User talk:Contribution: Difference between revisions

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: I agree with Xenwolf honestly, especially in light of some of the things currently being discussed on the Xenharmonic Alliance Discord Server. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:48, 13 April 2021 (UTC)

== equal contrary motion ==

Hi contribution, <br>

I think it would ease to understand this voice leading concept it there was some article of at least section (reachable via [[Help:redirect|redirect]]). Do you think you could explain (and illustrate) it a bit further? <br>

Thanks in advance. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:00, 3 October 2022 (UTC)

: According to [[Wikipedia: Contrapuntal motion]], another name for equal contrary motion is "strict contrary motion". I don't think it is necessary to redefine basic voice leading concepts here on the Xen Wiki, since it is possible to link to Wikipedia whenever such a definition might be judged necessary. I think adding pictures would help more than adding definitions.

: That said, I would see no problem if there were pages about examples of voice leading specific to some tunings, when there is too much content to keep it reasonably on the tuning's main page. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 02:28, 4 October 2022 (UTC)

:: Thanks for your opinion, Fredg999, so a page about (xenharmonic) counterpoint could help here (with ''strict contrary motion'' redirecting to it). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:33, 4 October 2022 (UTC)

Hello,

What kind of intervals does the concept of strict contrary motion refer to? Degrees of a scale (for example 1 degree of 12 tones), or size (for example 100 cents)? Could all contrary motion of the same amount of degrees in an irregular temperament still be called strict?

== Template: Infobox ZPI ==

The template you created calls an inexistent module. If this template is work in progress, please add <code><nowiki>[[Category:Draft templates]]</nowiki></code> and don't use it in other pages until its basic functionality is complete. Thank you in advance. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:19, 28 March 2024 (UTC)

= Recent edits to EDx pages =

Hello! May I know where you get your numbers from? For instance, you have written in the Ed11/9 page that:

''[[19ed11/9]], [[21ed11/9]] and [[40ed11/9]] are to the [[Ed11/9|division of 11/9]] what [[17ed5/4]], [[19ed5/4]], and [[36ed5/4]] are to the [[Ed5/4|division of 5/4]]... <long text omitted>''

May we know how you arrive at these values? I feel that without any context or explanation people are going to have a hard time understanding why you are editing these pages. Thank you! [[User:2^67-1|2^67-1]] 05:50, 28 August 2024 (UTC)

: Hi. For each pair of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math>, there exists a ratio <math>{a}/{b}</math> such that <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> are <math>{a}/{b}</math> complementary; it is observed that <math>a−b=1</math> or <math>a−b=2</math>.

: In other words, for each ratio <math>a/b</math> where <math>a−b=1</math> or <math>a−b=2</math>, there exists a pair of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> that are <math>{a}/{b}</math> complementary.

: Bellow is a Python code that show for equal divisions of <math>a/b</math> the cent error in the mapping of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> that are <math>a/b</math> complementary.

: When running the tests sequentially for equal divisions of 2/1, 5/3, 3/2, 7/5, 4/3, 9/7, 5/4, 11/9, 6/5, and so on, we observe a converging sequence and pattern for low errors: 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28; then 15, 17, 32; then 17, 19, 36; then 19, 21, 40; then 21, 23, 44; etc. --[[User:Contribution|Contribution]] ([[User talk:Contribution|talk]]) 11:08, 28 August 2024 (UTC)

<pre>

# Enter the values for the X ratio of EDX. Ensure the numerator and denominator differ by 1 or 2.

numerator, denominator = 3, 2

# Program

from math import log

def calculate_complementary_pair(numerator, denominator):

"""

Calculates the superparticular complementary pair based on the difference

between the numerator and denominator.

