User:Eufalesio/Important Tables - Revision history

Eufalesio: HSA5 to HSAF

2026-10-11T10:54:03Z

HSA5 to HSAF

← Older revision		Revision as of 10:54, 11 October 2026
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	==== CWE 31-limit ====		==== CWE 31-limit ====
	A good compromise, if you want to use 31 and 29 more readily specially in the context of [[User:Eufalesio/Harmonic Segments Along Fifths#HSA5 8\|~~HSA5~~ 8]].		A good compromise, if you want to use 31 and 29 more readily specially in the context of [[User:Eufalesio/Harmonic Segments Along Fifths#HSA5 8\|HSAF 8]].
	* PrimeMapping('''2, 1902.22, 2786.218''', 3368.927, 4151.049, 4440.416, 4904.8, 5097.316, ''23'', 5830.144, 5945.681)		* PrimeMapping('''2, 1902.22, 2786.218''', 3368.927, 4151.049, 4440.416, 4904.8, 5097.316, ''23'', 5830.144, 5945.681)

Eufalesio: /* Least error 13-limit: */

2026-10-04T14:43:19Z

Least error 13-limit:

← Older revision		Revision as of 14:43, 4 October 2026
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	* Generators: 1200., 702.23, 386.275		* Generators: 1200., 702.23, 386.275
	* (P8, P5, SP1, ^P1): 1200, 702.23, 26.76, 4.115		* (P8, P5, SP1, ^P1): 1200, 702.23, 26.76, 4.115
			* Error map: 0.000, 0.276, -0.008, -0.060, -0.005, -0.061, 0.355, -0.053, ''0.000'', 0.953, 1.104

	==== CWE 19-limit ====		==== CWE 19-limit ====
Line 16:		Line 17:
	* Generators: 1200., 702.228, 386.238		* Generators: 1200., 702.228, 386.238
	* (P8, P5, SP1, ^P1): 1200, 702.228, 26.736, 4.062		* (P8, P5, SP1, ^P1): 1200, 702.228, 26.736, 4.062
			* Error map: 0.000, 0.273, -0.075, -0.015, -0.078, -0.032, 0.148, -0.136, ''0.000'', 0.827, 0.964

	==== CWE 31-limit ====		==== CWE 31-limit ====
			A good compromise, if you want to use 31 and 29 more readily specially in the context of [[User:Eufalesio/Harmonic Segments Along Fifths#HSA5 8\|HSA5 8]].
	* PrimeMapping('''2, 1902.22, 2786.218''', 3368.927, 4151.049, 4440.416, 4904.8, 5097.316, ''23'', 5830.144, 5945.681)		* PrimeMapping('''2, 1902.22, 2786.218''', 3368.927, 4151.049, 4440.416, 4904.8, 5097.316, ''23'', 5830.144, 5945.681)

	*Generators: 1200., 702.22, 386.218		*Generators: 1200., 702.22, 386.218
	* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978		* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978
			* Error map: 0.000, 0.265, -0.095, 0.101, -0.269, -0.112, -0.155, -0.197, ''0.000'', 0.567, 0.645
	I don't recommend tempering octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy and tweaking octaves does close to nothing. Essentially, touch ~3 and ~5, not 2.		I don't recommend tempering octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy and tweaking octaves does close to nothing. Essentially, touch ~3 and ~5, not 2.

Eufalesio: Reorder and add (WIP)

2026-10-04T13:11:40Z

Reorder and add (WIP)

@@ Line 1: / Line 1: @@
 Data I deem important! <small>Note on shorthand: sk = k/(k-1)</small>
 == Temperament properties of septischismic temperaments (I care about) ==
 '''217 & 270 & 311: Ultimate {S49·S55, S64, S65} = {s2080, s4096, 35035/34992}'''
@@ Line 17: / Line 63: @@
 ! colspan="2" |
 ! colspan="2" |Gariwizmic
+! colspan="2" |Cotoneum
 ! rowspan="3" |Ultimate r3
 |-
@@ Line 23: / Line 69: @@
 ! colspan="4" |Cassandra
 ! colspan="2" |Vulture
 |- style="font-weight:bold;"
 ! 311
@@ Line 31: / Line 78: @@
 ! 270
 ! 217
 |-
-| colspan="8" | s2080
+| colspan="9" | S65
 |-
-| colspan="8" | s4096
+| colspan="9" | S76
 |-
-| colspan="8" | 35035/34492
+| colspan="9" |S77
 |-
-| colspan="2" | s2401
+| colspan="2" | S49
-| s676
+| S26
-| s81
+| S8
-| colspan="2" | s1716
+| colspan="2" | S99
-| s441
+| colspan="2" | S21
 | –
 |-
-| s625
+| S25
-| colspan="4" | s385
+| colspan="4" | S15
-| colspan="2" | s1001
+| colspan="2" | S26
 | –
 |}
 Any other join of Ultimate edos is ommited because I either don't know or don't care.
 == Table of Ultimate edos' intervals ==

