Porcupine/Chords: Difference between revisions

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Below are listed the [[15-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[porcupine|porcupine temperament]] that do not have generator steps 7 or 13 as [[dyad]]s. Typing the chords requires consideration of the fact that porcupine conflates [[10/9]], [[11/10]] and [[12/11]] and ~~also~~ [[16/9]] ~~and~~ [[7/4]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only [[64/63]] tempering are marked [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[121/120]] [[biyatismic chords|biyatismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], and by [[385/384]] [[keenanismic chords|keenanismic]]. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked [[ares chords|ares]], that require 100/99 and 385/384 tempering are marked [[keemic chords|keemic]], and that require any two of 121/120, 176/175 and 385/384 are marked [[zeus chords|zeus]]. Chords that receive tempering by three independent commas above are labeled porcupine.

Below are listed the [[15-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[porcupine|porcupine temperament]] that do not have generator steps 7 or 13 as [[dyad]]s. Typing the chords requires consideration of the fact that porcupine conflates [[10/9]], [[11/10]] and [[12/11]], [[11/9]] with [[6/5]], [[22/15]] with [[16/11]], and [[16/9]] with [[7/4]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only [[64/63]] tempering are marked [[archytas chords|archytas]], by [[100/99]] [[ptolemismic chords|ptolemismic]], by [[121/120]] [[biyatismic chords|biyatismic]], by [[176/175]] [[valinorsmic chords|valinorsmic]], and by [[385/384]] [[keenanismic chords|keenanismic]]. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked [[ares chords|ares]], that require 100/99 and 385/384 tempering are marked [[keemic chords|keemic]], and that require any two of 121/120, 176/175 and 385/384 are marked [[zeus chords|zeus]]. Chords that receive tempering by three independent commas above are labeled porcupine.

The transversal is in generator order. This is useful because it tells how common the chords are: For instance, a chord that appears on the sixth generation will appear exactly once in Porcupine[7], twice in Porcupine[8], and nine times in Porcupine[15].

Revision as of 11:07, 12 October 2025 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 23,908 edits m A little cleanup ← Older edit		Latest revision as of 23:50, 18 February 2026 view source Overthink (talk \| contribs) autopatrolled 2,695 edits complete conflations
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	Below are listed the [[15-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[porcupine\|porcupine temperament]] that do not have generator steps 7 or 13 as [[dyad]]s. Typing the chords requires consideration of the fact that porcupine conflates [[10/9]], [[11/10]] and [[12/11]] and ~~also~~ [[16/9]] ~~and~~ [[7/4]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only [[64/63]] tempering are marked [[archytas chords\|archytas]], by [[100/99]] [[ptolemismic chords\|ptolemismic]], by [[121/120]] [[biyatismic chords\|biyatismic]], by [[176/175]] [[valinorsmic chords\|valinorsmic]], and by [[385/384]] [[keenanismic chords\|keenanismic]]. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked [[ares chords\|ares]], that require 100/99 and 385/384 tempering are marked [[keemic chords\|keemic]], and that require any two of 121/120, 176/175 and 385/384 are marked [[zeus chords\|zeus]]. Chords that receive tempering by three independent commas above are labeled porcupine.		Below are listed the [[15-odd-limit]] [[dyadic chord]]s of [[11-limit]] [[porcupine\|porcupine temperament]] that do not have generator steps 7 or 13 as [[dyad]]s. Typing the chords requires consideration of the fact that porcupine conflates [[10/9]], [[11/10]] and [[12/11]], [[11/9]] with [[6/5]], [[22/15]] with [[16/11]], and [[16/9]] with [[7/4]]. If a [[transversal]] can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. If a chord is essentially tempered, the chord is analyzed in terms of the transversals 11/10, 6/5, 16/11 and 7/4. Chords that require only [[64/63]] tempering are marked [[archytas chords\|archytas]], by [[100/99]] [[ptolemismic chords\|ptolemismic]], by [[121/120]] [[biyatismic chords\|biyatismic]], by [[176/175]] [[valinorsmic chords\|valinorsmic]], and by [[385/384]] [[keenanismic chords\|keenanismic]]. Chords that require any two of 64/63, 100/99 and 176/175 tempering are marked [[ares chords\|ares]], that require 100/99 and 385/384 tempering are marked [[keemic chords\|keemic]], and that require any two of 121/120, 176/175 and 385/384 are marked [[zeus chords\|zeus]]. Chords that receive tempering by three independent commas above are labeled porcupine.

	The transversal is in generator order. This is useful because it tells how common the chords are: For instance, a chord that appears on the sixth generation will appear exactly once in Porcupine[7], twice in Porcupine[8], and nine times in Porcupine[15].		The transversal is in generator order. This is useful because it tells how common the chords are: For instance, a chord that appears on the sixth generation will appear exactly once in Porcupine[7], twice in Porcupine[8], and nine times in Porcupine[15].