Compton - Revision history

FloraC: /* Tunings */ + more edo tunings

2026-03-11T08:44:31Z

Tunings: + more edo tunings

@@ Line 257: / Line 257: @@
 | 49/48
 | 383.924
+|
 |-
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 | 21/20
 | 384.467
+|
 |-

FloraC: /* Tunings */ fix eigeninterval

2026-03-10T18:07:00Z

Tunings: fix eigeninterval

← Older revision		Revision as of 18:07, 10 March 2026
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	\|-		\|-
	\|		\|
	\| 5/4		\| 7/5
	\| 382.512		\| 382.512
	\|		\|

FloraC: + infobox

2026-03-10T18:06:03Z

+ infobox

← Older revision		Revision as of 18:06, 10 March 2026
Line 1:		Line 1:
			{{Infobox regtemp
			\| Title = Compton
			\| Subgroups = 2.3.5, 2.3.5.7
			\| Comma basis = [[531441/524288]] (5-limit); <br>[[225/224]], [[250047/250000]] (7-limit)
			\| Edo join 1 = 12 \| Edo join 2 = 72
			\| Mapping = 12; 0 1 2
			\| Generators = 5/4
			\| Generators tuning = 384.1
			\| Optimization method = CWE
			\| MOS scales = [[12L 12s]], [[12L 24s]]
			\| Odd limit 1 = 5 \| Mistuning 1 = 1.96 \| Complexity 1 = 24
			\| Odd limit 2 = 9 \| Mistuning 2 = 3.91 \| Complexity 2 = 36
			}}
	'''Compton''' is a [[regular temperament\|temperament]] that takes [[12edo]]'s [[circle of fifths]] for the [[3-limit]], but the [[5/1\|fifth harmonic]] is given its own generator instead of being mapped to one of 12edo's intervals. Essentially, it is the [[5-limit]] temperament which [[tempering out\|tempers out]] the Pythagorean comma, [[531441/524288]]. This equates any Pythagorean interval with its [[enharmonic]] counterparts, for example, the diminished fourth [[8192/6561]] with the major third [[81/64]], and the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], are merged into a single interval of 1/12 octave, which serves as the [[period]]. The [[generator]] can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a [[syntonic comma]]), but is most usefully [[5/4]], the ptolemaic major third, or 81/80, the syntonic comma itself.		'''Compton''' is a [[regular temperament\|temperament]] that takes [[12edo]]'s [[circle of fifths]] for the [[3-limit]], but the [[5/1\|fifth harmonic]] is given its own generator instead of being mapped to one of 12edo's intervals. Essentially, it is the [[5-limit]] temperament which [[tempering out\|tempers out]] the Pythagorean comma, [[531441/524288]]. This equates any Pythagorean interval with its [[enharmonic]] counterparts, for example, the diminished fourth [[8192/6561]] with the major third [[81/64]], and the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], are merged into a single interval of 1/12 octave, which serves as the [[period]]. The [[generator]] can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a [[syntonic comma]]), but is most usefully [[5/4]], the ptolemaic major third, or 81/80, the syntonic comma itself.

FloraC: No one calls 12edo compton

2025-10-08T09:26:22Z

No one calls 12edo compton

← Older revision		Revision as of 09:26, 8 October 2025
Line 1:		Line 1:
	~~''This page is about the 5-limit rank-2 temperament. For the 3-limit equal temperament, see [[12edo]].''~~

	'''Compton''' is a [[regular temperament\|temperament]] that takes [[12edo]]'s [[circle of fifths]] for the [[3-limit]], but the [[5/1\|fifth harmonic]] is given its own generator instead of being mapped to one of 12edo's intervals. Essentially, it is the [[5-limit]] temperament which [[tempering out\|tempers out]] the Pythagorean comma, [[531441/524288]]. This equates any Pythagorean interval with its [[enharmonic]] counterparts, for example, the diminished fourth [[8192/6561]] with the major third [[81/64]], and the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], are merged into a single interval of 1/12 octave, which serves as the [[period]]. The [[generator]] can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a [[syntonic comma]]), but is most usefully [[5/4]], the ptolemaic major third, or 81/80, the syntonic comma itself.		'''Compton''' is a [[regular temperament\|temperament]] that takes [[12edo]]'s [[circle of fifths]] for the [[3-limit]], but the [[5/1\|fifth harmonic]] is given its own generator instead of being mapped to one of 12edo's intervals. Essentially, it is the [[5-limit]] temperament which [[tempering out\|tempers out]] the Pythagorean comma, [[531441/524288]]. This equates any Pythagorean interval with its [[enharmonic]] counterparts, for example, the diminished fourth [[8192/6561]] with the major third [[81/64]], and the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], are merged into a single interval of 1/12 octave, which serves as the [[period]]. The [[generator]] can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a [[syntonic comma]]), but is most usefully [[5/4]], the ptolemaic major third, or 81/80, the syntonic comma itself.

