Mabilic and trismegistus - Revision history

Xenllium at 05:40, 21 June 2026

2026-06-21T05:40:55Z

← Older revision		Revision as of 05:40, 21 June 2026
Line 8:		Line 8:
	\| Generators tuning = 526.7		\| Generators tuning = 526.7
	\| Optimization method = CWE		\| Optimization method = CWE
			\| MOS scales = [[7L 2s]], [[9L 7s]]
	\| Ploidacot = alpha-triseph		\| Ploidacot = alpha-triseph
	\| Odd limit 1 = 2.5.7 35 \| Mistuning 1 = ? \| Complexity 1 = 16		\| Odd limit 1 = 2.5.7 7 \| Mistuning 1 = 4.76 \| Complexity 1 = 9
	\| Odd limit 2 = ~~add-~~25 add-35 7 \| Mistuning 2 = 5.9 \| Complexity 2 = 25		\| Odd limit 2 = 2.5.7 25 \| Mistuning 2 = 6.92 \| Complexity 2 = 16
	}}		\| Odd limit 3 = add-15, 21 7 \| Mistuning 3 = 5.92 \| Complexity 3 = 25
			\|}}
	'''Mabilic''' is a [[regular temperament\|temperament]] in the [[2.5.7 subgroup\|2.5.7]] [[subgroup]] where [[5/2]] is split into three [[generator]]s, five of which octave-reduced reach [[8/7]]. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 [[cent]]s. Mabilic, as a result, tempers out the [[mabilisma]] 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[armodue (temperament)\|armodue]] temperament. As such, mabilic can be associated with [[mos scale]]s like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not [[3/2]], [[2L 5s #Notation\|melodic]] [[chain-of-fifths notation]] makes some amount of sense to use here.		'''Mabilic''' is a [[regular temperament\|temperament]] in the [[2.5.7 subgroup\|2.5.7]] [[subgroup]] where [[5/2]] is split into three [[generator]]s, five of which octave-reduced reach [[8/7]]. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 [[cent]]s. Mabilic, as a result, tempers out the [[mabilisma]] 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[armodue (temperament)\|armodue]] temperament. As such, mabilic can be associated with [[mos scale]]s like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not [[3/2]], [[2L 5s #Notation\|melodic]] [[chain-of-fifths notation]] makes some amount of sense to use here.

FloraC: Cleanup on infobox

2026-02-09T10:15:12Z

Cleanup on infobox

← Older revision		Revision as of 10:15, 9 February 2026
Line 1:		Line 1:
	{{Infobox regtemp		{{Infobox regtemp
	\| ~~Optimization method~~ = ~~POTE~~		\| Title = Mabilic; Trismegistus
	\| ~~Generator tuning~~ = ~~527~~.~~236~~		\| Subgroups = 2.5.7; 2.3.5.7
			\| Comma basis = 1071875/1048576 (2.5.7); <br>1029/1024, 3125/3072 (2.3.5.7)
			\| Edo join 1 = 16 \| Edo join 2 = 25
	\| Mapping = 1; -15 -3 5		\| Mapping = 1; -15 -3 5
			\| Generators = 175/128
			\| Generators tuning = 526.7
			\| Optimization method = CWE
	\| Ploidacot = alpha-triseph		\| Ploidacot = alpha-triseph
	\| ~~Subgroups~~ = 2.5.7~~; 2.3.5.7~~		\| Odd limit 1 = 2.5.7 35 \| Mistuning 1 = ? \| Complexity 1 = 16
	\| ~~Title~~ = ~~Mabilic; Trismegistus~~		\| Odd limit 2 = add-25 add-35 7 \| Mistuning 2 = 5.9 \| Complexity 2 = 25
	\| ~~Comma basis = 1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)~~
	~~\| Generator = 175/128~~
	~~\| Edo join~~ 1 = 16 ~~\| Edo join 2 = 25~~
	~~\| Odd limit 1 = (2.5.7) 35~~ \| Odd limit 2 = add-25 add-35 7
	~~\| Mistuning 1 = ?~~ \| Mistuning 2 = 5.9
	~~\| Complexity 1 = 16~~ \| Complexity 2 = 25
	}}		}}
	'''Mabilic''' is a [[regular temperament\|temperament]] in the [[2.5.7 subgroup\|2.5.7]] [[subgroup]] where [[5/2]] is split into three [[generator]]s, five of which octave-reduced reach [[8/7]]. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 [[cent]]s. Mabilic, as a result, tempers out the [[mabilisma]] 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[armodue (temperament)\|armodue]] temperament. As such, mabilic can be associated with [[mos scale]]s like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not [[3/2]], [[2L 5s #Notation\|melodic]] [[chain-of-fifths notation]] makes some amount of sense to use here.		'''Mabilic''' is a [[regular temperament\|temperament]] in the [[2.5.7 subgroup\|2.5.7]] [[subgroup]] where [[5/2]] is split into three [[generator]]s, five of which octave-reduced reach [[8/7]]. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 [[cent]]s. Mabilic, as a result, tempers out the [[mabilisma]] 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[armodue (temperament)\|armodue]] temperament. As such, mabilic can be associated with [[mos scale]]s like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not [[3/2]], [[2L 5s #Notation\|melodic]] [[chain-of-fifths notation]] makes some amount of sense to use here.

