17edt: Difference between revisions
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In the no-twos subgroup, 17edt tempers out [[245/243]] and 16807/15625 in the 7-limit, 77/75 and [[1331/1323]] in the 11-limit, and 175/169 and 121/117 in the 13-limit. It [[support]]s the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written b17&b21. | In the no-twos subgroup, 17edt tempers out [[245/243]] and 16807/15625 in the 7-limit, 77/75 and [[1331/1323]] in the 11-limit, and 175/169 and 121/117 in the 13-limit. It [[support]]s the no-twos temperament tempering out 245/243 and 77/75, which in terms of tritave patent vals could be written b17&b21. | ||
17EDT is the sixth [[ | 17EDT is the sixth [[Riemann zeta function#Removing primes|zeta peak tritave division]]. | ||
{{Harmonics in equal|17|3|1|intervals=prime|columns=15}} | {{Harmonics in equal|17|3|1|intervals=prime|columns=15}} | ||
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Interval approximations shown in the 3.5''.14.16''.17 subgroup column are those within the 77-[[integer limit]] and less than 15 [[cents]] off, consistency is not taken into account. | Interval approximations shown in the 3.5''.14.16''.17 subgroup column are those within the 77-[[integer limit]] and less than 15 [[cents]] off, consistency is not taken into account. | ||
{| class="wikitable center-2 center-3 center-4 mw-collapsible" | {| class="wikitable center-2 center-3 center-4 center-5 mw-collapsible" | ||
|+ style="font-size: 105%;" | Intervals of 17edt | |+ style="font-size: 105%;" | Intervals of 17edt | ||
|- | |- | ||
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| K♯ | | K♯ | ||
| G♭ | | G♭ | ||
| | | [[17/15]] (+7.1¢); [[63/55]] (−11.3¢) | ||
| 16/14 ([[8/7]]) (-7.5¢) | | 16/14 ([[8/7]]) (-7.5¢) | ||
| 223.8 | | 223.8 | ||
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== Z function == | == Z function == | ||
Below is a plot of the [[ | Below is a plot of the [[Riemann zeta function#Removing primes|no-twos Z function]] in the vicinity of 17EDT. | ||
[[File:17edt.png|alt=17edt.png|17edt.png]] | [[File:17edt.png|alt=17edt.png|17edt.png]] | ||
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* "Circle is Square" from ''Xenharmonics, Vol. 5'' (2024) – [https://open.spotify.com/track/7aY59bxbyy17SZhBGTTJHF Spotify] | [https://togenom.bandcamp.com/track/circle-is-square Bandcamp] | [https://www.youtube.com/watch?v=WPR52uMkZK8 YouTube] | * "Circle is Square" from ''Xenharmonics, Vol. 5'' (2024) – [https://open.spotify.com/track/7aY59bxbyy17SZhBGTTJHF Spotify] | [https://togenom.bandcamp.com/track/circle-is-square Bandcamp] | [https://www.youtube.com/watch?v=WPR52uMkZK8 YouTube] | ||
[[Category:macrotonal]] | [[Category:macrotonal]] | ||
[[Category:tritave]] | [[Category:tritave]] | ||