Interval size measure - Revision history

FloraC: Update

2026-04-04T12:00:10Z

Update

← Older revision		Revision as of 12:00, 4 April 2026
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	\| [[Relative cent]] of [[6edo]]; proposed by [[Widogast Iring]] (1898), later by [[Joseph Yasser]] as a "centitone", a standard SI prefix + 12edo tone (1932)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft \| ''Centitone, iring'']</ref>.		\| [[Relative cent]] of [[6edo]]; proposed by [[Widogast Iring]] (1898), later by [[Joseph Yasser]] as a "centitone", a standard SI prefix + 12edo tone (1932)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft \| ''Centitone, iring'']</ref>.
	\|-		\|-
	\| [[~~Skisma~~]] (Sk)		\| [[Nil]] / [[skisma]] (Sk)
	\| [[612edo\|612]]		\| [[612edo\|612]]
	\| 2<sup>2</sup> × 3<sup>2</sup> × 17		\| 2<sup>2</sup> × 3<sup>2</sup> × 17
	\| ~~Edo representation of~~ [[~~Sagittal notation\|Sagittal~~]]~~'s Ultra~~ (~~Herculean~~) ~~precision level JI notation~~ (~~58eda~~)~~, where it is known~~ as ~~an "ultrina"~~<ref name="measure"/><ref>[http://tonalsoft.com/enc/s/sk.aspx Tonalsoft \| ''Sk, 612-edo'']</ref>.		\| Proposed by [[James Paul White]] (1894) as ''nil'', and by Gene Ward Smith (2007) as ''skisma''<ref name="measure"/><ref>[http://tonalsoft.com/enc/s/sk.aspx Tonalsoft \| ''Sk, 612-edo'']</ref>. Edo representation of [[Sagittal notation\|Sagittal]]'s Ultra (Herculean) precision level JI notation (58eda), where it is known as an "ultrina".
	\|-		\|-
	\| [[Delfi]]		\| [[Delfi]]

Tristanbay: /* Octave-based fine measures */Added table entry for 1\1395, propose another name if you want

2026-03-30T19:14:05Z

Octave-based fine measures: Added table entry for 1\1395, propose another name if you want

← Older revision		Revision as of 19:14, 30 March 2026
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	\| 2<sup>4</sup> × 3 × 5<sup>2</sup>		\| 2<sup>4</sup> × 3 × 5<sup>2</sup>
	\| See the dedicated page.		\| See the dedicated page.
			\|-
			\| Dingle
			\| [[1395edo\|1395]]
			\| 3<sup>2</sup> × 5 × 31
			\| Proposed by [[User:Tristanbay\|Tristan Bay]] (2026) as a 31edo-friendly fine-grain measure, shortened from "'''di'''esis a'''ngle'''".
	\|-		\|-
	\| Decifarab		\| Decifarab

Tristanbay: /* Octave-based fine measures */Added info about the name of the squb (1\494)

2025-08-04T09:20:13Z

Octave-based fine measures: Added info about the name of the squb (1\494)

← Older revision		Revision as of 09:20, 4 August 2025
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	\| [[494edo\|494]]		\| [[494edo\|494]]
	\| 2 × 13 × 19		\| 2 × 13 × 19
	\| ~~{{Citation needed}}~~		\| Named after [[729/728]], the squbema, due to its similar size.
	\|-		\|-
	\| [[Great iring]] / [[great centitone\|centitone]]		\| [[Great iring]] / [[great centitone\|centitone]]

Tristanbay: /* Octave-based fine measures */Got rid of a bunch of less-important MoreMajorThanMajor interval measures

2025-07-21T03:37:50Z

Octave-based fine measures: Got rid of a bunch of less-important MoreMajorThanMajor interval measures

@@ Line 170: / Line 170: @@
 | 2<sup>4</sup> × 3 × 5<sup>2</sup>
 | See the dedicated page.
 |-
 | Decifarab
@@ Line 205: / Line 175: @@
 | 2<sup>5</sup> × 3<sup>2</sup> × 5
 | Standard SI prefix + [[farab]]<ref name="measure"/>.
 |-
 | Heptamu (7mu)
@@ Line 225: / Line 180: @@
 | 2<sup>9</sup> × 3
 | Seventh MIDI-resolution unit, 1/128 (1/(2<sup>7</sup>)) of [[12edo]] semitone<ref>[http://tonalsoft.com/enc/number/7mu.aspx Tonalsoft | ''7mu / heptamu'']</ref>
 |-
 | śata
@@ Line 235: / Line 185: @@
 | 2<sup>6</sup> × 5<sup>2</sup>
 | From Sanskrit ''śatam'': hundred; [[relative cent]] of Armodue 16edo theory{{Citation needed}}
 |-
 | [[Iota]]

