Normal forms: Difference between revisions

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Since a [[regular temperament]] can be represented by multiple equivalent [[Vals and tuning space|val]] lists (aka [[mapping]]s) or [[Monzos and interval space|monzo]] lists (aka comma-bases), it can be helpful — e.g. when comparing or cataloguing temperaments — to choose a single one of these equivalent lists to use as its unique identifier. A set of rules that are consistently able to narrow the full set of equivalent lists down to a single list for each temperament may be called a ''normal form'', and accordingly, a list which uniquely identifies a temperament in this way may be called a '''normal list'''.

Since a [[regular temperament]] can be represented by multiple equivalent [[Vals and tuning space|val]] lists (aka [[mapping]]s) or [[Monzos and interval space|monzo]] lists (aka [[comma-basis|comma-bases]]), it can be helpful — e.g. when comparing or cataloguing temperaments — to choose a single one of these equivalent lists to use as its unique identifier. A set of rules that are consistently able to narrow the full set of equivalent lists down to a single list for each temperament may be called a ''normal form'', and accordingly, a list which uniquely identifies a temperament in this way may be called a '''normal list'''.

Because several different normal forms have been developed, each temperament has several different normal lists: one for each form. These normal lists are not all necessarily different; sometimes some or all of them may be the same.

Revision as of 21:40, 8 November 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,172 edits extract RREF from Mathematical theory of regular temperaments#Characterizing a regular temperament, because it is a subtopic of the Normal list characterization listed there ← Older edit		Revision as of 22:57, 8 November 2021 view source Cmloegcmluin (talk \| contribs) autopatrolled, emailconfirmed 5,172 edits link comma-basis Newer edit →
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	Since a [[regular temperament]] can be represented by multiple equivalent [[Vals and tuning space\|val]] lists (aka [[mapping]]s) or [[Monzos and interval space\|monzo]] lists (aka comma-bases), it can be helpful — e.g. when comparing or cataloguing temperaments — to choose a single one of these equivalent lists to use as its unique identifier. A set of rules that are consistently able to narrow the full set of equivalent lists down to a single list for each temperament may be called a ''normal form'', and accordingly, a list which uniquely identifies a temperament in this way may be called a '''normal list'''.		Since a [[regular temperament]] can be represented by multiple equivalent [[Vals and tuning space\|val]] lists (aka [[mapping]]s) or [[Monzos and interval space\|monzo]] lists (aka [[comma-basis\|comma-bases]]), it can be helpful — e.g. when comparing or cataloguing temperaments — to choose a single one of these equivalent lists to use as its unique identifier. A set of rules that are consistently able to narrow the full set of equivalent lists down to a single list for each temperament may be called a ''normal form'', and accordingly, a list which uniquely identifies a temperament in this way may be called a '''normal list'''.

	Because several different normal forms have been developed, each temperament has several different normal lists: one for each form. These normal lists are not all necessarily different; sometimes some or all of them may be the same.		Because several different normal forms have been developed, each temperament has several different normal lists: one for each form. These normal lists are not all necessarily different; sometimes some or all of them may be the same.

Normal forms: Difference between revisions

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