User:BudjarnLambeth/Bird’s eye view of rank-2 temperaments: Difference between revisions

'''This page has been deprecated, but it is being kept in place for longevity as a reference material. Please see [[User:BudjarnLambeth/Survey of efficient temperaments by subgroup]] for the new version.'''

 

This page is intended as that starting point. It does not aim to list every temperament. Instead it aims to list only the ones that are of high interest to a sizeable number of composers or theorists.

 

Composers and theorists disagree amongst themselves about what properties are desirable in a temperament, and you might over time find that you lean more towards one camp or another. This list arranges temperaments by their properties, allowing you the reader to seek out temperaments with whichever properties you value.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Alternatively, it can be interpreted as a high-accuracy 2.3.17.19 subgroup temperament, where all of the intervals have an error less than 5 cents.

So that should provide a point of comparison to help measure these other temperaments against.

* Medium accuracy: < 12c error on most targeted intervals

Rank 2 temperaments can generate scales with any number of notes per [[equave]]. However, if they have too few notes, they won't be able approximate enough targeted intervals to be useful, and if they have too many notes, they will be filled with extra notes that don't serve much purpose and get in the way. Just how many notes is about right, varies from temperament to temperament. In layman’s terms: More notes needed = more complexity, less notes needed = less complexity. The real definition of complexity is more involved and rigorous than this, but this is good enough for the purposes of a broad overview page.

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

| [[superpyth]]

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! Medium accuracy (7-12c)

| [[hanson]], [[magic]]

| [[valentine]]

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! High accuracy (3.5-7c)

| [[diaschismic]]

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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| schismic aka [[Helmholtz temperament|Helmholtz]]

| [[kwazy]]

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

| [[blacksmith]]

| [[augene]], [[godzilla]], [[pajara]], [[porcupine]], [[whitewood]]

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! Medium accuracy (7-12c)

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| [[magic]], [[meantone]], [[mothra]], [[sensi]], [[superpyth]]

| [[valentine]]

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! High accuracy (3.5-7c)

| [[orwell]]

| [[diaschismic]], [[garibaldi]]

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

| [[enneadecal]], [[trinity]]

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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| [[augene]], [[blacksmith]], [[pajara]], [[porcupine]], [[whitewood]]

| [[godzilla]], [[superpyth]]

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! Medium accuracy (7-12c)

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| [[magic]], [[meanpop]], [[meantone]], [[mothra]], [[valentine]]

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! High accuracy (3.5-7c)

| [[diaschismic]], [[orwell]]

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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| [[enneadecal]], [[trinity]]

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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| [[augene]], [[blacksmith]], [[pajara]], [[porcupine]], [[whitewood]]

| [[superpyth]]

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! Medium accuracy (7-12c)

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| [[magic]], [[meantone]], [[mothra]]

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! High accuracy (3.5-7c)

| [[diaschismic]], [[orwell]]

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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| [[enneadecal]], [[trinity]]

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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! High accuracy (3.5-7c)

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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| [[trinity]]

== Higher limits ==

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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! High accuracy (3.5-7c)

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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| [[trinity]]

== 3.5.7 and its extensions ==

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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! High accuracy (3.5-7c)

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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== Other no-2s subgroups ==

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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! High accuracy (3.5-7c)

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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== No-3s subgroups ==

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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| [[didacus]], [[orgone]]

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! High accuracy (3.5-7c)

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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== 2.3.7 and its extensions ==

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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! High accuracy (3.5-7c)

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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== No-7s subgroups ==

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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! High accuracy (3.5-7c)

| [[sensible]], [[srutal archagall]]

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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== No-11s subgroups ==

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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! High accuracy (3.5-7c)

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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== Other subgroups ==

! Approx. 30 notes

! Approx. 70 notes

! Exotemperament (18-∞c)

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! Low accuracy (12-18c)

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! Medium accuracy (7-12c)

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! High accuracy (3.5-7c)

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! Very high accuracy (1-3.5c)

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! Microtemperament (0-1c)

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