Sqrt(2187/2048): Difference between revisions

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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 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}} in most cases. [[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.

It is most often written in scores by a half-sharp, {{Sagittal|t}}. However, this does not mean E{{Sagittal|t}} = F{{Sagittal|d}} always; F{{Sagittal|d}} is a lower pitch than E{{Sagittal|t}} in most cases. [[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, resulting in E# ≠ F the same way. The equality holds true if and only if the pythagorean comma is tempered out.

Revision as of 16:52, 11 July 2026 view source Eufalesio (talk \| contribs) autopatrolled 739 edits No edit summary Tag: Visual edit ← Older edit		Latest revision as of 07:39, 12 July 2026 view source Eufalesio (talk \| contribs) autopatrolled 739 edits Fredg suggestions and fixed blunders Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit
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	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)]].		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 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}} in most cases. [[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.		It is most often written in scores by a half-sharp, {{Sagittal\|t}}. However, this does not mean E{{Sagittal\|t}} = F{{Sagittal\|d}} always; F{{Sagittal\|d}} is a lower pitch than E{{Sagittal\|t}} in most cases. [[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, resulting in E# ≠ F the same way. The equality holds true if and only if the pythagorean comma is tempered out.