"""

diff = numerator - denominator

if diff == 1:

# Case where numerator and denominator differ by 1

numerator_2 = numerator * 2

denominator_2 = numerator + denominator

numerator_3 = numerator + denominator

denominator_3 = denominator * 2

elif diff == 2:

# Case where numerator and denominator differ by 2

numerator_2 = numerator

denominator_2 = int((numerator + denominator) / 2)

numerator_3 = int((numerator + denominator) / 2)

denominator_3 = denominator

else:

raise ValueError("Invalid input: numerator and denominator must differ by 1 or 2.")

return (numerator_2, denominator_2), (numerator_3, denominator_3)

def calculate_log_ratio(ratio):

"""

Calculates the logarithmic value of a ratio in cents.

"""

return 1200 * log(ratio) / log(2)

def print_mappings(ratio_log, superparticular_log, numerator, denominator):

"""

Prints the mapping of ratios and their differences in logarithmic cents.

"""

for ed in range(1, 101):

mapping = int(superparticular_log / (ratio_log / ed) + 0.5) # Rounds to the nearest integer

error = mapping * (ratio_log / ed) - superparticular_log

print(f"scale: {ed}ed{numerator}/{denominator}, error: {error:.5f}")

# Calculate the superparticular complementary pairs

(pair_1, pair_2) = calculate_complementary_pair(numerator, denominator)

print(f"Successive superparticular complementary pair of {numerator}/{denominator}: {pair_1[0]}/{pair_1[1]} and {pair_2[0]}/{pair_2[1]}")

# Calculate ratios

ratio = numerator / denominator

superparticular_complementary_ratio = pair_1[0] / pair_1[1]

# Calculate the logarithmic values for the ratios in cents

ratio_log_cents = calculate_log_ratio(ratio)

superparticular_complementary_log_cents = calculate_log_ratio(superparticular_complementary_ratio)

# Output the mappings

print_mappings(ratio_log_cents, superparticular_complementary_log_cents, numerator, denominator)

