Syntonic–chromatic equivalence continuum: Difference between revisions
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! Monzo | ! Monzo | ||
|- | |- | ||
| | | −5 | ||
| | | −3 | ||
| [[Nadir]] | | [[Nadir]] | ||
| [[1162261467/1048576000]] | | [[1162261467/1048576000]] | ||
| {{monzo| -23 19 -3 }} | | {{monzo| -23 19 -3 }} | ||
|- | |- | ||
| | | −4 | ||
| | | −2 | ||
| Nethertone | | Nethertone | ||
| [[14348907/13107200]] | | [[14348907/13107200]] | ||
| {{monzo| -19 15 -2 }} | | {{monzo| -19 15 -2 }} | ||
|- | |- | ||
| | | −3 | ||
| | | −1 | ||
| Deeptone a.k.a. tragicomical | | Deeptone a.k.a. tragicomical | ||
| [[177147/163840]] | | [[177147/163840]] | ||
| {{monzo| -15 11 -1 }} | | {{monzo| -15 11 -1 }} | ||
|- | |- | ||
| | | −2 | ||
| 0 | | 0 | ||
| [[Whitewood]] | | [[Whitewood]] | ||
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| {{monzo| -11 7 }} | | {{monzo| -11 7 }} | ||
|- | |- | ||
| | | −1 | ||
| 1 | | 1 | ||
| [[Mavila]] | | [[Mavila]] | ||
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! Monzo | ! Monzo | ||
|- | |- | ||
| | | −1 | ||
| [[Shallowtone]] | | [[Shallowtone]] | ||
| [[295245/262144]] | | [[295245/262144]] | ||
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== Absurdity == | == Absurdity == | ||
: ''For extensions, see [[Porwell temperaments #Absurdity]].'' | |||
Absurdity corresponds to {{nowrap|''n'' {{=}} 7}}, and can be described as the {{nowrap|77 & 84}} temperament, so named because it truly is an absurd temperament. The generator is ~81/80 and the period is ~800/729, which is (10/9)/(81/80). | Absurdity corresponds to {{nowrap|''n'' {{=}} 7}}, and can be described as the {{nowrap|77 & 84}} temperament, so named because it truly is an absurd temperament. The generator is ~81/80 and the period is ~800/729, which is (10/9)/(81/80). | ||
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== Artoneutral == | == Artoneutral == | ||
: ''For extensions, see [[Hemifamity temperaments #Artoneutral]].'' | |||
5-limit artoneutral is generated by ~243/200 (or ~400/243), same as that of [[amity]] but sharper. This corresponds to {{nowrap|''n'' {{=}} 9/2}} and {{nowrap|''m'' {{=}} 9/7}} and can be described as the 80 & 87 temperament, though [[94edo]] is a notable tuning not appearing in the optimal ET sequence. | 5-limit artoneutral is generated by ~243/200 (or ~400/243), same as that of [[amity]] but sharper. This corresponds to {{nowrap|''n'' {{=}} 9/2}} and {{nowrap|''m'' {{=}} 9/7}} and can be described as the 80 & 87 temperament, though [[94edo]] is a notable tuning not appearing in the optimal ET sequence. | ||
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== Sevond == | == Sevond == | ||
: ''For extensions, see [[Keemic temperaments #Sevond]].'' | |||
Sevond is a fairly obvious temperament; it just equates a stack of seven ~10/9's with ~2/1, hence the period is ~10/9. One generator from 5\7 puts you at ~3/2, two generators from 2\7 puts you at ~5/4. This corresponds to {{nowrap|''n'' {{=}} 7/2}} and {{nowrap|''m'' {{=}} 7/5}} and can be described as the {{nowrap|56 & 63}} temperament. | Sevond is a fairly obvious temperament; it just equates a stack of seven ~10/9's with ~2/1, hence the period is ~10/9. One generator from 5\7 puts you at ~3/2, two generators from 2\7 puts you at ~5/4. This corresponds to {{nowrap|''n'' {{=}} 7/2}} and {{nowrap|''m'' {{=}} 7/5}} and can be described as the {{nowrap|56 & 63}} temperament. | ||
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== Deeptone a.k.a. tragicomical == | == Deeptone a.k.a. tragicomical == | ||
{{Main|Deeptone}} | {{Main| Deeptone }} | ||
Deeptone is generated by a fifth, which is typically sharper than in [[7edo]] but flatter than in [[flattone]]. The ~5/4 is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). | Deeptone is generated by a fifth, which is typically sharper than in [[7edo]] but flatter than in [[flattone]]. The ~5/4 is reached by eleven fifths octave-reduced, which is an augmented third (C–E♯). | ||
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== Shallowtone == | == Shallowtone == | ||
: ''For | : ''For extensions, see [[Mint temperaments #Shallowtone]].'' | ||
Shallowtone is generated by a fifth, which is typically sharper than in [[mavila]] but flatter than in [[7edo]]. The ~5/4 is reached by minus ten fifths octave-reduced, which is an augmented third (C-E𝄪) in melodic [[2L 5s|antidiatonic]] notation and a diminished third (C-E𝄫) in harmonic antidiatonic notation. | Shallowtone is generated by a fifth, which is typically sharper than in [[mavila]] but flatter than in [[7edo]]. The ~5/4 is reached by minus ten fifths octave-reduced, which is an augmented third (C-E𝄪) in melodic [[2L 5s|antidiatonic]] notation and a diminished third (C-E𝄫) in harmonic antidiatonic notation. | ||