VectorGraphics at 23:10, 7 October 2025

2025-10-07T23:10:52Z

← Older revision		Revision as of 23:10, 7 October 2025
Line 1:		Line 1:
			''This page is about the 5-limit rank-2 temperament. For the 3-limit equal temperament, see [[12edo]].''

	'''Compton''' is a [[regular temperament\|temperament]] that takes [[12edo]]'s [[circle of fifths]] for the [[3-limit]], but the [[5/1\|fifth harmonic]] is given its own generator instead of being mapped to one of 12edo's intervals. Essentially, it is the [[5-limit]] temperament which [[tempering out\|tempers out]] the Pythagorean comma, [[531441/524288]]. This equates any Pythagorean interval with its [[enharmonic]] counterparts, for example, the diminished fourth [[8192/6561]] with the major third [[81/64]], and the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], are merged into a single interval of 1/12 octave, which serves as the [[period]]. The [[generator]] can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a [[syntonic comma]]), but is most usefully [[5/4]], the ptolemaic major third, or 81/80, the syntonic comma itself.		'''Compton''' is a [[regular temperament\|temperament]] that takes [[12edo]]'s [[circle of fifths]] for the [[3-limit]], but the [[5/1\|fifth harmonic]] is given its own generator instead of being mapped to one of 12edo's intervals. Essentially, it is the [[5-limit]] temperament which [[tempering out\|tempers out]] the Pythagorean comma, [[531441/524288]]. This equates any Pythagorean interval with its [[enharmonic]] counterparts, for example, the diminished fourth [[8192/6561]] with the major third [[81/64]], and the two kinds of Pythagorean semitones, diatonic [[256/243]] and chromatic [[2187/2048]], are merged into a single interval of 1/12 octave, which serves as the [[period]]. The [[generator]] can then be seen as any ptolemaic interval (the alteration of a Pythagorean interval by a [[syntonic comma]]), but is most usefully [[5/4]], the ptolemaic major third, or 81/80, the syntonic comma itself.

FloraC: Text replacement - "prime-optimized" to "norm-based"

2025-09-12T14:05:59Z

Text replacement - "prime-optimized" to "norm-based"

← Older revision		Revision as of 14:05, 12 September 2025
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	== Tunings ==		== Tunings ==
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 5-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 5-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|
Line 163:		Line 163:

	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit ~~prime~~-~~optimized~~ tunings		\|+ style="font-size: 105%; white-space: nowrap;" \| 7-limit norm-based tunings
	\|-		\|-
	! rowspan="2" \|		! rowspan="2" \|

Lériendil: Text replacement - "Eigenmonzo
(unchanged-interval)" to "Unchanged interval
(eigenmonzo)"

2025-06-21T06:55:56Z

Text replacement - "Eigenmonzo<br>(unchanged-interval)" to "Unchanged interval<br>(eigenmonzo)"

← Older revision		Revision as of 06:55, 21 June 2025
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	\|-		\|-
	! Edo<br>generator		! Edo<br>generator
	! [[Eigenmonzo\|~~Eigenmonzo~~<br>(~~unchanged-interval~~)]]*		! [[Eigenmonzo\|Unchanged interval<br>(eigenmonzo)]]*
	! Generator (¢)		! Generator (¢)
	! Comments		! Comments

VectorGraphics at 21:27, 8 June 2025

2025-06-08T21:27:46Z

← Older revision		Revision as of 21:27, 8 June 2025
Line 10:		Line 10:
	Assuming one has chosen to approximate the 7-limit, the comma generator will be around 15–17 cents. This means that the [[11/1\|11th harmonic]] can be reached either by going up or down three steps. Going down three steps results in the canonical extension of compton. Stepping down one more comma, depending on the tuning, can lead to the [[13/1\|13th harmonic]], and results in the canonical tridecimal compton. This works best with tunings of the comma around 15 cents.		Assuming one has chosen to approximate the 7-limit, the comma generator will be around 15–17 cents. This means that the [[11/1\|11th harmonic]] can be reached either by going up or down three steps. Going down three steps results in the canonical extension of compton. Stepping down one more comma, depending on the tuning, can lead to the [[13/1\|13th harmonic]], and results in the canonical tridecimal compton. This works best with tunings of the comma around 15 cents.

