48ed5 - Revision history

Fredg999 category edits: Removing from Category:Edonoi using Cat-a-lot

2025-08-01T19:23:06Z

Removing from Category:Edonoi using Cat-a-lot

← Older revision		Revision as of 19:23, 1 August 2025
Line 274:		Line 274:
	48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val).		48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val).

	~~[[Category:Edonoi]]~~
	{{todo\|expand}}		{{todo\|expand}}

Fredg999 category edits: Removing from Category:Ed5 using Cat-a-lot

2025-08-01T18:39:06Z

Removing from Category:Ed5 using Cat-a-lot

← Older revision		Revision as of 18:39, 1 August 2025
Line 274:		Line 274:
	48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val).		48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val).

	~~[[Category:Ed5]]~~
	[[Category:Edonoi]]		[[Category:Edonoi]]
	{{todo\|expand}}		{{todo\|expand}}

BudjarnLambeth: Todo & collapsible

2024-12-22T04:08:10Z

Todo & collapsible

← Older revision		Revision as of 04:08, 22 December 2024
Line 3:		Line 3:

	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
			\|+ Intervals of 48ed5
	\|-		\|-
	! \| degree		! \| degree
Line 275:		Line 276:
	[[Category:Ed5]]		[[Category:Ed5]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
			{{todo\|expand}}

BudjarnLambeth: Harmonics

2024-10-06T01:29:09Z

Harmonics

@@ Line 2: / Line 2: @@
 '''[[Ed5|Division of the 5th harmonic]] into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.
 {| class="wikitable"
 |-
@@ Line 254: / Line 255: @@
 | | just major third plus two octaves
 |}
 ==48ed5 as a generator==

Plumtree: Infobox ET added

2022-10-05T20:42:06Z

Infobox ET added

← Older revision		Revision as of 20:42, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan\|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.		'''[[Ed5\|Division of the 5th harmonic]] into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan\|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.

Xenllium at 09:05, 1 January 2019

2019-01-01T09:05:38Z

← Older revision		Revision as of 09:05, 1 January 2019
Line 1:		Line 1:
	'''Division of the 5th harmonic into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan\|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.		'''[[Ed5\|Division of the 5th harmonic]] into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan\|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.

	{\| class="wikitable"		{\| class="wikitable"

Xenllium: Created page with "'''Division of the 5th harmonic into 48 equal parts''' (48ed5) is related to the semimiracle temperament. The step size is about 58.0482 cents. It is simil..."

2018-12-31T11:54:12Z

Created page with "'''Division of the 5th harmonic into 48 equal parts''' (48ed5) is related to the semimiracle temperament. The step size is about 58.0482 cents. It is simil..."

New page

'''Division of the 5th harmonic into 48 equal parts''' (48ed5) is related to the [[Gamelismic clan|semimiracle temperament]]. The step size is about 58.0482 cents. It is similar to every third step of [[62edo]], but with the 5/1 rather than the 2/1 being just. This tuning has a meantone fifth as the number of divisions of the 5th harmonic is multiple of 4.

