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Below are listed the [[15-odd-limit]] [[dyadic chord]]s of the [[buzzard]] temperament, subject to the condition that no interval smaller than [[12/11]], at 150 [[cent]]s, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[176/175]] are labeled [[ | Below are listed the [[15-odd-limit]] [[dyadic chord]]s of the [[13-limit]] [[buzzard]] temperament, subject to the condition that no interval smaller than [[12/11]], at 150 [[cent]]s, appears. The essentially just chords are typed as otonal, utonal, or ambitonal. Those requiring tempering only by [[176/175]] are labeled [[valinorsmic chords|valinorsmic]], by [[540/539]] [[swetismic chords|swetismic]], by [[351/350]] [[ratwolfsmic chords|ratwolfsmic]], by [[352/351]] [[major minthmic chords|minthmic]], by [[676/675]] [[island chords|island]], by [[729/728]] [[squbemic chords|squbemic]], by [[1001/1000]] [[sinbadmic chords|sinbadmic]], by [[640/637]] [[huntmic chords|huntmic]], by [[847/845]] [[cuthbert chords|cuthbert]], by [[1188/1183]] [[kestrel chords|kestrel]], and by [[2200/2197]] [[petrmic chords|petrmic]]. [[Codimension]]-2 temperaments are labeled valinorsmic-ratwolfsmic, valinorsmic-huntmic, valinorsmic-island, valinorsmic-swetismic, swetismic-ratwolfsmic, swetismic-minthmic, swetismic-cuthbert, ratwolfsmic-island, minthmic-squbemic, ratwolfsmic-kestrel, minthmic-island, cuthbert-sinbadmic according to the two commas which define it. Finally, rank-3 temperaments are labeled [[guanyin]], [[draco]] or [[persephone]]. | ||
Buzzard has [[mos scale]]s of size 5, 8, 13, 18, 28, 33, 38, 43, 48, 53, 58 and 111. The largest chords on these lists have complexity 42, and so would require the 43-note mos, but there are many chords of much lower complexity. The 8-note mos has a number of chords, the 13-note mos has a considerable store, and of course the 18-note mos many more. | Buzzard has [[mos scale]]s of size 5, 8, 13, 18, 28, 33, 38, 43, 48, 53, 58 and 111. The largest chords on these lists have complexity 42, and so would require the 43-note mos, but there are many chords of much lower complexity. The 8-note mos has a number of chords, the 13-note mos has a considerable store, and of course the 18-note mos many more. | ||
== Triads == | == Triads == | ||
The triads are listed in four ways. | The triads are listed in four ways. | ||
First, by number of generators, in the "transversal" column. This is a convenient way to see how many of these chords will appear in a given | First, by number of generators, in the "transversal" column. This is a convenient way to see how many of these chords will appear in a given mos: For example, since it takes four generators to get to 1–26/15–3/2, you will have four of these chords in the 8-note mos ({{nowrap| 8 - 4 {{=}} 4 }}). Note that 8 generators means 9 notes: 9/8 does not appear in the 8-note mos. | ||
However, the notes may not appear in size order; 26/15 is 952 cents and 3/2 is 702 cents, so the chord would normally be written | However, the notes may not appear in size order; 26/15 is 952 cents and 3/2 is 702 cents, so the chord would normally be written 1–3/2–26/15 – which leads us to the second way chords are listed. | ||
Second, as generated, but in size order. | Second, as generated, but in size order. | ||
| Line 17: | Line 16: | ||
Fourth, rotated to use the third note as the root. | Fourth, rotated to use the third note as the root. | ||
You can think of the third and fourth ways as the "first and second inversions" of the second way, but unlike conventional music theory, there | You can think of the third and fourth ways as the "first and second inversions" of the second way, but unlike conventional music theory, there is no preference for any one of the inversions over the other. Chords are chords are chords, and we look at the inversions because it can help to know that 1–8/7–12/7, 1–3/2–7/4, and 1–7/6–4/3 are all inversions or rotations of the same chord. | ||
Note that the values for these notes might have been attained by applying one of the commas noted in the introductory section. | Note that the values for these notes might have been attained by applying one of the commas noted in the introductory section. | ||
| Line 27: | Line 26: | ||
! Transversal | ! Transversal | ||
! Type | ! Type | ||
! Size | ! Size order | ||
! First | ! First rotation | ||
! Second | ! Second rotation | ||
|- | |- | ||
| 1 | | 1 | ||
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== Tetrads == | == Tetrads == | ||
{| class="wikitable center-1" | {| class="wikitable center-1" | ||
|- | |- | ||
| Line 928: | Line 926: | ||
! Transversal | ! Transversal | ||
! Type | ! Type | ||
! Size | ! Size order | ||
! First | ! First rotation | ||
! Second | ! Second rotation | ||
! Third | ! Third rotation | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 3,675: | Line 3,673: | ||
[[Category:Dyadic chords]] | [[Category:Dyadic chords]] | ||
[[Category:Buzzard]] | [[Category:Buzzard]] | ||
[[Category: | [[Category:Triads]] | ||
[[Category:Tetrads]] | |||
[[Category:Pentads]] | |||
[[Category:Hexads]] | |||