Overthink at 04:48, 19 October 2025

2025-10-19T04:48:50Z

← Older revision		Revision as of 04:48, 19 October 2025
Line 5:		Line 5:
	\| Ploidacot = alpha-triseph		\| Ploidacot = alpha-triseph
	\| Subgroups = 2.5.7; 2.3.5.7		\| Subgroups = 2.5.7; 2.3.5.7
	\| Title = Mabilic; ~~trismegistus~~		\| Title = Mabilic; Trismegistus
	\| Comma basis = 1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)		\| Comma basis = 1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)
	\| Generator = 175/128		\| Generator = 175/128
	\| Edo join 1 = 16 \| Edo join 2 = 25		\| Edo join 1 = 16 \| Edo join 2 = 25
	\| Odd limit 1 = (2.5.7) 35 \| Odd limit 2 = (7-~~limit)~~ 35		\| Odd limit 1 = (2.5.7) 35 \| Odd limit 2 = add-25 add-35 7
	\| Complexity 1 = 25 \| Complexity 2 = ~~107~~		\| Mistuning 1 = ? \| Mistuning 2 = 5.9
			\| Complexity 1 = 16 \| Complexity 2 = 25
	}}		}}
	'''Mabilic''' is a [[regular temperament\|temperament]] in the [[2.5.7 subgroup\|2.5.7]] [[subgroup]] where [[5/2]] is split into three [[generator]]s, five of which octave-reduced reach [[8/7]]. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 [[cent]]s. Mabilic, as a result, tempers out the [[mabilisma]] 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[armodue (temperament)\|armodue]] temperament. As such, mabilic can be associated with [[mos scale]]s like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not [[3/2]], [[2L 5s #Notation\|melodic]] [[chain-of-fifths notation]] makes some amount of sense to use here.		'''Mabilic''' is a [[regular temperament\|temperament]] in the [[2.5.7 subgroup\|2.5.7]] [[subgroup]] where [[5/2]] is split into three [[generator]]s, five of which octave-reduced reach [[8/7]]. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 [[cent]]s. Mabilic, as a result, tempers out the [[mabilisma]] 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[armodue (temperament)\|armodue]] temperament. As such, mabilic can be associated with [[mos scale]]s like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not [[3/2]], [[2L 5s #Notation\|melodic]] [[chain-of-fifths notation]] makes some amount of sense to use here.