{| class="wikitable"
|-
! | degree
! | cents value
! | corresponding <br>JI intervals
! | comments
|-
| | 0
| | 0.0000
| | '''exact [[1/1]]'''
| |
|-
| | 1
| | 58.0482
| | 31/30 ~ 30/29
| |
|-
| | 2
| | 116.0964
| | [[16/15]] ~ [[15/14]]
| |
|-
| | 3
| | 174.1446
| |
| |
|-
| | 4
| | 232.1928
| | [[8/7]]
| |
|-
| | 5
| | 290.2410
| | [[13/11]] ~ 45/38
| |
|-
| | 6
| | 348.2892
| | [[11/9]]
| |
|-
| | 7
| | 406.3374
| |
| |
|-
| | 8
| | 464.3856
| | [[17/13]]
| |
|-
| | 9
| | 522.4338
| | 23/17
| |
|-
| | 10
| | 580.4820
| | [[7/5]]
| |
|-
| | 11
| | 638.5302
| | [[13/9]] ~ 55/38
| |
|-
| | 12
| | 696.5784
| |
| | meantone fifth <br>(pseudo-[[3/2]])
|-
| | 13
| | 754.6266
| | [[17/11]]
| |
|-
| | 14
| | 812.6748
| | [[8/5]]
| |
|-
| | 15
| | 870.7230
| | 38/23
| |
|-
| | 16
| | 928.7712
| | 65/38
| |
|-
| | 17
| | 986.8194
| | 23/13
| |
|-
| | 18
| | 1044.8676
| | [[11/6]]
| |
|-
| | 19
| | 1102.9158
| | [[17/9]]
| |
|-
| | 20
| | 1160.9640
| | 45/23
| |
|-
| | 21
| | 1219.0122
| |
| |
|-
| | 22
| | 1277.0605
| | 23/11
| |
|-
| | 23
| | 1335.1087
| | [[13/6]]
| |
|-
| | 24
| | 1393.1569
| | [[19/17|38/17]] ~ 85/38
| | meantone major second plus an octave
|-
| | 25
| | 1451.2051
| | [[15/13|30/13]]
| |
|-
| | 26
| | 1509.2533
| | 55/23
| |
|-
| | 27
| | 1567.3015
| |
| |
|-
| | 28
| | 1625.3497
| | 23/9
| |
|-
| | 29
| | 1683.3979
| | 45/17
| |
|-
| | 30
| | 1741.4461
| | [[15/11|30/11]]
| |
|-
| | 31
| | 1799.4943
| | 65/23
| |
|-
| | 32
| | 1857.5425
| | [[19/13|38/13]]
| |
|-
| | 33
| | 1915.5907
| | 115/38
| |
|-
| | 34
| | 1973.6389
| | [[25/16|25/8]]
| |
|-
| | 35
| | 2031.6871
| | 55/17
| |
|-
| | 36
| | 2089.7353
| |
| | meantone major sixth plus an octave <br>(pseudo-[[10/3]])
|-
| | 37
| | 2147.7835
| | [[19/11|38/11]] ~ 45/13
| |
|-
| | 38
| | 2205.8317
| | 25/7
| |
|-
| | 39
| | 2263.8799
| | 85/23
| |
|-
| | 40
| | 2321.9281
| | 65/17
| |
|-
| | 41
| | 2379.9763
| |
| |
|-
| | 42
| | 2438.0245
| | [[45/44|45/11]]
| |
|-
| | 43
| | 2496.0727
| | [[19/18|38/9]] ~ 55/13
| |
|-
| | 44
| | 2554.1209
| | 35/8
| |
|-
| | 45
| | 2612.1691
| |
| |
|-
| | 46
| | 2670.2173
| | [[14/3]]
| |
|-
| | 47
| | 2728.2655
| | 29/6
| |
|-
| | 48
| | 2786.3137
| | '''exact [[5/1]]'''
| | just major third plus two octaves
|}

==48ed5 as a generator==
48ed5 can also be thought of as a [[generator]] of the 23-limit temperament which tempers out 169/168, 225/224, 243/242, 286/285, 385/384, 598/595, and 1445/1444 which is a [[cluster temperament]] with 21 clusters of notes in an octave. The large chroma interval between adjacent notes in each cluster is very versatile, representing 77/75 ~ 39/38 ~ 165/161 ~ 253/247 ~ 169/165 ~ 128/125 ~ 306/299 ~ 45/44 ~ 136/133 ~ 46/45 ~ 608/595 ~ 1292/1265 ~ 49/48 ~ 50/49 ~ 352/345 ~ 55/54 ~ 56/55 ~ 64/63 all tempered together. This temperament is supported by [[62edo]], [[82edo]] (82gh val), and [[144edo]] (144f val).

[[Category:Ed5]]
[[Category:Edonoi]]