Eufalesio: Unifying nomenclature

2026-10-02T09:30:55Z

Unifying nomenclature

← Older revision		Revision as of 09:30, 2 October 2026
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	==== Least error 13-limit: ====		==== Least error 13-limit: ====
	The best setting for general performance in the 13-limit. Error is going to be concentrated in the chain of fifths either way so at that point it's better to make all primes have minimal error. It also performs good with 19/16, and is basically identical to CE olympic.		The best setting for general performance in the 13-limit. Error is going to be concentrated in the chain of fifths either way so at that point it's better to make all primes have minimal error. It also performs good with 19/16, and is basically identical to CE olympic. It's my standard tuning of choice for Ultimate in most occassions because the 13-limit most important to me.
	* ~~Primes:~~ '''~~1200~~, 1902.23, 2786.275''', 3368.78, 4151.29, 4440.485, 4905.31, 5097.425, ''23'', 5830.53, 5946.14		* PrimeMapping('''2, 1902.23, 2786.275''', 3368.78, 4151.29, 4440.485, 4905.31, 5097.425, ''23'', 5830.53, 5946.14)
	* Generators: 1200, 702.23, 386.275		* Generators: 1200., 702.23, 386.275
	* (P8, P5, SP1, ^P1): 1200, 702.23, 26.76, 4.115		* (P8, P5, SP1, ^P1): 1200, 702.23, 26.76, 4.115

	==== CWE 19-limit ====		==== CWE 19-limit ====
	Detuning the basis a tiny bit so that 17/16 can be a bit purer. Error is still kept minimal for the yazalathana.		Detuning the basis a tiny bit so that septisperasmic 17/16 can be a bit purer. Error is still kept minimal for the yazalathana, though it can be used as a slight compromise for the rest of the primes.

	*~~Primes: '''1200.000~~''', ~~'''~~1902.228~~'''~~, ~~'''~~2786.238''', 3368.811, 4151.239, 4440.495, 4905.104, 5097.377, ''23'', 5830.404, 5946.~~000~~		*PrimeMapping('''2, 1902.228, 2786.238''', 3368.811, 4151.239, 4440.495, 4905.104, 5097.377, ''23'', 5830.404, 5946.)
	* Generators: 1200, 702.228, 386.238		* Generators: 1200., 702.228, 386.238
	* (P8, P5, SP1, ^P1): 1200, 702.228, 26.736, 4.062		* (P8, P5, SP1, ^P1): 1200, 702.228, 26.736, 4.062

	==== CWE 31-limit ====		==== CWE 31-limit ====

	* ~~Primes: 1200.000~~, 1902.22, 2786.218, 3368.927, 4151.049, 4440.416, 4904.8, 5097.316, ''23'', 5830.144, 5945.681		* PrimeMapping('''2, 1902.22, 2786.218''', 3368.927, 4151.049, 4440.416, 4904.8, 5097.316, ''23'', 5830.144, 5945.681)