FloraC: Sort of a cleanup

2025-10-10T07:40:11Z

Sort of a cleanup

Show changes

Overthink: added more to infobox

2025-10-10T07:29:52Z

added more to infobox

← Older revision		Revision as of 07:29, 10 October 2025
Line 1:		Line 1:
	{{Infobox regtemp\|Optimization method=POTE\|Generator tuning=527.236\|Mapping=1; -3 5\|Subgroups=2.5.7; 2.3.5.7\|Title=Mabilic; trismegistus\|Comma basis=1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)\|Generator=175/128\|Edo join 1=16\|Edo join 2=25}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 cents. Mabilic, as a result, tempers out the '''mabilisma''' 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[Mavila family#Armodue\|armodue]] temperament. As such, mabilic can be associated with MOS scales like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not 3/2, [[2L 5s#Notation\|melodic]] chain-of-fifths notation makes some amount of sense to use here.		{{Infobox regtemp\|Optimization method=POTE\|Generator tuning=527.236\|Mapping=1; -15 -3 5\|Ploidacot = alpha-triseph\|Subgroups=2.5.7; 2.3.5.7\|Title=Mabilic; trismegistus\|Comma basis=1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)\|Generator=175/128\|Edo join 1=16\|Edo join 2=25\|Odd limit 1 = (2.5.7) 35\|Odd limit 2=(7-limit) 35\|Complexity 1=25\|Complexity 2=107}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 cents. Mabilic, as a result, tempers out the '''mabilisma''' 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[Mavila family#Armodue\|armodue]] temperament. As such, mabilic can be associated with MOS scales like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not 3/2, [[2L 5s#Notation\|melodic]] chain-of-fifths notation makes some amount of sense to use here.

	Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Similarly, since 8/7 is at 5 steps, trismegistus is a slendric temperament.Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.		Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Similarly, since 8/7 is at 5 steps, trismegistus is a slendric temperament.Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.

VectorGraphics at 03:22, 27 August 2025

2025-08-27T03:22:38Z

← Older revision		Revision as of 03:22, 27 August 2025
Line 3:		Line 3:
	Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Similarly, since 8/7 is at 5 steps, trismegistus is a slendric temperament.Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.		Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Similarly, since 8/7 is at 5 steps, trismegistus is a slendric temperament.Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.

	There is an alternative extension, '''semabila''' ([[Mabila family#Semabila]]), which is a semaphore temperament (hence its name) and thus finds 4/3 at 10 generators.		There is an alternative extension, '''semabila''' ([[Mabila family#Semabila]]), which is a semaphore temperament (hence its name) and thus finds 4/3 at 10 generators. It is best tuned sharper than trismegistus.

	Making the generator itself 4/3 leads to the exotemperament [[mavila]], after which mabilic is named.		Making the generator itself 4/3 leads to the exotemperament [[mavila]], after which mabilic is named.

Fredg999 category edits: Categories

2025-08-01T19:15:56Z

VectorGraphics at 18:32, 30 July 2025

2025-07-30T18:32:36Z

← Older revision		Revision as of 18:32, 30 July 2025
Line 1:		Line 1:
	{{Infobox regtemp\|Optimization method=POTE\|Generator tuning=527.236\|Mapping=1; -3 5\|Subgroups=2.5.7; 2.3.5.7\|Title=Mabilic; trismegistus\|Comma basis=1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)\|Generator=175/128\|Edo join 1=16\|Edo join 2=25}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 cents. Mabilic, as a result, tempers out the '''mabilisma''' 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[Mavila family#Armodue\|armodue]] temperament. As such, mabilic can be associated with MOS scales like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not 3/2, [[2L 5s#Notation\|melodic]] chain-of-fifths notation makes some amount of sense to use here.		{{Infobox regtemp\|Optimization method=POTE\|Generator tuning=527.236\|Mapping=1; -3 5\|Subgroups=2.5.7; 2.3.5.7\|Title=Mabilic; trismegistus\|Comma basis=1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)\|Generator=175/128\|Edo join 1=16\|Edo join 2=25}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 cents. Mabilic, as a result, tempers out the '''mabilisma''' 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[Mavila family#Armodue\|armodue]] temperament. As such, mabilic can be associated with MOS scales like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not 3/2, [[2L 5s#Notation\|melodic]] chain-of-fifths notation makes some amount of sense to use here.

	Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.		Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Similarly, since 8/7 is at 5 steps, trismegistus is a slendric temperament.Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.

	There is an alternative extension, '''semabila''' ([[Mabila family#Semabila]]), which is a semaphore temperament (hence its name) and thus finds 4/3 at 10 generators.		There is an alternative extension, '''semabila''' ([[Mabila family#Semabila]]), which is a semaphore temperament (hence its name) and thus finds 4/3 at 10 generators.

