Septimal ennealimma: Difference between revisions
Created page with "'''Septimal ennealimma''', '''no-five ennealimma''', or '''tritrizo comma''' is an unnoticeable 7-limit comma defined as 40353607/40310784 and measuring 1.838 cents. It arises..." |
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''' | {{Infobox Interval | ||
| Ratio = 40353607/40310784 | |||
| Name = septimal ennealimma, septiennealimma, no-five ennealimma | |||
| Color name = tritrizo comma | |||
| Comma = yes | |||
}} | |||
The '''septimal ennealimma''', '''septiennealimma''' or '''no-five ennealimma''' is an [[unnoticeable comma|unnoticeable]] [[7-limit]] [[comma]] measuring 1.838 [[cent]]s. It is the difference between a stack of nine [[7/6|septimal minor thirds (7/6)]] and two [[2/1|octaves]], or ([[7/6]])<sup>9</sup> / ([[2/1]])<sup>2</sup>. | |||
== Temperaments == | |||
In the [[2.3.7 subgroup]], tempering it out leads to the 2.3.7-subgroup [[restriction]] of the [[ennealimmal]] temperament, which is the head of the [[septiennealimmal clan]]. It can only possibly be tempered out in an edo if that edo is a multiple of 9. | |||
In the full 7-limit, tempering it out leads to the '''septiennealimmal temperament''' (''cf''. septimal ennealimmal temperament). You may find a list of good equal temperaments that support this temperament below. | |||
=== Septiennealimmal === | |||
[[Subgroup]]: 2.3.5.7 | |||
{{Mapping|legend=1| 9 0 0 11 | 0 1 0 1 | 0 0 1 0 }} | |||
: mapping generators: ~2592/2401, ~3, ~5 | |||
[[Optimal tuning]]s: | |||
* [[WE]]: ~2592/2401 = 133.3357{{c}}, ~3/2 = 701.9772{{c}}, ~5/4 = 386.2717{{c}} | |||
: [[error map]]: {{val| +0.021 +0.043 -0.000 -0.135 }} | |||
* [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~3/2 = 701.9833{{c}}, ~5/4 = 386.2877{{c}} | |||
: error map: {{val| 0.000 +0.028 -0.026 -0.176 }} | |||
{{Optimal ET sequence|legend=1| 27, 45, 63, 72, 99, 171, 441, 612 }} | |||
[[Badness]] (Sintel): 2.21 | |||
== See also == | |||
* [[Ennealimma]] | |||
[[Category:Septiennealimmal]] | |||
[[Category:Commas named for their periods per equave]] | |||
Latest revision as of 11:05, 23 February 2026
| Interval information |
septiennealimma,
no-five ennealimma
The septimal ennealimma, septiennealimma or no-five ennealimma is an unnoticeable 7-limit comma measuring 1.838 cents. It is the difference between a stack of nine septimal minor thirds (7/6) and two octaves, or (7/6)9 / (2/1)2.
Temperaments
In the 2.3.7 subgroup, tempering it out leads to the 2.3.7-subgroup restriction of the ennealimmal temperament, which is the head of the septiennealimmal clan. It can only possibly be tempered out in an edo if that edo is a multiple of 9.
In the full 7-limit, tempering it out leads to the septiennealimmal temperament (cf. septimal ennealimmal temperament). You may find a list of good equal temperaments that support this temperament below.
Septiennealimmal
Subgroup: 2.3.5.7
Mapping: [⟨9 0 0 11], ⟨0 1 0 1], ⟨0 0 1 0]]
- mapping generators: ~2592/2401, ~3, ~5
- WE: ~2592/2401 = 133.3357 ¢, ~3/2 = 701.9772 ¢, ~5/4 = 386.2717 ¢
- error map: ⟨+0.021 +0.043 -0.000 -0.135]
- CWE: ~2592/2401 = 133.3333 ¢, ~3/2 = 701.9833 ¢, ~5/4 = 386.2877 ¢
- error map: ⟨0.000 +0.028 -0.026 -0.176]
Optimal ET sequence: 27, 45, 63, 72, 99, 171, 441, 612
Badness (Sintel): 2.21