	Alternatively, any prime may be merged into its 12edo mapping, making the smallest available prime the generator. This is done in [[catler]] (which shares 12edo's 5-limit and is generated by 7) and [[duodecim]] (which shares 12edo's 7-limit and is generated by 11). This is a natural choice for 17 and 19, as 12edo tunes those primes especially well, so compton can be seen as a 19-limit temperament. The next step down, which ends up at around 75 cents flat of the corresponding 12edo interval, can be used for 23 and 29, though two steps up (30 ~~steps~~ sharp) is also a reasonable (but less intuitive) choice.		Alternatively, any prime may be merged into its 12edo mapping, making the smallest available prime the generator. This is done in [[catler]] (which shares 12edo's 5-limit and is generated by 7) and [[duodecim]] (which shares 12edo's 7-limit and is generated by 11). This is a natural choice for 17 and 19, as 12edo tunes those primes especially well, so compton can be seen as a 19-limit temperament. The next step down, which ends up at around 75 cents flat of the corresponding 12edo interval, can be used for 23 and 29, though two steps up (30 cents sharp) is also a reasonable (but less intuitive) choice.

	== Interval chain ==		== Interval chain ==

VectorGraphics at 21:27, 8 June 2025

2025-06-08T21:27:24Z

← Older revision		Revision as of 21:27, 8 June 2025
Line 10:		Line 10:
	Assuming one has chosen to approximate the 7-limit, the comma generator will be around 15–17 cents. This means that the [[11/1\|11th harmonic]] can be reached either by going up or down three steps. Going down three steps results in the canonical extension of compton. Stepping down one more comma, depending on the tuning, can lead to the [[13/1\|13th harmonic]], and results in the canonical tridecimal compton. This works best with tunings of the comma around 15 cents.		Assuming one has chosen to approximate the 7-limit, the comma generator will be around 15–17 cents. This means that the [[11/1\|11th harmonic]] can be reached either by going up or down three steps. Going down three steps results in the canonical extension of compton. Stepping down one more comma, depending on the tuning, can lead to the [[13/1\|13th harmonic]], and results in the canonical tridecimal compton. This works best with tunings of the comma around 15 cents.

	Alternatively, any prime may be merged into its 12edo mapping, making the smallest available prime the generator. This is done in [[catler]] (which shares 12edo's 5-limit and is generated by 7) and [[duodecim]] (which shares 12edo's 7-limit and is generated by 11). This is a natural choice for 17 and 19, as 12edo tunes those primes especially well, so compton can be seen as a 19-limit temperament.		Alternatively, any prime may be merged into its 12edo mapping, making the smallest available prime the generator. This is done in [[catler]] (which shares 12edo's 5-limit and is generated by 7) and [[duodecim]] (which shares 12edo's 7-limit and is generated by 11). This is a natural choice for 17 and 19, as 12edo tunes those primes especially well, so compton can be seen as a 19-limit temperament. The next step down, which ends up at around 75 cents flat of the corresponding 12edo interval, can be used for 23 and 29, though two steps up (30 steps sharp) is also a reasonable (but less intuitive) choice.

	== Interval chain ==		== Interval chain ==

FloraC: +tunings

2025-04-24T13:00:23Z

+tunings

Show changes

Compton - Revision history

FloraC: /* Tunings */ + more edo tunings

FloraC: /* Tunings */ fix eigeninterval

FloraC: + infobox

FloraC: No one calls 12edo compton

VectorGraphics at 23:10, 7 October 2025

FloraC: Text replacement - "prime-optimized" to "norm-based"

Lériendil: Text replacement - "Eigenmonzo(unchanged-interval)" to "Unchanged interval(eigenmonzo)"

VectorGraphics at 21:27, 8 June 2025

VectorGraphics at 21:27, 8 June 2025

FloraC: +tunings

Lériendil: Text replacement - "Eigenmonzo
(unchanged-interval)" to "Unchanged interval
(eigenmonzo)"