VectorGraphics: Created page with "{{Infobox regtemp|Optimization method=POTE|Generator tuning=527.236|Mapping=1; -3 5|Subgroups=2.5.7; 2.3.5.7|Title=Mabilic; trismegistus|Comma basis=1071875/1048576 (2.5.7);
1029/1024, 3125/3072 (2.3.5.7)|Generator=175/128|Edo join 1=16|Edo join 2=25}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, b..."

2025-07-30T07:38:11Z

Created page with "{{Infobox regtemp|Optimization method=POTE|Generator tuning=527.236|Mapping=1; -3 5|Subgroups=2.5.7; 2.3.5.7|Title=Mabilic; trismegistus|Comma basis=1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)|Generator=175/128|Edo join 1=16|Edo join 2=25}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, b..."

New page

{{Infobox regtemp|Optimization method=POTE|Generator tuning=527.236|Mapping=1; -3 5|Subgroups=2.5.7; 2.3.5.7|Title=Mabilic; trismegistus|Comma basis=1071875/1048576 (2.5.7); <br> 1029/1024, 3125/3072 (2.3.5.7)|Generator=175/128|Edo join 1=16|Edo join 2=25}}'''Mabilic''' is a temperament in the 2.5.7 subgroup where 5/2 is split into three generators, five of which octave-reduced reach 8/7. The generator is a sharpened fourth (or, conversely, a flattened fifth) in size, best tuned around 528 cents. Mabilic, as a result, tempers out the '''mabilisma''' 1071875/1048576. Mabilic is arrived at by removing the inaccurate 3/2 mapping from [[Mavila family#Armodue|armodue]] temperament. As such, mabilic can be associated with MOS scales like [[antidiatonic]] and [[armotonic]]. Thus, while the generating interval is not 3/2, [[2L 5s#Notation|melodic]] chain-of-fifths notation makes some amount of sense to use here.

Mabilic can be extended into a full 7-limit temperament called '''trismegistus''' in which 3 is found at 15 steps. Since 5 is at 3 steps, that makes trismegistus a magic temperament. Trismegistus is associated with the MOS scale [[9L 7s]], where 3/2 is found as the "augmented" version of the generator, and 25edo, 41edo, and 66edo make for good tunings.

There is an alternative extension, '''semabila''' ([[Mabila family#Semabila]]), which is a semaphore temperament (hence its name) and thus finds 4/3 at 10 generators.

Making the generator itself 4/3 leads to the exotemperament [[mavila]], after which mabilic is named.

The tuning optimum of mabilic is 527.2 cents, which is almost exactly the [[Golden sequences and tuning|golden]] antidiatonic generator.

For technical data, see [[No-threes subgroup temperaments#Mabilic]] and [[Magic family#Trismegistus]].

== Intervals ==
In the following tables, odd harmonics and subharmonics 1–15 are labeled in '''bold'''.
{| class="wikitable"
|+
!
! colspan="2" |Generators up
! colspan="2" |Generators down
|-
!#
!Cents
!Approximate ratios
!Cents
!Approximate ratios
|-
|0
|0
|'''1/1'''
|1200
|'''2/1'''
|-
|1
|527.236
|
|672.764
|
|-
|2
|1054.472
|64/35
|145.528
|35/32
|-
|3
|381.708
|'''5/4'''
|818.292
|'''8/5'''
|-
|4
|908.944
|42/25
|291.056
|25/21
|-
|5
|236.18
|'''8/7'''
|963.82
|'''7/4'''
|-
|6
|763.416
|25/16
|436.584
|32/25
|-
|7
|90.652
|
|1109.348
|
|-
|8
|617.888
|10/7
|582.112
|7/5
|-
|9
|1145.124
|
|54.876
|
|-
|10
|472.36
|21/16
|727.64
|32/21
|-
|11
|999.596
|25/14
|200.404
|28/25
|-
|12
|326.832
|6/5
|873.168
|5/3
|-
|13
|854.068
|
|345.932
|
|-
|14
|181.304
|
|1018.696
|
|-
|15
|708.54
|'''3/2'''
|491.46
|'''4/3'''
|-
|16
|35.776
|
|1164.224
|
|}

← Older revision		Revision as of 19:15, 1 August 2025
Line 127:		Line 127:
	\|		\|
	\|}		\|}

			[[Category:Subgroup temperaments]]
			[[Category:Magic family]]