	*Generators: 1200, 702.22, 386.218		*Generators: 1200., 702.22, 386.218
	* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978		* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978
	I don't recommend tempering octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy and tweaking octaves does close to nothing. Essentially, touch ~3 and ~5, not 2.		I don't recommend tempering octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy and tweaking octaves does close to nothing. Essentially, touch ~3 and ~5, not 2.
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	\|[[11/10]]		\|[[11/10]]
	\| rowspan="2" \|16.8		\| rowspan="2" \|16.8
	\|~~vsMM2~~		\|vrsM2
	\|165.015		\|165.015
	\|-		\|-
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	\|[[15/13]]		\|[[15/13]]
	\| rowspan="2" \|18.53		\| rowspan="2" \|18.53
	\|^^~~SMM2~~		\|^^rSM2
	\|248.02		\|248.02
	\|-		\|-
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	\|[[22/15]]		\|[[22/15]]
	\| rowspan="2" \|39.445		\| rowspan="2" \|39.445
	\|~~vsMP5~~		\|vrsP5
	\|662.785		\|662.785
	\|-		\|-
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	\|[[26/15]]		\|[[26/15]]
	\| rowspan="2" \|16.8		\| rowspan="2" \|16.8
	\|~~vvsmm7~~		\|vvrsm7
	\|951.98		\|951.98
	\|-		\|-
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	\|[[20/11]]		\|[[20/11]]
	\| rowspan="2" \|14.075		\| rowspan="2" \|14.075
	\|^~~Smm7~~		\|^rSm7
	\|1034.985		\|1034.985
	\|-		\|-
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	\|[[13/7]]		\|[[13/7]]
	\| rowspan="2" \|8.57		\| rowspan="2" \|8.57
	\|~~vsMM7~~		\|vrsM7
	\|1071.705		\|1071.705
	\|-		\|-

Eufalesio: Every byte counts.

2026-10-01T18:21:05Z

Every byte counts.

Eufalesio at 18:04, 1 October 2026

2026-10-01T18:04:26Z

← Older revision		Revision as of 18:04, 1 October 2026
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	==== Least error 13-limit: ====		==== Least error 13-limit: ====
	The best setting for general performance in the 13-limit. Error is going to be concentrated in the chain of fifths either way so at that point it's better to make all primes have minimal error. ~~Also~~ performs good with ~~the~~ 19/16.		The best setting for general performance in the 13-limit. Error is going to be concentrated in the chain of fifths either way so at that point it's better to make all primes have minimal error. It also performs good with 19/16, and is basically identical to CE olympic.
	* Primes: '''1200, 1902.23, 2786.275''', 3368.78, 4151.29, 4440.485, 4905.31, 5097.425, ''23'', 5830.53, 5946.14		* Primes: '''1200, 1902.23, 2786.275''', 3368.78, 4151.29, 4440.485, 4905.31, 5097.425, ''23'', 5830.53, 5946.14
	* Generators: 1200, 702.23, 386.275		* Generators: 1200, 702.23, 386.275
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	*Generators: 1200, 702.22, 386.218		*Generators: 1200, 702.22, 386.218
	* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978		* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978
	I don't recommend ~~detempering~~ octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy. Essentially~~, if need be~~, touch 3/2 and 5/4, not 2/1.		I don't recommend tempering octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy and tweaking octaves does close to nothing. Essentially, touch 3/2 and 5/4, not 2/1.

	== Table of Ultimate edos' intervals ==		== Table of Ultimate edos' intervals ==

Eufalesio at 17:56, 1 October 2026

2026-10-01T17:56:11Z

Eufalesio: /* Temperament properties of Ultimate edos (I care about) */

2026-09-30T17:20:09Z

Temperament properties of Ultimate edos (I care about)

Eufalesio: Added septischismic recommended tunings and fixed 270 225-odd-limit table blunders

2026-09-30T17:13:06Z

Added septischismic recommended tunings and fixed 270 225-odd-limit table blunders

Show changes

Eufalesio: /* Table of Ultimate edos' intervals */

2026-08-14T17:01:01Z

Table of Ultimate edos' intervals

Show changes

← Older revision		Revision as of 18:21, 1 October 2026
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	== Temperament properties of septischismic temperaments (I care about) ==		== Temperament properties of septischismic temperaments (I care about) ==
	'''217 & 270 & 311: Ultimate {~~S49*S55~~, S64, S65} = {s2080, s4096, 35035/34992}'''		'''217 & 270 & 311: Ultimate {S49·S55, S64, S65} = {s2080, s4096, 35035/34992}'''

