Musical Calendar

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Musical Calendar

Karl Palmen

Dear Calendar People

 

If the 31-day months were the white notes on a piano, we’d get

 

A  May

A#/Bb  June

B  July

C  August

C#/Db September

D October

D#/Eb November

E December

F January

F#/Gb February

G March

G#/Ab April

 

 

Also I’d like to remind calendar people of the Leuconic Calendars from March (G) 2002.

 

 

I came a across a set of calendars in which the year was divided into seven leucons.

 

The new year begins at or near the June Solstice and the seven leucons are named as follows:

 

1: Dodiros

2: Reisunos

3: Mimyos

4: Farunos

5: Sothredos

6: Lasos

7: Tibredos

 

A long leucon has 59 days and a short leucon has 35 days. Each year has five long leucons and two short leucons. The short leucons are as evenly spaced as possible.

 

There were seven varieties of this leuconic calendar. The number of days in leucons of each of these varieties is as follows:

 

Variety    Do Re Mi Fa So La Ti sequence

Lydian     59 59 59 35 59 59 35 LLLsLLs

Ionian     59 59 35 59 59 59 35 LLsLLLs

Myxolydian 59 59 35 59 59 35 59 LLsLLsL

Dorian     59 35 59 59 59 35 59 LsLLLsL

Aolian     59 35 59 59 35 59 59 LsLLsLL

Phrygian   35 59 59 59 35 59 59 sLLLsLL

Locrian    35 59 59 35 59 59 59 sLLsLLL

 

In a leap year, an extra day was added to Tibredos. It was not known what the leap year rule was, but it was known that all 7 varieties celebrated the new year on exactly the same day, so must have agreed on an (equivalent) leap year rule.

 

So Dodiros begins on the same day in all 7 varieties. Each of the other 6 leucons begins on either of two days 24 days apart. The table below shows the day of year each leucon begins in each variety

 

Variety    Dod Rei Mim Far Sot Las Tib

Lydian     001 060 119 178 213 272 331

Ionian     001 060 119 154 213 272 331

Myxolydian 001 060 119 154 213 272 307

Dorian     001 060 095 154 213 272 307

Aolian     001 060 095 154 213 248 307

Phrygian   001 036 095 154 213 248 307

Locrian    001 036 095 154 189 248 307

 

At later times only two varieties survived. The Ionian variety, which became known as the Major Leuconic Calendar and the Aolian variety, which became known as the Minor Leuconic Calendar.

 

 

Karl

 

15(01(30

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Re: Musical Calendar

Vladimir Pakhomov-2

The musical interpretation of our perpetual calendar.

http://dominorus.site50.net/seals.html

You can listen to this melody.

 

Vladimir Pakhomov

 

 

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Karl Palmen
Sent: Thursday, July 16, 2015 3:38 PM
To: [hidden email]
Subject: Musical Calendar

 

Dear Calendar People

 

If the 31-day months were the white notes on a piano, we’d get

 

A  May

A#/Bb  June

B  July

C  August

C#/Db September

D October

D#/Eb November

E December

F January

F#/Gb February

G March

G#/Ab April

 

 

Also I’d like to remind calendar people of the Leuconic Calendars from March (G) 2002.

 

 

I came a across a set of calendars in which the year was divided into seven leucons.

 

The new year begins at or near the June Solstice and the seven leucons are named as follows:

 

1: Dodiros

2: Reisunos

3: Mimyos

4: Farunos

5: Sothredos

6: Lasos

7: Tibredos

 

A long leucon has 59 days and a short leucon has 35 days. Each year has five long leucons and two short leucons. The short leucons are as evenly spaced as possible.

