148edo: Difference between revisions

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~~'''~~148edo''' is the [[equal division of the octave]] into 148 equal parts of 8.108 cents each, near a [[kleisma|kleisma]]. It provides the [[Optimal_patent_val|optimal patent val]] for 11-limit [[Diaschismic_family|echidnic temperament]], the 10&46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the [[~~Patent_val|~~patent val]] tempers out 686/675 and 1029/1024, but an alternative mapping ~~<~~148 235 344 416| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of [[~~80edo|~~80edo]] for 7- and 13- limit [[~~Diaschismic_family|~~bidia ~~temperament~~]], the 12&68 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. In the 13-limit, the patent val tempers out 325/324 and 364/363, and the alternative val 325/324 again, as well as 640/637 and 847/845.

{{EDO intro}} 148edo has a fifth on the sharp side, 3.45 cents sharp. The equal temperament tempers out [[2048/2025]] in the 5-limit, making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val| 148 235 344 416 }} with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7- and 13- limit [[bidia]], the 12 & 68 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for 11-limit [[echidnic]], the 10 & 46 temperament.

~~148 = 4 * 37~~, ~~with divisors 2, 4, 37, 74~~.

=== Prime harmonics ===

~~[[Category:Equal divisions of the octave~~|~~###]] ~~

=== Subsets and supersets ===

Since 148 = 4 × 37, 148edo has subset edos {{EDOs| 2, 4, 37, and 74 }}.

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 {{Infobox ET}}
-'''148edo''' is the [[equal division of the octave]] into 148 equal parts of 8.108 cents each, near a [[kleisma|kleisma]]. It provides the [[Optimal_patent_val|optimal patent val]] for 11-limit [[Diaschismic_family|echidnic temperament]], the 10&amp;46 temperament. It has a fifth on the sharp side, 3.45 cents sharp. It tempers out 2048/2025 in the 5-limit, making it a diaschismic system. In the 7-limit, the [[Patent_val|patent val]] tempers out 686/675 and 1029/1024, but an alternative mapping &lt;148 235 344 416| with a sharp rather than a flat 7 tempers out 3136/3125 instead, and provides a better tuning than the patent val tuning of [[80edo|80edo]] for 7- and 13- limit [[Diaschismic_family|bidia temperament]], the 12&amp;68 temperament. In the 11-limit, the patent val tempers out 385/384 and 441/440, and the alternative mapping with the sharp 7 tempers out 176/175, 896/891 and 1375/1372 instead. In the 13-limit, the patent val tempers out 325/324 and 364/363, and the alternative val 325/324 again, as well as 640/637 and 847/845.
+{{EDO intro}} 148edo has a fifth on the sharp side, 3.45 cents sharp. The equal temperament tempers out [[2048/2025]] in the 5-limit, making it a [[diaschismic]] system. In the 7-limit, the [[patent val]] tempers out [[686/675]] and [[1029/1024]], but the alternative mapping {{val| 148 235 344 416 }} with a sharp rather than a flat 7 tempers out [[3136/3125]] instead, and provides a better tuning than the patent val tuning of [[80edo]] for 7- and 13- limit [[bidia]], the 12 &amp; 68 temperament. In the 11-limit, the patent val tempers out [[385/384]] and [[441/440]], and the alternative mapping with the sharp 7 tempers out [[176/175]], [[896/891]] and [[1375/1372]] instead. In the 13-limit, the patent val tempers out [[325/324]] and [[364/363]], and the alternative val 325/324 again, as well as [[640/637]] and [[847/845]]. It provides the [[optimal patent val]] for 11-limit [[echidnic]], the 10 &amp; 46 temperament.
-= 4 * 37, with divisors 2, 4, 37, 74.
 === Prime harmonics ===
 {{Harmonics in equal|148}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+=== Subsets and supersets ===
+Since 148 = 4 × 37, 148edo has subset edos {{EDOs| 2, 4, 37, and 74 }}.