	* '''270 & 311''': Newt {S49, S55, S64, S65} = {s2080, s2401, s3025, s4096}; supported trivially by 41edo		* '''270 & 311''': Newt {S49, S55, S64, S65} = {s2080, s2401, s3025, s4096}; supported trivially by 41edo
	* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {s1716, <span data-darkreader-inline-color="">s2080, s4096, 35035/34992}; supported trivially by 94edo</span>		* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {s1716, <span data-darkreader-inline-color="">s2080, s4096, 35035/34992}; supported trivially by 94edo</span>
	* '''41 & 217''': Cotoneum {S21, ~~S28<sup>2</sup>*S29~~, S64, S65} = {<span data-darkreader-inline-color="">s364,</span> s441, <span data-darkreader-inline-color="">s2080, s4096}; supported trivially by 41edo</span>		* '''41 & 217''': Cotoneum {S21, S28²·S29, S64, S65} = {<span data-darkreader-inline-color="">s364,</span> s441, <span data-darkreader-inline-color="">s2080, s4096}; supported trivially by 41edo</span>
	* '''41 & 53''': Cassandra {S25*S26, S15, S64, S65} = {s225, s325, s352, s385}; supported trivially by 12e		* '''41 & 53''': Cassandra {S25*S26, S15, S64, S65} = {s225, s325, s352, s385}; supported trivially by 12e
	** '''270:''' {S49, S55, S64, S65, S99} = {s1001, s2401, s2080, s3025, s4096}		** '''270:''' {S49, S55, S64, S65, S99} = {s1001, s2401, s2080, s3025, s4096}
	** '''94:''' {S15, S11/S12, S64, S65, S99} = {s225, s325, s352, s385, s1716}		** '''94:''' {S15, S11/S12, S64, S65, S99} = {s225, s325, s352, s385, s1716}
	** '''12e:''' {S8, S9, S15, S64, S65} = {~~22/21~~, ~~50/49~~, ~~64/63~~, ~~65/63~~, ~~81/80~~}		** '''12e:''' {S8, S9, S15, S64, S65} = {s22, s50, s64, s65, s81}

	Which can implicitly be seen in this table:		Which can implicitly be seen in this table:
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	*Generators: 1200, 702.22, 386.218		*Generators: 1200, 702.22, 386.218
	* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978		* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978
	I don't recommend tempering octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy and tweaking octaves does close to nothing. Essentially, touch 3/2 and 5/4, not 2/1.		I don't recommend tempering octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy and tweaking octaves does close to nothing. Essentially, touch ~3 and ~5, not 2.

	== Table of Ultimate edos' intervals ==		== Table of Ultimate edos' intervals ==

← Older revision		Revision as of 17:56, 1 October 2026
Line 56:		Line 56:

	=== Recommended tunings of Ultimate r3 (septisperasmic - septifantasious): ===		=== Recommended tunings of Ultimate r3 (septisperasmic - septifantasious): ===
			The 31-limit is provided with 23 in italic because it isn't part of the temperament, but is intended to be used for prime mappings in Scale workshop. 23 is there so that scale workshop doesn't go bonkers when you accidentally input the mapping for 29 in the 23 slot.

	==== Least error 13-limit: ====		==== Least error 13-limit: ====
	The best setting for general performance in the 13-limit. Error is going to be concentrated in the chain of fifths either way so at that point it's better to make all primes have minimal error. Also performs good with the 19/16.		The best setting for general performance in the 13-limit. Error is going to be concentrated in the chain of fifths either way so at that point it's better to make all primes have minimal error. Also performs good with the 19/16.
	* Primes: '''1200, 1902.23, 2786.275''', 3368.78, 4151.29, 4440.485, 4905.31, 5097.425, 5830.53, 5946.14		* Primes: '''1200, 1902.23, 2786.275''', 3368.78, 4151.29, 4440.485, 4905.31, 5097.425, ''23'', 5830.53, 5946.14
	* Generators: 1200, 702.23, 386.275		* Generators: 1200, 702.23, 386.275
	* (P8, P5, SP1, ^P1): 1200, 702.23, 26.76, 4.115		* (P8, P5, SP1, ^P1): 1200, 702.23, 26.76, 4.115

	==== CWE 19-limit ====		==== CWE 19-limit ====
	Detuning a tiny bit ~~the 5/4~~ so that 17/16 can be a bit purer. Error is still kept minimal for the yazalathana.		Detuning the basis a tiny bit so that 17/16 can be a bit purer. Error is still kept minimal for the yazalathana.

