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Golden sequences and tuning: Difference between revisions

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Golden generators can be named after temperaments which they generate, or MOS scales they are found in, i.e. "golden meantone", "golden mavila". "The golden generator" usually refers to the golden generator of oneirotonic, or [[logarithmic phi]].
Golden generators can be named after temperaments which they generate, or MOS scales they are found in, i.e. "golden meantone", "golden mavila". "The golden generator" usually refers to the golden generator of oneirotonic, or [[logarithmic phi]].


== Golden generators for common temperaments ==
Here are some golden generators for many rank-2 octave-periodic temperaments on [[Bird's eye view of temperaments by accuracy|this page]] as well as some other well-known temperaments. Buzzard and trienstonian were omitted because of their very awkward tuning ranges (both extremely close to 5edo) for the purposes of generating scales.
{| class="wikitable"
|+Common temperaments
!Temperament
!Generator
!Golden tuning
!MOS
|-
|Schismic/Garibaldi
|3/2
|702.75c
|12L 17s
|-
|Kleismic/Cata
|6/5
|317.17c
|4L 11s
|-
|Sensi
|9/7
|440.59c
|3L 5s
|-
|Wurschmidt
|5/4
|387.82c
|3L 28s
|-
|MIRACLE
|16/15
|115.59c
|10L 11s
|-
|Meantone
|3/2
|696.21c
|2L 3s
|-
|Mothra/Slendric
|8/7
|231.74c
|5L 21s
|-
|Didacus
|28/25
|191.13c
|6L 13s
|-
|Superpyth
|3/2
|708.05c
|5L 12s
|-
|Mohajira
|11/9
|348.91c
|7L 17s
|-
|Semaphore
|8/7
|254.04c
|5L 9s
|-
|Negri
|16/15
|124.77c
|1L 8s
|-
|Flattone
|3/2
|693.06c
|7L 12s
|-
|Porcupine
|10/9
|162.56c
|7L 8s
|-
|Magic
|5/4
|380.82c<ref group="note">Also has another tuning of 377.6 cents for 3L 13s. This results in a fifth almost as flat as in 7edo, but is a simpler scale of 16 notes rather than 19.</ref>
|3L 16s
|}
Exotemperaments are tuned to the simplest MOS that has a golden generator in the correct range.
{| class="wikitable"
|+Exotemperaments
!Temperament
!Generator
!Golden tuning
!MOS
|-
|Father
|8/5
|741.64c
|1L 1s
|-
|Mavila
|3/2
|672.85c
|2L 5s
|-
|Bug
|5/3
|940.15c
|1L 3s
|-
|Dicot
|5/4
|354.83c
|3L 4s
|}
Yo shares sensi's golden generator, so it is excluded here.
== Big table of golden generators ==
This table originated on the page "Golden MOS" and has moved here. It shows the golden generators for a large number of simple MOSes. Many have the same generator, so they've been placed in the same row.
{| class="wikitable sortable"
!MOS
!Generator (¢)
|-
|1L&nbsp;1s, 2L 1s, 3L 2s, 5L 3s, 8L 5s
|741.6408
|-
|1L&nbsp;2s, 3L 1s, 4L 3s, 7L 4s
|868.3282
|-
|1L&nbsp;3s, 4L 1s, 5L 4s
|940.1492
|-
|2L&nbsp;3s, 5L 2s, 7L 5s
|503.7855
|-
|1L&nbsp;4s, 5L 1s, 6L 5s
|986.4021
|-
|1L&nbsp;5s, 6L 1s, 7L 6s
|1018.6773
|-
|3L&nbsp;4s, 7L 3s
|354.8232
|-
|2L&nbsp;5s, 7L 2s
|527.1497
|-
|1L&nbsp;6s, 7L 1s
|1042.4790
|-
|3L&nbsp;5s, 8L 3s
|759.4078
|-
|1L&nbsp;7s, 8L 1s
|1060.7571
|-
|4L&nbsp;5s, 9L 4s
|273.8497
|-
|2L&nbsp;7s, 9L 2s
|541.3837
|-
|1L&nbsp;8s, 9L 1s
|1075.2344
|-
|3L&nbsp;7s, 10L 3s
|366.2564
|-
|1L&nbsp;9s, 10L 1s
|1086.9847
|-
|5L&nbsp;6s
|222.9668
|-
|4L&nbsp;7s
|877.7318
|-
|3L&nbsp;8s
|768.8815
|-
|2L&nbsp;9s, 11L 2s
|550.9646
|-
|1L&nbsp;10s, 11L 1s
|1096.7123
|-
|5L&nbsp;7s
|704.0956
|-
|1L&nbsp;11s, 12L 1s
|1104.8980
|-
|6L&nbsp;7s
|188.0298
|-
|5L&nbsp;8s
|465.0841
|-
|4L&nbsp;9s
|280.6103
|-
|3L&nbsp;10s
|373.0714
|-
|2L&nbsp;11s
|557.8535
|-
|1L&nbsp;12s
|1111.8816
|}


== Notes ==
== Notes ==
Retrieved from "https://en.xen.wiki/w/Golden_sequences_and_tuning"