48edo: Difference between revisions
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=== Subsets and supersets === | === Subsets and supersets === | ||
48edo is the 10th [[highly composite edo]]. Since 48 factors into {{factorization|48}}, 48edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 16, and 24 }}. | 48edo is the 10th [[highly composite edo]]. Since 48 factors into {{factorization|48}}, 48edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 16, and 24 }}. | ||
== Intervals == | == Intervals == | ||
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| 1200.0 | | 1200.0 | ||
| {{UDnote|step=48}} | | {{UDnote|step=48}} | ||
|} | |||
== Notation == | |||
=== Ups and downs notation === | |||
48edo can be notated using [[ups and downs notation]]. This can be accomplished by combining [[Helmholtz-Ellis]] accidentals with semisharps and semiflats: | |||
{{Sharpness-sharp4|48}} | |||
=== Sagittal notation === | |||
This notation is a superset of the notations for EDOs [[24edo#Sagittal notation|24]], [[12edo#Sagittal notation|12]], [[8edo#Sagittal notation|8]], and [[6edo#Sagittal notation|6]]. | |||
==== Evo flavor ==== | |||
<imagemap> | |||
File:48-EDO_Evo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 535 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 140 106 [[736/729]] | |||
rect 140 80 260 106 [[33/32]] | |||
default [[File:48-EDO_Evo_Sagittal.svg]] | |||
</imagemap> | |||
==== Revo flavor ==== | |||
<imagemap> | |||
File:48-EDO_Revo_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 535 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 140 106 [[736/729]] | |||
rect 140 80 260 106 [[33/32]] | |||
default [[File:48-EDO_Revo_Sagittal.svg]] | |||
</imagemap> | |||
==== Evo-SZ flavor ==== | |||
<imagemap> | |||
File:48-EDO_Evo-SZ_Sagittal.svg | |||
desc none | |||
rect 80 0 300 50 [[Sagittal_notation]] | |||
rect 300 0 519 80 [https://sagittal.org#periodic-table Periodic table of EDOs with sagittal notation] | |||
rect 20 80 140 106 [[736/729]] | |||
rect 140 80 260 106 [[33/32]] | |||
default [[File:48-EDO_Evo-SZ_Sagittal.svg]] | |||
</imagemap> | |||
== Approximation to JI == | |||
=== Zeta peak index === | |||
{| class="wikitable center-all" | |||
|- | |||
! colspan="3" | Tuning | |||
! colspan="3" | Strength | |||
! colspan="2" | Closest edo | |||
! colspan="2" | Integer limit | |||
|- | |||
! ZPI | |||
! Steps per octave | |||
! Step size (cents) | |||
! Height | |||
! Integral | |||
! Gap | |||
! Edo | |||
! Octave (cents) | |||
! Consistent | |||
! Distinct | |||
|- | |||
| [[226zpi]] | |||
| 47.9883202080850 | |||
| 25.0060847055410 | |||
| 5.843508 | |||
| 0.890480 | |||
| 13.888482 | |||
| 48edo | |||
| 1200.29206586597 | |||
| 6 | |||
| 6 | |||
|} | |} | ||
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|} | |} | ||
<nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
== Music == | == Music == | ||