Tristanbay: /* Octave-based fine measures */Added 1\41 as a Dea unit

2025-07-21T02:54:09Z

Octave-based fine measures: Added 1\41 as a Dea unit

← Older revision		Revision as of 02:54, 21 July 2025
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	\| 31 (prime)		\| 31 (prime)
	\| See the dedicated page.		\| See the dedicated page.
			\|-
			\| [[Dea]]
			\| [[41edo\|41]]
			\| 41 (prime)
			\| Proposed by [[User:Tristanbay\|Tristan Bay]] (2025) to reflect that a mina is a "minute" (1/60 the width) of a 1\41 "degree".
	\|-		\|-
	\| [[Méride]]		\| [[Méride]]

FloraC: Just use standard reading!

2025-06-30T13:14:04Z

Just use standard reading!

← Older revision		Revision as of 13:14, 30 June 2025
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	=== Backslash notation ===		=== Backslash notation ===
	A common shorthand in use in the microtonal community is ''k''\''N'', written with a backslash (\) instead of a forwardslash (/), to refer to an interval with a frequency ratio of 2<sup>''k''/''N''</sup>. ''k''\''N'' is pronounced "''k'' steps of ''N'' [[edo]]" ~~or "''k'' out of ''N''"[[Template:Idiosyncratic]]~~, and can be derived from the meaning of "[[step]]s" in the context of edos (unless talking about steps of specific subsets/scales of some edo).		A common shorthand in use in the microtonal community is ''k''\''N'', written with a backslash (\) instead of a forwardslash (/), to refer to an interval with a frequency ratio of 2<sup>''k''/''N''</sup>. ''k''\''N'' is pronounced "''k'' steps of ''N'' [[edo]]", and can be derived from the meaning of "[[step]]s" in the context of edos (unless talking about steps of specific subsets/scales of some edo).

	Steps are linear in the log-frequency domain, so expressions like {{nowrap\|11\19 − 6\19 {{=}} 5\19}} hold. In general, we have		Steps are linear in the log-frequency domain, so expressions like {{nowrap\|11\19 − 6\19 {{=}} 5\19}} hold. In general, we have

VectorGraphics at 02:53, 14 April 2025

2025-04-14T02:53:28Z

← Older revision		Revision as of 02:53, 14 April 2025
Line 5:		Line 5:

	=== Backslash notation ===		=== Backslash notation ===
	A common shorthand in use in the microtonal community is ''k''\''N'', written with a backslash (\) instead of a forwardslash (/), to refer to an interval with a frequency ratio of 2<sup>''k''/''N''</sup>. ''k''\''N'' is pronounced "''k'' steps of ''N'' [[edo]]", and can be derived from the meaning of "[[step]]s" in the context of edos (unless talking about steps of specific subsets/scales of some edo).		A common shorthand in use in the microtonal community is ''k''\''N'', written with a backslash (\) instead of a forwardslash (/), to refer to an interval with a frequency ratio of 2<sup>''k''/''N''</sup>. ''k''\''N'' is pronounced "''k'' steps of ''N'' [[edo]]" or "''k'' out of ''N''"[[Template:Idiosyncratic]], and can be derived from the meaning of "[[step]]s" in the context of edos (unless talking about steps of specific subsets/scales of some edo).

	Steps are linear in the log-frequency domain, so expressions like {{nowrap\|11\19 − 6\19 {{=}} 5\19}} hold. In general, we have		Steps are linear in the log-frequency domain, so expressions like {{nowrap\|11\19 − 6\19 {{=}} 5\19}} hold. In general, we have

Angekallikoita: /* Octave-based fine measures */

2025-03-27T13:08:39Z

Octave-based fine measures

← Older revision		Revision as of 13:08, 27 March 2025
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	\| 2<sup>2</sup> × 5<sup>2</sup> x 43		\| 2<sup>2</sup> × 5<sup>2</sup> x 43
	\| {{Citation needed}}		\| {{Citation needed}}
			\|-
			\| [[4320edo\|Click]]
			\| [[4320edo\|4320]]
			\| 2<sup>5</sup> × 3<sup>3</sup> × 5
			\| Proposed by [[User:Eliora\|Eliora]]. See the dedicated page.
	\|-		\|-
	\| [[Major tina]]		\| [[Major tina]]

Lériendil: based on a proposal from Oct 2024 to rededicate "euhekts" from 19edt to 39edt. The rationale here is that "euhekts" in the 19edt sense seem to have entirely been an invention of MoreMajorThanMajor, and not used anywhere else on the internet than this page. 39 is a much more useful amount to subdivide the tritave into than 19, considering 19 is more or less the same as cents.