 

There were seven varieties of this leuconic calendar. The number of days in leucons of each of these varieties is as follows:

 

Variety    Do Re Mi Fa So La Ti sequence

Lydian     59 59 59 35 59 59 35 LLLsLLs

Ionian     59 59 35 59 59 59 35 LLsLLLs

Myxolydian 59 59 35 59 59 35 59 LLsLLsL

Dorian     59 35 59 59 59 35 59 LsLLLsL

Aolian     59 35 59 59 35 59 59 LsLLsLL

Phrygian   35 59 59 59 35 59 59 sLLLsLL

Locrian    35 59 59 35 59 59 59 sLLsLLL

 

In a leap year, an extra day was added to Tibredos. It was not known what the leap year rule was, but it was known that all 7 varieties celebrated the new year on exactly the same day, so must have agreed on an (equivalent) leap year rule.

 

So Dodiros begins on the same day in all 7 varieties. Each of the other 6 leucons begins on either of two days 24 days apart. The table below shows the day of year each leucon begins in each variety

 

Variety    Dod Rei Mim Far Sot Las Tib

Lydian     001 060 119 178 213 272 331

Ionian     001 060 119 154 213 272 331

Myxolydian 001 060 119 154 213 272 307

Dorian     001 060 095 154 213 272 307

Aolian     001 060 095 154 213 248 307

Phrygian   001 036 095 154 213 248 307

Locrian    001 036 095 154 189 248 307

 

At later times only two varieties survived. The Ionian variety, which became known as the Major Leuconic Calendar and the Aolian variety, which became known as the Minor Leuconic Calendar.

 

 

Karl

 

15(01(30

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Re: Musical Calendar

Karl Palmen

Dear Vladimir and Calendar People

 

The link raises some issues. I saw a table that looks a little bit like a table of Dominical letters of years over a 28-year cycle, but the letters go forward rather than backwards and the leap years have one letter rather than two. So I went to

http://dominorus.site50.net/calendar.html  

 

While reading that I found out that Vladimir asserted the existence of a Seleucid Calendar, which had 365 days in a common year and 366 days in a leap year and was adopted in 312 BC. In Wikipedia I find no such calendar, only a Seleucid era.

 

Also Wikipedia has no page for  Leuconic calendar. This is because such a calendar never really existed. It’s something I made up to amuse musically minded calendar people. The names of the Leucons are based on the lyrics of a song from “The Sound Of Music” and the names of  seven varieties are names of 7 modes of music

https://en.wikipedia.org/wiki/Mode_(music)#Modern such that the long leucon corresponds to a tone and the short leucon corresponds to a semitone.

 

I don’t know of any leap day calendar that was used before the Julian calendar.

 

I found that Vladimir uses a calendar who’s year begins on March 1, this gets rid of complications caused by days of the year that may occur after a leap day.

 

He then gives letters to the days of the week: A for  Friday, B for Saturday to G for Thursday. The choice of Friday for A seems to arise from the seemingly arbitrary choice of the year stating of March 1, 1997  Julian calendar as the first year of his 28-year cycle (1997 has remainder 9 when divided by 28). 

 

I then go back to the first link, which is really part 2. I see something about the 4 columns of the table of 28-year table forming an error, detecting code.

He changes the letters A to F to numbers 1 to 6 and G to 0. The table of the days of week each March 1 occurs starting from 1997 in Julian calendar is then

1 2 3 5

6 0 1 3

4 5 6 1

2 3 4 6

0 1 2 4

5 6 0 2

3 4 5 0

He then arranges this into dominoes by placing two dominoes along each row

[1 2][3 5]

[6 0][1 3]

[4 5][6 1]

[2 3][4 6]

[0 1][2 4]

[5 6][0 2]

[3 4][5 0]

He then observes that the dominoes in the first column have their numbers differ by 1 or 6 and all such dominoes are included and the dominoes in the second column have their numbers differ by 2 or 5 and all such dominoes are included.

I observe that this relies on the 28-year cycle starting in a year after a leap year. If it started in a leap year or 2 years after a leap year, every domino would have their numbers differ by 1 or 6 and each of these dominoes would appear once in each column.

 

Even with the 28-year cycle starting on a year after a leap year or any odd-numbered year, only 14 of the 28 dominoes are used and so Vladimir extends it to use all  28 of the dominoes.

