Tempered monzos and vals: Difference between revisions

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'''~~Tmonzos''' (for '''tempered~~ monzos''') and ~~'''tvals''' (for~~ '''tempered vals''') are like regular [[monzo]]s and [[val]]s, except they work in a space of tempered intervals (for example, the intervals found in meantone) rather than in [[just intonation]]. A tval specifies a tuning or further temperament of the [[generator]]s of a temperament. For example, the 31edo tval for meantone is {{val| 31 49 }}, assume the generators are ~2 and ~3. A tmonzo specifies a particular tempered interval in terms of stacking the temperament's generators. For example, the tmonzo form of the major third in meantone is {{monzo| -6 4 }}. Taking the {{w|dot product}} of these (multiplying corresponding elements and adding up the results) yields the tuning of the major third in 31edo, 10\31.

'''Tempered monzos''' and '''tempered vals''' are like regular [[monzo]]s and [[val]]s, except they work in a space of tempered intervals (for example, the intervals found in meantone) rather than in [[just intonation]]. A tempered val (for short, "'''tval'''") specifies a tuning or further temperament of the [[generator]]s of a temperament. For example, the 31edo tval for meantone is {{val| 31 49 }}, assume the generators are ~2 and ~3. A tempered monzo (for short, "'''tmonzo'''") specifies a particular tempered interval in terms of stacking the temperament's generators. For example, the tmonzo form of the major third in meantone is {{monzo| -6 4 }}. Taking the {{w|dot product}} of these (multiplying corresponding elements and adding up the results) yields the tuning of the major third in 31edo, 10\31.

Tmonzos are rather straightforward, and tvals act on tmonzos in the same way that vals act on monzos, in that they map from tmonzos to a scalar representing a certain number of steps. A similar concept is a generator [[tuning map]], which maps from tmonzos to tunings in cents (or another logarithmic measure).

Revision as of 04:37, 16 May 2025 view source VectorGraphics (talk \| contribs) 2,399 edits m VectorGraphics moved page Tmonzos and tvals to Tempered monzos and vals ← Older edit		Latest revision as of 10:31, 17 May 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 23,893 edits m - breadcrumbs (this isn't a subpage).
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	'''~~Tmonzos''' (for '''tempered~~ monzos''') and ~~'''tvals''' (for~~ '''tempered vals''') are like regular [[monzo]]s and [[val]]s, except they work in a space of tempered intervals (for example, the intervals found in meantone) rather than in [[just intonation]]. A tval specifies a tuning or further temperament of the [[generator]]s of a temperament. For example, the 31edo tval for meantone is {{val\| 31 49 }}, assume the generators are ~2 and ~3. A tmonzo specifies a particular tempered interval in terms of stacking the temperament's generators. For example, the tmonzo form of the major third in meantone is {{monzo\| -6 4 }}. Taking the {{w\|dot product}} of these (multiplying corresponding elements and adding up the results) yields the tuning of the major third in 31edo, 10\31.		'''Tempered monzos''' and '''tempered vals''' are like regular [[monzo]]s and [[val]]s, except they work in a space of tempered intervals (for example, the intervals found in meantone) rather than in [[just intonation]]. A tempered val (for short, "'''tval'''") specifies a tuning or further temperament of the [[generator]]s of a temperament. For example, the 31edo tval for meantone is {{val\| 31 49 }}, assume the generators are ~2 and ~3. A tempered monzo (for short, "'''tmonzo'''") specifies a particular tempered interval in terms of stacking the temperament's generators. For example, the tmonzo form of the major third in meantone is {{monzo\| -6 4 }}. Taking the {{w\|dot product}} of these (multiplying corresponding elements and adding up the results) yields the tuning of the major third in 31edo, 10\31.

	Tmonzos are rather straightforward, and tvals act on tmonzos in the same way that vals act on monzos, in that they map from tmonzos to a scalar representing a certain number of steps. A similar concept is a generator [[tuning map]], which maps from tmonzos to tunings in cents (or another logarithmic measure).		Tmonzos are rather straightforward, and tvals act on tmonzos in the same way that vals act on monzos, in that they map from tmonzos to a scalar representing a certain number of steps. A similar concept is a generator [[tuning map]], which maps from tmonzos to tunings in cents (or another logarithmic measure).