2025-03-14T23:02:34Z

based on a proposal from Oct 2024 to rededicate "euhekts" from 19edt to 39edt. The rationale here is that "euhekts" in the 19edt sense seem to have entirely been an invention of MoreMajorThanMajor, and not used anywhere else on the internet than this page. 39 is a much more useful amount to subdivide the tritave into than 19, considering 19 is more or less the same as cents.

← Older revision		Revision as of 23:02, 14 March 2025
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	\| Euhekt		\| Euhekt
	\| 3/1 (twelfth)		\| 3/1 (twelfth)
	\| ~~1900~~		\| 3900
	\| 1/100 of ~~19edt~~ (~~OnlyPure~~) scale step		\| 1/100 of 39edt (Triboh) scale step
	\|-		\|-
	\| Grad		\| Grad

FloraC: /* Logarithmic */ update

2025-03-05T11:58:41Z

Logarithmic: update

← Older revision		Revision as of 11:58, 5 March 2025
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	\| [[16edo\|16]]		\| [[16edo\|16]]
	\| 2<sup>4</sup>		\| 2<sup>4</sup>
	\| From Sanskrit ''eka'': one, unit; chromatic unit of Armodue 16edo ~~Theory~~<ref>[http://www.armodue.com/risorse.htm Armodue: le risorse di un nuovo sistema musicale]</ref>.		\| From Sanskrit ''eka'': one, unit; chromatic unit of Armodue 16edo theory<ref>[http://www.armodue.com/risorse.htm Armodue: le risorse di un nuovo sistema musicale]</ref>.
	\|-		\|-
	\| [[Normal shruti]]		\| [[Normal shruti]]
	\| [[22edo\|22]]		\| [[22edo\|22]]
	\| 2 × 11		\| 2 × 11
	\| Proposed by [[User:Tristanbay\|Tristan Bay]] in reference to the Indian tradition of dividing the octave into 22 unequal parts.		\| Proposed by [[User:Tristanbay\|Tristan Bay]] (2025) in reference to the Indian tradition of dividing the octave into 22 unequal parts.
	\|-		\|-
	\| [[Normal diesis]]		\| [[Normal diesis]]
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	\| See the dedicated page.		\| See the dedicated page.
	\|-		\|-
	\| [[Holdrian comma\|~~Mercator’s~~ old comma]]		\| [[Holdrian comma\|Mercator's old comma]]
	\| [[55edo\|55]]		\| [[55edo\|55]]
	\| 5 × 11		\| 5 × 11
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	\| [[60edo\|60]]		\| [[60edo\|60]]
	\| 2<sup>2</sup> × 3 × 5		\| 2<sup>2</sup> × 3 × 5
	\|		\| Standard SI prefix + 12edo tone
	\|-		\|-
	\| [[Morion]]		\| [[Morion]]
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	\| [[144edo\|144]]		\| [[144edo\|144]]
	\| 2<sup>4</sup> × 3<sup>2</sup>		\| 2<sup>4</sup> × 3<sup>2</sup>
	\| 1/12 of [[12edo]] semitone; ~~Proposed~~ by [[al-Farabi]] in 10th century<ref name="measure"/><ref>[http://tonalsoft.com/enc/f/farab.aspx Tonalsoft \| ''Farab''].</ref>.		\| 1/12 of [[12edo]] semitone; proposed by [[al-Farabi]] in 10th century<ref name="measure"/><ref>[http://tonalsoft.com/enc/f/farab.aspx Tonalsoft \| ''Farab''].</ref>.
	\|-		\|-
	\| [[Mem]]		\| [[Mem]]
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	\| {{Citation needed}}		\| {{Citation needed}}
	\|-		\|-
	\| ~~Great~~ [[iring]] / [[centitone]]		\| [[Great iring]] / [[great centitone\|centitone]]
	\| [[500edo\|500]]		\| [[500edo\|500]]
	\| 2<sup>2</sup> × 5<sup>3</sup>		\| 2<sup>2</sup> × 5<sup>3</sup>
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	\| [[600edo\|600]]		\| [[600edo\|600]]
	\| 2<sup>3</sup> × 3 × 5<sup>2</sup>		\| 2<sup>3</sup> × 3 × 5<sup>2</sup>
	\| [[Relative cent]] of [[6edo]] ~~([[12edo]] tone)~~; ~~Proposed~~ by [[Widogast Iring]] (1898), later by [[Joseph Yasser]] as a "centitone" (1932)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft \| ''Centitone, iring'']</ref>.		\| [[Relative cent]] of [[6edo]]; proposed by [[Widogast Iring]] (1898), later by [[Joseph Yasser]] as a "centitone", a standard SI prefix + 12edo tone (1932)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/c/centitone.aspx Tonalsoft \| ''Centitone, iring'']</ref>.
