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46edo: Difference between revisions

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! #
! #
! Cents
! Cents
! Approximate Ratios*
! Approximate Ratios<ref name="interval ratios" group="note">Based on treating 46edo as a 2.3.5.7.11.13.17.23 subgroup, without ratios of 15 (except the superparticulars). 46edo has intervals involving the 15th harmonic poorly approximated, except for 15/8 and 16/15 themselves, because, while the 3rd and 5th harmonics are sharp and their deviations from just intonation add up, 7, 11, and 13 are all tuned flat, making the difference even larger, preventing it from being [[consistent]] in the [[15-odd-limit]]. This can be demonstrated with the discrepancy approximating [[15/13]] and [[26/15]]. 9\46 is closer to 15/13 by a hair; 10\46 represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13.</ref>
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[SKULO interval names| SKULO notation]] (K or S = 1, U = 2)
! colspan="3" | [[SKULO interval names| SKULO notation]] (K or S = 1, U = 2)
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| UEb, D#
| UEb, D#
| fri
| fri
| ru &#42;&#42;
| ru<ref name="intervals2" group="note">/u/ as in s'''u'''praminor</ref>
|-
|-
| 6
| 6
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| uE, sD#
| uE, sD#
| ri
| ri
| ruh &#42;&#42;&#42;
| ruh<ref name="intervals3" group="note">/ʌ/ as in s'''u'''bmajor</ref>
|-
|-
| 7
| 7
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| UF
| UF
| ni
| ni
| mu &#42;&#42;
| mu<ref name="intervals2" group="note" />
|-
|-
| 14
| 14
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| uF#
| uF#
| mi
| mi
| muh &#42;&#42;&#42;
| muh<ref name="intervals3" group="note" />
|-
|-
| 15
| 15
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| UBb
| UBb
| fli
| fli
| lu &#42;&#42;
| lu<ref name="intervals2" group="note" />
|-
|-
| 33
| 33
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| uB
| uB
| li
| li
| luh &#42;&#42;&#42;
| luh<ref name="intervals3" group="note" />
|-
|-
| 34
| 34
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| UC, sDb
| UC, sDb
| thi
| thi
| tu &#42;&#42;
| tu<ref name="intervals2" group="note" />
|-
|-
| 41
| 41
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| uC#, Db
| uC#, Db
| ti
| ti
| tuh &#42;&#42;&#42;
| tuh<ref name="intervals3" group="note" />
|-
|-
| 42
| 42
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| da
| da
| do
| do
{{table notes|cols=11
| Based on treating 46edo as a 2.3.5.7.11.13.17.23 subgroup, without ratios of 15 (except the superparticulars). 46edo has intervals involving the 15th harmonic poorly approximated, except for 15/8 and 16/15 themselves, because, while the 3rd and 5th harmonics are sharp and their deviations from just intonation add up, 7, 11, and 13 are all tuned flat, making the difference even larger, preventing it from being [[consistent]] in the [[15-odd-limit]]. This can be demonstrated with the discrepancy approximating [[15/13]] and [[26/15]]. 9\46 is closer to 15/13 by a hair; 10\46 represents the difference between, for instance, 46edo's 15/8 and 13/8, and is more likely to appear in chords actually functioning as 15/13.
| &thinsp;/u/ as in s'''u'''praminor
| /ʌ/ as in s'''u'''bmajor
}}
|}
|}


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