</pre>

@@ Line 152: / Line 152: @@
 : I agree with Xenwolf honestly, especially in light of some of the things currently being discussed on the Xenharmonic Alliance Discord Server. --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 20:48, 13 April 2021 (UTC)
+== equal contrary motion ==
+Hi contribution, <br>
+I think it would ease to understand this voice leading concept it there was some article of at least section (reachable via [[Help:redirect|redirect]]). Do you think you could explain (and illustrate) it a bit further? <br>
+Thanks in advance. --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 21:00, 3 October 2022 (UTC)
+: According to [[Wikipedia: Contrapuntal motion]], another name for equal contrary motion is "strict contrary motion". I don't think it is necessary to redefine basic voice leading concepts here on the Xen Wiki, since it is possible to link to Wikipedia whenever such a definition might be judged necessary. I think adding pictures would help more than adding definitions.
+: That said, I would see no problem if there were pages about examples of voice leading specific to some tunings, when there is too much content to keep it reasonably on the tuning's main page. --[[User:Fredg999|Fredg999]] ([[User talk:Fredg999|talk]]) 02:28, 4 October 2022 (UTC)
+:: Thanks for your opinion, Fredg999, so a page about (xenharmonic) counterpoint could help here (with ''strict contrary motion'' redirecting to it). --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 06:33, 4 October 2022 (UTC)
+Hello,
+What kind of intervals does the concept of strict contrary motion refer to? Degrees of a scale (for example 1 degree of 12 tones), or size (for example 100 cents)? Could all contrary motion of the same amount of degrees in an irregular temperament still be called strict?
+== Template: Infobox ZPI ==
+The template you created calls an inexistent module. If this template is work in progress, please add <code><nowiki>[[Category:Draft templates]]</nowiki></code> and don't use it in other pages until its basic functionality is complete. Thank you in advance. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 13:19, 28 March 2024 (UTC)
+= Recent edits to EDx pages =
+Hello! May I know where you get your numbers from? For instance, you have written in the Ed11/9 page that:
+''[[19ed11/9]], [[21ed11/9]] and [[40ed11/9]] are to the [[Ed11/9|division of 11/9]] what [[17ed5/4]], [[19ed5/4]], and [[36ed5/4]] are to the [[Ed5/4|division of 5/4]]... <long text omitted>''
+May we know how you arrive at these values? I feel that without any context or explanation people are going to have a hard time understanding why you are editing these pages. Thank you!     [[User:2^67-1|2^67-1]] 05:50, 28 August 2024 (UTC)
+: Hi. For each pair of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math>, there exists a ratio <math>{a}/{b}</math> such that <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> are <math>{a}/{b}</math> complementary; it is observed that <math>a−b=1</math> or <math>a−b=2</math>.
+: In other words, for each ratio <math>a/b</math> where <math>a−b=1</math> or <math>a−b=2</math>, there exists a pair of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> that are <math>{a}/{b}</math> complementary.
+: Bellow is a Python code that show for equal divisions of <math>a/b</math> the cent error in the mapping of superparticular ratios <math>{s1}/{s2}</math> and <math>{s2}/{s3}</math> that are <math>a/b</math> complementary.
+: When running the tests sequentially for equal divisions of 2/1, 5/3, 3/2, 7/5, 4/3, 9/7, 5/4, 11/9, 6/5, and so on, we observe a converging sequence and pattern for low errors: 5, 7, 12; then 7, 9, 16; then 9, 11, 20; then 11, 13, 24; then 13, 15, 28; then 15, 17, 32; then 17, 19, 36; then 19, 21, 40; then 21, 23, 44; etc. --[[User:Contribution|Contribution]] ([[User talk:Contribution|talk]]) 11:08, 28 August 2024 (UTC)
+<pre>
+# Enter the values for the X ratio of EDX. Ensure the numerator and denominator differ by 1 or 2.
+numerator, denominator = 3, 2
+# Program
+from math import log
+def calculate_complementary_pair(numerator, denominator):
+    """
+    Calculates the superparticular complementary pair based on the difference
+    between the numerator and denominator.
+    """
+    diff = numerator - denominator
+    if diff == 1:
+        # Case where numerator and denominator differ by 1
+        numerator_2 = numerator * 2
+        denominator_2 = numerator + denominator
+        numerator_3 = numerator + denominator
+        denominator_3 = denominator * 2
+    elif diff == 2:
+        # Case where numerator and denominator differ by 2
+        numerator_2 = numerator
+        denominator_2 = int((numerator + denominator) / 2)
+        numerator_3 = int((numerator + denominator) / 2)
+        denominator_3 = denominator
+    else:
+        raise ValueError("Invalid input: numerator and denominator must differ by 1 or 2.")
+    return (numerator_2, denominator_2), (numerator_3, denominator_3)
+def calculate_log_ratio(ratio):
+    """
+    Calculates the logarithmic value of a ratio in cents.
+    """
+    return 1200 * log(ratio) / log(2)
+def print_mappings(ratio_log, superparticular_log, numerator, denominator):
+    """
+    Prints the mapping of ratios and their differences in logarithmic cents.
+    """
+    for ed in range(1, 101):
+        mapping = int(superparticular_log / (ratio_log / ed) + 0.5)  # Rounds to the nearest integer
+        error = mapping * (ratio_log / ed) - superparticular_log
+        print(f"scale: {ed}ed{numerator}/{denominator}, error: {error:.5f}")
+# Calculate the superparticular complementary pairs
+(pair_1, pair_2) = calculate_complementary_pair(numerator, denominator)
+print(f"Successive superparticular complementary pair of {numerator}/{denominator}: {pair_1[0]}/{pair_1[1]} and {pair_2[0]}/{pair_2[1]}")
+# Calculate ratios
+ratio = numerator / denominator
+superparticular_complementary_ratio = pair_1[0] / pair_1[1]
+# Calculate the logarithmic values for the ratios in cents
+ratio_log_cents = calculate_log_ratio(ratio)
+superparticular_complementary_log_cents = calculate_log_ratio(superparticular_complementary_ratio)
+# Output the mappings
+print_mappings(ratio_log_cents, superparticular_complementary_log_cents, numerator, denominator)
+</pre>