	\|-		\|-
	\| [[Skisma]] (Sk)		\| [[Skisma]] (Sk)
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	\| <ref name="measure"/>		\| <ref name="measure"/>
	\|-		\|-
	\| ~~Small~~ [[iring]] / [[centitone]]		\| [[Small iring]] / [[small centitone\|centitone]]
	\| [[700edo\|700]]		\| [[700edo\|700]]
	\| 2<sup>2</sup> × 5<sup>2</sup> x 7		\| 2<sup>2</sup> × 5<sup>2</sup> x 7
	\| {{Citation needed}}		\| {{Citation needed}}
	\|-		\|-
	\| [[Woolhouse]]		\| [[Woolhouse unit]]
	\| [[730edo\|730]]		\| [[730edo\|730]]
	\| 2 × 5 × 73		\| 2 × 5 × 73
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	\| [[1440edo\|1440]]		\| [[1440edo\|1440]]
	\| 2<sup>5</sup> × 3<sup>2</sup> × 5		\| 2<sup>5</sup> × 3<sup>2</sup> × 5
	\| ~~1/10 of~~ [[~~Farab~~]] ~~unit~~<ref name="measure"/>.		\| Standard SI prefix + [[farab]]<ref name="measure"/>.
	\|-		\|-
	\| Quadratic cent		\| Quadratic cent
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	\| [[1600edo\|1600]]		\| [[1600edo\|1600]]
	\| 2<sup>6</sup> × 5<sup>2</sup>		\| 2<sup>6</sup> × 5<sup>2</sup>
	\| From Sanskrit ''śatam'': hundred; [[~~Relative~~ cent]] of Armodue 16edo ~~Theory~~{{Citation needed}}		\| From Sanskrit ''śatam'': hundred; [[relative cent]] of Armodue 16edo theory{{Citation needed}}
	\|-		\|-
	\| Tile		\| Tile
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	\| [[9900edo\|9900]]		\| [[9900edo\|9900]]
	\| 2<sup>2</sup> × 3<sup>2</sup> × 5<sup>2</sup> × 11		\| 2<sup>2</sup> × 3<sup>2</sup> × 5<sup>2</sup> × 11
	\| [[Relative cent]] of [[99edo]]; ~~Suggested~~ by [[Osmiorisbendi]], advocated by [[Tútim Dennsuul Wafiil]]. See the dedicated page.		\| [[Relative cent]] of [[99edo]]; suggested by [[Osmiorisbendi]], advocated by [[Tútim Dennsuul Wafiil]]. See the dedicated page.
	\|-		\|-
	\| [[Türk sent]] / [[Turkish cent]]		\| [[Türk sent]] / [[Turkish cent]]
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	\| [[30103edo\|30103]]		\| [[30103edo\|30103]]
	\| 30103 (prime)		\| 30103 (prime)
	\| 30103 ≃ 100,000 × log<sub>10</sub>2; ~~Proposed~~ by [[Augustus de Morgan]] (1864)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/j/jot.aspx Tonalsoft \| ''Jot'']</ref><ref name="equal"/>.		\| 30103 ≃ 100,000 × log<sub>10</sub>2; proposed by [[Augustus de Morgan]] (1864)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/j/jot.aspx Tonalsoft \| ''Jot'']</ref><ref name="equal"/>.
	\|-		\|-
	\| [[Imp]]		\| [[Imp]]
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	\| [[78005edo\|78005]]		\| [[78005edo\|78005]]
	\| 5 × 15601		\| 5 × 15601
	\| ~~Name proposed~~ by Tristan Bay in 2023; 78005edo consistently maps Kirnberger's atom to 1 edostep and is a very strong 5-limit system. ~~{{Citation needed}}~~		\| Proposed by Tristan Bay (2023); 78005edo consistently maps Kirnberger's atom to 1 edostep and is a very strong 5-limit system.
	\|-		\|-
	\| [[MIDI Tuning Standard unit]] (14mu)		\| [[MIDI Tuning Standard unit]] (14mu)
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	=== Relative measures ===		=== Relative measures ===
	Within a given [[~~Equal~~-step tuning\|equal-stepped]] ~~tonal system~~, the [[relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[Just intonation\|JI]] intervals). It is defined as on 100th (or 1 percent) of the interval between two neighbouring pitches in the used equal tuning.		Within a given [[equal-step tuning\|equal-stepped tuning system]], the [[relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[Just intonation\|JI]] intervals). It is defined as on 100th (or 1 percent) of the interval between two neighbouring pitches in the used equal tuning.

	== Ratio ==		== Ratio ==