Eufalesio at 18:26, 9 June 2026

2026-06-09T18:26:17Z

← Older revision		Revision as of 18:26, 9 June 2026
Line 1:		Line 1:
	{{Infobox interval\|Name=half-apotome<br>semiaugmented unison\|Ratio=\sqrt{2187/2048}\|Cents=56.8425}}'''sqrt(2187/2048)''', the '''half-apotome, or semiaugmented unison''', is a [[radical interval]] of about 57 cents, in the [[Hemipyth\|sqrt(2).sqrt(3) subgroup]] or [[Ploidacot/Dicot\|dicot (ploidacot)]] more precisely. It is a quartertone-like interval; differing from the smaller quartertone [[sqrt(256/243)]] by half a [[pythagorean comma]]. It is reached by +7 hemififths octave reduced, with a fractional monzo of {{Monzo\|-11/2 7/2}}.		{{Infobox interval\|Name=half-apotome<br>semiaugmented unison\|Ratio=\sqrt{2187/2048}\|Cents=56.8425}}'''sqrt(2187/2048)''', the '''half-apotome, or semiaugmented unison''', is a [[radical interval]] of about 57 cents, in the [[Hemipyth\|sqrt(2).sqrt(3) subgroup]] or [[Ploidacot/Dicot\|dicot (ploidacot)]] more precisely. It is a [[quartertone]]-like interval; differing from the smaller quartertone [[sqrt(256/243)]] by half a [[pythagorean comma]]. It is reached by +7 [[Hemififth\|hemififths]] octave reduced, with a fractional monzo of {{Monzo\|-11/2 7/2}}.

	== In temperaments ==		== In temperaments ==
	The half-apotome can be made equal to many rational intervals, most notably, to [[33/32]], tempering out the [[rastma]], or much more accurately to [[1323/1280]], tempering out the [[breedsma]].		The half-apotome can be made equal to many rational intervals, most notably, to [[33/32]], tempering out the [[rastma\|rastma (243/242)]], or much more accurately to [[1323/1280]], tempering out the [[breedsma\|breedsma (2401/2400)]].

	It is most often ~~represented~~ in scores by a half-sharp, {{Sagittal\|t}}. However, this does not mean C{{Sagittal\|t}} = D{{Sagittal\|d}} always; the ~~latter~~ is ~~the smaller quartertone sqrt(256/243)~~. ~~This~~ equality ~~only~~ holds true if the pythagorean comma is tempered out ~~too~~.		It is most often written in scores by a half-sharp, {{Sagittal\|t}}. However, this does not mean C{{Sagittal\|t}} = D{{Sagittal\|d}} always; D{{Sagittal\|d}} is a lower pitch than C{{Sagittal\|t}}. [[Pythagorean comma#Importance in diatonic\|This antiintuitive notion]] is due to the fact that the apotome - an augmented unison - is wider than a minor second in [[Pythagorean tuning]], and [[JI]] more generally. The equality holds true if and only if the pythagorean comma is tempered out.

Eufalesio: Birth

2026-06-09T15:21:10Z

Birth

New page

{{Infobox interval|Name=half-apotome<br>semiaugmented unison|Ratio=\sqrt{2187/2048}|Cents=56.8425}}'''sqrt(2187/2048)''', the '''half-apotome, or semiaugmented unison''', is a [[radical interval]] of about 57 cents, in the [[Hemipyth|sqrt(2).sqrt(3) subgroup]] or [[Ploidacot/Dicot|dicot (ploidacot)]] more precisely. It is a quartertone-like interval; differing from the smaller quartertone [[sqrt(256/243)]] by half a [[pythagorean comma]]. It is reached by +7 hemififths octave reduced, with a fractional monzo of {{Monzo|-11/2 7/2}}.

== In temperaments ==
The half-apotome can be made equal to many rational intervals, most notably, to [[33/32]], tempering out the [[rastma]], or much more accurately to [[1323/1280]], tempering out the [[breedsma]].

It is most often represented in scores by a half-sharp, {{Sagittal|t}}. However, this does not mean C{{Sagittal|t}} = D{{Sagittal|d}} always; the latter is the smaller quartertone sqrt(256/243). This equality only holds true if the pythagorean comma is tempered out too.

Sqrt(2187/2048) - Revision history

Eufalesio at 18:26, 9 June 2026

Eufalesio: Birth