth, 49/40 to the hemififth, and 99/70 to the semioctave. It is quite accurate, and solid as a hemififths extension, where primes 5 and 7 are along the dicot chain, and primes 11 and 13 are along the diploid chain. | |||