72edo: Difference between revisions
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== Theory == | == Theory == | ||
72edo approximates [[11-limit]] [[just intonation]] exceptionally well, is [[consistent]] in the [[17-limit]], and is the ninth [[The Riemann | 72edo approximates [[11-limit]] [[just intonation]] exceptionally well, is [[consistent]] in the [[17-limit]], and is the ninth [[The Riemann zeta function and tuning #Zeta EDO lists|zeta integral tuning]]. The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33. | ||
72edo is an excellent tuning for the [[miracle]] temperament, especially the 11-limit version, and the related rank-3 temperament [[prodigy]], and is a good tuning for other temperaments and scales, including [[wizard]], [[harry]], [[catakleismic]], [[compton]], [[unidec]] and [[tritikleismic]]. | 72edo is an excellent tuning for the [[miracle]] temperament, especially the 11-limit version, and the related rank-3 temperament [[prodigy]], and is a good tuning for other temperaments and scales, including [[wizard]], [[harry]], [[catakleismic]], [[compton]], [[unidec]] and [[tritikleismic]]. | ||
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=== 15-odd-limit interval mappings === | === 15-odd-limit interval mappings === | ||
The following table shows how [[15-odd-limit intervals]] are represented in 72edo. Prime harmonics are in '''bold'''. As 72edo is consistent in the 15-odd-limit, the results by direct approximation and patent val mapping are the same. | The following table shows how [[15-odd-limit intervals]] are represented in 72edo. Prime harmonics are in '''bold'''. As 72edo is consistent in the 15-odd-limit, the results by direct approximation and patent val mapping are the same. | ||
{{15-odd-limit|72}} | {{15-odd-limit|72}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
! rowspan="2" | Subgroup | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br>8ve Stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning Error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
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{| class="wikitable center-1 center-2" | {| class="wikitable center-1 center-2" | ||
|- | |- | ||
! Periods<br>per | ! Periods<br>per 8ve | ||
! Generator | ! Generator | ||
! Names | ! Names | ||
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| 1 | | 1 | ||
| 7\72 | | 7\72 | ||
| [[Miracle]]/benediction/manna | | [[Miracle]] / benediction / manna | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 995: | Line 996: | ||
| 1 | | 1 | ||
| 31\72 | | 31\72 | ||
| [[Marvo]]/zarvo | | [[Marvo]] / zarvo | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 1,011: | Line 1,012: | ||
| 2 | | 2 | ||
| 7\72 | | 7\72 | ||
| [[ | | [[Semimiracle]] | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 1,019: | Line 1,020: | ||
| 2 | | 2 | ||
| 13\72 | | 13\72 | ||
| [[Wizard]]/lizard/gizzard | | [[Wizard]] / lizard / gizzard | ||
|- | |- | ||
| 2 | | 2 | ||
| 19\72 | | 19\72 | ||
| [[ | | [[Bikleismic]] | ||
|- | |- | ||
| 3 | | 3 | ||
| Line 1,079: | Line 1,080: | ||
| 9 | | 9 | ||
| 3\72 | | 3\72 | ||
| [[Ennealimmal]]/ | | [[Ennealimmal]] / ennealimnic | ||
|- | |- | ||
| 12 | | 12 | ||
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* [https://www.myspace.com/dawier Danny Wier, composer and musician who specializes in 72-edo] | * [https://www.myspace.com/dawier Danny Wier, composer and musician who specializes in 72-edo] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Marvel]] | [[Category:Marvel]] | ||
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[[Category:Prodigy]] | [[Category:Prodigy]] | ||
[[Category:Wizard]] | [[Category:Wizard]] | ||