So that

(1) each number occurs in each column once (so total 21),

(2) each row has the same total (which must be 24),

(3) each column of dominoes has the dominoes whose numbers differ by the same amount or 7 minus that amount

Vladimir found the following solution:

[1 2][3 5][3 3][2 5]

[6 0][1 3][5 5][4 0]

[4 5][6 1][1 1][5 1]

[2 3][4 6][0 0][3 6]

[0 1][2 4][6 6][1 4]

[5 6][0 2][4 4][0 3]

[3 4][5 0][2 2][6 2]

Vladimir claims without any presenting any evidence that numbers in the right half represent a lunar calendar. The right half is quite irregular compared to the left half.

Is this solution unique?

 

Then comes the musical calendar. The music is come from Vladimir’s solution. I’ll listen to it during the weekend.  The first 4 notes of each row are the same, except for the key and octave. The remaining 4 notes vary more.

 

Karl

 

15(02(01

 

From: East Carolina University Calendar discussion List [mailto:[hidden email]] On Behalf Of Vladimir Pakhomov
Sent: 16 July 2015 20:39
To: [hidden email]
Subject: Re: Musical Calendar

 

The musical interpretation of our perpetual calendar.

http://dominorus.site50.net/seals.html

You can listen to this melody.

 

Vladimir Pakhomov

 

 

 

From: East Carolina University Calendar discussion List [[hidden email]] On Behalf Of Karl Palmen
Sent: Thursday, July 16, 2015 3:38 PM
To: [hidden email]
Subject: Musical Calendar

 

Dear Calendar People

 

If the 31-day months were the white notes on a piano, we’d get

 

A  May

A#/Bb  June

B  July

C  August

C#/Db September

D October

D#/Eb November

E December

F January

F#/Gb February

G March

G#/Ab April

 

 

Also I’d like to remind calendar people of the Leuconic Calendars from March (G) 2002.

 

 

I came a across a set of calendars in which the year was divided into seven leucons.

 

The new year begins at or near the June Solstice and the seven leucons are named as follows:

 

1: Dodiros

2: Reisunos

3: Mimyos

4: Farunos

5: Sothredos

6: Lasos

7: Tibredos

 

A long leucon has 59 days and a short leucon has 35 days. Each year has five long leucons and two short leucons. The short leucons are as evenly spaced as possible.

 

There were seven varieties of this leuconic calendar. The number of days in leucons of each of these varieties is as follows:

 

Variety    Do Re Mi Fa So La Ti sequence

Lydian     59 59 59 35 59 59 35 LLLsLLs

Ionian     59 59 35 59 59 59 35 LLsLLLs

Myxolydian 59 59 35 59 59 35 59 LLsLLsL

Dorian     59 35 59 59 59 35 59 LsLLLsL

Aolian     59 35 59 59 35 59 59 LsLLsLL

Phrygian   35 59 59 59 35 59 59 sLLLsLL

Locrian    35 59 59 35 59 59 59 sLLsLLL

 

In a leap year, an extra day was added to Tibredos. It was not known what the leap year rule was, but it was known that all 7 varieties celebrated the new year on exactly the same day, so must have agreed on an (equivalent) leap year rule.

 

So Dodiros begins on the same day in all 7 varieties. Each of the other 6 leucons begins on either of two days 24 days apart. The table below shows the day of year each leucon begins in each variety

 

Variety    Dod Rei Mim Far Sot Las Tib

Lydian     001 060 119 178 213 272 331

Ionian     001 060 119 154 213 272 331

Myxolydian 001 060 119 154 213 272 307

Dorian     001 060 095 154 213 272 307

Aolian     001 060 095 154 213 248 307

Phrygian   001 036 095 154 213 248 307

Locrian    001 036 095 154 189 248 307

 

At later times only two varieties survived. The Ionian variety, which became known as the Major Leuconic Calendar and the Aolian variety, which became known as the Minor Leuconic Calendar.

 

 

Karl

 

15(01(30