	*Primes: '''1200.000''', '''1902.228''', '''2786.238''', 3368.811, 4151.239, 4440.495, 4905.104, 5097.377, 5830.404, 5946.000		*Primes: '''1200.000''', '''1902.228''', '''2786.238''', 3368.811, 4151.239, 4440.495, 4905.104, 5097.377, ''23'', 5830.404, 5946.000
	* Generators: 1200, 702.228, 386.238		* Generators: 1200, 702.228, 386.238
	* (P8, P5, SP1, ^P1): 1200, 702.228, 26.736, 4.062		* (P8, P5, SP1, ^P1): 1200, 702.228, 26.736, 4.062
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	==== CWE 31-limit ====		==== CWE 31-limit ====

	* Primes: 1200.000, 1902.~~220~~, 2786.218, 3368.927, 4151.049, 4440.416, 4904.~~800~~, 5097.316, 5830.144, 5945.681		* Primes: 1200.000, 1902.22, 2786.218, 3368.927, 4151.049, 4440.416, 4904.8, 5097.316, ''23'', 5830.144, 5945.681

	*Generators: 1200, 702.22, 386.218		*Generators: 1200, 702.22, 386.218
	* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978		* (P8, P5, SP1, ^P1): 1200, 702.22, 26.64, 3.978
			I don't recommend detempering octaves in Ultimate because error is already close to 0 in the 13-limit except for p3. For the rest of more compromised tunings, error is messy. Essentially, if need be, touch 3/2 and 5/4, not 2/1.

	== Table of Ultimate edos' intervals ==		== Table of Ultimate edos' intervals ==

← Older revision		Revision as of 17:20, 30 September 2026
Line 1:		Line 1:
	Data I deem important! <small>Note on shorthand: sk = k/(k-1)</small>		Data I deem important! <small>Note on shorthand: sk = k/(k-1)</small>

	== Temperament properties of ~~Ultimate edos~~ (I care about) ==		== Temperament properties of septischismic temperaments (I care about) ==
	'''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {s2080, s4096, 35035/34992}'''		'''217 & 270 & 311: Ultimate {S49*S55, S64, S65} = {s2080, s4096, 35035/34992}'''

	* '''270 & 311''': Newt {S49, S55, S64, S65} = {s2080, s2401, s3025, s4096}; supported trivially by 41edo		* '''270 & 311''': Newt {S49, S55, S64, S65} = {s2080, s2401, s3025, s4096}; supported trivially by 41edo
	* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {s1716, <span data-darkreader-inline-color="">s2080, s4096, 35035/34992}; supported trivially by 94edo</span>		* '''94 & 270''': Gariwizmic {S11/S12, S64, S65, S99) = {s1716, <span data-darkreader-inline-color="">s2080, s4096, 35035/34992}; supported trivially by 94edo</span>
	* '''~~41g~~ & 217''': Cotoneum {S21, S28<sup>2</sup>*S29, S64, S65} = {s441, <span data-darkreader-inline-color="">s2080, s4096~~, 10976/10935~~}; supported trivially by 41edo</span>		* '''41 & 217''': Cotoneum {S21, S28<sup>2</sup>*S29, S64, S65} = {<span data-darkreader-inline-color="">s364,</span> s441, <span data-darkreader-inline-color="">s2080, s4096}; supported trivially by 41edo</span>
	* '''~~41g~~ & 53''': Cassandra {S25*S26, S15, S64, S65} = {s225, s325, s352, s385}; supported trivially by 12e		* '''41 & 53''': Cassandra {S25*S26, S15, S64, S65} = {s225, s325, s352, s385}; supported trivially by 12e
	** '''270:''' {S49, S55, S64, S65, S99} = {s1001, s2401, s2080, s3025, s4096}		** '''270:''' {S49, S55, S64, S65, S99} = {s1001, s2401, s2080, s3025, s4096}
	** '''94:''' {S15, S11/S12, S64, S65, S99} = {s225, s325, s352, s385, s1716}		** '''94:''' {S15, S11/S12, S64, S65, S99} = {s225, s325, s352, s385, s1716}
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	Ultimate can be easily defined in 19-limit as {S50, S64, S65, S76, S77} = {s1540, s1729, s2080, s2500, s4096}.		Ultimate can be easily defined in 19-limit as {S50, S64, S65, S76, S77} = {s1540, s1729, s2080, s2500, s4096}.

	=== Recommended tunings of Ultimate r3 (~~Septifantasious~~): ===		=== Recommended tunings of Ultimate r3 (septisperasmic - septifantasious): ===

	==== Least error 13-limit: ====		==== Least error 13-limit: ====